Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Attractors of equations of non-Newtonian fluid dynamics

NASA Astrophysics Data System (ADS)

Zvyagin, V. G.; Kondrat'ev, S. K.

2014-10-01

This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

A phase-field method to analyze the dynamics of immiscible fluids in porous media

NASA Astrophysics Data System (ADS)

de Paoli, Marco; Roccon, Alessio; Zonta, Francesco; Soldati, Alfredo

2017-11-01

Liquid carbon dioxide (CO2) injected into geological formations (filled with brine) is not completely soluble in the surrounding fluid. For this reason, complex transport phenomena may occur across the interface that separates the two phases (CO2+brine and brine). Inspired by this geophysical instance, we used a Phase-Field Method (PFM) to describe the dynamics of two immiscible fluids in satured porous media. The basic idea of the PFM is to introduce an order parameter (ϕ) that varies continuously across the interfacial layer between the phases and is uniform in the bulk. The equation that describes the distribution of ϕ is the Cahn-Hilliard (CH) equation, which is coupled with the Darcy equation (to evaluate fluid velocity) through the buoyancy and Korteweg stress terms. The governing equations are solved through a pseudo-spectral technique (Fourier-Chebyshev). Our results show that the value of the surface tension between the two phases strongly influences the initial and the long term dynamics of the system. We believe that the proposed numerical approach, which grants an accurate evaluation of the interfacial fluxes of momentum/energy/species, is attractive to describe the transfer mechanism and the overall dynamics of immiscible and partially miscible phases.

A theory for the retrieval of virtual temperature from winds, radiances and the equations of fluid dynamics

NASA Technical Reports Server (NTRS)

Tzvi, G. C.

1986-01-01

A technique to deduce the virtual temperature from the combined use of the equations of fluid dynamics, observed wind and observed radiances is described. The wind information could come from ground-based sensitivity very high frequency (VHF) Doppler radars and/or from space-borne Doppler lidars. The radiometers are also assumed to be either space-borne and/or ground-based. From traditional radiometric techniques the vertical structure of the temperature can be estimated only crudely. While it has been known for quite some time that the virtual temperature could be deduced from wind information only, such techniques had to assume the infallibility of certain diagnostic relations. The proposed technique is an extension of the Gal-Chen technique. It is assumed that due to modeling uncertainties the equations of fluid dynamics are satisfied only in the least square sense. The retrieved temperature, however, is constrained to reproduce the observed radiances. It is shown that the combined use of the three sources of information (wind, radiances and fluid dynamical equations) can result in a unique determination of the vertical temperature structure with spatial and temporal resolution comparable to that of the observed wind.

Polymer Fluid Dynamics.

ERIC Educational Resources Information Center

Bird, R. Byron

1980-01-01

Problems in polymer fluid dynamics are described, including development of constitutive equations, rheometry, kinetic theory, flow visualization, heat transfer studies, flows with phase change, two-phase flow, polymer unit operations, and drag reduction. (JN)

Nanoscale hydrodynamics near solids

NASA Astrophysics Data System (ADS)

Camargo, Diego; de la Torre, J. A.; Duque-Zumajo, D.; Español, Pep; Delgado-Buscalioni, Rafael; Chejne, Farid

2018-02-01

Density Functional Theory (DFT) is a successful and well-established theory for the study of the structure of simple and complex fluids at equilibrium. The theory has been generalized to dynamical situations when the underlying dynamics is diffusive as in, for example, colloidal systems. However, there is no such a clear foundation for Dynamic DFT (DDFT) for the case of simple fluids in contact with solid walls. In this work, we derive DDFT for simple fluids by including not only the mass density field but also the momentum density field of the fluid. The standard projection operator method based on the Kawasaki-Gunton operator is used for deriving the equations for the average value of these fields. The solid is described as featureless under the assumption that all the internal degrees of freedom of the solid relax much faster than those of the fluid (solid elasticity is irrelevant). The fluid moves according to a set of non-local hydrodynamic equations that include explicitly the forces due to the solid. These forces are of two types, reversible forces emerging from the free energy density functional, and accounting for impenetrability of the solid, and irreversible forces that involve the velocity of both the fluid and the solid. These forces are localized in the vicinity of the solid surface. The resulting hydrodynamic equations should allow one to study dynamical regimes of simple fluids in contact with solid objects in isothermal situations.

Equation of state and some structural and dynamical properties of the confined Lennard-Jones fluid into carbon nanotube: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Abbaspour, Mohsen; Akbarzadeh, Hamed; Salemi, Sirous; Abroodi, Mousarreza

2016-11-01

By considering the anisotropic pressure tensor, two separate equations of state (EoS) as functions of the density, temperature, and carbon nanotube (CNT) diameter have been proposed for the radial and axial directions for the confined Lennard-Jones (LJ) fluid into (11,11), (12,10), and (19,0) CNTs from 120 to 600 K using molecular dynamics (MD) simulations. We have also investigated the effects of the pore size, pore loading, chirality, and temperature on some of the structural and dynamical properties of the confined LJ fluid into (11,11), (12,10), (19,0), and (19,19) CNTs such as the radial density profile and self-diffusion coefficient. We have also determined the EoS for the confined LJ fluid into double and triple walled CNTs.

Foundations of radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Mihalas, D.; Mihalas, B. W.

This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.

Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements

NASA Astrophysics Data System (ADS)

Liburdy, James

2017-11-01

Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Profeta, Christophe

2015-11-01

This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Zp=(xp,Up) and is represented by its PDF p (t ;yp,Vp) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Zp=(xp,Up,Us) , and, consequently, handles an extended PDF p (t ;yp,Vp,Vs) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to describe physical systems and guidelines are formulated to emphasize the key role played by the notion of slow and fast variables.

Fundamental Study on Quantum Nanojets

DTIC Science & Technology

2004-08-01

Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantum mechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantum mechanical perspectives; Schrödinger’s wave mechanics and quantum fluid dynamics based on Hamilton-Jacoby...References 8 2). Direct Problems a). Quantum fluid dynamics formalism based on Hamilton-Jacoby equation are adapted for the numerical

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardall, Christian Y.

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

DOE PAGES

Cardall, Christian Y.

2017-12-15

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

On the kinetics of the capillary imbibition of a simple fluid through a designed nanochannel using the molecular dynamics simulation approach.

PubMed

Ahadian, Samad; Mizuseki, Hiroshi; Kawazoe, Yoshiyuki

2010-12-15

A molecular dynamics (MD) approach was employed to simulate the imbibition of a designed nanopore by a simple fluid (i.e., a Lennard-Jones (LJ) fluid). The length of imbibition as a function of time for various interactions between the LJ fluid and the pore wall was recorded for this system (i.e., the LJ fluid and the nanopore). By and large, the kinetics of imbibition was successfully described by the Lucas-Washburn (LW) equation, although deviation from it was observed in some cases. This lack of agreement is due to the neglect of the dynamic contact angle (DCA) in the LW equation. Two commonly used models (i.e., hydrodynamic and molecular-kinetic (MK) models) were thus employed to calculate the DCA. It is demonstrated that the MK model is able to justify the simulation results in which are not in good agreement with the simple LW equation. However, the hydrodynamic model is not capable of doing that. Further investigation of the MD simulation data revealed an interesting fact that there is a direct relationship between the wall-fluid interaction and the speed of the capillary imbibition. More evidence to support this claim is presented. Copyright © 2010 Elsevier Inc. All rights reserved.

Multipole Vortex Blobs (MVB): Symplectic Geometry and Dynamics.

PubMed

Holm, Darryl D; Jacobs, Henry O

2017-01-01

Vortex blob methods are typically characterized by a regularization length scale, below which the dynamics are trivial for isolated blobs. In this article, we observe that the dynamics need not be trivial if one is willing to consider distributional derivatives of Dirac delta functionals as valid vorticity distributions. More specifically, a new singular vortex theory is presented for regularized Euler fluid equations of ideal incompressible flow in the plane. We determine the conditions under which such regularized Euler fluid equations may admit vorticity singularities which are stronger than delta functions, e.g., derivatives of delta functions. We also describe the symplectic geometry associated with these augmented vortex structures, and we characterize the dynamics as Hamiltonian. Applications to the design of numerical methods similar to vortex blob methods are also discussed. Such findings illuminate the rich dynamics which occur below the regularization length scale and enlighten our perspective on the potential for regularized fluid models to capture multiscale phenomena.

Direct modeling for computational fluid dynamics

NASA Astrophysics Data System (ADS)

Xu, Kun

2015-06-01

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of discrete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydrodynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Fluid equations in the presence of electron cyclotron current drive

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Kruger, Scott E.

2012-12-01

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

Fluid equations in the presence of electron cyclotron current drive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jenkins, Thomas G.; Kruger, Scott E.

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

Finite Element Modeling of Coupled Flexible Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2006-09-01

tanks is presented. The semi-discrete combined solid and fluid equations of motions are integrated using a time- accurate parallel explicit solver...Incompressible fluid flow in a moving/deforming container including accurate modeling of the free-surface, turbulence, and viscous effects ...paper, a single computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of

Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

NASA Astrophysics Data System (ADS)

Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao

2018-04-01

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.

Fluid Dynamics of the Heart and its Valves

NASA Astrophysics Data System (ADS)

Peskin, Charles S.

1997-11-01

The fluid dynamics of the heart involve the interaction of blood, a viscous incompressible fluid, with the flexible, elastic, fiber-reinforced heart valve leaflets that are immersed in that fluid. Neither the fluid motion nor the valve leaflet motion are known in advance: both must be computed simultaneously by solving their coupled equations of motion. This can be done by the immersed boundary method(Peskin CS and McQueen DM: A general method for the computer simulation of biological systems interacting with fluids. In: Biological Fluid Dynamics (Ellington CP and Pedley TJ, eds.), The Company of Biologists Limited, Cambridge UK, 1995, pp. 265-276.), which can be extended to incorporate the contractile fiber architecture of the muscular heart walls as well as the valve leaflets and the blood. In this way we arrive at a three-dimensional computer model of the heart(Peskin CS and McQueen DM: Fluid dynamics of the heart and its valves. In: Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology (Othmer HG, Adler FR, Lewis MA, and Dallon JC, eds.), Prentice-Hall, Englewood Cliffs NJ, 1996, pp. 309-337.), which can be used as a test chamber for the design of prosthetic cardiac valves, and also to study the function of the heart in health and in disease. Numerical solutions of the equations of cardiac fluid dynamics obtained by the immersed boundary method will be presented in the form of a video animation of the beating heart.

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

NASA Astrophysics Data System (ADS)

Hu, Wei; Tian, Qiang; Hu, HaiYan

2018-04-01

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

A study analysis of cable-body systems totally immersed in a fluid stream

NASA Technical Reports Server (NTRS)

Delaurier, J. D.

1972-01-01

A general stability analysis of a cable-body system immersed in a fluid stream is presented. The analytical portion of this analysis treats the system as being essentially a cable problem, with the body dynamics giving the end conditions. The mathematical form of the analysis consists of partial differential wave equations, with the end and auxiliary conditions being determined from the body equations of motion. The equations uncouple to give a lateral problem and a longitudinal problem as in first order airplane dynamics. A series of tests on a tethered wind tunnel model provide a comparison of the theory with experiment.

Advances in Quantum Trajectory Approaches to Dynamics

NASA Astrophysics Data System (ADS)

Askar, Attila

2001-03-01

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

Brownian microhydrodynamics of active filaments.

PubMed

Laskar, Abhrajit; Adhikari, R

2015-12-21

Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian motion, and the elasticity of the body presents a challenging fluid-structure interaction problem. Here, we model this problem by approximating the slender body as an elastic filament that can impose non-equilibrium velocities or stresses at the fluid-structure interface. We derive equations of motion for such an active filament by enforcing momentum conservation in the fluid-structure interaction and assuming slow viscous flow in the fluid. The fluid-structure interaction is obtained, to any desired degree of accuracy, through the solution of an integral equation. A simplified form of the equations of motion, which allows for efficient numerical solutions, is obtained by applying the Kirkwood-Riseman superposition approximation to the integral equation. We use this form of equation of motion to study dynamical steady states in free and hinged minimally active filaments. Our model provides the foundation to study collective phenomena in momentum-conserving, Brownian, active filament suspensions.

A Multiscale Model for Virus Capsid Dynamics

PubMed Central

Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei

2010-01-01

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. PMID:20224756

Flow of variably fluidized granular masses across three-dimensional terrain I. Coulomb mixture theory

USGS Publications Warehouse

Iverson, R.M.; Denlinger, R.P.

2001-01-01

Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces, govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, threedimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Flow of variably fluidized granular masses across three-dimensional terrain: 1. Coulomb mixture theory

NASA Astrophysics Data System (ADS)

Iverson, Richard M.; Denlinger, Roger P.

2001-01-01

Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, three-dimensional mathematical model that accounts explicitly for solid- and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force

NASA Astrophysics Data System (ADS)

Tort, Marine; Dubos, Thomas; Bouchut, François; Zeitlin, Vladimir

2014-05-01

Dynamically Consistent Shallow-Atmosphere Equations with a Complete Coriolis force Marine Tort1, Thomas Dubos1, François Bouchut2 & Vladimir Zeitlin1,3 1 Laboratoire of Dynamical Meteorology, Univ. P. and M. Curie, Ecole Normale Supérieure, and Ecole Polytechnique, FRANCE 2 Université Paris-Est, Laboratoire d'Analyse et de Mathématiques Appliquées, FRANCE 3 Institut Universitaire de France Atmospheric and oceanic motion are usually modeled within the shallow-fluid approximation, which simplifies the 3D spherical geometry. For dynamical consistency, i.e. to ensure conservation laws for potential vorticity, energy and angular momentum, the horizontal component of the Coriolis force is neglected. Here new equation sets combining consistently a simplified shallow-fluid geometry with a complete Coriolis force is presented. The derivation invokes Hamilton's principle of least action with an approximate Lagrangian capturing the small increase with height of the solid-body entrainment velocity due to planetary rotation. A three-dimensional compressible model and a one-layer shallow-water model are obtained. The latter extends previous work done on the f-plane and β-plane. Preliminary numerical results confirm the accuracy of the 3D model within the range of parameters for which the equations are relevant. These new models could be useful to incorporate a full Coriolis force into existing numerical models and to disentangle the effects of the shallow-atmosphere approximation from those of the traditional approximation. Related papers: Tort M., Dubos T., Bouchut F. and Zeitlin V. Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography. J. Fluid Mech. (under revisions) Tort M. and Dubos T. Dynamically consistent shallow-atmosphere equations with a complete Coriolis force. Q.J.R. Meteorol. Soc. (DOI: 10.1002/qj.2274)

Three-Dimensional Coupled Dynamics of The Two-Fluid Model in Superfluid 4He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow

NASA Astrophysics Data System (ADS)

Yui, Satoshi; Tsubota, Makoto; Kobayashi, Hiromichi

2018-04-01

The coupled dynamics of the two-fluid model of superfluid 4He is numerically studied for quantum turbulence of the thermal counterflow in a square channel. We combine the vortex filament model of the superfluid and the Navier-Stokes equations of normal fluid. Simulations of the coupled dynamics show that the velocity profile of the normal fluid is deformed significantly by superfluid turbulence as the vortices become dense. This result is consistent with recently performed visualization experiments. We introduce a dimensionless parameter that characterizes the deformation of the velocity profile.

Application of wave mechanics theory to fluid dynamics problems: Fundamentals

NASA Technical Reports Server (NTRS)

Krzywoblocki, M. Z. V.

1974-01-01

The application of the basic formalistic elements of wave mechanics theory is discussed. The theory is used to describe the physical phenomena on the microscopic level, the fluid dynamics of gases and liquids, and the analysis of physical phenomena on the macroscopic (visually observable) level. The practical advantages of relating the two fields of wave mechanics and fluid mechanics through the use of the Schroedinger equation constitute the approach to this relationship. Some of the subjects include: (1) fundamental aspects of wave mechanics theory, (2) laminarity of flow, (3) velocity potential, (4) disturbances in fluids, (5) introductory elements of the bifurcation theory, and (6) physiological aspects in fluid dynamics.

Pairwise Force Smoothed Particle Hydrodynamics model for multiphase flow: Surface tension and contact line dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tartakovsky, Alexandre M.; Panchenko, Alexander

2016-01-01

We present a novel formulation of the Pairwise Force Smoothed Particle Hydrodynamics Model (PF-SPH) and use it to simulate two- and three-phase flows in bounded domains. In the PF-SPH model, the Navier-Stokes equations are discretized with the Smoothed Particle Hydrodynamics (SPH) method and the Young-Laplace boundary condition at the fluid-fluid interface and the Young boundary condition at the fluid-fluid-solid interface are replaced with pairwise forces added into the Navier-Stokes equations. We derive a relationship between the parameters in the pairwise forces and the surface tension and static contact angle. Next, we demonstrate the accuracy of the model under static andmore » dynamic conditions. Finally, to demonstrate the capabilities and robustness of the model we use it to simulate flow of three fluids in a porous material.« less

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Parallel computational fluid dynamics '91; Conference Proceedings, Stuttgart, Germany, Jun. 10-12, 1991

NASA Technical Reports Server (NTRS)

Reinsch, K. G. (Editor); Schmidt, W. (Editor); Ecer, A. (Editor); Haeuser, Jochem (Editor); Periaux, J. (Editor)

1992-01-01

A conference was held on parallel computational fluid dynamics and produced related papers. Topics discussed in these papers include: parallel implicit and explicit solvers for compressible flow, parallel computational techniques for Euler and Navier-Stokes equations, grid generation techniques for parallel computers, and aerodynamic simulation om massively parallel systems.

Design and dynamic modeling of electrorheological fluid-based variable-stiffness fin for robotic fish

NASA Astrophysics Data System (ADS)

Bazaz Behbahani, Sanaz; Tan, Xiaobo

2017-08-01

Fish actively control their stiffness in different swimming conditions. Inspired by such an adaptive behavior, in this paper we study the design, prototyping, and dynamic modeling of compact, tunable-stiffness fins for robotic fish, where electrorheological (ER) fluid serves as the enabling element. A multi-layer composite fin with an ER fluid core is prototyped and utilized to investigate the influence of electrical field on its performance. Hamilton's principle is used to derive the dynamic equations of motion of the flexible fin, and Lighthill's large-amplitude elongated-body theory is adopted to estimate the hydrodynamic force when the fin undergoes base-actuated rotation. The dynamic equations are then discretized using the finite element method, to obtain an approximate numerical solution. Experiments are conducted on the prototyped flexible ER fluid-filled beam for parameter identification and validation of the proposed model, and for examining the effectiveness of electrically controlled stiffness tuning. In particular, it is found that the natural frequency is increased by almost 40% when the applied electric field changes from 0 to 1.5× {10}6 {{V}} {{{m}}}-1.

SPAR improved structure/fluid dynamic analysis capability

NASA Technical Reports Server (NTRS)

Oden, J. T.; Pearson, M. L.

1983-01-01

The capability of analyzing a coupled dynamic system of flowing fluid and elastic structure was added to the SPAR computer code. A method, developed and adopted for use in SPAR utilizes the existing assumed stress hybrid plan element in SPAR. An operational mode was incorporated in SPAR which provides the capability for analyzing the flaw of a two dimensional, incompressible, viscous fluid within rigid boundaries. Equations were developed to provide for the eventual analysis of the interaction of such fluids with an elastic solid.

The use of numerical programs in research and academic institutions

NASA Astrophysics Data System (ADS)

Scupi, A. A.

2016-08-01

This paper is conceived on the idea that numerical programs using computer models of physical processes can be used both for scientific research and academic teaching to study different phenomena. Computational Fluid Dynamics (CFD) is used today on a large scale in research and academic institutions. CFD development is not limited to computer simulations of fluid flow phenomena. Analytical solutions for most fluid dynamics problems are already available for ideal or simplified situations for different situations. CFD is based on the Navier- Stokes (N-S) equations characterizing the flow of a single phase of any liquid. For multiphase flows the integrated N-S equations are complemented with equations of the Volume of Fluid Model (VOF) and with energy equations. Different turbulent models were used in the paper, each one of them with practical engineering applications: the flow around aerodynamic surfaces used as unconventional propulsion system, multiphase flows in a settling chamber and pneumatic transport systems, heat transfer in a heat exchanger etc. Some of them numerical results were validated by experimental results. Numerical programs are also used in academic institutions where certain aspects of various phenomena are presented to students (Bachelor, Master and PhD) for a better understanding of the phenomenon itself.

Proper Orthogonal Decomposition in Optimal Control of Fluids

NASA Technical Reports Server (NTRS)

Ravindran, S. S.

1999-01-01

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.

Interfacial fluid instabilities and Kapitsa pendula.

PubMed

Krieger, Madison S

2017-07-01

The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilized by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum-type equation, we demonstrate how stability can be induced in fluid systems by properly tuned vibrations. We construct a "dictionary"-type relationship between various pendula and the classical Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational instabilities. This makes several results in control theory and dynamical systems directly applicable to the study of tunable fluid instabilities, where the critical wavelength depends on the external forces or the instability is suppressed entirely. We suggest some applications and instances of the effect ranging in scale from microns to the radius of a galaxy.

Frequency-dependent hydrodynamic interaction between two solid spheres

NASA Astrophysics Data System (ADS)

Jung, Gerhard; Schmid, Friederike

2017-12-01

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions between finite-sized particles in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that at high frequencies, the compressibility of the fluid has a significant impact on the frequency-dependent pair interactions. The predictions of hydrodynamic theory are compared to molecular dynamics simulations of two nanocolloids in a Lennard-Jones fluid. For this system, we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.

Fluid dynamics of out of equilibrium boost invariant plasmas

NASA Astrophysics Data System (ADS)

Blaizot, Jean-Paul; Yan, Li

2018-05-01

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

Sedimentation of Inertialess Particles in Stokes Flows

NASA Astrophysics Data System (ADS)

Höfer, Richard M.

2018-05-01

We investigate the sedimentation of a cloud of rigid, spherical particles of identical radii under gravity in a Stokes fluid. Both inertia and rotation of particles are neglected. We consider the homogenization limit of many small particles in the case of a dilute system in which interactions between particles are still important. In the relevant time scale, we rigorously prove convergence of the dynamics to the solution of a macroscopic equation. This macroscopic equation resembles the Stokes equations for a fluid of variable density subject to gravitation.

Instability analysis of expansion-free sphere in f(𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Ikram, Ayesha

The aim of this paper is to study the dynamical instability of expansion-free spherically symmetric anisotropic fluid in the framework of f(𝒢) gravity. We apply perturbation scheme of the first-order to the metric functions as well as matter variables and construct modified field equations for both static and perturbed configurations using power-law f(𝒢) model. To discuss the instability dynamics, we use the contracted Bianchi identities to formulate the dynamical equations in both Newtonian and post-Newtonian regimes. It is found that the range of instability is independent of adiabatic index for expansion-free fluid but depends on anisotropic pressures, energy density and Gauss-Bonnet (GB) terms.

Relativistic fluid dynamics with spin

NASA Astrophysics Data System (ADS)

Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico

2018-04-01

Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Astrophysical fluid dynamics

NASA Astrophysics Data System (ADS)

Ogilvie, Gordon I.

2016-06-01

> These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.-Israel Workshop, Jerusalem, Israel, December 1984

NASA Technical Reports Server (NTRS)

Murman, E. M. (Editor); Abarbanel, S. S. (Editor)

1985-01-01

Current developments and future trends in the application of supercomputers to computational fluid dynamics are discussed in reviews and reports. Topics examined include algorithm development for personal-size supercomputers, a multiblock three-dimensional Euler code for out-of-core and multiprocessor calculations, simulation of compressible inviscid and viscous flow, high-resolution solutions of the Euler equations for vortex flows, algorithms for the Navier-Stokes equations, and viscous-flow simulation by FEM and related techniques. Consideration is given to marching iterative methods for the parabolized and thin-layer Navier-Stokes equations, multigrid solutions to quasi-elliptic schemes, secondary instability of free shear flows, simulation of turbulent flow, and problems connected with weather prediction.

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

NASA Technical Reports Server (NTRS)

Newman, Perry A.; Newman, James C., III; Barnwell, Richard W.; Taylor, Arthur C., III; Hou, Gene J.-W.

1998-01-01

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

u-w formulation for dynamic problems in large deformation regime solved through an implicit meshfree scheme

NASA Astrophysics Data System (ADS)

Navas, Pedro; Sanavia, Lorenzo; López-Querol, Susana; Yu, Rena C.

2017-12-01

Solving dynamic problems for fluid saturated porous media at large deformation regime is an interesting but complex issue. An implicit time integration scheme is herein developed within the framework of the u-w (solid displacement-relative fluid displacement) formulation for the Biot's equations. In particular, liquid water saturated porous media is considered and the linearization of the linear momentum equations taking into account all the inertia terms for both solid and fluid phases is for the first time presented. The spatial discretization is carried out through a meshfree method, in which the shape functions are based on the principle of local maximum entropy LME. The current methodology is firstly validated with the dynamic consolidation of a soil column and the plastic shear band formulation of a square domain loaded by a rigid footing. The feasibility of this new numerical approach for solving large deformation dynamic problems is finally demonstrated through the application to an embankment problem subjected to an earthquake.

Derivation of a continuum model and the energy law for moving contact lines with insoluble surfactants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zhen, E-mail: matzz@nus.edu.sg; Xu, Shixin, E-mail: matxs@nus.edu.sg; Ren, Weiqing, E-mail: matrw@nus.edu.sg

2014-06-15

A continuous model is derived for the dynamics of two immiscible fluids with moving contact lines and insoluble surfactants based on thermodynamic principles. The continuum model consists of the Navier-Stokes equations for the dynamics of the two fluids and a convection-diffusion equation for the evolution of the surfactant on the fluid interface. The interface condition, the boundary condition for the slip velocity, and the condition for the dynamic contact angle are derived from the consideration of energy dissipations. Different types of energy dissipations, including the viscous dissipation, the dissipations on the solid wall and at the contact line, as wellmore » as the dissipation due to the diffusion of surfactant, are identified from the analysis. A finite element method is developed for the continuum model. Numerical experiments are performed to demonstrate the influence of surfactant on the contact line dynamics. The different types of energy dissipations are compared numerically.« less

Stratified rotating Boussinesq equations in geophysical fluid dynamics: Dynamic bifurcation and periodic solutions

NASA Astrophysics Data System (ADS)

Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong

2007-06-01

The main objective of this article is to study the dynamics of the stratified rotating Boussinesq equations, which are a basic model in geophysical fluid dynamics. First, for the case where the Prandtl number is greater than 1, a complete stability and bifurcation analysis near the first critical Rayleigh number is carried out. Second, for the case where the Prandtl number is smaller than 1, the onset of the Hopf bifurcation near the first critical Rayleigh number is established, leading to the existence of nontrivial periodic solutions. The analysis is based on a newly developed bifurcation and stability theory for nonlinear dynamical systems (both finite and infinite dimensional) by two of the authors [T. Ma and S. Wang, Bifurcation Theory and Applications, World Scientific Series on Nonlinear Sciences Vol. 53 (World Scientific, Singapore, 2005)].

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

PubMed

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-11-25

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

A Fluid Dynamic Approach to the Dust-Acoustic Soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2002-12-01

The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.

Dynamic density functional theory with hydrodynamic interactions: theoretical development and application in the study of phase separation in gas-liquid systems.

PubMed

Kikkinides, E S; Monson, P A

2015-03-07

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van der Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.

Dynamic density functional theory with hydrodynamic interactions: Theoretical development and application in the study of phase separation in gas-liquid systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kikkinides, E. S.; Monson, P. A.

Building on recent developments in dynamic density functional theory, we have developed a version of the theory that includes hydrodynamic interactions. This is achieved by combining the continuity and momentum equations eliminating velocity fields, so the resulting model equation contains only terms related to the fluid density and its time and spatial derivatives. The new model satisfies simultaneously continuity and momentum equations under the assumptions of constant dynamic or kinematic viscosity and small velocities and/or density gradients. We present applications of the theory to spinodal decomposition of subcritical temperatures for one-dimensional and three-dimensional density perturbations for both a van dermore » Waals fluid and for a lattice gas model in mean field theory. In the latter case, the theory provides a hydrodynamic extension to the recently studied dynamic mean field theory. We find that the theory correctly describes the transition from diffusive phase separation at short times to hydrodynamic behaviour at long times.« less

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

Estimating dynamic permeability in fractal pore network saturated by Maxwellian fluid

NASA Astrophysics Data System (ADS)

Sun, W.

2017-12-01

The frequency dependent flow of fluid in porous media is an important issue in geophysical prospecting. Oscillating flow in pipe leads to frequency dependent dynamic permeability and has been studied in pore network containing Newtonian fluid. But there is little work on oscillating complex fluid in pipe network, especially in irregular network. Here we formulated frequency dependent permeability for Maxwellian fluid and estimated the permeability in three-dimensional fractal network model. We consider an infinitely long cylindrical pipe with rigid solid wall. The pipe is filled with Maxwellian fluids. Based on the mass conservation equation, the equilibrium equation of force and Maxwell constitutive relationship, we formulated the flux by integration of axial velocity component over the pipe's cross section. Then we extend single pipe formulation to a 3D irregular network. Flux balance condition yields a set of linear equations whose unknowns are the fluid pressure at each node. By evaluating the total flow flux through the network, the dynamic permeability can be calculated.We investigated the dynamic permeability of brine and CPyCl/NaSal in a 3D porous sample with a cubic side length 1 cm. The pore network is created by a Voronoi cell filling method. The porosity, i.e., volume ratio between pore/pipe network and the overall cubic, is set as 0.1. The irregular pore network has a fractal structure. The dimension d of the pore network is defined by the relation between node number M within a sphere and the radius r of the sphere,M=rd.The results show that both brine and Maxwellian fluid's permeability maintain a stable value at low frequency, then decreases with fluctuating peaks. The dynamic permeability in pore networks saturated by Maxwellian fluid (CPyCl/NaSal (60 mM)) show larger peaks during the decline process at high frequency, which represents the typical resonance behavior. Dynamic permeability shows clear dependence on the dimension of the fractal network. Small-scale network has higher dimension than large-scale networks. The reason is that in larger networks pore and inter-pore connections are so dense that the probability P(r) to have a neighboring pore at distance r decays faster. The proposed model may be used to explain velocity dispersion in unconventional reservoir rocks observed in laboratory.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

PubMed

Hoover, Wm G; Hoover, Carol G

2010-04-01

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Filtering of non-linear instabilities. [from finite difference solution of fluid dynamics equations

NASA Technical Reports Server (NTRS)

Khosla, P. K.; Rubin, S. G.

1979-01-01

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

Lagrangian fluid description with simple applications in compressible plasma and gas dynamics

NASA Astrophysics Data System (ADS)

Schamel, Hans

2004-03-01

The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D). In cosmology referring to the pancake model of Zel'dovich and the adhesion model of Gurbatov and Saichev, both assuming a clumping of matter at the intersection points of fluid particle trajectories (i.e. at the caustics), the foam-like large-scale structure of our Universe observed recently by Chandra X-ray observatory may be explained by the 3D convection of weakly interacting dark matter. Recent developments in plasma and nanotechnology-the miniaturization and fabrication of nanoelectronic devices being one example-have reinforced the interest in the quasi-ballistic electron transport in diodes and triodes, a field which turns out to be best treated by the Lagrangian fluid description. It is shown that the well-known space-charge-limited flow given by Child-Langmuir turns out to be incorrect in cases of finite electron injection velocities at the emitting electrode. In that case it is an intrinsic bifurcation scenario which is responsible for current limitation rather than electron reflection at the virtual cathode as intuitively assumed by Langmuir. The inclusion of a Drude friction term in the electron momentum equation can be handled solely by the Lagrangian fluid description. Exploiting the formula in case of field emission it is possible to bridge ballistic and drift-dominated transport. Furthermore, the transient processes in the electron transport triggered by the switching of the anode potential are shown to be perfectly accounted for by means of the Lagrangian fluid description. Finally, by use of the Lagrangian ion fluid equations in case of a two component, current driven plasma we derive a system of two coupled scalar wave equations which involve the specific volume of ions and electrons, respectively. It has a small amplitude strange soliton solution with unusual scaling properties. In case of charge neutrality the existence of two types of collapses are predicted, one being associated with a density excavation, the other one with a density clumping as in the laser induced ion expansion problem and in the cosmic sticking matter problem. However, only the latter will survive charge separation and hence be observable. In summary, the Lagrangian method of solving fluid equations turns out to be a powerful tool for compressible media in general. It offers new perspectives and addresses to a broad audience of physicists with interest in fields such as plasma and fluid dynamics, semiconductor- and astrophysics, to mention few of them.

Dynamics of dense granular flows of small-and-large-grain mixtures in an ambient fluid.

PubMed

Meruane, C; Tamburrino, A; Roche, O

2012-08-01

Dense grain flows in nature consist of a mixture of solid constituents that are immersed in an ambient fluid. In order to obtain a good representation of these flows, the interaction mechanisms between the different constituents of the mixture should be considered. In this article, we study the dynamics of a dense granular flow composed of a binary mixture of small and large grains immersed in an ambient fluid. In this context, we extend the two-phase approach proposed by Meruane et al. [J. Fluid Mech. 648, 381 (2010)] to the case of flowing dense binary mixtures of solid particles, by including in the momentum equations a constitutive relation that describes the interaction mechanisms between the solid constituents in a dense regime. These coupled equations are solved numerically and validated by comparing the numerical results with experimental measurements of the front speed of gravitational granular flows resulting from the collapse, in ambient air or water, of two-dimensional granular columns that consisted of mixtures of small and large spherical particles of equal mass density. Our results suggest that the model equations include the essential features that describe the dynamics of grains flows of binary mixtures in an ambient fluid. In particular, it is shown that segregation of small and large grains can increase the front speed because of the volumetric expansion of the flow. This increase in flow speed is damped by the interaction forces with the ambient fluid, and this behavior is more pronounced in water than in air.

3-Dimensional Modeling of Capacitively and Inductively Coupled Plasma Etching Systems

NASA Astrophysics Data System (ADS)

Rauf, Shahid

2008-10-01

Low temperature plasmas are widely used for thin film etching during micro and nano-electronic device fabrication. Fluid and hybrid plasma models were developed 15-20 years ago to understand the fundamentals of these plasmas and plasma etching. These models have significantly evolved since then, and are now a major tool used for new plasma hardware design and problem resolution. Plasma etching is a complex physical phenomenon, where inter-coupled plasma, electromagnetic, fluid dynamics, and thermal effects all have a major influence. The next frontier in the evolution of fluid-based plasma models is where these models are able to self-consistently treat the inter-coupling of plasma physics with fluid dynamics, electromagnetics, heat transfer and magnetostatics. We describe one such model in this paper and illustrate its use in solving engineering problems of interest for next generation plasma etcher design. Our 3-dimensional plasma model includes the full set of Maxwell equations, transport equations for all charged and neutral species in the plasma, the Navier-Stokes equation for fluid flow, and Kirchhoff's equations for the lumped external circuit. This model also includes Monte Carlo based kinetic models for secondary electrons and stochastic heating, and can take account of plasma chemistry. This modeling formalism allows us to self-consistently treat the dynamics in commercial inductively and capacitively coupled plasma etching reactors with realistic plasma chemistries, magnetic fields, and reactor geometries. We are also able to investigate the influence of the distributed electromagnetic circuit at very high frequencies (VHF) on the plasma dynamics. The model is used to assess the impact of azimuthal asymmetries in plasma reactor design (e.g., off-center pump, 3D magnetic field, slit valve, flow restrictor) on plasma characteristics at frequencies from 2 -- 180 MHz. With Jason Kenney, Ankur Agarwal, Ajit Balakrishna, Kallol Bera, and Ken Collins.

Dynamic fluid sloshing in a one-dimensional array of coupled vessels

NASA Astrophysics Data System (ADS)

Huang, Y. H.; Turner, M. R.

2017-12-01

This paper investigates the coupled motion between the dynamics of N vessels coupled together in a one-dimensional array by springs and the motion of the inviscid fluid sloshing within each vessel. We develop a fully nonlinear model for the system relative to a moving frame such that the fluid in each vessel is governed by the Euler equations and the motion of each vessel is modeled by a forced spring equation. By considering a linearization of the model, the characteristic equation for the natural frequencies of the system is derived and analyzed for a variety of nondimensional parameter regimes. It is found that the problem can exhibit a variety of resonance situations from the 1 :1 resonance to (N +1 ) -fold 1 :⋯:1 resonance, as well as more general r :s :⋯:t resonances for natural numbers r ,s ,t . This paper focuses in particular on determining the existence of regions of parameter space where the (N +1 ) -fold 1 :⋯:1 resonance can be found.

Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas

NASA Astrophysics Data System (ADS)

Zhu, Jian-Zhou

2018-03-01

The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.

Summer Study Program in Geophysical Fluid Dynamics, The Woods Hole Oceanographic Institution. Baroclinic Instability and Ocean Fronts.

DTIC Science & Technology

1983-11-01

spectrum of the linear stability theory has multiple roots with zero real parts. Then the general forms of the amplitude equations may be found for given...76 Dynamical Generation of Eastern Boundary Currents George eronis. .......................... 77 ..Amplitude Equations Edward...Associated Countercurrent. Benoit Cushman-Roisin ....... .................... ... 103 Turbulently Generated Eastern Boundary Currents Roger L. Hughes

An analysis of dynamic stability for a flexible rotor filled with liquid

NASA Astrophysics Data System (ADS)

Wang, Guangding; Yuan, Huiqun

2018-03-01

The investigation of dynamic stability for a flexible rotor completely filled with liquid is carried out. The perturbation differential equations of infinitesimal fluid are established on the basis of three-dimensional flow analysis in the rotor cavity. The analytical expression of the hydrodynamic force exerted on the rotor inner wall is obtained by using the Fourier series expansion. Assuming that both ends of the rotor are simply supported and the fluid motion is axially symmetric, the nondimensional whirling frequency equation of the system is derived. According to the obtained frequency equation, the system stability is analyzed and the results are compared with a rigid rotor system. Moreover, the effects of the mass ratio and system parameter on the stability of a flexible liquid-filled rotor system are discussed.

Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory

NASA Astrophysics Data System (ADS)

Bouras, I.; Molnár, E.; Niemi, H.; Xu, Z.; El, A.; Fochler, O.; Greiner, C.; Rischke, D. H.

2010-08-01

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio η/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn<1/2.

Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouras, I.; El, A.; Fochler, O.

2010-08-15

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio {eta}/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn<1/2.

Local equilibrium solutions in simple anisotropic cosmological models, as described by relativistic fluid dynamics

NASA Astrophysics Data System (ADS)

Shogin, Dmitry; Amund Amundsen, Per

2016-10-01

We test the physical relevance of the full and the truncated versions of the Israel-Stewart (IS) theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the IS theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the IS theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated IS equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the IS transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation

PubMed Central

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-01-01

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design. PMID:25404761

The Equations of Oceanic Motions

NASA Astrophysics Data System (ADS)

Müller, Peter

2006-10-01

Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kordilla, Jannes, E-mail: jkordil@gwdg.de; Pan, Wenxiao, E-mail: Wenxiao.Pan@pnnl.gov; Tartakovsky, Alexandre, E-mail: alexandre.tartakovsky@pnnl.gov

2014-12-14

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formationmore » of the so-called “giant fluctuations” of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power −4 of the wavenumber—except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.« less

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

PubMed

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre

2014-12-14

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

Smoothed particle hydrodynamics model for Landau-Lifshitz Navier-Stokes and advection-diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre M.

2014-12-14

We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation ofmore » the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.« less

Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications. Volume 24. Note on Numerical Fluid Mechanics

DTIC Science & Technology

1989-01-01

Calculations and Experiments (B.van den Berg/ D.A. Humphreysl E. Krause /J.P. F. Lindhout) Volume 20 Proceedings of the Seventh GAMM-Conference on...GRID METHODS FOR HYPERBOLIC PROBLEMS Wolfgang Hackbusch Sigrid Hagemann Institut fUr Informatik und Praktische Mathematik Christian-Albrechts...Euler Equations. Proceedings of the 8th Inter- national Conference on Numerical Methods in Fluid Dynamics (E. Krause , ed.), Aachen, 1988. Springer

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions

NASA Astrophysics Data System (ADS)

Ahuja, V. R.; van der Gucht, J.; Briels, W. J.

2018-01-01

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Hydrodynamically Coupled Brownian Dynamics: A coarse-grain particle-based Brownian dynamics technique with hydrodynamic interactions for modeling self-developing flow of polymer solutions.

PubMed

Ahuja, V R; van der Gucht, J; Briels, W J

2018-01-21

We present a novel coarse-grain particle-based simulation technique for modeling self-developing flow of dilute and semi-dilute polymer solutions. The central idea in this paper is the two-way coupling between a mesoscopic polymer model and a phenomenological fluid model. As our polymer model, we choose Responsive Particle Dynamics (RaPiD), a Brownian dynamics method, which formulates the so-called "conservative" and "transient" pair-potentials through which the polymers interact besides experiencing random forces in accordance with the fluctuation dissipation theorem. In addition to these interactions, our polymer blobs are also influenced by the background solvent velocity field, which we calculate by solving the Navier-Stokes equation discretized on a moving grid of fluid blobs using the Smoothed Particle Hydrodynamics (SPH) technique. While the polymers experience this frictional force opposing their motion relative to the background flow field, our fluid blobs also in turn are influenced by the motion of the polymers through an interaction term. This makes our technique a two-way coupling algorithm. We have constructed this interaction term in such a way that momentum is conserved locally, thereby preserving long range hydrodynamics. Furthermore, we have derived pairwise fluctuation terms for the velocities of the fluid blobs using the Fokker-Planck equation, which have been alternatively derived using the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) approach in Smoothed Dissipative Particle Dynamics (SDPD) literature. These velocity fluctuations for the fluid may be incorporated into the velocity updates for our fluid blobs to obtain a thermodynamically consistent distribution of velocities. In cases where these fluctuations are insignificant, however, these additional terms may well be dropped out as they are in a standard SPH simulation. We have applied our technique to study the rheology of two different concentrations of our model linear polymer solutions. The results show that the polymers and the fluid are coupled very well with each other, showing no lag between their velocities. Furthermore, our results show non-Newtonian shear thinning and the characteristic flattening of the Poiseuille flow profile typically observed for polymer solutions.

Effect of fluid compressibility on journal bearing performance

NASA Technical Reports Server (NTRS)

Dimofte, Florin

1993-01-01

An analysis was undertaken to determine the effect of fluid film compressibility on the performance of fluid film bearings. A new version of the Reynolds equation was developed, using a polytropic expansion, for both steady-state and dynamic conditions. Polytropic exponents from 1 (isothermal) to 1000 (approaching an incompressible liquid) were evaluated for two bearing numbers, selected from a range of practical interest for cryogenic application, and without cavitation. Bearing loads were insensitive to fluid compressibility for low bearing numbers, as was expected. The effect of compressibility on attitude angle was significant, even when the bearing number was low. A small amount of fluid compressibility was enough to obtain stable running conditions. Incompressible liquid lacked stability at all conditions. Fluid compressibility can be used to control the bearing dynamic coefficients, thereby influencing the dynamic behavior of the rotor-bearing system.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

The Statistical Mechanics of Ideal Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2002-01-01

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows

NASA Astrophysics Data System (ADS)

Zhao, Lifei; Li, Zhen; Caswell, Bruce; Ouyang, Jie; Karniadakis, George Em

2018-06-01

We simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics. In particular, a continuum model of polymeric fluids is constructed without a pre-specified constitutive relation, but instead it is actively learned from mesoscopic simulations where the dynamics of polymer chains is explicitly computed. To couple the bulk rheology of polymeric fluids and the microscale dynamics of polymer chains, the continuum approach (based on the finite volume method) provides the transient flow field as inputs for the (mesoscopic) dissipative particle dynamics (DPD), and in turn DPD returns an effective constitutive relation to close the continuum equations. In this multiscale modeling procedure, we employ an active learning strategy based on Gaussian process regression (GPR) to minimize the number of expensive DPD simulations, where adaptively selected DPD simulations are performed only as necessary. Numerical experiments are carried out for flow past a circular cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by bead-spring chains. The results show that only five DPD simulations are required to achieve an effective closure of the continuum equations at Reynolds number Re = 10. Furthermore, when Re is increased to 100, only one additional DPD simulation is required for constructing an extended GPR-informed model closure. Compared to traditional message-passing multiscale approaches, applying an active learning scheme to multiscale modeling of non-Newtonian fluids can significantly increase the computational efficiency. Although the method demonstrated here obtains only a local viscosity from the polymer dynamics, it can be extended to other multiscale models of complex fluids whose macro-rheology is unknown.

The coupling of fluids, dynamics, and controls on advanced architecture computers

NASA Technical Reports Server (NTRS)

Atwood, Christopher

1995-01-01

This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.

The Jungle Universe: coupled cosmological models in a Lotka-Volterra framework

NASA Astrophysics Data System (ADS)

Perez, Jérôme; Füzfa, André; Carletti, Timoteo; Mélot, Laurence; Guedezounme, Lazare

2014-06-01

In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaître universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaître cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserves the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain the general Lyapunov function of the system when one of the fluids is coupled to dark energy. This provides in a rigorous form a generic asymptotic behavior for cosmic expansion in presence of coupled species, beyond the standard de Sitter, Einstein-de Sitter and Milne cosmologies. Finally, we conjecture that chaos can appear for at least four interacting fluids.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Fluid dynamical description of relativistic nuclear collisions

NASA Technical Reports Server (NTRS)

Nix, J. R.; Strottman, D.

1982-01-01

On the basis of both a conventional relativistic nuclear fluid dynamic model and a two fluid generalization that takes into account the interpenetration of the target and projectile upon contact, collisions between heavy nuclei moving at relativistic speeds are calculated. This is done by solving the relevant equations of motion numerically in three spatial dimensions by use of particle in cell finite difference computing techniques. The effect of incorporating a density isomer, or quasistable state, in the nuclear equation of state at three times normal nuclear density, and the effect of doubling the nuclear compressibility coefficient are studied. For the reaction 20Ne + 238U at a laboratory bombarding energy per nucleon of 393 MeV, the calculated distributions in energy and angle of outgoing charged particles are compared with recent experimental data both integrated over all impact parameters and for nearly central collisions.

Magnetofluid dynamics in curved spacetime

NASA Astrophysics Data System (ADS)

Bhattacharjee, Chinmoy; Das, Rupam; Mahajan, S. M.

2015-03-01

A grand unified field Mμ ν is constructed from Maxwell's field tensor and an appropriately modified flow field, both nonminimally coupled to gravity, to analyze the dynamics of hot charged fluids in curved background space-time. With a suitable 3 +1 decomposition, this new formalism of the hot fluid is then applied to investigate the vortical dynamics of the system. Finally, the equilibrium state for plasma with nonminimal coupling through Ricci scalar R to gravity is investigated to derive a double Beltrami equation in curved space-time.

A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL NUMERICAL SCHEME FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp

A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron–positron or an electron–proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten–Lax–Van Leer) Riemann solver is proposed that exactlymore » preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.« less

An examination of the rheology of flocculated clay suspensions

NASA Astrophysics Data System (ADS)

Spearman, Jeremy

2017-04-01

A dense cohesive sediment suspension, sometimes referred to as fluid mud, is a thixotropic fluid with a true yield stress. Current rheological formulations struggle to reconcile the structural dynamics of cohesive sediment suspensions with the equilibrium behaviour of these suspensions across the range of concentrations and shear. This paper is concerned with establishing a rheological framework for the range of sediment concentrations from the yield point to Newtonian flow. The shear stress equation is based on floc fractal theory, put forward by Mills and Snabre (1988). This results in a Casson-like rheology equation. Additional structural dynamics is then added, using a theory on the self-similarity of clay suspensions proposed by Coussot (1995), giving an equation which has the ability to match the equilibrium and time-dependent viscous rheology of a wide range of suspensions of different concentration and mineralogy.

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

NASA Technical Reports Server (NTRS)

Engquist, B. E. (Editor); Osher, S. (Editor); Somerville, R. C. J. (Editor)

1985-01-01

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Axisymmetric contour dynamics for buoyant vortex rings

NASA Astrophysics Data System (ADS)

Chang, Ching; Llewellyn Smith, Stefan

2017-11-01

Vortex rings are important in many fluid flows in engineering and environmental applications. A family of steady propagating vortex rings including thin-core rings and Hill's spherical vortex was obtained by Norbury (1973). However, the dynamics of vortex rings in the presence of buoyancy has not been investigated yet in detail. When the core of a ring is thin, we may formulate reduced equations using momentum balance for vortex filaments, but that is not the case for ``fat'' rings. In our study, we use contour dynamics to study the time evolution of axisymmetric vortex rings when the density of the fluid inside the ring differs from that of the ambient. Axisymmetry leads to an almost-conserved material variable when the Boussinesq approximation is made. A set of integro-differential equations is solved numerically for these buoyant vortex rings. The same physical settings are also used to run a DNS code and compare to the results from contour dynamics.

Wetting dynamics of a collapsing fluid hole

NASA Astrophysics Data System (ADS)

Bostwick, J. B.; Dijksman, J. A.; Shearer, M.

2017-01-01

The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the governing field equations for the thin film to yield an evolution equation that captures the effect of capillary, gravitational, and centrifugal forces on this converging flow. The focus is on the quasistatic spreading regime, whereby contact-line motion is governed by a constitutive law relating the contact-angle to the contact-line speed. Surface tension forces dominate the collapse dynamics for small holes with the collapse time appearing as a power law whose exponent compares favorably to experiments in the literature. Gravity accelerates the collapse process. Volume dependence is predicted and compared with experiment. Centrifugal forces slow the collapse process and lead to complex dynamics characterized by stalled spreading behavior that separates the large and small hole asymptotic regimes.

Computational Fluid Dynamics for Atmospheric Entry

DTIC Science & Technology

2009-09-01

equations. This method is a parallelizable variant of the Gauss - Seidel line-relaxation method of MacCormack (Ref. 33, 35), and is at the core of the...G.V. Candler, “The Solution of the Navier-Stokes Equations Gauss - Seidel Line Relaxation,” Computers and Fluids, Vol. 17, No. 1, 1989, pp. 135-150. 35... solution differs by 5% from the results obtained using the direct simulation Monte Carlo method . 3 Some authors advocate the use of higher-order continuum

Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid

NASA Astrophysics Data System (ADS)

Oveissi, Soheil; Toghraie, Davood; Eftekhari, Seyyed Ali

2016-09-01

Nowadays, carbon nanotubes (CNT) play an important role in practical applications in fluidic devices. To this end, researchers have studied various aspects of vibration analysis of a behavior of CNT conveying fluid. In this paper, based on nonlocal elasticity theory, single-walled carbon nanotube (SWCNT) is simulated. To investigate and analyze the effect of internal fluid flow on the longitudinal vibration and stability of SWCNT, the equation of motion for longitudinal vibration is obtained by using Navier-Stokes equations. In the governing equation of motion, the interaction of fluid-structure, dynamic and fluid flow velocity along the axial coordinate of the nanotube and the nano-scale effect of the structure are considered. To solve the nonlocal longitudinal vibration equation, the approximate Galerkin method is employed and appropriate simply supported boundary conditions are applied. The results show that the axial vibrations of the nanotubesstrongly depend on the small-size effect. In addition, the fluid flowing in nanotube causes a decrease in the natural frequency of the system. It is obvious that the system natural frequencies reach zero at lower critical flow velocities as the wave number increases. Moreover, the critical flow velocity decreases as the nonlocal parameter increases.

Bayesian Inference of High-Dimensional Dynamical Ocean Models

NASA Astrophysics Data System (ADS)

Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.

2015-12-01

This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.

Existence of the passage to the limit of an inviscid fluid.

PubMed

Goldobin, Denis S

2017-11-24

In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.

Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves

PubMed Central

Velescu, Cornel; Popa, Nicolae Calin

2014-01-01

We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances) and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc.), for the laminar and permanent motion regime. PMID:24526896

Laminar motion of the incompressible fluids in self-acting thrust bearings with spiral grooves.

PubMed

Velescu, Cornel; Popa, Nicolae Calin

2014-01-01

We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the "pumping" direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances) and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc.), for the laminar and permanent motion regime.

The dynamic two-fluid model OLGA; Theory and application

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bendiksen, K.H.; Maines, D.; Moe, R.

1991-05-01

Dynamic two-fluid models have found a wide range of application in the simulation of two-phase-flow systems, particularly for the analysis of steam/water flow in the core of a nuclear reactor. Until quite recently, however, very few attempts have been made to use such models in the simulation of two-phase oil and gas flow in pipelines. This paper presents a dynamic two-fluid model, OLGA, in detail, stressing the basic equations and the two-fluid models applied. Predictions of steady-state pressure drop, liquid hold-up, and flow-regime transitions are compared with data from the SINTEF Two-Phase Flow Laboratory and from the literature. Comparisons withmore » evaluated field data are also presented.« less

[Study on the dynamic model with supercritical CO2 fluid extracting the lipophilic components in Panax notoginseng].

PubMed

Duan, Xian-Chun; Wang, Yong-Zhong; Zhang, Jun-Ru; Luo, Huan; Zhang, Heng; Xia, Lun-Zhu

2011-08-01

To establish a dynamics model for extracting the lipophilic components in Panax notoginseng with supercritical carbon dioxide (CO2). Based on the theory of counter-flow mass transfer and the molecular mass transfer between the material and the supercritical CO2 fluid under differential mass-conservation equation, a dynamics model was established and computed to compare forecasting result with the experiment process. A dynamics model has been established for supercritical CO2 to extract the lipophilic components in Panax notoginseng, the computed result of this model was consistent with the experiment process basically. The supercritical fluid extract dynamics model established in this research can expound the mechanism in the extract process of which lipophilic components of Panax notoginseng dissolve the mass transfer and is tallied with the actual extract process. This provides certain instruction for the supercritical CO2 fluid extract' s industrialization enlargement.

Interfacial gauge methods for incompressible fluid dynamics

PubMed Central

Saye, Robert

2016-01-01

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of “gauge freedom” to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work, high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena. PMID:27386567

Fluid Dynamics of Bottle Filling

NASA Astrophysics Data System (ADS)

McGough, Patrick; Gao, Haijing; Appathurai, Santosh; Basaran, Osman

2011-11-01

Filling of bottles is a widely practiced operation in a large number of industries. Well known examples include filling of ``large'' bottles with shampoos and cleaners in the household products and beauty care industries and filling of ``small'' bottles in the pharmaceutical industry. Some bottle filling operations have recently drawn much attention from the fluid mechanics community because of the occurrence of a multitude of complex flow regimes, transitions, and instabilities such as mounding and coiling that occur as a bottle is filled with a fluid. In this talk, we present a primarily computational study of the fluid dynamical challenges that can arise during the rapid filling of bottles. Given the diversity of fluids used in filling applications, we consider four representative classes of fluids that exhibit Newtonian, shear-thinning, viscoelastic, and yield-stress rheologies. The equations governing the dynamics of bottle filling are solved either in their full 3D but axisymmetric form or using the slender-jet approximation.

Unsteady Magnetized Flow and Heat Transfer of a Viscoelastic fluid over a Stretching Surface

NASA Astrophysics Data System (ADS)

Ghosh, Sushil Kumar

2017-12-01

This paper is to study the flow of heated ferro-fluid over a stretching sheet under the influence of magnetic field. The fluid considered in the present investigation is a mixture of blood as well as fluid-dispersed magnetic nano particles and under this context blood is found to be the appropriate choice of viscoelastic, Walter's B fluid. The objective of the present work is to study the effect of various parameters found in the mathematical analysis. Taking into account the blood has zero electrical conductivity, magnetization effect has been considered in the governing equation of the present study with the use of ferro-fluid dynamics principle. By introducing appropriate non-dimensional variables into the governing equations of unsteady two-dimensional flow of viscoelastic fluid with heat transfer are converted to a set of ordinary differential equations with appropriate boundary conditions. Newton's linearization technique has been employed for the solution of non-linear ordinary differential equations. Important results found in the present investigation are the substantial influence of ferro-magnetic parameter, Prandlt number and the parameter associated with the thermal conductivity on the flow and heat transfer. It is observed that the presence of magnetic dipole essentially reduces the flow velocity in the vertical direction and that helps to damage the cancer cells in the tumor region.

Coupling of electromagnetics and structural/fluid dynamics - application to the dual coolant blanket subjected to plasma disruptions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jordan, T.

Some aspects concerning the coupling of quasi-stationary electromagnetics and the dynamics of structure and fluid are investigated. The necessary equations are given in a dimensionless form. The dimensionless parameters in these equations are used to evaluate the importance of the different coupling effects. A finite element formulation of the eddy-current damping in solid structures is developed. With this formulation, an existing finite element method (FEM) structural dynamics code is extended and coupled to an FEM eddy-current code. With this program system, the influence of the eddy-current damping on the dynamic loading of the dual coolant blanket during a centered plasmamore » disruption is determined. The analysis proves that only in loosely fixed or soft structures will eddy-current damping considerably reduce the resulting stresses. Additionally, the dynamic behavior of the liquid metal in the blankets` poloidal channels is described with a simple two-dimensional magnetohydrodynamic approach. The analysis of the dimensionless parameters shows that for small-scale experiments, which are designed to model the coupled electromagnetic and structural/fluid dynamic effects in such a blanket, the same magnetic fields must be applied as in the real fusion device. This will be the easiest way to design experiments that produce transferable results. 10 refs., 7 figs.« less

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Cole, Helen; Chen, C. P.

2005-01-01

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Sun, Yan

2018-01-01

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

A finite difference method for a coupled model of wave propagation in poroelastic materials.

PubMed

Zhang, Yang; Song, Limin; Deffenbaugh, Max; Toksöz, M Nafi

2010-05-01

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.

A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

NASA Astrophysics Data System (ADS)

Halpern, Federico

2017-10-01

The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

Numerical models analysis of energy conversion process in air-breathing laser propulsion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong Yanji; Song Junling; Cui Cunyan

Energy source was considered as a key essential in this paper to describe energy conversion process in air-breathing laser propulsion. Some secondary factors were ignored when three independent modules, ray transmission module, energy source term module and fluid dynamic module, were established by simultaneous laser radiation transportation equation and fluid mechanics equation. The incidence laser beam was simulated based on ray tracing method. The calculated results were in good agreement with those of theoretical analysis and experiments.

Experimental Validation of a Coupled Fluid-Multibody Dynamics Model for Tanker Trucks

DTIC Science & Technology

2007-11-08

order to accurately predict the dynamic response of tanker trucks, the model must accurately account for the following effects : • Incompressible...computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of motion. Many commercial...position vector, τ is the deviatoric stress tensor, D is the rate of deformation tensor, f r is the body force vector, r is the artificial

Rogue waves and lump solitons for a ?-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Yin, Hui-Min

2018-07-01

Under investigation is a ?-dimensional B-type Kadomtsev-Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, ?, increasing when ?. In addition, dark rogue waves are derived when ?. Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter ?, and amplitude of the lump soliton is negatively correlated with ? when ?.

A nonequilibrium model for a moderate pressure hydrogen microwave discharge plasma

NASA Technical Reports Server (NTRS)

Scott, Carl D.

1993-01-01

This document describes a simple nonequilibrium energy exchange and chemical reaction model to be used in a computational fluid dynamics calculation for a hydrogen plasma excited by microwaves. The model takes into account the exchange between the electrons and excited states of molecular and atomic hydrogen. Specifically, electron-translation, electron-vibration, translation-vibration, ionization, and dissociation are included. The model assumes three temperatures, translational/rotational, vibrational, and electron, each describing a Boltzmann distribution for its respective energy mode. The energy from the microwave source is coupled to the energy equation via a source term that depends on an effective electric field which must be calculated outside the present model. This electric field must be found by coupling the results of the fluid dynamics and kinetics solution with a solution to Maxwell's equations that includes the effects of the plasma permittivity. The solution to Maxwell's equations is not within the scope of this present paper.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Application research of computational mass-transfer differential equation in MBR concentration field simulation.

PubMed

Li, Chunqing; Tie, Xiaobo; Liang, Kai; Ji, Chanjuan

2016-01-01

After conducting the intensive research on the distribution of fluid's velocity and biochemical reactions in the membrane bioreactor (MBR), this paper introduces the use of the mass-transfer differential equation to simulate the distribution of the chemical oxygen demand (COD) concentration in MBR membrane pool. The solutions are as follows: first, use computational fluid dynamics to establish a flow control equation model of the fluid in MBR membrane pool; second, calculate this model by adopting direct numerical simulation to get the velocity field of the fluid in membrane pool; third, combine the data of velocity field to establish mass-transfer differential equation model for the concentration field in MBR membrane pool, and use Seidel iteration method to solve the equation model; last but not least, substitute the real factory data into the velocity and concentration field model to calculate simulation results, and use visualization software Tecplot to display the results. Finally by analyzing the nephogram of COD concentration distribution, it can be found that the simulation result conforms the distribution rule of the COD's concentration in real membrane pool, and the mass-transfer phenomenon can be affected by the velocity field of the fluid in membrane pool. The simulation results of this paper have certain reference value for the design optimization of the real MBR system.

Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

PubMed

Felderhof, B U

2013-08-01

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

A GPU-based incompressible Navier-Stokes solver on moving overset grids

NASA Astrophysics Data System (ADS)

Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

2013-07-01

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

Fluid dynamics of the magnetic field dependent thermosolutal convection and viscosity between coaxial contracting discs

NASA Astrophysics Data System (ADS)

Khan, Aamir; Shah, Rehan Ali; Shuaib, Muhammad; Ali, Amjad

2018-06-01

The effects of magnetic field dependent (MFD) thermosolutal convection and MFD viscosity of the fluid dynamics are investigated between squeezing discs rotating with different velocities. The unsteady constitutive expressions of mass conservation, modified Navier-Stokes, Maxwell and MFD thermosolutal convection are coupled as a system of ordinary differential equations. The corresponding solutions for the transformed radial and azimuthal momentum as well as solutions for the azimuthal and axial induced magnetic field equations are determined, also the MHD pressure and torque which the fluid exerts on the upper disc is derived and discussed in details. In the case of smooth discs the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The validity and accuracy of HAM results is proved by comparison of the HAM solutions with numerical solver package BVP4c. It has been shown that magnetic Reynolds number causes to decrease magnetic field distributions, fluid temperature, axial and tangential velocity. Also azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems, heating up or cooling processes, biological sensor systems and biological prosthetic etc.

Dynamics of Robertson–Walker spacetimes with diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alho, A., E-mail: aalho@math.ist.utl.pt; Calogero, S., E-mail: calogero@chalmers.se; Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt

2015-03-15

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.

Prediction of pressure drop in fluid tuned mounts using analytical and computational techniques

NASA Technical Reports Server (NTRS)

Lasher, William C.; Khalilollahi, Amir; Mischler, John; Uhric, Tom

1993-01-01

A simplified model for predicting pressure drop in fluid tuned isolator mounts was developed. The model is based on an exact solution to the Navier-Stokes equations and was made more general through the use of empirical coefficients. The values of these coefficients were determined by numerical simulation of the flow using the commercial computational fluid dynamics (CFD) package FIDAP.

Coarsening dynamics of binary liquids with active rotation.

PubMed

Sabrina, Syeda; Spellings, Matthew; Glotzer, Sharon C; Bishop, Kyle J M

2015-11-21

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.

The Mochi project: a field theory approach to plasma dynamics and self-organization

NASA Astrophysics Data System (ADS)

You, Setthivoine; von der Linden, Jens; Lavine, Eric Sander; Card, Alexander; Carroll, Evan

2016-10-01

The Mochi project is designed to study the interaction between plasma flows and magnetic fields from the point-of-view of canonical flux tubes. The Mochi Labjet experiment is being commissioned after achieving first plasma. Analytical and numerical tools are being developed to visualize canonical flux tubes. One analytical tool described here is a field theory approach to plasma dynamics and self-organization. A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. This work is supported by by US DOE Grant DE-SC0010340.

A Smoluchowski model of crystallization dynamics of small colloidal clusters

NASA Astrophysics Data System (ADS)

Beltran-Villegas, Daniel J.; Sehgal, Ray M.; Maroudas, Dimitrios; Ford, David M.; Bevan, Michael A.

2011-10-01

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

Advances in modelling of biomimetic fluid flow at different scales

PubMed Central

2011-01-01

The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed. PMID:21711847

Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Padmanabhan, T.

2011-02-15

It has been known for several decades that Einstein's field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather thanmore » a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.« less

Interfacial gauge methods for incompressible fluid dynamics

DOE PAGES

Saye, R.

2016-06-10

Designing numerical methods for incompressible fluid flow involving moving interfaces, for example, in the computational modeling of bubble dynamics, swimming organisms, or surface waves, presents challenges due to the coupling of interfacial forces with incompressibility constraints. A class of methods, denoted interfacial gauge methods, is introduced for computing solutions to the corresponding incompressible Navier-Stokes equations. These methods use a type of "gauge freedom" to reduce the numerical coupling between fluid velocity, pressure, and interface position, allowing high-order accurate numerical methods to be developed more easily. Making use of an implicit mesh discontinuous Galerkin framework, developed in tandem with this work,more » high-order results are demonstrated, including surface tension dynamics in which fluid velocity, pressure, and interface geometry are computed with fourth-order spatial accuracy in the maximum norm. Applications are demonstrated with two-phase fluid flow displaying fine-scaled capillary wave dynamics, rigid body fluid-structure interaction, and a fluid-jet free surface flow problem exhibiting vortex shedding induced by a type of Plateau-Rayleigh instability. The developed methods can be generalized to other types of interfacial flow and facilitate precise computation of complex fluid interface phenomena.« less

Molecular dynamics studies of transport properties and equation of state of supercritical fluids

NASA Astrophysics Data System (ADS)

Nwobi, Obika C.

Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the coefficients.

Turbulent motion of mass flows. Mathematical modeling

NASA Astrophysics Data System (ADS)

Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana

2016-04-01

New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

Multiscale turbulence models based on convected fluid microstructure

NASA Astrophysics Data System (ADS)

Holm, Darryl D.; Tronci, Cesare

2012-11-01

The Euler-Poincaré approach to complex fluids is used to derive multiscale equations for computationally modeling Euler flows as a basis for modeling turbulence. The model is based on a kinematic sweeping ansatz (KSA) which assumes that the mean fluid flow serves as a Lagrangian frame of motion for the fluctuation dynamics. Thus, we regard the motion of a fluid parcel on the computationally resolvable length scales as a moving Lagrange coordinate for the fluctuating (zero-mean) motion of fluid parcels at the unresolved scales. Even in the simplest two-scale version on which we concentrate here, the contributions of the fluctuating motion under the KSA to the mean motion yields a system of equations that extends known results and appears to be suitable for modeling nonlinear backscatter (energy transfer from smaller to larger scales) in turbulence using multiscale methods.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

The Kantowski-Sachs Quantum Model with Stiff Matter Fluid

NASA Astrophysics Data System (ADS)

Alvarenga, F. G.; Fracalossi, R.; Freitas, R. C.; Gonçalves, S. V. B.

2018-05-01

In this paper, we study the quantum cosmological Kantowski-Sachs model and we solve the Wheeler-DeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The viability of this model is analyzed and discussed.

Computational fluid dynamics: Transition to design applications

NASA Technical Reports Server (NTRS)

Bradley, R. G.; Bhateley, I. C.; Howell, G. A.

1987-01-01

The development of aerospace vehicles, over the years, was an evolutionary process in which engineering progress in the aerospace community was based, generally, on prior experience and data bases obtained through wind tunnel and flight testing. Advances in the fundamental understanding of flow physics, wind tunnel and flight test capability, and mathematical insights into the governing flow equations were translated into improved air vehicle design. The modern day field of Computational Fluid Dynamics (CFD) is a continuation of the growth in analytical capability and the digital mathematics needed to solve the more rigorous form of the flow equations. Some of the technical and managerial challenges that result from rapidly developing CFD capabilites, some of the steps being taken by the Fort Worth Division of General Dynamics to meet these challenges, and some of the specific areas of application for high performance air vehicles are presented.

Dynamics modeling and vibration analysis of a piezoelectric diaphragm applied in valveless micropump

NASA Astrophysics Data System (ADS)

He, Xiuhua; Xu, Wei; Lin, Nan; Uzoejinwa, B. B.; Deng, Zhidan

2017-09-01

This paper presents the dynamical model involved with load of fluid pressure, electric-solid coupling simulation and experimental performance of the piezoelectric diaphragm fabricated and applied in valveless micropump. The model is based on the theory of plate-shell with small deflection, considering the two-layer structure of piezoelectric ceramic and elastic substrate. The high-order non-homogeneous vibration equation of the piezoelectric diaphragm, derived in the course of the study, was solved by being divided into a homogeneous Bessel equation and a non-homogeneous static equation according to the superposition principle. The amplitude of the piezoelectric diaphragm driven by sinusoidal voltage against the load of fluid pressure was obtained from the solution of the vibration equation. Also, finite element simulation of electric-solid coupling between displacement of piezoelectric diaphragm due to an applied voltage and resulting deformation of membrane was considered. The simulation result showed that the maximum deflection of diaphragm is 9.51 μm at a quarter cycle time when applied a peak-to-peak voltage of 150VP-P with a frequency of 90 Hz, and the displacement distribution according to the direction of the radius was demonstrated. Experiments were performed to verify the prediction of the dynamic modeling and the coupling simulation, the experimental data showed a good agreement with the dynamical model and simulation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbante, Paolo; Frezzotti, Aldo; Gibelli, Livio

The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviationsmore » of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.« less

Parallel aeroelastic computations for wing and wing-body configurations

NASA Technical Reports Server (NTRS)

Byun, Chansup

1994-01-01

The objective of this research is to develop computationally efficient methods for solving fluid-structural interaction problems by directly coupling finite difference Euler/Navier-Stokes equations for fluids and finite element dynamics equations for structures on parallel computers. This capability will significantly impact many aerospace projects of national importance such as Advanced Subsonic Civil Transport (ASCT), where the structural stability margin becomes very critical at the transonic region. This research effort will have direct impact on the High Performance Computing and Communication (HPCC) Program of NASA in the area of parallel computing.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Fluid dynamics following flow shut-off in bottle filling

NASA Astrophysics Data System (ADS)

Thete, Sumeet; Appathurai, Santosh; Gao, Haijing; Basaran, Osman

2012-11-01

Bottle filling is ubiquitous in industry. Examples include filling of bottles with shampoos and cleaners, engine oil and pharmaceuticals. In these examples, fluid flows out of a nozzle to fill bottles in an assembly line. Once the required volume of fluid has flowed out of the nozzle, the flow is shut off. However, an evolving fluid thread or string may remain suspended from the nozzle following flow shut-off and persist. This stringing phenomenon can be detrimental to a bottle filling operation because it can adversely affect line speed and filling accuracy by causing uncertainty in fill volume, product loss and undesirable marring of the bottles' exterior surfaces. The dynamics of stringing are studied numerically primarily by using the 1D, slender-jet approximation of the flow equations. A novel feature entails development and use of a new boundary condition downstream of the nozzle exit to expedite the computations. While the emphasis is on stringing of Newtonian fluids and use of 1D approximations, results will also be presented for situations where (a) the fluids are non-Newtonian and (b) the full set of equations are solved without invoking the 1D approximation. Phase diagrams will be presented that identify conditions for which stringing can be problematic.

Extension of Miles Equation for Ring Baffle Damping Predictions to Small Slosh Amplitudes and Large Baffle Widths

NASA Technical Reports Server (NTRS)

West, Jeff; Yang, H. Q.; Brodnick, Jacob; Sansone, Marco; Westra, Douglas

2016-01-01

The Miles equation has long been used to predict slosh damping in liquid propellant tanks due to ring baffles. The original work by Miles identifies defined limits to its range of application. Recent evaluations of the Space Launch System identified that the Core Stage baffle designs resulted in violating the limits of the application of the Miles equation. This paper describes the work conducted by NASA/MSFC to develop methods to predict slosh damping from ring baffles for conditions for which Miles equation is not applicable. For asymptotically small slosh amplitudes or conversely large baffle widths, an asymptotic expression for slosh damping was developed and calibrated using historical experimental sub-scale slosh damping data. For the parameter space that lies between region of applicability of the asymptotic expression and the Miles equation, Computational Fluid Dynamics simulations of slosh damping were used to develop an expression for slosh damping. The combined multi-regime slosh prediction methodology is shown to be smooth at regime boundaries and consistent with both sub-scale experimental slosh damping data and the results of validated Computational Fluid Dynamics predictions of slosh damping due to ring baffles.

Formulation and closure of compressible turbulence equations in the light of kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.; Sagara, K.

1976-01-01

Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

On the inclusion of mass source terms in a single-relaxation-time lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Aursjø, Olav; Jettestuen, Espen; Vinningland, Jan Ludvig; Hiorth, Aksel

2018-05-01

We present a lattice Boltzmann algorithm for incorporating a mass source in a fluid flow system. The proposed mass source/sink term, included in the lattice Boltzmann equation, maintains the Galilean invariance and the accuracy of the overall method, while introducing a mass source/sink term in the fluid dynamical equations. The method can, for instance, be used to inject or withdraw fluid from any preferred lattice node in a system. This suggests that injection and withdrawal of fluid does not have to be introduced through cumbersome, and sometimes less accurate, boundary conditions. The method also suggests that, through a chosen equation of state relating mass density to pressure, the proposed mass source term will render it possible to set a preferred pressure at any lattice node in a system. We demonstrate how this model handles injection and withdrawal of a fluid. And we show how it can be used to incorporate pressure boundaries. The accuracy of the algorithm is identified through a Chapman-Enskog expansion of the model and supported by the numerical simulations.

Analysis of Two-Phase Flow in Damper Seals for Cryogenic Turbopumps

NASA Technical Reports Server (NTRS)

Arauz, Grigory L.; SanAndres, Luis

1996-01-01

Cryogenic damper seals operating close to the liquid-vapor region (near the critical point or slightly su-cooled) are likely to present two-phase flow conditions. Under single phase flow conditions the mechanical energy conveyed to the fluid increases its temperature and causes a phase change when the fluid temperature reaches the saturation value. A bulk-flow analysis for the prediction of the dynamic force response of damper seals operating under two-phase conditions is presented as: all-liquid, liquid-vapor, and all-vapor, i.e. a 'continuous vaporization' model. The two phase region is considered as a homogeneous saturated mixture in thermodynamic equilibrium. Th flow in each region is described by continuity, momentum and energy transport equations. The interdependency of fluid temperatures and pressure in the two-phase region (saturated mixture) does not allow the use of an energy equation in terms of fluid temperature. Instead, the energy transport is expressed in terms of fluid enthalpy. Temperature in the single phase regions, or mixture composition in the two phase region are determined based on the fluid enthalpy. The flow is also regarded as adiabatic since the large axial velocities typical of the seal application determine small levels of heat conduction to the walls as compared to the heat carried by fluid advection. Static and dynamic force characteristics for the seal are obtained from a perturbation analysis of the governing equations. The solution expressed in terms of zeroth and first order fields provide the static (leakage, torque, velocity, pressure, temperature, and mixture composition fields) and dynamic (rotordynamic force coefficients) seal parameters. Theoretical predictions show good agreement with experimental leakage pressure profiles, available from a Nitrogen at cryogenic temperatures. Force coefficient predictions for two phase flow conditions show significant fluid compressibility effects, particularly for mixtures with low mass content of vapor. Under these conditions, an increase on direct stiffness and reduction of whirl frequency ratio are shown to occur. Prediction of such important effects will motivate experimental studies as well as a more judicious selection of the operating conditions for seals used in cryogenic turbomachinery.

NASA Computational Fluid Dynamics Conference. Volume 1: Sessions 1-6

NASA Technical Reports Server (NTRS)

1989-01-01

Presentations given at the NASA Computational Fluid Dynamics (CFD) Conference held at the NASA Ames Research Center, Moffett Field, California, March 7-9, 1989 are given. Topics covered include research facility overviews of CFD research and applications, validation programs, direct simulation of compressible turbulence, turbulence modeling, advances in Runge-Kutta schemes for solving 3-D Navier-Stokes equations, grid generation and invicid flow computation around aircraft geometries, numerical simulation of rotorcraft, and viscous drag prediction for rotor blades.

Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons.

PubMed

Cerfon, Antoine J

2016-04-29

We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

Test of a new heat-flow equation for dense-fluid shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

Studies of the nucler equation of state using numerical calculations of nuclear drop collisions

NASA Technical Reports Server (NTRS)

Alonso, C. T.; Leblanc, J. M.; Wilson, J. R.

1982-01-01

A numerical calculation for the full thermal dynamics of colliding nuclei was developed. Preliminary results are reported for the thermal fluid dynamics in such processes as Coulomb scattering, fusion, fusion-fission, bulk oscillations, compression with heating, and collisions of heated nuclei.

Fast methods to numerically integrate the Reynolds equation for gas fluid films

NASA Technical Reports Server (NTRS)

Dimofte, Florin

1992-01-01

The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid films. An efficient code is developed to predict both the steady-state and dynamic performance of an aerodynamic journal bearing. An alternative approach is shown for hybrid journal gas bearings by using Liebmann's iterative solution (LIS) for elliptic partial differential equations. The results are compared with known design criteria from experimental data. The developed methods show good accuracy and very short computer running time in comparison with methods based on an inverting of a matrix. The computer codes need a small amount of memory and can be run on either personal computers or on mainframe systems.

Crystal Growth and Fluid Mechanics Problems in Directional Solidification

NASA Technical Reports Server (NTRS)

Tanveer, Saleh A.; Baker, Gregory R.; Foster, Michael R.

2001-01-01

Our work in directional solidification has been in the following areas: (1) Dynamics of dendrites including rigorous mathematical analysis of the resulting equations; (2) Examination of the near-structurally unstable features of the mathematically related Hele-Shaw dynamics; (3) Numerical studies of steady temperature distribution in a vertical Bridgman device; (4) Numerical study of transient effects in a vertical Bridgman device; (5) Asymptotic treatment of quasi-steady operation of a vertical Bridgman furnace for large Rayleigh numbers and small Biot number in 3D; and (6) Understanding of Mullins-Sererka transition in a Bridgman device with fluid dynamics is accounted for.

International Congress of Fluid Mechanics, 3rd, Cairo, Egypt, Jan. 2-4, 1990, Proceedings. Volumes 1, 2, 3, & 4

NASA Astrophysics Data System (ADS)

Nayfeh, A. H.; Mobarak, A.; Rayan, M. Abou

This conference presents papers in the fields of flow separation, unsteady aerodynamics, fluid machinery, boundary-layer control and stability, grid generation, vorticity dominated flows, and turbomachinery. Also considered are propulsion, waves and sound, rotor aerodynamics, computational fluid dynamics, Euler and Navier-Stokes equations, cavitation, mixing and shear layers, mixing layers and turbulent flows, and fluid machinery and two-phase flows. Also addressed are supersonic and reacting flows, turbulent flows, and thermofluids.

Holographic DC conductivity and Onsager relations

NASA Astrophysics Data System (ADS)

Donos, Aristomenis; Gauntlett, Jerome P.; Griffin, Tom; Lohitsiri, Nakarin; Melgar, Luis

2017-07-01

Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.

A unified equation of state for fluids of C-H-O-N-S-Ar composition and their mixtures up to very high temperatures and pressures

NASA Astrophysics Data System (ADS)

Belonoshko, A. B.; Saxena, S. K.

1992-10-01

A unified equation of state (EOS) is derived for 13 gases (including H2O, CO2, CH4, CO, O2, H2, Ar, N2, NH3, H2S, SO2, COS, and S2) in C-H-O-N-S-Ar system, on the basis of molecular dynamical simulated PVT data, assuming these species to be alpha-exponential-6 fluids at high temperature and pressure. The EOS equation is parameterized for these gases in the ranges of temperature and pressure 400-4000 K and 5-1000 kbar, respectively. It is shown that the equation reproduces most of the available experimental data in the limits of experimental accuracy of volume measurements.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

Lectures series in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Thompson, Kevin W.

1987-01-01

The lecture notes cover the basic principles of computational fluid dynamics (CFD). They are oriented more toward practical applications than theory, and are intended to serve as a unified source for basic material in the CFD field as well as an introduction to more specialized topics in artificial viscosity and boundary conditions. Each chapter in the test is associated with a videotaped lecture. The basic properties of conservation laws, wave equations, and shock waves are described. The duality of the conservation law and wave representations is investigated, and shock waves are examined in some detail. Finite difference techniques are introduced for the solution of wave equations and conservation laws. Stability analysis for finite difference approximations are presented. A consistent description of artificial viscosity methods are provided. Finally, the problem of nonreflecting boundary conditions are treated.

Simple waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.

2018-04-01

We study the dynamics of so-called simple waves in a two-component Bose-Einstein condensate. The evolution of the condensate is described by Gross-Pitaevskii equations which can be reduced for these simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fluid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between interspecies and intraspecies nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.

Static and dynamic characteristics of parallel-grooved seals

NASA Technical Reports Server (NTRS)

Iwatsubo, Takuzo; Yang, Bo-Suk; Ibaraki, Ryuji

1987-01-01

Presented is an analytical method to determine static and dynamic characteristics of annular parallel-grooved seals. The governing equations were derived by using the turbulent lubrication theory based on the law of fluid friction. Linear zero- and first-order perturbation equations of the governing equations were developed, and these equations were analytically investigated to obtain the reaction force of the seals. An analysis is presented that calculates the leakage flow rate, the torque loss, and the rotordynamic coefficients for parallel-grooved seals. To demonstrate this analysis, we show the effect of changing number of stages, land and groove width, and inlet swirl on stability of the boiler feed water pump seals. Generally, as the number of stages increased or the grooves became wider, the leakage flow rate and rotor-dynamic coefficients decreased and the torque loss increased.

Prediction and control of slender-wing rock

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Salman, Ahmed A.

1992-01-01

The unsteady Euler equations and the Euler equations of rigid-body dynamics, both written in the moving frame of reference, are sequentially solved to simulate the limit-cycle rock motion of slender delta wings. The governing equations of the fluid flow and the dynamics of the present multidisciplinary problem are solved using an implicit, approximately-factored, central-difference-like, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. For the control of wing-rock motion, leading-edge flaps are forced to oscillate anti-symmetrically at prescribed frequency and amplitude, which are tuned in order to suppress the rock motion. Since the computational grid deforms due to the leading-edge flaps motion, the grid is dynamically deformed using the Navier-displacement equations. Computational applications cover locally-conical and three-dimensional solutions for the wing-rock simulation and its control.

Dynamics of charged viscous dissipative cylindrical collapse with full causal approach

NASA Astrophysics Data System (ADS)

Shah, S. M.; Abbas, G.

2017-11-01

The aim of this paper is to investigate the dynamical aspects of a charged viscous cylindrical source by using the Misner approach. To this end, we have considered the more general charged dissipative fluid enclosed by the cylindrical symmetric spacetime. The dissipative nature of the source is due to the presence of dissipative variables in the stress-energy tensor. The dynamical equations resulting from such charged cylindrical dissipative source have been coupled with the causal transport equations for heat flux, shear and bulk viscosity, in the context of the Israel-Steward theory. In this case, we have the considered Israel-Steward transportation equations without excluding the thermodynamics viscous/heat coupling coefficients. The results are compared with the previous works in which such coefficients were excluded and viscosity variables do not satisfy the casual transportation equations.

Running interfacial waves in a two-layer fluid system subject to longitudinal vibrations.

PubMed

Goldobin, D S; Pimenova, A V; Kovalevskaya, K V; Lyubimov, D V; Lyubimova, T P

2015-05-01

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

Large-eddy simulation of oxygen transport and depletion in waterbodies

NASA Astrophysics Data System (ADS)

Scalo, Carlo; Piomelli, Ugo; Boegman, Leon

2010-11-01

Dissolved oxygen (DO) in water plays an important role in lake and marine ecosystems. Agricultural runoff may spur excessive plant growth on the water surface; when the plants die they sink to the bottom of the water bodies and decompose, consuming oxygen. Significant environmental (and economic) damage may result from the loss of aquatic life caused by the oxygen depletion. The study of DO transport and depletion dynamics in water bodies has, therefore, become increasingly important. We study this phenomenon by large-eddy simulations performed at laboratory scale. The equations governing the transport of momentum and of a scalar (the DO) in the fluid are coupled to a biochemical model for DO depletion in the permeable sediment bed [Higashino et al., Water Res. (38) 1, 2004)], and to an equation for the fluid transpiration in the porous medium. The simulations are in good agreement with previous calculations and experiments. We show that the results are sensitive to the biochemical and fluid dynamical properties of the sediment, which are very difficult to determine experimentally.

Automating the parallel processing of fluid and structural dynamics calculations

NASA Technical Reports Server (NTRS)

Arpasi, Dale J.; Cole, Gary L.

1987-01-01

The NASA Lewis Research Center is actively involved in the development of expert system technology to assist users in applying parallel processing to computational fluid and structural dynamic analysis. The goal of this effort is to eliminate the necessity for the physical scientist to become a computer scientist in order to effectively use the computer as a research tool. Programming and operating software utilities have previously been developed to solve systems of ordinary nonlinear differential equations on parallel scalar processors. Current efforts are aimed at extending these capabilities to systems of partial differential equations, that describe the complex behavior of fluids and structures within aerospace propulsion systems. This paper presents some important considerations in the redesign, in particular, the need for algorithms and software utilities that can automatically identify data flow patterns in the application program and partition and allocate calculations to the parallel processors. A library-oriented multiprocessing concept for integrating the hardware and software functions is described.

Vibration analysis of partially cracked plate submerged in fluid

NASA Astrophysics Data System (ADS)

Soni, Shashank; Jain, N. K.; Joshi, P. V.

2018-01-01

The present work proposes an analytical model for vibration analysis of partially cracked rectangular plates coupled with fluid medium. The governing equation of motion for the isotropic plate based on the classical plate theory is modified to accommodate a part through continuous line crack according to simplified line spring model. The influence of surrounding fluid medium is incorporated in the governing equation in the form of inertia effects based on velocity potential function and Bernoulli's equations. Both partially and totally submerged plate configurations are considered. The governing equation also considers the in-plane stretching due to lateral deflection in the form of in-plane forces which introduces geometric non-linearity into the system. The fundamental frequencies are evaluated by expressing the lateral deflection in terms of modal functions. The assessment of the present results is carried out for intact submerged plate as to the best of the author's knowledge the literature lacks in analytical results for submerged cracked plates. New results for fundamental frequencies are presented as affected by crack length, fluid level, fluid density and immersed depth of plate. By employing the method of multiple scales, the frequency response and peak amplitude of the cracked structure is analyzed. The non-linear frequency response curves show the phenomenon of bending hardening or softening and the effect of fluid dynamic pressure on the response of the cracked plate.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy: II. Numerical predictions and experimental tests.

USGS Publications Warehouse

George, David L.; Iverson, Richard M.

2014-01-01

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model’s five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure, and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here we recapitulate the equations and analyze their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout, and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses, and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

A numerical relativity scheme for cosmological simulations

NASA Astrophysics Data System (ADS)

Daverio, David; Dirian, Yves; Mitsou, Ermis

2017-12-01

Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chang, E-mail: cliuaa@ust.hk; Xu, Kun, E-mail: makxu@ust.hk; Sun, Quanhua, E-mail: qsun@imech.ac.cn

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, themore » dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region where it is needed. The central ingredient of the UGKS is the coupled treatment of particle transport and collision in the flux evaluation across a cell interface, where a continuous flow dynamics from kinetic to hydrodynamic scales is modeled. The newly developed UGKS has the asymptotic preserving (AP) property of recovering the NS solutions in the continuum flow regime, and the full Boltzmann solution in the rarefied regime. In the mostly unexplored transition regime, the UGKS itself provides a valuable tool for the non-equilibrium flow study. The mathematical properties of the scheme, such as stability, accuracy, and the asymptotic preserving, will be analyzed in this paper as well.« less

Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Yan, Zhenya

2017-02-01

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.

Role of computational fluid dynamics in unsteady aerodynamics for aeroelasticity

NASA Technical Reports Server (NTRS)

Guruswamy, Guru P.; Goorjian, Peter M.

1989-01-01

In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized.

Normal compression wave scattering by a permeable crack in a fluid-saturated poroelastic solid

NASA Astrophysics Data System (ADS)

Song, Yongjia; Hu, Hengshan; Rudnicki, John W.

2017-04-01

A mathematical formulation is presented for the dynamic stress intensity factor (mode I) of a finite permeable crack subjected to a time-harmonic propagating longitudinal wave in an infinite poroelastic solid. In particular, the effect of the wave-induced fluid flow due to the presence of a liquid-saturated crack on the dynamic stress intensity factor is analyzed. Fourier sine and cosine integral transforms in conjunction with Helmholtz potential theory are used to formulate the mixed boundary-value problem as dual integral equations in the frequency domain. The dual integral equations are reduced to a Fredholm integral equation of the second kind. It is found that the stress intensity factor monotonically decreases with increasing frequency, decreasing the fastest when the crack width and the slow wave wavelength are of the same order. The characteristic frequency at which the stress intensity factor decays the fastest shifts to higher frequency values when the crack width decreases.

Transition and separation process in brine channels formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berti, Alessia, E-mail: alessia.berti@unibs.it; Bochicchio, Ivana, E-mail: ibochicchio@unisa.it; Fabrizio, Mauro, E-mail: mauro.fabrizio@unibo.it

2016-02-15

In this paper, we discuss the formation of brine channels in sea ice. The model includes a time-dependent Ginzburg-Landau equation for the solid-liquid phase change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics, and the heat equation for the temperature change. The macroscopic motion of the fluid is also considered, so the resulting differential system couples with the Navier-Stokes equation. The compatibility of this system with the thermodynamic laws and a maximum theorem is proved.

Simple cubic equation of state applied to hard-sphere, Lennard-Jones fluids, simple fluids and solids

NASA Astrophysics Data System (ADS)

Sun, Jiu-Xun; Cai, Ling-Cang; Wu, Qiang; Jin, Ke

2013-09-01

Based on the expansion and extension of the virial equation of state (EOS) of hard-sphere fluids solved by the Percus-Yevick integration equation, a universal cubic (UC) EOS is developed. The UC EOS is applied to model hard-sphere and Lennard-Jones (LJ) fluids, simple Ar and N2 liquids at low temperatures, and supercritical Ar and N2 fluids at high temperatures, as well as ten solids, respectively. The three parameters are determined for the hard-sphere fluid by fitting molecular dynamics (MD) simulation data of the third to eighth virial coefficients in the literature; for other fluids by fitting isothermal compression data; and for solids by using the Einstein model. The results show that the UC EOS gives better results than the Carnahan-Starling EOS for compressibility of hard-sphere fluids. The Helmholtz free energy and internal energy for LJ fluids are predicted and compared with MD simulation data. The calculated pressures for simple Ar and N2 liquids are compared with experimental data. The agreement is fairly good. Eight three-parameter EOSs are applied to describe isothermals of ten typical solids. It is shown that the UC EOS gives the best precision with correct behavior at high-pressure limitation. The UC EOS considering thermal effects is used to analytically evaluate the isobaric thermal expansivity and isothermal compressibility coefficients. The results are in good agreement with experimental data.

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

NASA Technical Reports Server (NTRS)

Barth, Timothy (Editor); Deconinck, Herman (Editor)

1999-01-01

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Dynamic Modeling Strategy for Flow Regime Transition in Gas-Liquid Two-Phase Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia Wang; Xiaodong Sun; Benjamin Doup

In modeling gas-liquid two-phase flows, the concept of flow regimes has been widely used to characterize the global interfacial structure of the flows. Nearly all constitutive relations that provide closures to the interfacial transfers in two-phase flow models, such as the two-fluid model, are flow regime dependent. Current nuclear reactor safety analysis codes, such as RELAP5, classify flow regimes using flow regime maps or transition criteria that were developed for steady-state, fully-developed flows. As twophase flows are dynamic in nature, it is important to model the flow regime transitions dynamically to more accurately predict the two-phase flows. The present workmore » aims to develop a dynamic modeling strategy to determine flow regimes in gas-liquid two-phase flows through introduction of interfacial area transport equations (IATEs) within the framework of a two-fluid model. The IATE is a transport equation that models the interfacial area concentration by considering the creation of the interfacial area, fluid particle (bubble or liquid droplet) disintegration, boiling and evaporation, and the destruction of the interfacial area, fluid particle coalescence and condensation. For flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and shapes, namely group-1 and group-2 bubbles. A preliminary approach to dynamically identify the flow regimes is discussed, in which discriminator s are based on the predicted information, such as the void fraction and interfacial area concentration. The flow regime predicted with this method shows good agreement with the experimental observations.« less

Numerical Simulation of Two-Fluid Mingling Using the Particle Finite Element Method with Applications to Magmatic and Volcanic Processes

NASA Astrophysics Data System (ADS)

de Mier, M.; Costa, F.; Idelsohn, S.

2008-12-01

Many magmatic and volcanic processes (e.g., magma differentiation, mingling, transport in the volcanic conduit) are controlled by the physical properties and flow styles of high-temperature silicate melts. Such processes can be experimentally investigated using analog systems and scaling methods, but it is difficult to find the suitable material and it is generally not possible to quantitatively extrapolate the results to the natural system. An alternative means of studying fluid dynamics in volcanic systems is with numerical models. We have chosen the Particle Finite Element Method (PFEM), which is based on a Delaunay mesh that moves with the fluid velocity, the Navier-Stokes equations in Lagrangian formulation, and linear elements for velocity, pressure, and temperature. Remeshing is performed when the grid becomes too distorted [E. Oñate et al., 2004. The Particle Finite Element Method: An Overview. Int. J. Comput. Meth. 1, 267-307]. The method is ideal for tracking material interfaces between different fluids or media. Methods based on Eulerian reference frames need special techniques, such as level-set or volume-of-fluid, to capture the interface position, and these techniques add a significant numerical diffusion at the interface. We have performed a series of two-dimensional simulations of a classical problem of fluid dynamics in magmatic and volcanic systems: intrusion of a basaltic melt in a silica-rich magma reservoir. We have used realistic physical properties and equations of state for the silicate melts (e.g., temperature, viscosity, and density) and tracked the changes in the system for geologically relevant time scales (up to 100 years). The problem is modeled by the low-Mach-number equations derived from an asymptotic analysis of the compressible Navier-Stokes equations that removes shock waves from the flow but allows however large variations of density due to temperature variations. Non-constant viscosity and volume changes are taken into account in the momentum conservation equation through the full shear-stress tensor. The implications of different magma intrusion rates, volumes, and times will be discussed in the context of mafic-silicic magma mixing and eruption triggers.

Toroidal gyrofluid equations for simulations of tokamak turbulence

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1996-11-01

A set of nonlinear gyrofluid equations for simulations of tokamak turbulence are derived by taking moments of the nonlinear toroidal gyrokinetic equation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5, 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal ∇B and curvature drifts take the basic form presented in Waltz et al. [Phys. Fluids B 4, 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamak turbulence, and is simple enough to be used in high resolution direct numerical simulations.

Kinetically reduced local Navier-Stokes equations: an alternative approach to hydrodynamics.

PubMed

Karlin, Iliya V; Tomboulides, Ananias G; Frouzakis, Christos E; Ansumali, Santosh

2006-09-01

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers.

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Education and research in fluid dynamics

NASA Astrophysics Data System (ADS)

López González-Nieto, P.; Redondo, J. M.; Cano, J. L.

2009-04-01

Fluid dynamics constitutes an essential subject for engineering, since auronautic engineers (airship flights in PBL, flight processes), industrial engineers (fluid transportation), naval engineers (ship/vessel building) up to agricultural engineers (influence of the weather conditions on crops/farming). All the above-mentioned examples possess a high social and economic impact on mankind. Therefore, the fluid dynamics education of engineers is very important, and, at the same time, this subject gives us an interesting methodology based on a cycle relation among theory, experiments and numerical simulation. The study of turbulent plumes -a very important convective flow- is a good example because their theoretical governing equations are simple; it is possible to make experimental plumes in an aesy way and to carry out the corresponding numerical simulatons to verify experimental and theoretical results. Moreover, it is possible to get all these aims in the educational system (engineering schools or institutions) using a basic laboratory and the "Modellus" software.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

2D Mesh Manipulation

DTIC Science & Technology

2011-11-01

the Poisson form of the equations can also be generated by manipulating the computational space , so forcing functions become superfluous . The...ABSTRACT Unstructured methods for region discretization have become common in computational fluid dynamics (CFD) analysis because of certain benefits...application of Winslow elliptic smoothing equations to unstructured meshes. It has been shown that it is not necessary for the computational space of

The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics

PubMed Central

Walker, Wade A.

2012-01-01

In this paper we describe the repeated replacement method (RRM), a new meshfree method for computational fluid dynamics (CFD). RRM simulates fluid flow by modeling compressible fluids’ tendency to evolve towards a state of constant density, velocity, and pressure. To evolve a fluid flow simulation forward in time, RRM repeatedly “chops out” fluid from active areas and replaces it with new “flattened” fluid cells with the same mass, momentum, and energy. We call the new cells “flattened” because we give them constant density, velocity, and pressure, even though the chopped-out fluid may have had gradients in these primitive variables. RRM adaptively chooses the sizes and locations of the areas it chops out and replaces. It creates more and smaller new cells in areas of high gradient, and fewer and larger new cells in areas of lower gradient. This naturally leads to an adaptive level of accuracy, where more computational effort is spent on active areas of the fluid, and less effort is spent on inactive areas. We show that for common test problems, RRM produces results similar to other high-resolution CFD methods, while using a very different mathematical framework. RRM does not use Riemann solvers, flux or slope limiters, a mesh, or a stencil, and it operates in a purely Lagrangian mode. RRM also does not evaluate numerical derivatives, does not integrate equations of motion, and does not solve systems of equations. PMID:22866175

A Spalart-Allmaras local correlation-based transition model for Thermo-fuid dynamics

NASA Astrophysics Data System (ADS)

D'Alessandro, V.; Garbuglia, F.; Montelpare, S.; Zoppi, A.

2017-11-01

The study of innovative energy systems often involves complex fluid flows problems and the Computational Fluid-Dynamics (CFD) is one of the main tools of analysis. It is important to put in evidence that in several energy systems the flow field experiences the laminar-to-turbulent transition. Direct Numerical Simulations (DNS) or Large Eddy Simulation (LES) are able to predict the flow transition but they are still inapplicable to the study of real problems due to the significant computational resources requirements. Differently standard Reynolds Averaged Navier Stokes (RANS) approaches are not always reliable since they assume a fully turbulent regime. In order to overcome this drawback in the recent years some locally formulated transition RANS models have been developed. In this work, we present a local correlation-based transition approach adding two equations that control the laminar-toturbulent transition process -γ and \\[\\overset{}{\\mathop{{{\\operatorname{Re}}θ, \\text{t}}}} \\] - to the well-known Spalart-Allmaras (SA) turbulence model. The new model was implemented within OpenFOAM code. The energy equation is also implemented in order to evaluate the model performance in thermal-fluid dynamics applications. In all the considered cases a very good agreement between numerical and experimental data was observed.

Dynamical behavior for the three-dimensional generalized Hasegawa-Mima equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Ruifeng; Guo Boling; Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088

2007-01-15

The long time behavior of solution of the three-dimensional generalized Hasegawa-Mima [Phys. Fluids 21, 87 (1978)] equations with dissipation term is considered. The global attractor problem of the three-dimensional generalized Hasegawa-Mima equations with periodic boundary condition was studied. Applying the method of uniform a priori estimates, the existence of global attractor of this problem was proven, and also the dimensions of the global attractor are estimated.

Joseph Boussinesq et son approximation : un aperçu actuel

NASA Astrophysics Data System (ADS)

Zeytounian, Radyadour Kh.

2003-08-01

A hundred years ago, in his 1903 volume II of the monograph devoted to 'Théorie Analytique de la Chaleur', Joseph Valentin Boussinesq observes that: "The v ariations of density can be ignored except were they are multiplied by the acceleration of gravity in equation of motion for the vertical component of the velocity vector." A spectacular consequence of this Boussinesq observation (called, in 1916, by Rayleigh, the 'Boussinesq approximation') is the possibility to work with a quasi-incompressible system of coupled dynamic, (Navier) and thermal (Fourier) equations where buoyancy is the main driving force. After a few words on the life of Boussinesq and on his observation, the applicability of this approximation is briefly discussed for various thermal, geophysical, astrophysical and magnetohydrodynamic problems in the framework of 'Boussinesquian fluid dynamics'. An important part of our contemporary view is devoted to a logical (100 years later) justification of this Boussinesq approximation for a perfect gas and an ideal liquid in the framework of an asymptotic modelling of the full fluid dynamics (Euler and Navier-Stokes-Fourier) equations with especially careful attention given to the validity of this approximation. To cite this article: R.Kh. Zeytounian, C. R. Mecanique 331 (2003).

Lie symmetry analysis, conservation laws, solitary and periodic waves for a coupled Burger equation

NASA Astrophysics Data System (ADS)

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian

2017-01-01

Under investigation in this paper is a generalized (2 + 1)-dimensional coupled Burger equation with variable coefficients, which describes lots of nonlinear physical phenomena in geophysical fluid dynamics, condense matter physics and lattice dynamics. By employing the Lie group method, the symmetry reductions and exact explicit solutions are obtained, respectively. Based on a direct method, the conservations laws of the equation are also derived. Furthermore, by virtue of the Painlevé analysis, we successfully obtain the integrable condition on the variable coefficients, which plays an important role in further studying the integrability of the equation. Finally, its auto-Bäcklund transformation as well as some new analytic solutions including solitary and periodic waves are also presented via algebraic and differential manipulation.

Modeling the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics and molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Voulgarakis, Nikolaos K.; Satish, Siddarth; Chu, Jhih-Wei

2009-12-01

A multiscale computational method is developed to model the nanoscale viscoelasticity of fluids by bridging non-Markovian fluctuating hydrodynamics (FHD) and molecular dynamics (MD) simulations. To capture the elastic responses that emerge at small length scales, we attach an additional rheological model parallel to the macroscopic constitutive equation of a fluid. The widely used linear Maxwell model is employed as a working choice; other models can be used as well. For a fluid that is Newtonian in the macroscopic limit, this approach results in a parallel Newtonian-Maxwell model. For water, argon, and an ionic liquid, the power spectrum of momentum field autocorrelation functions of the parallel Newtonian-Maxwell model agrees very well with those calculated from all-atom MD simulations. To incorporate thermal fluctuations, we generalize the equations of FHD to work with non-Markovian rheological models and colored noise. The fluctuating stress tensor (white noise) is integrated in time in the same manner as its dissipative counterpart and numerical simulations indicate that this approach accurately preserves the set temperature in a FHD simulation. By mapping position and velocity vectors in the molecular representation onto field variables, we bridge the non-Markovian FHD with atomistic MD simulations. Through this mapping, we quantitatively determine the transport coefficients of the parallel Newtonian-Maxwell model for water and argon from all-atom MD simulations. For both fluids, a significant enhancement in elastic responses is observed as the wave number of hydrodynamic modes is reduced to a few nanometers. The mapping from particle to field representations and the perturbative strategy of developing constitutive equations provide a useful framework for modeling the nanoscale viscoelasticity of fluids.

A Study of Flow Separation in Transonic Flow Using Inviscid and Viscous Computational Fluid Dynamics (CFD) Schemes

NASA Technical Reports Server (NTRS)

Rhodes, J. A.; Tiwari, S. N.; Vonlavante, E.

1988-01-01

A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation

PubMed Central

Ma, Xianghong

2016-01-01

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate–fluid interaction problem is developed on the basis of linearized Navier–Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions. PMID:27118914

Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation.

PubMed

Wu, Zhangming; Ma, Xianghong

2016-03-01

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate-fluid interaction problem is developed on the basis of linearized Navier-Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Analogy between the Navier-Stokes equations and Maxwell's equations: Application to turbulence

NASA Astrophysics Data System (ADS)

Marmanis, Haralambos

1998-06-01

A new theory of turbulence is initiated, based on the analogy between electromagnetism and turbulent hydrodynamics, for the purpose of describing the dynamical behavior of averaged flow quantities in incompressible fluid flows of high Reynolds numbers. The starting point is the recognition that the vorticity (w=∇×u) and the Lamb vector (l=w×u) should be taken as the kernel of a dynamical theory of turbulence. The governing equations for these fields can be obtained by the Navier-Stokes equations, which underlie the whole evolution. Then whatever parts are not explicitly expressed as a function of w or l only are gathered and treated as source terms. This is done by introducing the concepts of turbulent charge and turbulent current. Thus we are led to a closed set of linear equations for the averaged field quantities. The premise is that the earlier introduced sources will be apt for modeling, in the sense that their distribution will depend only on the geometry and the total energetics of the flow. The dynamics described in the preceding manner is what we call the metafluid dynamics.

Comparison of Hydrodynamic Load Predictions Between Engineering Models and Computational Fluid Dynamics for the OC4-DeepCwind Semi-Submersible: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benitz, M. A.; Schmidt, D. P.; Lackner, M. A.

Hydrodynamic loads on the platforms of floating offshore wind turbines are often predicted with computer-aided engineering tools that employ Morison's equation and/or potential-flow theory. This work compares results from one such tool, FAST, NREL's wind turbine computer-aided engineering tool, and the computational fluid dynamics package, OpenFOAM, for the OC4-DeepCwind semi-submersible analyzed in the International Energy Agency Wind Task 30 project. Load predictions from HydroDyn, the offshore hydrodynamics module of FAST, are compared with high-fidelity results from OpenFOAM. HydroDyn uses a combination of Morison's equations and potential flow to predict the hydrodynamic forces on the structure. The implications of the assumptionsmore » in HydroDyn are evaluated based on this code-to-code comparison.« less

Stability of gravito-coupled complex gyratory astrofluids

NASA Astrophysics Data System (ADS)

Kumar Karmakar, Pralay; Das, Papari

2017-07-01

We analyze the gravitational instability of complex rotating astrofluids in the presence of dynamic role of dark matter in a homogeneous hydrostatic equilibrium framework. The effects of the lowest-order fluid viscoelasticity, Coriolis force, fluid turbulence and inter-layer frictional coupling dynamics are concurrently considered in spatially-flat geometry. The Coriolis rotation is relative to the center of the entire fluid mass distribution, contributed by both the gyratory bright (visible) and dark (invisible) sectors, conjugated via the mutual gravitational interaction. The turbulence effects are included via the modified Larson equation of state. We use a regular Fourier-based linear perturbation analysis over the rotating fluid field equations to obtain a unique form of quartic dispersion relation with variable coefficients. We numerically carry out the dispersion analysis in two extreme limits: hydrodynamic (low-frequency) and kinetic (high-frequency) regimes. It is demonstrated that, in the former regime, the gas as well as dark matter rotations have stabilizing effects on the Jeans instability of the bi-fluidic admixture. In contrast, in the latter, the rotations play destabilizing roles on the instability. An interesting feature noted here is that the magnitude of the group velocity of the fluctuations throughout increases with both the gas and dark matter rotation frequencies, and vice-versa. We, finally, hope that the obtained results could be helpful in understanding the top-down kinetic mechanisms of bounded structure formation via gravitational collapse dynamics.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

TEMPEST: A computer code for three-dimensional analysis of transient fluid dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fort, J.A.

TEMPEST (Transient Energy Momentum and Pressure Equations Solutions in Three dimensions) is a powerful tool for solving engineering problems in nuclear energy, waste processing, chemical processing, and environmental restoration because it analyzes and illustrates 3-D time-dependent computational fluid dynamics and heat transfer analysis. It is a family of codes with two primary versions, a N- Version (available to public) and a T-Version (not currently available to public). This handout discusses its capabilities, applications, numerical algorithms, development status, and availability and assistance.

H-division quarterly report, October--December 1977. [Lawrence Livermore Laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1978-02-10

The Theoretical EOS Group develops theoretical techniques for describing material properties under extreme conditions and constructs equation-of-state (EOS) tables for specific applications. Work this quarter concentrated on a Li equation of state, equation of state for equilibrium plasma, improved ion corrections to the Thomas--Fermi--Kirzhnitz theory, and theoretical estimates of high-pressure melting in metals. The Experimental Physics Group investigates properties of materials at extreme conditions of pressure and temperature, and develops new experimental techniques. Effort this quarter concerned the following: parabolic projectile distortion in the two-state light-gas gun, construction of a ballistic range for long-rod penetrators, thermodynamics and sound velocities inmore » liquid metals, isobaric expansion measurements in Pt, and calculation of the velocity--mass profile of a jet produced by a shaped charge. Code development was concentrated on the PELE code, a multimaterial, multiphase, explicit finite-difference Eulerian code for pool suppression dynamics of a hypothetical loss-of-coolant accident in a nuclear reactor. Activities of the Fluid Dynamics Group were directed toward development of a code to compute the equations of state and transport properties of liquid metals (e.g. Li) and partially ionized dense plasmas, jet stability in the Li reactor system, and the study and problem application of fluid dynamic turbulence theory. 19 figures, 5 tables. (RWR)« less

Simulation of dynamic magnetic particle capture and accumulation around a ferromagnetic wire

NASA Astrophysics Data System (ADS)

Choomphon-anomakhun, Natthaphon; Ebner, Armin D.; Natenapit, Mayuree; Ritter, James A.

2017-04-01

A new approach for modeling high gradient magnetic separation (HGMS)-type systems during the time-dependent capture and accumulation of magnetic particles by a ferromagnetic wire was developed. This new approach assumes the fluid (slurry) viscosity, comprised of water and magnetic particles, is a function of the magnetic particle concentration in the fluid, with imposed maxima on both the particle concentration and fluid viscosity to avoid unrealistic limits. In 2-D, the unsteady-state Navier-Stokes equations for compressible fluid flow and the unsteady-state continuity equations applied separately to the water and magnetic particle phases in the slurry were solved simultaneously, along with the Laplace equations for the magnetic potential applied separately to the slurry and wire, to evaluate the velocities and concentrations around the wire in a narrow channel using COMSOL Multiphysics. The results from this model revealed very realistic magnetically attractive and repulsive zones forming in time around the wire. These collection zones formed their own impermeable viscous phase during accumulation that was also magnetic with its area and magnetism impacting locally both the fluid flow and magnetic fields around the wire. These collection zones increased with an increase in the applied magnetic field. For a given set of conditions, the capture ability peaked and then decreased to zero at infinite time during magnetic particle accumulation in the collection zones. Predictions of the collection efficiency from a steady-state, clean collector, trajectory model could not show this behavior; it also agreed only qualitatively with the dynamic model and then only at the early stages of collection and more so at a higher applied magnetic field. Also, the collection zones decreased in size when the accumulation regions included magnetic particle magnetization (realistic) compared to when they excluded it (unrealistic). Overall, this might be the first time a mathematical model was shown to be capable of realistically predicting the dynamic nature of magnetic particle capture and accumulation around a wire in HGMS-type systems.

An immersed-shell method for modelling fluid–structure interactions

PubMed Central

Viré, A.; Xiang, J.; Pain, C. C.

2015-01-01

The paper presents a novel method for numerically modelling fluid–structure interactions. The method consists of solving the fluid-dynamics equations on an extended domain, where the computational mesh covers both fluid and solid structures. The fluid and solid velocities are relaxed to one another through a penalty force. The latter acts on a thin shell surrounding the solid structures. Additionally, the shell is represented on the extended domain by a non-zero shell-concentration field, which is obtained by conservatively mapping the shell mesh onto the extended mesh. The paper outlines the theory underpinning this novel method, referred to as the immersed-shell approach. It also shows how the coupling between a fluid- and a structural-dynamics solver is achieved. At this stage, results are shown for cases of fundamental interest. PMID:25583857

Physical Principle for Generation of Randomness

NASA Technical Reports Server (NTRS)

Zak, Michail

2009-01-01

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

NASA Astrophysics Data System (ADS)

Loureiro, Nuno; Dorland, William; Fazendeiro, Luis; Kanekar, Anjor; Mallet, Alfred; Zocco, Alessandro

2015-11-01

We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model equations [Zocco & Schekochihin, 2011] and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., 2009]. Two main applications of these equations are magnetised (Alfvnénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, with focus on 3D decaying kinetic turbulence. Work partially supported by Fundação para a Ciência e Tecnologia via Grants UID/FIS/50010/2013 and IF/00530/2013.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Error Propagation Dynamics of PIV-based Pressure Field Calculations: How well does the pressure Poisson solver perform inherently?

PubMed

Pan, Zhao; Whitehead, Jared; Thomson, Scott; Truscott, Tadd

2016-08-01

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Three-dimensional simulation of beam propagation and heat transfer in static gas Cs DPALs using wave optics and fluid dynamics models

NASA Astrophysics Data System (ADS)

Waichman, Karol; Barmashenko, Boris D.; Rosenwaks, Salman

2017-10-01

Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C2H6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 62S1/2, (2) 62P1/2 and (3) 62P3/2. The kinetic processes include absorption due to the 1->3 D2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2->1 D1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.

Analysis of the autonomous problem about coupled active non-Newtonian multi-seepage in sparse medium

NASA Astrophysics Data System (ADS)

Deng, Shuxian; Li, Hongen

2017-10-01

The flow field of non-Newtonian fluid in sparse medium was analyzed by computational fluid dynamics (CFD) method. The results show that the axial velocity and radial velocity of the non-Newtonian fluid are larger than those of the Newtonian fluid due to the coupling of the viscosity of the non-Newtonian fluid and the shear rate, and the tangential velocity is less than that of the Newtonian fluid. These differences lead to the difference in the sparse medium Non-Newtonian fluids are of a special nature. The influence of the weight function on the global existence and blasting of the problem is discussed by analyzing the non-Newtonian percolation equation with nonlocal and weighted non-local Dirichlet boundary conditions. According to the non-Newtonian percolation equation, we define the weak solution of the problem and expound the local existence of the weak solution. Then we construct the test function and prove the weak comparison principle by using the Grown well inequality. The overall existence and blasting are analyzed by constructing the upper and lower solutions.

Numerical computations of the dynamics of fluidic membranes and vesicles

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-11-01

Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.

Differential invariants in nonclassical models of hydrodynamics

NASA Astrophysics Data System (ADS)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with analytical methods makes it possible to make the results of mathematical modeling more accurate and reliable.

Methodology Development of a Gas-Liquid Dynamic Flow Regime Transition Model

NASA Astrophysics Data System (ADS)

Doup, Benjamin Casey

Current reactor safety analysis codes, such as RELAP5, TRACE, and CATHARE, use flow regime maps or flow regime transition criteria that were developed for static fully-developed two-phase flows to choose interfacial transfer models that are necessary to solve the two-fluid model. The flow regime is therefore difficult to identify near the flow regime transitions, in developing two-phase flows, and in transient two-phase flows. Interfacial area transport equations were developed to more accurately predict the dynamic nature of two-phase flows. However, other model coefficients are still flow regime dependent. Therefore, an accurate prediction of the flow regime is still important. In the current work, the methodology for the development of a dynamic flow regime transition model that uses the void fraction and interfacial area concentration obtained by solving three-field the two-fluid model and two-group interfacial area transport equation is investigated. To develop this model, detailed local experimental data are obtained, the two-group interfacial area transport equations are revised, and a dynamic flow regime transition model is evaluated using a computational fluid dynamics model. Local experimental data is acquired for 63 different flow conditions in bubbly, cap-bubbly, slug, and churn-turbulent flow regimes. The measured parameters are the group-1 and group-2 bubble number frequency, void fraction, interfacial area concentration, and interfacial bubble velocities. The measurements are benchmarked by comparing the prediction of the superficial gas velocities, determined using the local measurements with those determined from volumetric flow rate measurements and the agreement is generally within +/-20%. The repeatability four-sensor probe construction process is within +/-10%. The repeatability of the measurement process is within +/-7%. The symmetry of the test section is examined and the average agreement is within +/-5.3% at z/D = 10 and +/-3.4% at z/D = 32. Revised source/sink terms for the two-group interfacial area transport equations are derived and fit to area-averaged experimental data to determine new model coefficients. The average agreement between this model and the experiment data for the void fraction and interfacial area concentration is 10.6% and 15.7%, respectively. This revised two-group interfacial area transport equation and the three-field two-fluid model are used to solve for the group-1 and group-2 interfacial area concentration and void fraction. These values and a dynamic flow regime transition model are used to classify the flow regimes. The flow regimes determined using this model are compared with the flow regimes based on the experimental data and on a flow regime map using Mishima and Ishii's (1984) transition criteria. The dynamic flow regime transition model is shown to predict the flow regimes dynamically and has improved the prediction of the flow regime over that using a flow regime map. Safety codes often employ the one-dimensional two-fluid model to model two-phase flows. The area-averaged relative velocity correlation necessary to close this model is derived from the drift flux model. The effects of the necessary assumptions used to derive this correlation are investigated using local measurements and these effects are found to have a limited impact on the prediction of the area-averaged relative velocity.

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions.

PubMed

Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

2018-04-14

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

NASA Astrophysics Data System (ADS)

Rivas, Nicolas; Frijters, Stefan; Pagonabarraga, Ignacio; Harting, Jens

2018-04-01

A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a Bhatnagar-Gross-Krook collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics through appropriate boundary conditions. We present the first full integration of these three elements. The model is validated by comparing with known analytic solutions of ionic distributions at fluid interfaces, dielectric droplet deformations, and the electrophoretic mobility of colloidal suspensions. Its possibilities are explored by considering various physical systems, such as breakup of charged and neutral droplets and colloidal dynamics at either planar or spherical fluid interfaces.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

Smoothed Particle Hydrodynamics Simulations of Ultrarelativistic Shocks with Artificial Viscosity

NASA Astrophysics Data System (ADS)

Siegler, S.; Riffert, H.

2000-03-01

We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing suitable Lagrangian time evolution variables, from which the generic fluid variables of rest-mass density, 3-velocity, and thermodynamic pressure have to be determined. We present the corresponding equations for an ideal gas and show the existence and uniqueness of the solution. On the basis of the Lagrangian formulation we have developed a three-dimensional general relativistic smoothed particle hydrodynamics (SPH) code using the standard SPH formalism as known from nonrelativistic fluid dynamics. One-dimensional simulations of a shock tube and a wall shock are presented together with a two-dimensional test calculation of an inclined shock tube. With our method we can model ultrarelativistic fluid flows including shocks with Lorentz factors of even 1000.

Experimental Validation of a Time-Accurate Finite Element Model for Coupled Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2007-04-16

velocity of the fluid mesh, P is the relative pressure, xr is the position vector, τ is the deviatoric stress tensor, D is the rate of deformation...corresponds to a slip factor of zero. The slip factor determines how much of the fluid and structure forces are mutually exchanged. Equations 22 and 23...updated from last to first. viii.Average the fluid pressure (This step eliminates the pressure checker-boarding effect and allows use of equal

Causal dissipation for the relativistic dynamics of ideal gases

NASA Astrophysics Data System (ADS)

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Causal dissipation for the relativistic dynamics of ideal gases

PubMed Central

2017-01-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier–Stokes equations. PMID:28588397

Causal dissipation for the relativistic dynamics of ideal gases.

PubMed

Freistühler, Heinrich; Temple, Blake

2017-05-01

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

Impact of the Equation of State in Models for Surfactant Spreading Experiments

NASA Astrophysics Data System (ADS)

Levy, Rachel

2014-11-01

Pulmonary surfactant spreading models often rely on an equation of state relating surfactant concentration to surface tension. Mathematically, these models have been analyzed with simple functional relationships. However, to model an experiment with a given fluid and surfactant, a physically meaningful equation of state can be derived from experimentally obtained isotherms. We discuss the comparison between model and experiment for NBD-PC lipid (surfactant) spreading on glycerol for an empirically-determined equation of state, and compare those results to simulations with traditionally employed functional forms. In particular we compare the timescales by tracking the leading edge of surfactant, the central fluid height and dynamics of the Marangoni ridge. We consider both outward spreading of a disk-shaped region of surfactant and the hole-closure problem in which a disk-shaped surfactant-free region self-heals. Support from NSF-DMS-FRG 0968154, RCSA-CCS-19788, and HHMI.

A CFD Approach to Modeling Spacecraft Fuel Slosh

NASA Technical Reports Server (NTRS)

Marsell, Brandon; Gangadharan, Sathya; Chatman, Yadira; Sudermann, James; Schlee, Keith; Ristow, James E.

2009-01-01

Energy dissipation and resonant coupling from sloshing fuel in spacecraft fuel tanks is a problem that occurs in the design of many spacecraft. In the case of a spin stabilized spacecraft, this energy dissipation can cause a growth in the spacecrafts' nutation (wobble) that may lead to disastrous consequences for the mission. Even in non-spinning spacecraft, coupling between the spacecraft or upper stage flight control system and an unanticipated slosh resonance can result in catastrophe. By using a Computational Fluid Dynamics (CFD) solver such as Fluent, a model for this fuel slosh can be created. The accuracy of the model must be tested by comparing its results to an experimental test case. Such a model will allow for the variation of many different parameters such as fluid viscosity and gravitational field, yielding a deeper understanding of spacecraft slosh dynamics. In order to gain a better understanding of the dynamics behind sloshing fluids, the Launch Services Program (LSP) at the NASA Kennedy Space Center (KSC) is interested in finding ways to better model this behavior. Thanks to past research, a state-of-the-art fuel slosh research facility was designed and fabricated at Embry Riddle Aeronautical University (ERAU). This test facility has produced interesting results and a fairly reliable parameter estimation process to predict the necessary values that accurately characterize a mechanical pendulum analog model. The current study at ERAU uses a different approach to model the free surface sloshing of liquid in a spherical tank using Computational Fluid Dynamics (CFD) methods. Using a software package called Fluent, a model was created to simulate the sloshing motion of the propellant. This finite volume program uses a technique called the Volume of Fluid (VOF) method to model the interaction between two fluids [4]. For the case of free surface slosh, the two fluids are the propellant and air. As the fuel sloshes around in the tank, it naturally displaces the air. Using the conservation of mass, momentum, and energy equations, as well as the VOF equations, one can predict the behavior of the sloshing fluid and calculate the forces, pressure gradients, and velocity field for the entire liquid as a function of time.

A thermodynamically consistent model for granular-fluid mixtures considering pore pressure evolution and hypoplastic behavior

NASA Astrophysics Data System (ADS)

Hess, Julian; Wang, Yongqi

2016-11-01

A new mixture model for granular-fluid flows, which is thermodynamically consistent with the entropy principle, is presented. The extra pore pressure described by a pressure diffusion equation and the hypoplastic material behavior obeying a transport equation are taken into account. The model is applied to granular-fluid flows, using a closing assumption in conjunction with the dynamic fluid pressure to describe the pressure-like residual unknowns, hereby overcoming previous uncertainties in the modeling process. Besides the thermodynamically consistent modeling, numerical simulations are carried out and demonstrate physically reasonable results, including simple shear flow in order to investigate the vertical distribution of the physical quantities, and a mixture flow down an inclined plane by means of the depth-integrated model. Results presented give insight in the ability of the deduced model to capture the key characteristics of granular-fluid flows. We acknowledge the support of the Deutsche Forschungsgemeinschaft (DFG) for this work within the Project Number WA 2610/3-1.

Fluid flow and heat transfer characteristics of an enclosure with fin as a top cover of a solar collector

NASA Astrophysics Data System (ADS)

Ambarita, H.; Ronowikarto, A. D.; Siregar, R. E. T.; Setyawan, E. Y.

2018-03-01

To reduce heat loses in a flat plate solar collector, double glasses cover is employed. Several studies show that the heat loss from the glass cover is still very significant in comparison with other losses. Here, double glasses cover with attached fins is proposed. In the present work, the fluid flow and heat transfer characteristics of the enclosure between the double glass cover are investigated numerically. The objective is to examine the effect of the fin to the heat transfer rate of the cover. Two-dimensional governing equations are developed. The governing equations and the boundary conditions are solved using commercial Computational Fluid Dynamics code. The fluid flow and heat transfer characteristics are plotted, and numerical results are compared with empirical correlation. The results show that the presence of the fin strongly affects the fluid flow and heat transfer characteristics. The fin can reduce the heat transfer rate up to 22.42% in comparison with double glasses cover without fins.

Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

NASA Astrophysics Data System (ADS)

Thete, Sumeet Suresh; Anthony, Christopher; Doshi, Pankaj; Harris, Michael T.; Basaran, Osman A.

2016-09-01

Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. For sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid's viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance each other while capillary force remains negligible, in accordance with the results of Vaynblat, Lister, and Witelski.

Parallel Simulation of Three-Dimensional Free-Surface Fluid Flow Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

BAER,THOMAS A.; SUBIA,SAMUEL R.; SACKINGER,PHILIP A.

2000-01-18

We describe parallel simulations of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact lines. The Galerlin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of problem unknowns. Issues concerning the proper constraints along the solid-fluid dynamic contact line inmore » three dimensions are discussed. Parallel computations are carried out for an example taken from the coating flow industry, flow in the vicinity of a slot coater edge. This is a three-dimensional free-surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another part of the flow domain. Discussion focuses on parallel speedups for fixed problem size, a class of problems of immediate practical importance.« less

Aeroelastic Analysis Of Joined Wing Of High Altitude Long Endurance (HALE) Aircraft Based On The Sensor-Craft Configuration

NASA Astrophysics Data System (ADS)

Marisarla, Soujanya; Ghia, Urmila; "Karman" Ghia, Kirti

2002-11-01

Towards a comprehensive aeroelastic analysis of a joined wing, fluid dynamics and structural analyses are initially performed separately. Steady flow calculations are currently performed using 3-D compressible Navier-Stokes equations. Flow analysis of M6-Onera wing served to validate the software for the fluid dynamics analysis. The complex flow field of the joined wing is analyzed and the prevailing fluid dynamic forces are computed using COBALT software. Currently, these forces are being transferred as fluid loads on the structure. For the structural analysis, several test cases were run considering the wing as a cantilever beam; these served as validation cases. A nonlinear structural analysis of the wing is being performed using ANSYS software to predict the deflections and stresses on the joined wing. Issues related to modeling, and selecting appropriate mesh for the structure were addressed by first performing a linear analysis. The frequencies and mode shapes of the deformed wing are obtained from modal analysis. Both static and dynamic analyses are carried out, and the results obtained are carefully analyzed. Loose coupling between the fluid and structural analyses is currently being examined.

Attractors of three-dimensional fast-rotating Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Trahe, Markus

The three-dimensional (3-D) rotating Navier-Stokes equations describe the dynamics of rotating, incompressible, viscous fluids. In this work, they are considered with smooth, time-independent forces and the original statements implied by the classical "Taylor-Proudman Theorem" of geophysics are rigorously proved. It is shown that fully developed turbulence of 3-D fast-rotating fluids is essentially characterized by turbulence of two-dimensional (2-D) fluids in terms of numbers of degrees of freedom. In this context, the 3-D nonlinear "resonant limit equations", which arise in a non-linear averaging process as the rotation frequency O → infinity, are studied and optimal (2-D-type) upper bounds for fractal box and Hausdorff dimensions of the global attractor as well as upper bounds for box dimensions of exponential attractors are determined. Then, the convergence of exponential attractors for the full 3-D rotating Navier-Stokes equations to exponential attractors for the resonant limit equations as O → infinity in the sense of full Hausdorff-metric distances is established. This provides upper and lower semi-continuity of exponential attractors with respect to the rotation frequency and implies that the number of degrees of freedom (attractor dimension) of 3-D fast-rotating fluids is close to that of 2-D fluids. Finally, the algebraic-geometric structure of the Poincare curves, which control the resonances and small divisor estimates for partial differential equations, is further investigated; the 3-D nonlinear limit resonant operators are characterized by three-wave interactions governed by these curves. A new canonical transformation between those curves is constructed; with far-reaching consequences on the density of the latter.

Fluid-structure interaction analysis on the effect of vessel wall hypertrophy and stiffness on the blood flow in carotid artery bifurcation

NASA Astrophysics Data System (ADS)

Lee, Sang Hoon; Choi, Hyoung Gwon; Yoo, Jung Yul

2012-11-01

The effect of artery wall hypertrophy and stiffness on the flow field is investigated using three-dimensional finite element method for simulating the blood flow. To avoid the complexity due to the necessity of additional mechanical constraints, we use the combined formulation which includes both the fluid and structural equations of motion into single coupled variational equation. A P2P1 Galerkin finite element method is used to solve the Navier-Stokes equations for fluid flow and arbitrary Lagrangian-Eulerian formulation is used to achieve mesh movement. The Newmark method is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics. The pulsatile, incompressible flows of Newtonian fluids constrained in the flexible wall are analyzed with Womersley velocity profile at the inlet and constant pressure at the outlet. The study shows that the stiffness of carotid artery wall affects significantly the flow phenomena during the pulse cycle. Similarly, it is found that the flow field is also strongly influenced by wall hypertrophy. This work was supported by Mid-career Researcher Program and Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0079936 & 2011-0029613).

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

NASA Astrophysics Data System (ADS)

Brenier, Yann

2009-10-01

We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations. Finally, we show how a “stringy” generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology (see Arnold and Khesin in Topological methods in hydrodynamics. Applied mathematical sciences, vol. 125, Springer, Berlin, 1998; Moffatt in J. Fluid Mech. 159:359-378, 1985, Topological aspects of the dynamics of fluids and plasmas. NATO adv. sci. inst. ser. E, appl. sci., vol. 218, Kluwer, Dordrecht, 1992; Schonbek in Theory of the Navier-Stokes equations, Ser. adv. math. appl. sci., vol. 47, pp. 179-184, World Sci., Singapore, 1998; Vladimirov et al. in J. Fluid Mech. 390:127-150, 1999; Nishiyama in Bull. Inst. Math. Acad. Sin. (N.S.) 2:139-154, 2007).

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Numerical modeling of multidimensional flow in seals and bearings used in rotating machinery

NASA Technical Reports Server (NTRS)

Hendricks, R. C.; Tam, L. T.; Przekwas, A.; Muszynska, A.; Braun, M. J.; Mullen, R. L.

1988-01-01

The rotordynamic behavior of turbomachinery is critically dependent on fluid dynamic rotor forces developed by various types of seals and bearings. The occurrence of self-excited vibrations often depends on the rotor speed and load. Misalignment and rotor wobbling motion associated with differential clearance were often attributed to stability problems. In general, the rotative character of the flowfield is a complex three dimensional system with secondary flow patterns that significantly alter the average fluid circumferential velocity. A multidimensional, nonorthogonal, body-fitted-grid fluid flow model is presented that describes the fluid dynamic forces and the secondary flow pattern development in seals and bearings. Several numerical experiments were carried out to demonstrate the characteristics of this complex flowfield. Analyses were performed by solving a conservation form of the three dimensional Navier-Stokes equations transformed to those for a rotating observer and using the general-purpose computer code PHOENICS with the assumptions that the rotor orbit is circular and that static eccentricity is zero. These assumptions have enabled a precise steady-state analysis to be used. Fluid injection from ports near the seal or bearing center increased fluid-film direct dynamic stiffness and, in some cases, significantly increased quadrature dynamic stiffness. Injection angle and velocity could be used for active rotordynamic control; for example, injection, when compared with no injection, increased direct dynamic stiffness, which is an important factor for hydrostatic bearings.

von Kármán-Howarth equation for three-dimensional two-fluid plasmas.

PubMed

Andrés, N; Mininni, P D; Dmitruk, P; Gómez, D O

2016-06-01

We derive the von Kármán-Howarth equation for a full three-dimensional incompressible two-fluid plasma. In the long-time limit and for very large Reynolds numbers we obtain the equivalent of the hydrodynamic "four-fifths" law. This exact law predicts the scaling of the third-order two-point correlation functions, and puts a strong constraint on the plasma turbulent dynamics. Finally, we derive a simple expression for the 4/5 law in terms of third-order structure functions, which is appropriate for comparison with in situ measurements in the solar wind at different spatial ranges.

Numerical Modeling of Unsteady Thermofluid Dynamics in Cryogenic Systems

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2003-01-01

A finite volume based network analysis procedure has been applied to model unsteady flow without and with heat transfer. Liquid has been modeled as compressible fluid where the compressibility factor is computed from the equation of state for a real fluid. The modeling approach recognizes that the pressure oscillation is linked with the variation of the compressibility factor; therefore, the speed of sound does not explicitly appear in the governing equations. The numerical results of chilldown process also suggest that the flow and heat transfer are strongly coupled. This is evident by observing that the mass flow rate during 90-second chilldown process increases by factor of ten.

Combined effects of heat and mass transfer to magneto hydrodynamics oscillatory dusty fluid flow in a porous channel

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Vijayalakshmi, R.; Ramamurthy, V.

2018-04-01

The main aim of this article is to study the combined effects of heat and mass transfer to radiative Magneto Hydro Dynamics (MHD) oscillatory optically thin dusty fluid in a saturated porous medium channel. Based on certain assumptions, the momentum, energy, concentration equations are obtained.The governing equations are non-dimensionalised, simplified and solved analytically. The closed analytical form solutions for velocity, temperature, concentration profiles are obtained. Numerical computations are presented graphically to show the salient features of various physical parameters. The shear stress, the rate of heat transfer and the rate of mass transfer are also presented graphically.

Power loss for a periodically driven ferromagnetic nanoparticle in a viscous fluid: The finite anisotropy aspects

NASA Astrophysics Data System (ADS)

Lyutyy, T. V.; Hryshko, O. M.; Kovner, A. A.

2018-01-01

The coupled magnetic and mechanical motion of a ferromagnetic nanoparticle in a viscous fluid is considered within the dynamical approach. The equation based on the total momentum conservation law is used for the description of the mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is utilized for the description of the internal magnetic dynamics. The exact expressions for the particles trajectories and the power loss are obtained in the linear approximation. The comparison with the results of other widespread approaches, such as the model of fixed particle and the model of rigid dipole, is performed. It is established that in the small oscillations mode the damping precession of the nanoparticle magnetic moment is the main channel of energy dissipation, but the motion of the nanoparticle easy axis can significantly influence the value of the resulting power loss.

[Quantitative Evaluation of Intracardiac Blood Flow by Left Ventricle Dynamic Anatovy Based On Exact Solutions of Non-Stationary Navier-Stocks Equations for Selforganized tornado-Like Flows of Viscous Incompresssible Fluid].

PubMed

Talygin, E A; Zazybo, N A; Zhorzholiany, S T; Krestinich, I M; Mironov, A A; Kiknadze, G I; Bokerya, L A; Gorodkov, A Y; Makarenko, V N; Alexandrova, S A

2016-01-01

New approach to intracardiac blood flow condition analysis based on geometric parameters of left ventricle flow channel has been suggested. Parameters, that used in this method, follow from exact solutions of nonstationary Navier-Stocks equations for selforganized tornado-like flows of viscous incompressible fluid. The main advantage of this method is considering dynamic anatomy of intracardiac cavity and trabeculae relief of left ventricle streamlined surface, both registered in a common mri-process, as flow condition indicator. Calculated quantity options that characterizes blood flow condition can be use as diagnostic criterias for estimation of violation in blood circulation function which entails heart ejection reduction. Developed approach allows to clarify heart jet organization mechanism and estimate the share of the tornado-like flow self-organization in heart ejection structure.

CFD analysis of hypersonic, chemically reacting flow fields

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1993-01-01

Design studies are underway for a variety of hypersonic flight vehicles. The National Aero-Space Plane will provide a reusable, single-stage-to-orbit capability for routine access to low earth orbit. Flight-capable satellites will dip into the atmosphere to maneuver to new orbits, while planetary probes will decelerate at their destination by atmospheric aerobraking. To supplement limited experimental capabilities in the hypersonic regime, computational fluid dynamics (CFD) is being used to analyze the flow about these configurations. The governing equations include fluid dynamic as well as chemical species equations, which are being solved with new, robust numerical algorithms. Examples of CFD applications to hypersonic vehicles suggest an important role this technology will play in the development of future aerospace systems. The computational resources needed to obtain solutions are large, but solution adaptive grids, convergence acceleration, and parallel processing may make run times manageable.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

Nature of self-diffusion in two-dimensional fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Transient multi-physics analysis of a magnetorheological shock absorber with the inverse Jiles-Atherton hysteresis model

NASA Astrophysics Data System (ADS)

Zheng, Jiajia; Li, Yancheng; Li, Zhaochun; Wang, Jiong

2015-10-01

This paper presents multi-physics modeling of an MR absorber considering the magnetic hysteresis to capture the nonlinear relationship between the applied current and the generated force under impact loading. The magnetic field, temperature field, and fluid dynamics are represented by the Maxwell equations, conjugate heat transfer equations, and Navier-Stokes equations. These fields are coupled through the apparent viscosity and the magnetic force, both of which in turn depend on the magnetic flux density and the temperature. Based on a parametric study, an inverse Jiles-Atherton hysteresis model is used and implemented for the magnetic field simulation. The temperature rise of the MR fluid in the annular gap caused by core loss (i.e. eddy current loss and hysteresis loss) and fluid motion is computed to investigate the current-force behavior. A group of impulsive tests was performed for the manufactured MR absorber with step exciting currents. The numerical and experimental results showed good agreement, which validates the effectiveness of the proposed multi-physics FEA model.

Hypersonic Magneto-Fluid-Dynamic Compression in Cylindrical Inlet

NASA Technical Reports Server (NTRS)

Shang, Joseph S.; Chang, Chau-Lyan

2007-01-01

Hypersonic magneto-fluid-dynamic interaction has been successfully performed as a virtual leading-edge strake and a virtual cowl of a cylindrical inlet. In a side-by-side experimental and computational study, the magnitude of the induced compression was found to be depended on configuration and electrode placement. To better understand the interacting phenomenon the present investigation is focused on a direct current discharge at the leading edge of a cylindrical inlet for which validating experimental data is available. The present computational result is obtained by solving the magneto-fluid-dynamics equations at the low magnetic Reynolds number limit and using a nonequilibrium weakly ionized gas model based on the drift-diffusion theory. The numerical simulation provides a detailed description of the intriguing physics. After validation with experimental measurements, the computed results further quantify the effectiveness of a magnet-fluid-dynamic compression for a hypersonic cylindrical inlet. At a minuscule power input to a direct current surface discharge of 8.14 watts per square centimeter of electrode area produces an additional compression of 6.7 percent for a constant cross-section cylindrical inlet.

Marangoni-driven chemotaxis, chemotactic collapse, and the Keller-Segel equation

NASA Astrophysics Data System (ADS)

Shelley, Michael; Masoud, Hassan

2013-11-01

Almost by definition, chemotaxis involves the biased motion of motile particles along gradients of a chemical concentration field. Perhaps the most famous model for collective chemotaxis in mathematical biology is the Keller-Segel model, conceived to describe collective aggregation of slime mold colonies in response to an intrinsically produced, and diffusing, chemo-attractant. Heavily studied, particularly in 2D where the system is ``super-critical'', it has been proved that the KS model can develop finite-time singularities - so-called chemotactic collapse - of delta-function type. Here, we study the collective dynamics of immotile particles bound to a 2D interface above a 3D fluid. These particles are chemically active and produce a diffusing field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. Remarkably, we show that this system involving 3D diffusion and fluid dynamics, exactly yields the 2D Keller-Segel model for the surface-flow of active particles. We discuss the consequences of collapse on the 3D fluid dynamics, and generalizations of the fluid-dynamical model.

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach

NASA Astrophysics Data System (ADS)

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.; Marone, Chris; Carmeliet, Jan

2017-05-01

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this paper, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that the (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.

Boundary Layer Measurements in the Trisonic Gas-dynamics Facility Using Particle Image Velocimetery with CO2 Seeding

DTIC Science & Technology

2012-03-22

understanding of fluid mechanics and aircraft design. The fundamental theories, concepts and equations developed by men like Newton, Bernoulli ...resulting instantaneous flow field data from PIV, boundary layer effects, turbulence characteristics, vortex formation, and momentum thickness, for...divided by the momentum thickness, δ2, and displacement thickness, δ1, as seen in Equations (2.8) and (2.9

The shallow water equation and the vorticity equation for a change in height of the topography.

PubMed

Da, ChaoJiu; Shen, BingLu; Yan, PengCheng; Ma, DeShan; Song, Jian

2017-01-01

We consider the shallow water equation and the vorticity equations for a variable height of topography. On the assumptions that the atmosphere is incompressible and a constant density, we simplify the coupled dynamic equations. The change in topographic height is handled as the sum of the inherent and changing topography using the perturbation method, together with appropriate boundary conditions of the atmosphere, to obtain the relationship between the relative height of the flow, the inherent topography and the changing topography. We generalize the conservation of the function of relative position, and quantify the relationship between the height of the topography and the relative position of a fluid element. If the height of the topography increases (decreases), the relative position of a fluid element descends (ascends). On this basis, we also study the relationship between the vorticity and the topography to find the vorticity decreasing (increasing) for an increasing (decreasing) height of the topography.

The shallow water equation and the vorticity equation for a change in height of the topography

PubMed Central

Shen, BingLu; Yan, PengCheng; Ma, DeShan; Song, Jian

2017-01-01

We consider the shallow water equation and the vorticity equations for a variable height of topography. On the assumptions that the atmosphere is incompressible and a constant density, we simplify the coupled dynamic equations. The change in topographic height is handled as the sum of the inherent and changing topography using the perturbation method, together with appropriate boundary conditions of the atmosphere, to obtain the relationship between the relative height of the flow, the inherent topography and the changing topography. We generalize the conservation of the function of relative position, and quantify the relationship between the height of the topography and the relative position of a fluid element. If the height of the topography increases (decreases), the relative position of a fluid element descends (ascends). On this basis, we also study the relationship between the vorticity and the topography to find the vorticity decreasing (increasing) for an increasing (decreasing) height of the topography. PMID:28591129

Modeling meniscus rise in capillary tubes using fluid in rigid-body motion approach

NASA Astrophysics Data System (ADS)

Hamdan, Mohammad O.; Abu-Nabah, Bassam A.

2018-04-01

In this study, a new term representing net flux rate of linear momentum is introduced to Lucas-Washburn equation. Following a fluid in rigid-body motion in modeling the meniscus rise in vertical capillary tubes transforms the nonlinear Lucas-Washburn equation to a linear mass-spring-damper system. The linear nature of mass-spring-damper system with constant coefficients offers a nondimensional analytical solution where meniscus dynamics are dictated by two parameters, namely the system damping ratio and its natural frequency. This connects the numerous fluid-surface interaction physical and geometrical properties to rather two nondimensional parameters, which capture the underlying physics of meniscus dynamics in three distinct cases, namely overdamped, critically damped, and underdamped systems. Based on experimental data available in the literature and the understanding meniscus dynamics, the proposed model brings a new approach of understanding the system initial conditions. Accordingly, a closed form relation is produced for the imbibition velocity, which equals half of the Bosanquet velocity divided by the damping ratio. The proposed general analytical model is ideal for overdamped and critically damped systems. While for underdamped systems, the solution shows fair agreement with experimental measurements once the effective viscosity is determined. Moreover, the presented model shows meniscus oscillations around equilibrium height occur if the damping ratio is less than one.

The fluid dynamic approach to equidistribution methods for grid generation and adaptation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delzanno, Gian Luca; Finn, John M

2009-01-01

The equidistribution methods based on L{sub p} Monge-Kantorovich optimization [Finn and Delzanno, submitted to SISC, 2009] and on the deformation [Moser, 1965; Dacorogna and Moser, 1990, Liao and Anderson, 1992] method are analyzed primarily in the context of grid generation. It is shown that the first class of methods can be obtained from a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density, arising from a variational principle. In this context, deformation methods arise from a fluid formulation by making a specific assumption on the time evolution of the density (but with some degreemore » of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L{sub 1} Monge-Kantorovich optimization, by making a further assumption on the momentum density. Some applications of the L{sub p} fluid dynamic formulation to imaging are also explored.« less

Computational Flow Modeling of Hydrodynamics in Multiphase Trickle-Bed Reactors

NASA Astrophysics Data System (ADS)

Lopes, Rodrigo J. G.; Quinta-Ferreira, Rosa M.

2008-05-01

This study aims to incorporate most recent multiphase models in order to investigate the hydrodynamic behavior of a TBR in terms of pressure drop and liquid holdup. Taking into account transport phenomena such as mass and heat transfer, an Eulerian k-fluid model was developed resulting from the volume averaging of the continuity and momentum equations and solved for a 3D representation of the catalytic bed. Computational fluid dynamics (CFD) model predicts hydrodynamic parameters quite well if good closures for fluid/fluid and fluid/particle interactions are incorporated in the multiphase model. Moreover, catalytic performance is investigated with the catalytic wet oxidation of a phenolic pollutant.

Effect of micropolar fluids on the squeeze film elliptical plates

NASA Astrophysics Data System (ADS)

Rajashekhar Anagod, Roopa; Hanumagowda, B. N.; Santhosh Kumar, J.

2018-04-01

This paper elaborates on the theoretical analysis of squeeze film characteristics between elliptical plates lubricated with non-Newtonian micro-polar fluid on the basis of Eringen's micropolar fluid theory. The modified Reynold’s equations governing flow of micro-polar fluid is mathematically derived and the outcome reveals distribution of film pressure which determines the dynamic performance characteristics in terms of load and squeezing time for various values of coupling number and micro structure size parameter. Based on the results reported, The influence of non-Newtonian micropolar fluids is examined in enhancing the time of approach and load carrying capacity to the case of classical Newtonian lubricant.

Analysis of material parameter effects on fluidlastic isolators performance

NASA Astrophysics Data System (ADS)

Cheng, Q. Y.; Deng, J. H.; Feng, Z. Z.; Qian, F.

2018-01-01

Control of vibration in helicopters has always been a complex and challenging task. The fluidlastic isolators become more and more widely used because the fluids are non-toxic, non-corrosive, nonflammable, and compatible with most elastomers and adhesives. In the field of the fluidlastic isolators design, the selection of design parameters of fluid and rubber is very important to obtain efficient vibration-suppressed. Aiming at getting the property of fluidlastic isolator to material design parameters, a dynamic equation is set up based on the dynamic theory. And the dynamic analysis is carried out. The influences of design parameters on the property of fluidlastic isolator are calculated. The material parameters examined are the properties of fluid and rubber. Analysis results showed that the design parameters such as density of fluid, viscosity coefficient of fluid, stiffness of rubber (K1) and loss coefficient of rubber have obvious influence on the performance of isolator. Base on the results of the study it is concluded that the efficient vibration-suppressed can be obtained by the selection of design parameters.

Three-dimensional simulations of thin ferro-fluid films and drops in magnetic fields

NASA Astrophysics Data System (ADS)

Conroy, Devin; Wray, Alex; Matar, Omar

2016-11-01

We consider the interfacial dynamics of a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly-conducting. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and continuity equations. The magnetisation of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved with the use of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We consider the three-dimensional evolution of the film to spawise perturbations by solving the non-linear equations numerically. The constant flux configuration is considered, which corresponds to a thin film and drop flowing down an incline, and a parametric study is performed to understand the effect of a magnetic field on the stability and structure of the formed drops. EPSRC UK platform Grant MACIPh (EP/L020564/1) and programme Grant MEMPHIS (EP/K003976/1).

Study of the flow field past dimpled aerodynamic surfaces: numerical simulation and experimental verification

NASA Astrophysics Data System (ADS)

Binci, L.; Clementi, G.; D'Alessandro, V.; Montelpare, S.; Ricci, R.

2017-11-01

This work presents the study of the flow field past of dimpled laminar airfoil. Fluid dynamic behaviour of these elements has been not still deeply studied in the scientific community. Therefore Computational Fluid-Dynamics (CFD) is here used to analyze the flow field induced by dimples on the NACA 64-014A laminar airfoil at Re = 1.75 · 105 at α = 0°. Reynolds Averaged Navier-Stokes (RANS) equations and Large-Eddy Simulations (LES) were compared with wind tunnel measurements in order to evaluate their effectiveness in the modeling this kind of flow field. LES equations were solved using a specifically developed OpenFOAM solver adopting an L-stable Singly Diagonally Implicit Runge-Kutta (SDIRK) technique with an iterated PISO-like procedure for handling pressure-velocity coupling within each RK stage. Dynamic Smagorinsky subgrid model was employed. LES results provided good agreement with experimental data, while RANS equations closed with \\[k-ω -γ -\\overset{}{\\mathop{{{\\operatorname{Re}}θ, \\text{t}}}} \\] approach overstimates laminar separation bubble (LSB) extension of dimpled and un-dimpled configurations. Moreover, through skin friction coefficient analysis, we found a different representation of the turbulent zone between the numerical models; indeed, with RANS model LSB seems to be divided in two different parts, meanwhile LES model shows a LSB global reduction.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.

Departure of microscopic friction from macroscopic drag in molecular fluid dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hanasaki, Itsuo; Fujiwara, Daiki; Kawano, Satoyuki, E-mail: kawano@me.es.osaka-u.ac.jp

2016-03-07

Friction coefficient of the Langevin equation and drag of spherical macroscopic objects in steady flow at low Reynolds numbers are usually regarded as equivalent. We show that the microscopic friction can be different from the macroscopic drag when the mass is taken into account for particles with comparable scale to the surrounding fluid molecules. We illustrate it numerically by molecular dynamics simulation of chloride ion in water. Friction variation by the atomistic mass effect beyond the Langevin regime can be of use in the drag reduction technology as well as the electro or thermophoresis.

Diffuse interface models of locally inextensible vesicles in a viscous fluid

PubMed Central

Aland, Sebastian; Egerer, Sabine; Lowengrub, John; Voigt, Axel

2014-01-01

We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid with inertial forces. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. We introduce a new equation for the local Lagrange multiplier whose solution essentially provides a harmonic extension of the multiplier off the interface while maintaining the local inextensibility constraint near the interface. We also develop a local relaxation scheme that dynamically corrects local stretching/compression errors thereby preventing their accumulation. Asymptotic analysis is presented that shows that our new system converges to a relaxed version of the inextensible sharp interface model. This is also verified numerically. To solve the equations, we use an adaptive finite element method with implicit coupling between the Navier-Stokes and the diffuse interface inextensibility equations. Numerical simulations of a single vesicle in a shear flow at different Reynolds numbers demonstrate that errors in enforcing local inextensibility may accumulate and lead to large differences in the dynamics in the tumbling regime and smaller differences in the inclination angle of vesicles in the tank-treading regime. The local relaxation algorithm is shown to prevent the accumulation of stretching and compression errors very effectively. Simulations of two vesicles in an extensional flow show that local inextensibility plays an important role when vesicles are in close proximity by inhibiting fluid drainage in the near contact region. PMID:25246712

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

NASA Astrophysics Data System (ADS)

Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.

2017-07-01

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.

Computational Fluid Dynamics (CFD) simulations of a Heisenberg Vortex Tube

NASA Astrophysics Data System (ADS)

Bunge, Carl; Sitaraman, Hariswaran; Leachman, Jake

2017-11-01

A 3D Computational Fluid Dynamics (CFD) simulation of a Heisenberg Vortex Tube (HVT) is performed to estimate cooling potential with cryogenic hydrogen. The main mechanism driving operation of the vortex tube is the use of fluid power for enthalpy streaming in a highly turbulent swirl in a dual-outlet tube. This enthalpy streaming creates a temperature separation between the outer and inner regions of the flow. Use of a catalyst on the peripheral wall of the centrifuge enables endothermic conversion of para-ortho hydrogen to aid primary cooling. A κ- ɛ turbulence model is used with a cryogenic, non-ideal equation of state, and para-orthohydrogen species evolution. The simulations are validated with experiments and strategies for parametric optimization of this device are presented.

On the slow dynamics of near-field acoustically levitated objects under High excitation frequencies

NASA Astrophysics Data System (ADS)

Ilssar, Dotan; Bucher, Izhak

2015-10-01

This paper introduces a simplified analytical model describing the governing dynamics of near-field acoustically levitated objects. The simplification converts the equation of motion coupled with the partial differential equation of a compressible fluid, into a compact, second order ordinary differential equation, where the local stiffness and damping are transparent. The simplified model allows one to more easily analyse and design near-field acoustic levitation based systems, and it also helps to devise closed-loop controller algorithms for such systems. Near-field acoustic levitation employs fast ultrasonic vibrations of a driving surface and exploits the viscosity and the compressibility of a gaseous medium to achieve average, load carrying pressure. It is demonstrated that the slow dynamics dominates the transient behaviour, while the time-scale associated with the fast, ultrasonic excitation has a small presence in the oscillations of the levitated object. Indeed, the present paper formulates the slow dynamics under an ultrasonic excitation without the need to explicitly consider the latter. The simplified model is compared with a numerical scheme based on Reynolds equation and with experiments, both showing reasonably good results.

Hybrid Method for Power Control Simulation of a Single Fluid Plasma Thruster

NASA Astrophysics Data System (ADS)

Jaisankar, S.; Sheshadri, T. S.

2018-05-01

Propulsive plasma flow through a cylindrical-conical diverging thruster is simulated by a power controlled hybrid method to obtain the basic flow, thermodynamic and electromagnetic variables. Simulation is based on a single fluid model with electromagnetics being described by the equations of potential Poisson, Maxwell and the Ohm's law while the compressible fluid dynamics by the Navier Stokes in cylindrical form. The proposed method solved the electromagnetics and fluid dynamics separately, both to segregate the two prominent scales for an efficient computation and for the delivery of voltage controlled rated power. The magnetic transport is solved for steady state while fluid dynamics is allowed to evolve in time along with an electromagnetic source using schemes based on generalized finite difference discretization. The multistep methodology with power control is employed for simulating fully ionized propulsive flow of argon plasma through the thruster. Numerical solution shows convergence of every part of the solver including grid stability causing the multistep hybrid method to converge for a rated power delivery. Simulation results are reasonably in agreement with the reported physics of plasma flow in the thruster thus indicating the potential utility of this hybrid computational framework, especially when single fluid approximation of plasma is relevant.

Analytical Model For Fluid Dynamics In A Microgravity Environment

NASA Technical Reports Server (NTRS)

Naumann, Robert J.

1995-01-01

Report presents analytical approximation methodology for providing coupled fluid-flow, heat, and mass-transfer equations in microgravity environment. Experimental engineering estimates accurate to within factor of 2 made quickly and easily, eliminating need for time-consuming and costly numerical modeling. Any proposed experiment reviewed to see how it would perform in microgravity environment. Model applied in commercial setting for preliminary design of low-Grashoff/Rayleigh-number experiments.

Flapping Wing Flight Dynamic Modeling

DTIC Science & Technology

2011-08-22

cases. Pesavento and Wang [24] solved the two dimensional Navier-Stokes equations in relation to a piece of free falling paper at Reynolds number near...von Karman, T. and Burgers, J. M., Gerneral Aerodynamic Theory - Perfect Fluids , Vol. II, Julius Springer, Berlin, 1935. [24] Pesavento , U. and Wang...2004, pp. 14. [25] Andersen, A., Pesavento , U., and Wang, Z. J., Unsteady aerodynamics of uttering and tumbling plates, Journal of Fluid Mechanics

The effect of sediments on turbulent plume dynamics in a stratified fluid

NASA Astrophysics Data System (ADS)

Stenberg, Erik; Ezhova, Ekaterina; Brandt, Luca

2017-11-01

We report large eddy simulation results of sediment-loaded turbulent plumes in a stratified fluid. The configuration, where the plume is discharged from a round source, provides an idealized model of subglacial discharge from a submarine tidewater glacier and is a starting point for understanding the effect of sediments on the dynamics of the rising plume. The transport of sediments is modeled by means of an advection-diffusion equation where sediment settling velocity is taken into account. We initially follow the experimental setup of Sutherland (Phys. Rev. Fluids, 2016), considering uniformly stratified ambients and further extend the work to pycnocline-type stratifications typical of Greenland fjords. Apart from examining the rise height, radial spread and intrusion of the rising plume, we gain further insights of the plume dynamics by extracting turbulent characteristics and the distribution of the sediments inside the plume.

Two-dimensional fluid dynamics in a sharply bent channel: Laminar flow, separation bubble, and vortex dynamics

NASA Astrophysics Data System (ADS)

Matsumoto, Daichi; Fukudome, Koji; Wada, Hirofumi

2016-10-01

Understanding the hydrodynamic properties of fluid flow in a curving pipe and channel is important for controlling the flow behavior in technologies and biomechanics. The nature of the resulting flow in a bent pipe is extremely complicated because of the presence of a cross-stream secondary flow. In an attempt to disentangle this complexity, we investigate the fluid dynamics in a bent channel via the direct numerical simulation of the Navier-Stokes equation in two spatial dimensions. We exploit the absence of secondary flow from our model and systematically investigate the flow structure along the channel as a function of both the bend angle and Reynolds number of the laminar-to-turbulent regime. We numerically suggest a scaling relation between the shape of the separation bubble and the flow conductance, and construct an integrated phase diagram.

On locally and nonlocally related potential systems

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.; Bluman, George W.

2010-07-01

For any partial differential equation (PDE) system, a local conservation law yields potential equations in terms of some potential variable, which normally is a nonlocal variable. The current paper examines situations when such a potential variable is a local variable, i.e., is a function of the independent and dependent variables of a given PDE system, and their derivatives. In the case of two independent variables, a simple necessary and sufficient condition is presented for the locality of such a potential variable, and this is illustrated by several examples. As a particular example, two-dimensional reductions of equilibrium equations for fluid and plasma dynamics are considered. It is shown that such reductions with respect to helical, axial, and translational symmetries have conservation laws which yield local potential variables. This leads to showing that the well-known Johnson-Frieman-Kruskal-Oberman (JFKO) and Bragg-Hawthorne (Grad-Shafranov) equations are locally related to the corresponding helically and axially symmetric PDE systems of fluid/plasma dynamics. For the axially symmetric case, local symmetry classifications and arising invariant solutions are compared for the original PDE system and the Bragg-Hawthorne (potential) equation. The potential equation is shown to have additional symmetries, denoted as restricted symmetries. Restricted symmetries leave invariant a family of solutions of a given PDE system but not the whole solution manifold, and hence are not symmetries of the given PDE system. Corresponding reductions are shown to yield solutions, which are not obtained as invariant solutions from local symmetry reduction.

Two-dimensional extended fluid model for a dc glow discharge with nonlocal ionization source term

NASA Astrophysics Data System (ADS)

Rafatov, Ismail; Bogdanov, Eugeny; Kudryavtsev, Anatoliy

2013-09-01

Numerical techniques applied to the gas discharge plasma modelling are generally grouped into fluid and kinetic (particle) methods, and their combinations which lead to the hybrid models. Hybrid models usually employ Monte Carlo method to simulate fast electron dynamics, while slow plasma species are described as fluids. However, since fast electrons contribution to these models is limited to deriving the ionization rate distribution, their effect can be expressed by the analytical approximation of the ionization source function, and then integrating it into the fluid model. In the context of this approach, we incorporated effect of fast electrons into the ``extended fluid model'' of glow discharge, using two spatial dimensions. Slow electrons, ions and excited neutral species are described by the fluid plasma equations. Slow electron transport (diffusion and mobility) coefficients as well as electron induced reaction rates are determined from the solutions of the electron Boltzmann equation. The self-consistent electric field is calculated using the Poisson equation. We carried out test calculations for the discharge in argon gas. Comparison with the experimental data as well as with the hybrid model results exhibits good applicability of the proposed model. The work was supported by the joint research grant from the Scientific and Technical Research Council of Turkey (TUBITAK) 212T164 and Russian Foundation for Basic Research (RFBR).

Integral equation methods for vesicle electrohydrodynamics in three dimensions

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan

2016-12-01

In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor-Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations.

Equation of state of solid, liquid and gaseous tantalum from first principles

DOE PAGES

Miljacic, Ljubomir; Demers, Steven; Hong, Qi-Jun; ...

2015-09-18

Here, we present ab initio calculations of the phase diagram and the equation of state of Ta in a wide range of volumes and temperatures, with volumes from 9 to 180 Å 3/atom, temperature as high as 20000 K, and pressure up to 7 Mbars. The calculations are based on first principles, in combination with techniques of molecular dynamics, thermodynamic integration, and statistical modeling. Multiple phases are studied, including the solid, fluid, and gas single phases, as well as two-phase coexistences. We calculate the critical point by direct molecular dynamics sampling, and extend the equation of state to very lowmore » density through virial series fitting. The accuracy of the equation of state is assessed by comparing both the predicted melting curve and the critical point with previous experimental and theoretical investigations.« less

Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

NASA Astrophysics Data System (ADS)

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

2018-04-01

Relativistic fluid dynamics is a major component in dynamical simulations of the quark-gluon plasma created in relativistic heavy-ion collisions. Simulations of the full three-dimensional dissipative dynamics of the quark-gluon plasma with fluctuating initial conditions are computationally expensive and typically require some degree of parallelization. In this paper, we present a GPU implementation of the Kurganov-Tadmor algorithm which solves the 3 + 1d relativistic viscous hydrodynamics equations including the effects of both bulk and shear viscosities. We demonstrate that the resulting CUDA-based GPU code is approximately two orders of magnitude faster than the corresponding serial implementation of the Kurganov-Tadmor algorithm. We validate the code using (semi-)analytic tests such as the relativistic shock-tube and Gubser flow.

Reduced order modeling of fluid/structure interaction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph

2009-11-01

This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preservesmore » numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.« less

Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment

NASA Astrophysics Data System (ADS)

Liang, Feng; Yang, Xiao-Dong; Zhang, Wei; Qian, Ying-Jing

2018-03-01

In this paper, a dynamical model of simply-supported spinning pipes conveying fluid with axial deployment is proposed and the transverse free vibration and stability for such a doubly gyroscopic system involving time-dependent parameters are investigated. The partial differential equations of motion are derived by the extended Hamilton principle and then truncated by the Galerkin technique. The time-variant frequencies, mode shapes and responses to initial conditions are comprehensively investigated to reveal the dynamical essence of the system. It is indicated that the qualitative stability evolution of the system mainly depends on the effect of fluid-structure interaction (FSI), while the spinning motion will enhance the pipe rigidity and eliminate the buckling instability. The dynamical evolution of a retracting pipe is almost inverse to that of the deploying one. The pipe possesses different mode configurations of spatial curves as the pipe length increases and some modal and response characteristics of the present system are found rather distinct from those of deploying cantilevered structures.

Transient Nonequilibrium Molecular Dynamic Simulations of Thermal Conductivity: 1. Simple Fluids

NASA Astrophysics Data System (ADS)

Hulse, R. J.; Rowley, R. L.; Wilding, W. V.

2005-01-01

Thermal conductivity has been previously obtained from molecular dynamics (MD) simulations using either equilibrium (EMD) simulations (from Green--Kubo equations) or from steady-state nonequilibrium (NEMD) simulations. In the case of NEMD, either boundary-driven steady states are simulated or constrained equations of motion are used to obtain steady-state heat transfer rates. Like their experimental counterparts, these nonequilibrium steady-state methods are time consuming and may have convection problems. Here we report a new transient method developed to provide accurate thermal conductivity predictions from MD simulations. In the proposed MD method, molecules that lie within a specified volume are instantaneously heated. The temperature decay of the system of molecules inside the heated volume is compared to the solution of the transient energy equation, and the thermal diffusivity is regressed. Since the density of the fluid is set in the simulation, only the isochoric heat capacity is needed in order to obtain the thermal conductivity. In this study the isochoric heat capacity is determined from energy fluctuations within the simulated fluid. The method is valid in the liquid, vapor, and critical regions. Simulated values for the thermal conductivity of a Lennard-Jones (LJ) fluid were obtained using this new method over a temperature range of 90 to 900 K and a density range of 1-35 kmol · m-3. These values compare favorably with experimental values for argon. The new method has a precision of ±10%. Compared to other methods, the algorithm is quick, easy to code, and applicable to small systems, making the simulations very efficient.

Optimal sensor placement for control of a supersonic mixed-compression inlet with variable geometry

NASA Astrophysics Data System (ADS)

Moore, Kenneth Thomas

A method of using fluid dynamics models for the generation of models that are useable for control design and analysis is investigated. The problem considered is the control of the normal shock location in the VDC inlet, which is a mixed-compression, supersonic, variable-geometry inlet of a jet engine. A quasi-one-dimensional set of fluid equations incorporating bleed and moving walls is developed. An object-oriented environment is developed for simulation of flow systems under closed-loop control. A public interface between the controller and fluid classes is defined. A linear model representing the dynamics of the VDC inlet is developed from the finite difference equations, and its eigenstructure is analyzed. The order of this model is reduced using the square root balanced model reduction method to produce a reduced-order linear model that is suitable for control design and analysis tasks. A modification to this method that improves the accuracy of the reduced-order linear model for the purpose of sensor placement is presented and analyzed. The reduced-order linear model is used to develop a sensor placement method that quantifies as a function of the sensor location the ability of a sensor to provide information on the variable of interest for control. This method is used to develop a sensor placement metric for the VDC inlet. The reduced-order linear model is also used to design a closed loop control system to control the shock position in the VDC inlet. The object-oriented simulation code is used to simulate the nonlinear fluid equations under closed-loop control.

Solving Navier-Stokes equations on a massively parallel processor; The 1 GFLOP performance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saati, A.; Biringen, S.; Farhat, C.

This paper reports on experience in solving large-scale fluid dynamics problems on the Connection Machine model CM-2. The authors have implemented a parallel version of the MacCormack scheme for the solution of the Navier-Stokes equations. By using triad floating point operations and reducing the number of interprocessor communications, they have achieved a sustained performance rate of 1.42 GFLOPS.

Surfactant effects on the dynamics of an intravascular bubble

NASA Astrophysics Data System (ADS)

Zhang, Jie; Eckmann, David; Ayyaswamy, P. S.

2004-11-01

The effects of a surfactant on the dynamics of gas bubble behavior in the arteriolar vasculature are numerically investigated. The equations for momentum in the bulk fluid (blood) and the bubble, and the convection-diffusion equations for mass transport both in the bulk fluid and on the gas-liquid interface are numerically solved using a front tracking method. Both soluble and insoluble surfactants are considered. The adsorption/desorption dynamics of the soluble surfactant is accurately resolved. For a nearly occluded bubble, a faster rate of depletion of the surfactant from the region adjacent to the wall of the vessel is observed. In several cases studied here, the bulk medium is treated as non-Newtonian (power law, Casson), although the majority of cases treat blood as Newtonian. Results show that the adsorbed surfactant serves to prevent blood proteins and other macromolecules from occupying the interface. This prevents clotting or adhesion of the bubble to the vessel wall. The results obtained have significance in the study of intravascular gas embolism. Supported by NIH R01 HL67986

Improved computational fluid dynamic simulations of blood flow in membrane oxygenators from X-ray imaging.

PubMed

Jones, Cameron C; McDonough, James M; Capasso, Patrizio; Wang, Dongfang; Rosenstein, Kyle S; Zwischenberger, Joseph B

2013-10-01

Computational fluid dynamics (CFD) is a useful tool in characterizing artificial lung designs by providing predictions of device performance through analyses of pressure distribution, perfusion dynamics, and gas transport properties. Validation of numerical results in membrane oxygenators has been predominantly based on experimental pressure measurements with little emphasis placed on confirmation of the velocity fields due to opacity of the fiber membrane and limitations of optical velocimetric methods. Biplane X-ray digital subtraction angiography was used to visualize flow of a blood analogue through a commercial membrane oxygenator at 1-4.5 L/min. Permeability and inertial coefficients of the Ergun equation were experimentally determined to be 180 and 2.4, respectively. Numerical simulations treating the fiber bundle as a single momentum sink according to the Ergun equation accurately predicted pressure losses across the fiber membrane, but significantly underestimated velocity magnitudes in the fiber bundle. A scaling constant was incorporated into the numerical porosity and reduced the average difference between experimental and numerical values in the porous media regions from 44 ± 4% to 6 ± 5%.

Formation of curvature singularities on the interface between dielectric liquids in a strong vertical electric field.

PubMed

Kochurin, Evgeny A; Zubarev, Nikolay M; Zubareva, Olga V

2013-08-01

The nonlinear dynamics of the interface between two deep dielectric fluids in the presence of a vertical electric field is studied. We consider the limit of a strong external electric field where electrostatic forces dominate over gravitational and capillary forces. The nonlinear integrodifferential equations for the interface motion are derived under the assumption of small interfacial slopes. It is shown in the framework of these equations that, in the generic case, the instability development leads to the formation of root singularities at the interface in a finite time. The interfacial curvature becomes infinite at singular points, while the slope angles remain relatively small. The curvature is negative in the vicinity of singularities if the ratio of the permittivities of the fluids exceeds the inverse ratio of their densities, and it is positive in the opposite case (we consider that the lower fluid is heavier than the upper one). In the intermediate case, the interface evolution equations describe the formation and sharpening of dimples at the interface. The results obtained are applicable for the description of the instability of the interface between two magnetic fluids in a vertical magnetic field.

Accelerating dark energy cosmological model in two fluids with hybrid scale factor

NASA Astrophysics Data System (ADS)

Mishra, B.; Sahoo, P. K.; Ray, Pratik P.

In this paper, we have investigated the anisotropic behavior of the accelerating universe in Bianchi V spacetime in the framework of General Relativity (GR). The matter field we have considered is of two non-interacting fluids, i.e. the usual string fluid and dark energy (DE) fluid. In order to represent the pressure anisotropy, the skewness parameters are introduced along three different spatial directions. To achieve a physically realistic solutions to the field equations, we have considered a scale factor, known as hybrid scale factor, which is generated by a time-varying deceleration parameter. This simulates a cosmic transition from early deceleration to late time acceleration. It is observed that the string fluid dominates the universe at early deceleration phase but does not affect nature of cosmic dynamics substantially at late phase, whereas the DE fluid dominates the universe in present time, which is in accordance with the observations results. Hence, we analyzed here the role of two fluids in the transitional phases of universe with respect to time which depicts the reason behind the cosmic expansion and DE. The role of DE with variable equation of state parameter (EoS) and skewness parameters, is also discussed along with physical and geometrical properties.

Dynamic compression of dense oxide (Gd3Ga5O12) from 0.4 to 2.6 TPa: Universal Hugoniot of fluid metals

PubMed Central

Ozaki, N.; Nellis, W. J.; Mashimo, T.; Ramzan, M.; Ahuja, R.; Kaewmaraya, T.; Kimura, T.; Knudson, M.; Miyanishi, K.; Sakawa, Y.; Sano, T.; Kodama, R.

2016-01-01

Materials at high pressures and temperatures are of great current interest for warm dense matter physics, planetary sciences, and inertial fusion energy research. Shock-compression equation-of-state data and optical reflectivities of the fluid dense oxide, Gd3Ga5O12 (GGG), were measured at extremely high pressures up to 2.6 TPa (26 Mbar) generated by high-power laser irradiation and magnetically-driven hypervelocity impacts. Above 0.75 TPa, the GGG Hugoniot data approach/reach a universal linear line of fluid metals, and the optical reflectivity most likely reaches a constant value indicating that GGG undergoes a crossover from fluid semiconductor to poor metal with minimum metallic conductivity (MMC). These results suggest that most fluid compounds, e.g., strong planetary oxides, reach a common state on the universal Hugoniot of fluid metals (UHFM) with MMC at sufficiently extreme pressures and temperatures. The systematic behaviors of warm dense fluid would be useful benchmarks for developing theoretical equation-of-state and transport models in the warm dense matter regime in determining computational predictions. PMID:27193942

Dynamic compression of dense oxide (Gd 3Ga 5O 12) from 0.4 to 2.6 TPa: Universal Hugoniot of fluid metals

DOE PAGES

Ozaki, N.; Nellis, W. J.; Mashimo, T.; ...

2016-05-19

Materials at high pressures and temperatures are of great current interest for warm dense matter physics, planetary sciences, and inertial fusion energy research. Shock-compression equation-of-state data and optical reflectivities of the fluid dense oxide, Gd 3Ga 5O 12 (GGG), were measured at extremely high pressures up to 2.6 TPa (26 Mbar) generated by high-power laser irradiation and magnetically-driven hypervelocity impacts. Above 0.75 TPa, the GGG Hugoniot data approach/reach a universal linear line of fluid metals, and the optical reflectivity most likely reaches a constant value indicating that GGG undergoes a crossover from fluid semiconductor to poor metal with minimum metallicmore » conductivity (MMC). These results suggest that most fluid compounds, e.g., strong planetary oxides, reach a common state on the universal Hugoniot of fluid metals (UHFM) with MMC at sufficiently extreme pressures and temperatures. Lastly, the systematic behaviors of warm dense fluid would be useful benchmarks for developing theoretical equation-of-state and transport models in the warm dense matter regime in determining computational predictions.« less

Dynamic compression of dense oxide (Gd3Ga5O12) from 0.4 to 2.6 TPa: Universal Hugoniot of fluid metals.

PubMed

Ozaki, N; Nellis, W J; Mashimo, T; Ramzan, M; Ahuja, R; Kaewmaraya, T; Kimura, T; Knudson, M; Miyanishi, K; Sakawa, Y; Sano, T; Kodama, R

2016-05-19

Materials at high pressures and temperatures are of great current interest for warm dense matter physics, planetary sciences, and inertial fusion energy research. Shock-compression equation-of-state data and optical reflectivities of the fluid dense oxide, Gd3Ga5O12 (GGG), were measured at extremely high pressures up to 2.6 TPa (26 Mbar) generated by high-power laser irradiation and magnetically-driven hypervelocity impacts. Above 0.75 TPa, the GGG Hugoniot data approach/reach a universal linear line of fluid metals, and the optical reflectivity most likely reaches a constant value indicating that GGG undergoes a crossover from fluid semiconductor to poor metal with minimum metallic conductivity (MMC). These results suggest that most fluid compounds, e.g., strong planetary oxides, reach a common state on the universal Hugoniot of fluid metals (UHFM) with MMC at sufficiently extreme pressures and temperatures. The systematic behaviors of warm dense fluid would be useful benchmarks for developing theoretical equation-of-state and transport models in the warm dense matter regime in determining computational predictions.

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid.

PubMed

Xiao, Li; Luo, Ray

2017-12-07

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Spherically symmetric Einstein-aether perfect fluid models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coley, Alan A.; Latta, Joey; Leon, Genly

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysicalmore » objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.« less

The instanton method and its numerical implementation in fluid mechanics

NASA Astrophysics Data System (ADS)

Grafke, Tobias; Grauer, Rainer; Schäfer, Tobias

2015-08-01

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional (2D or 3D) fluid dynamical problems. We illustrate these ideas using the 2D Burgers equation and the 3D Navier-Stokes equations.

Numerical Simulations of Free Surface Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Glimm, James; Oh, Wonho; Prykarpatskyy, Yarema

2003-11-01

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations are based on a finite element discretization on moving grids dynamically conforming to fluid interfaces. The method has been implemented as an MHD extension of the FronTier code. The code has been applied for modeling the behavior of lithium and mercury jets in magnetic fields, laser ablation plumes, and the Richtmyer-Meshkov instability of a liquid mercury jet interacting with a high energy proton pulse in a strong magnetic field. Such an instability occurs in the target for the Muon Collider.

Implementation of parallel moment equations in NIMROD

NASA Astrophysics Data System (ADS)

Lee, Hankyu Q.; Held, Eric D.; Ji, Jeong-Young

2017-10-01

As collisionality is low (the Knudsen number is large) in many plasma applications, kinetic effects become important, particularly in parallel dynamics for magnetized plasmas. Fluid models can capture some kinetic effects when integral parallel closures are adopted. The adiabatic and linear approximations are used in solving general moment equations to obtain the integral closures. In this work, we present an effort to incorporate non-adiabatic (time-dependent) and nonlinear effects into parallel closures. Instead of analytically solving the approximate moment system, we implement exact parallel moment equations in the NIMROD fluid code. The moment code is expected to provide a natural convergence scheme by increasing the number of moments. Work in collaboration with the PSI Center and supported by the U.S. DOE under Grant Nos. DE-SC0014033, DE-SC0016256, and DE-FG02-04ER54746.

Dust cyclone research in the 21st century

USDA-ARS?s Scientific Manuscript database

Research to meet the demand for ever more efficient dust cyclones continues after some eighty years. Recent trends emphasize design optimization through computational fluid dynamics (CFD) and testing design subtleties not modeled by semi-empirical equations. Improvements to current best available ...

PHYSICS REQUIRES A SIMPLE LOW MACH NUMBER FLOW TO BE COMPRESSIBLE

EPA Science Inventory

Radial, laminar, plane, low velocity flow represents the simplest, non-linear fluid dynamics problem. Ostensibly this apparently trivial flow could be solved using the incompressible Navier-Stokes equations, universally believed to be adequate for such problems. Most researchers ...

The complex dynamics of wishful thinking: the critical positivity ratio.

PubMed

Brown, Nicholas J L; Sokal, Alan D; Friedman, Harris L

2013-12-01

We examine critically the claims made by Fredrickson and Losada (2005) concerning the construct known as the "positivity ratio." We find no theoretical or empirical justification for the use of differential equations drawn from fluid dynamics, a subfield of physics, to describe changes in human emotions over time; furthermore, we demonstrate that the purported application of these equations contains numerous fundamental conceptual and mathematical errors. The lack of relevance of these equations and their incorrect application lead us to conclude that Fredrickson and Losada's claim to have demonstrated the existence of a critical minimum positivity ratio of 2.9013 is entirely unfounded. More generally, we urge future researchers to exercise caution in the use of advanced mathematical tools, such as nonlinear dynamics, and in particular to verify that the elementary conditions for their valid application have been met. PsycINFO Database Record (c) 2013 APA, all rights reserved.

Dynamics of a spherical particle in an acoustic field: A multiscale approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk; Vanneste, Jacques

2014-10-15

A rigid spherical particle in an acoustic wave field oscillates at the wave period but has also a mean motion on a longer time scale. The dynamics of this mean motion is crucial for numerous applications of acoustic microfluidics, including particle manipulation and flow visualisation. It is controlled by four physical effects: acoustic (radiation) pressure, streaming, inertia, and viscous drag. In this paper, we carry out a systematic multiscale analysis of the problem in order to assess the relative importance of these effects depending on the parameters of the system that include wave amplitude, wavelength, sound speed, sphere radius, andmore » viscosity. We identify two distinguished regimes characterised by a balance among three of the four effects, and we derive the equations that govern the mean particle motion in each regime. This recovers and organises classical results by King [“On the acoustic radiation pressure on spheres,” Proc. R. Soc. A 147, 212–240 (1934)], Gor'kov [“On the forces acting on a small particle in an acoustical field in an ideal fluid,” Sov. Phys. 6, 773–775 (1962)], and Doinikov [“Acoustic radiation pressure on a rigid sphere in a viscous fluid,” Proc. R. Soc. London A 447, 447–466 (1994)], clarifies the range of validity of these results, and reveals a new nonlinear dynamical regime. In this regime, the mean motion of the particle remains intimately coupled to that of the surrounding fluid, and while viscosity affects the fluid motion, it plays no part in the acoustic pressure. Simplified equations, valid when only two physical effects control the particle motion, are also derived. They are used to obtain sufficient conditions for the particle to behave as a passive tracer of the Lagrangian-mean fluid motion.« less

Hydrodynamical processes in coalescing binary stars

NASA Astrophysics Data System (ADS)

Lai, Dong

1994-01-01

Coalescing neutron star binaries are considered to be the most promising sources of gravitational waves that could be detected by the planned laser-interferometer LIGO/VIRGO detectors. Extracting gravity wave signals from noisy data requires accurate theoretical waveforms in the frequency range 10-1000 Hz end detailed understanding of the dynamics of the binary orbits. We investigate the quasi-equilibrium and dynamical tidal interactions in coalescing binary stars, with particular focus on binary neutron stars. We develop a new formalism to study the equilibrium and dynamics of fluid stars in binary systems. The stars are modeled as compressible ellipsoids, and satisfy polytropic equation of state. The hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. The equilibrium binary structure is determined by a set of algebraic equations. We consider both synchronized and nonsynchronized systems, obtaining the generalizations to compressible fluid of the classical results for the ellipsoidal binary configurations. Our method can be applied to a wide variety of astrophysical binary systems containing neutron stars, white dwarfs, main-sequence stars and planets. We find that both secular and dynamical instabilities can develop in close binaries. The quasi-static (secular) orbital evolution, as well as the dynamical evolution of binaries driven by viscous dissipation and gravitational radiation reaction are studied. The development of the dynamical instability accelerates the binary coalescence at small separation, leading to appreciable radial infall velocity near contact. We also study resonant excitations of g-mode oscillations in coalescing binary neutron stars. A resonance occurs when the frequency of the tidal driving force equals one of the intrinsic g-mode frequencies. Using realistic microscopic nuclear equations of state, we determine the g-modes in a cold neutron atar. Resonant excitations of these g-modes during the last few minutes of the binary coalescence result in energy transfer and angular momentum transfer from the binary orbit to the neutron star. Because of the weak coupling between the g-modes and the tidal potential, the induced orbital phase errors due to resonances are small. However, resonant excitations of the g-modes play an important role in the tidal heating of binary neutron stars.

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach: STICK-SLIP IN SATURATED FAULT GOUGE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this study, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that themore » (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Finally, our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.« less

On the role of fluids in stick-slip dynamics of saturated granular fault gouge using a coupled computational fluid dynamics-discrete element approach: STICK-SLIP IN SATURATED FAULT GOUGE

DOE PAGES

Dorostkar, Omid; Guyer, Robert A.; Johnson, Paul A.; ...

2017-05-01

The presence of fault gouge has considerable influence on slip properties of tectonic faults and the physics of earthquake rupture. The presence of fluids within faults also plays a significant role in faulting and earthquake processes. In this study, we present 3-D discrete element simulations of dry and fluid-saturated granular fault gouge and analyze the effect of fluids on stick-slip behavior. Fluid flow is modeled using computational fluid dynamics based on the Navier-Stokes equations for an incompressible fluid and modified to take into account the presence of particles. Analysis of a long time train of slip events shows that themore » (1) drop in shear stress, (2) compaction of granular layer, and (3) the kinetic energy release during slip all increase in magnitude in the presence of an incompressible fluid, compared to dry conditions. We also observe that on average, the recurrence interval between slip events is longer for fluid-saturated granular fault gouge compared to the dry case. This observation is consistent with the occurrence of larger events in the presence of fluid. It is found that the increase in kinetic energy during slip events for saturated conditions can be attributed to the increased fluid flow during slip. Finally, our observations emphasize the important role that fluid flow and fluid-particle interactions play in tectonic fault zones and show in particular how discrete element method (DEM) models can help understand the hydromechanical processes that dictate fault slip.« less

Dynamic colloidal assembly pathways via low dimensional models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu; Thyagarajan, Raghuram

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterizedmore » by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.« less

Generalized Forchheimer Flows of Isentropic Gases

NASA Astrophysics Data System (ADS)

Celik, Emine; Hoang, Luan; Kieu, Thinh

2018-03-01

We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat's and Ward's general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L^∞ and W^{1,2-a} (with 0

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azhar, Mueed; Greiner, Andreas; Korvink, Jan G., E-mail: jan.korvink@kit.edu, E-mail: david.kauzlaric@imtek.uni-freiburg.de

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. Aftermore » a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.« less

Mechanics of couple-stress fluid coatings

NASA Technical Reports Server (NTRS)

Waxman, A. M.

1982-01-01

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

A stochastic differential equation analysis of cerebrospinal fluid dynamics.

PubMed

Raman, Kalyan

2011-01-18

Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.

ARCTIC SEA ICE EXTENT AND DRIFT, MODELED AS A VISCOUS FLUID.

USGS Publications Warehouse

Ling, Chi-Hai; Parkinson, Claire L.

1986-01-01

A dynamic/thermodynamic numerical model of sea ice has been used to calculate the yearly cycle of sea ice thicknesses, concentrations, and velocities in the Arctic Ocean and surrounding seas. The model combines the formulations of two previous models, taking the thermodynamics and momentum equations from the model of Parkinson and Washington and adding the constitutive equation and equation of state from the model of Ling, Rasmussen, and Campbell. Simulated annually averaged ice drift vectors compare well with observed ice drift from the Arctic Ocean Buoy Program.

Pseudo-compressibility methods for the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, Eli; Arnone, A.

1993-01-01

Preconditioning methods to accelerate convergence to a steady state for the incompressible fluid dynamics equations are considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Thus the steady state of the preconditioned system is the same as the steady state of the original system. The method is compared to other types of pseudo-compressibility. For finite difference methods preconditioning can change and improve the steady state solutions. An application to viscous flow around a cascade with a non-periodic mesh is presented.

An evaluation of Computational Fluid dynamics model for flood risk analysis

NASA Astrophysics Data System (ADS)

Di Francesco, Silvia; Biscarini, Chiara; Montesarchio, Valeria

2014-05-01

This work presents an analysis of the hydrological-hydraulic engineering requisites for Risk evaluation and efficient flood damage reduction plans. Most of the research efforts have been dedicated to the scientific and technical aspects of risk assessment, providing estimates of possible alternatives and of the risk associated. In the decision making process for mitigation plan, the contribute of scientist is crucial, due to the fact that Risk-Damage analysis is based on evaluation of flow field ,of Hydraulic Risk and on economical and societal considerations. The present paper will focus on the first part of process, the mathematical modelling of flood events which is the base for all further considerations. The evaluation of potential catastrophic damage consequent to a flood event and in particular to dam failure requires modelling of the flood with sufficient detail so to capture the spatial and temporal evolutions of the event, as well of the velocity field. Thus, the selection of an appropriate mathematical model to correctly simulate flood routing is an essential step. In this work we present the application of two 3D Computational fluid dynamics models to a synthetic and real case study in order to evaluate the correct evolution of flow field and the associated flood Risk . The first model is based on a opensource CFD platform called openFoam. Water flow is schematized with a classical continuum approach based on Navier-Stokes equation coupled with Volume of fluid (VOF) method to take in account the multiphase character of river bottom-water- air systems. The second model instead is based on the Lattice Boltzmann method, an innovative numerical fluid dynamics scheme based on Boltzmann's kinetic equation that represents the flow dynamics at the macroscopic level by incorporating a microscopic kinetic approach. Fluid is seen as composed by particles that can move and collide among them. Simulation results from both models are promising and congruent to experimental results available in literature, thought the LBM model requires less computational effort respect to the NS one.

Geophysical aspects of underground fluid dynamics and mineral transformation process

NASA Astrophysics Data System (ADS)

Khramchenkov, Maxim; Khramchenkov, Eduard

2014-05-01

The description of processes of mass exchange between fluid and poly-minerals material in porous media from various kinds of rocks (primarily, sedimentary rocks) have been examined. It was shown that in some important cases there is a storage equation of non-linear diffusion equation type. In addition, process of filtration in un-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and particles material were considered. In the latter case equations of physical-chemical mechanics of conservation of mass for fluid and particles material were used. As it is well known, the mechanics of porous media is theoretical basis of such branches of science as rock mechanics, soil physics and so on. But at the same moment some complex processes in the geosystems lacks full theoretical description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The process of rocks consolidation which happens due to filtration of underground fluids is described from the position of rock mechanics. As an additional impact, let us consider the porous media consolidating under the weight of overlying rock with coupled complex geological processes, as a continuous porous medium of variable mass. Problems of obtaining of correct storage equations for coupled processes of consolidation and mass exchange between underground fluid and skeleton material are often met in catagenesi processes description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The present work is dedicated to the retrieval of new ways to formulate and construct such models. It was shown that in some important cases there is a governing equation of non-linear diffusion equation type (well-known Fisher equation). In addition, some geophysical aspects of filtration process in usual non-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and skeleton material, including earth quakes, are considered.

A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

NASA Astrophysics Data System (ADS)

Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

2014-11-01

We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

Flocking from a quantum analogy: spin-orbit coupling in an active fluid

NASA Astrophysics Data System (ADS)

Loewe, Benjamin; Souslov, Anton; Goldbart, Paul M.

2018-01-01

Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of the fluid can yield insights into experimentally realizable active flows, but this connection is well understood in only a few select cases. We introduce a model of self-propelled particles based on an analogy with the motion of electrons that have strong spin-orbit coupling. We find that, within our model, self-propelled particles are subject to an analog of the Heisenberg uncertainty principle that relates translational and rotational noise. Furthermore, by coarse-graining this microscopic model, we establish expressions for the coefficients of the Toner-Tu equations—the hydrodynamic equations that describe an active fluid composed of these ‘active spins.’ The connection between stochastic self-propelled particles and quantum particles with spin may help realize exotic phases of matter using active fluids via analogies with systems composed of strongly correlated electrons.

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

NASA Astrophysics Data System (ADS)

Shams, Mosayeb; Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko

2018-03-01

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier-Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier-Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas.

Computer code for gas-liquid two-phase vortex motions: GLVM

NASA Technical Reports Server (NTRS)

Yeh, T. T.

1986-01-01

A computer program aimed at the phase separation between gas and liquid at zero gravity, induced by vortex motion, is developed. It utilizes an explicit solution method for a set of equations describing rotating gas-liquid flows. The vortex motion is established by a tangential fluid injection. A Lax-Wendroff two-step (McCormack's) numerical scheme is used. The program can be used to study the fluid dynamical behavior of the rotational two-phase fluids in a cylindrical tank. It provides a quick/easy sensitivity test on various parameters and thus provides the guidance for the design and use of actual physical systems for handling two-phase fluids.

Numerical Simulation Of Flow Through An Artificial Heart

NASA Technical Reports Server (NTRS)

Rogers, Stuart; Kutler, Paul; Kwak, Dochan; Kiris, Centin

1991-01-01

Research in both artificial hearts and fluid dynamics benefits from computational studies. Algorithm that implements Navier-Stokes equations of flow extended to simulate flow of viscous, incompressible blood through articifial heart. Ability to compute details of such flow important for two reasons: internal flows with moving boundaries of academic interest in their own right, and many of deficiencies of artificial hearts attributable to dynamics of flow.

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

NASA Technical Reports Server (NTRS)

Revenaugh, Justin; Parsons, Barry

1987-01-01

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Multitasking the code ARC3D. [for computational fluid dynamics

NASA Technical Reports Server (NTRS)

Barton, John T.; Hsiung, Christopher C.

1986-01-01

The CRAY multitasking system was developed in order to utilize all four processors and sharply reduce the wall clock run time. This paper describes the techniques used to modify the computational fluid dynamics code ARC3D for this run and analyzes the achieved speedup. The ARC3D code solves either the Euler or thin-layer N-S equations using an implicit approximate factorization scheme. Results indicate that multitask processing can be used to achieve wall clock speedup factors of over three times, depending on the nature of the program code being used. Multitasking appears to be particularly advantageous for large-memory problems running on multiple CPU computers.

Hydrodynamics of confined colloidal fluids in two dimensions

NASA Astrophysics Data System (ADS)

Sané, Jimaan; Padding, Johan T.; Louis, Ard A.

2009-05-01

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two-dimensional colloidal disks in confined geometries. We calculate the velocity autocorrelation functions and observe the predicted t-1 long-time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the t-1 tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system. The Langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times.

A Landau fluid model for dispersive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.

2004-11-01

A monofluid model with Landau damping is presented for strongly magnetized electron-proton collisionless plasmas whose distribution functions are close to bi-Maxwellians. This description that includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors, extends the Landau-fluid model of Snyder, Hammett, and Dorland [Phys. Plasmas 4, 3974 (1997)] by retaining Hall effect and finite Larmor radius corrections. It accurately reproduces the weakly nonlinear dynamics of dispersive Alfvén waves whose wavelengths are large compared to the ion inertial length, whatever their direction of propagation, and also the rapid Landau dissipation of long magnetosonic waves in a warm plasma.

Dynamic Deployment Simulations of Inflatable Space Structures

NASA Technical Reports Server (NTRS)

Wang, John T.

2005-01-01

The feasibility of using Control Volume (CV) method and the Arbitrary Lagrangian Eulerian (ALE) method in LSDYNA to simulate the dynamic deployment of inflatable space structures is investigated. The CV and ALE methods were used to predict the inflation deployments of three folded tube configurations. The CV method was found to be a simple and computationally efficient method that may be adequate for modeling slow inflation deployment sine the inertia of the inflation gas can be neglected. The ALE method was found to be very computationally intensive since it involves the solving of three conservative equations of fluid as well as dealing with complex fluid structure interactions.

Dynamic force response of spherical hydrostatic journal bearing for cryogenic applications

NASA Technical Reports Server (NTRS)

Sanandres, Luis

1994-01-01

Hydrostatic Journal Bearings (HJB's) are reliable and resilient fluid film rotor support elements ideal to replace roller bearings in cryogenic turbomachinery. HJB' will be used for primary space-power applications due to their long lifetime, low friction and wear, large load capacity, large direct stiffness, and damping force coefficients. An analysis for the performance characteristics of turbulent flow, orifice compensated, spherical hydrostatic journal bearings (HJB's) is presented. Spherical bearings allow tolerance for shaft misalignment without force performance degradation and have also the ability to support axial loads. The spherical HJB combines these advantages to provide a bearing design which could be used efficiently on high performance turbomachinery. The motion of a barotropic liquid on the thin film bearing lands is described by bulk-flow mass and momentum equations. These equations are solved numerically using an efficient CFD method. Numerical predictions of load capacity and force coefficients for a 6 recess, spherical HJB in a LO2 environment are presented. Fluid film axial forces and force coefficients of a magnitude about 20% of the radial load capacity are predicted for the case analyzed. Fluid inertia effects, advective and centrifugal, are found to affect greatly the static and dynamic force performance of the bearing studied.

A patient-specific aortic valve model based on moving resistive immersed implicit surfaces.

PubMed

Fedele, Marco; Faggiano, Elena; Dedè, Luca; Quarteroni, Alfio

2017-10-01

In this paper, we propose a full computational framework to simulate the hemodynamics in the aorta including the valve. Closed and open valve surfaces, as well as the lumen aorta, are reconstructed directly from medical images using new ad hoc algorithms, allowing a patient-specific simulation. The fluid dynamics problem that accounts from the movement of the valve is solved by a new 3D-0D fluid-structure interaction model in which the valve surface is implicitly represented through level set functions, yielding, in the Navier-Stokes equations, a resistive penalization term enforcing the blood to adhere to the valve leaflets. The dynamics of the valve between its closed and open position is modeled using a reduced geometric 0D model. At the discrete level, a finite element formulation is used and the SUPG stabilization is extended to include the resistive term in the Navier-Stokes equations. Then, after time discretization, the 3D fluid and 0D valve models are coupled through a staggered approach. This computational framework, applied to a patient-specific geometry and data, allows to simulate the movement of the valve, the sharp pressure jump occurring across the leaflets, and the blood flow pattern inside the aorta.

Viscous dissipation in a flow with power law, temperature-dependent rheology: Application to channeled lava flows

NASA Astrophysics Data System (ADS)

Filippucci, Marilena; Tallarico, Andrea; Dragoni, Michele

2017-05-01

The cooling and the dynamics of a lava flowing down an inclined channel under the effect of the gravity force is studied through the finite volume method, taking into account the effect of viscous dissipation in the heat equation. The considered rheology is shear thinning and temperature dependent. The numerical solution is tested in order to verify the independence from the mesh. The dynamic and heat problems are addressed obtaining both the stationary and the transient solution. Results indicate that, considering viscous dissipation in the heat equation, a fluid with temperature-dependent nonlinear viscosity is faster and hotter with respect to the case in which viscous dissipation is neglected. The most important effect of viscous dissipation is on the solid boundaries where the fluid warms up, and the use of a variable Reynolds number allowed us to conclude that areas in which the flow is in the laminar regime and areas in which the flow is in the turbulent regime can coexist inside the fluid. This behavior seems independent of the channel shape and can explain the observed warming back after the initial cooling in the lava flow lobes emplacement on Kilauea Volcano.

Computational Fluid Dynamics.

DTIC Science & Technology

1986-06-01

this area concentrated first on the compu- tation of foldpoints by means of one of the many possible forms of augmented equations. One approach in this...this area is, of course, the deter- mination of the principal characteristic features of the solution manifold of the given parametrized equation. This...into Spanish and appeared in Metodos Numericos Para Calculo y Diseno en Ingeniera 1 (1985), 67-80. [5] J. P. Fink and W. C. Rheinboldt, "Folds on the

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Electroosmotic flow and Joule heating in preparative continuous annular electrochromatography.

PubMed

Laskowski, René; Bart, Hans-Jörg

2015-09-01

An openFOAM "computational fluid dynamic" simulation model was developed for the description of local interaction of hydrodynamics and Joule heating in annular electrochromatography. A local decline of electrical conductivity of the background eluent is caused by an electrokinetic migration of ions resulting in higher Joule heat generation. The model equations consider the Navier-Stokes equation for incompressible fluids, the energy equation for stationary temperature fields, and the mass transfer equation for the electrokinetic flow. The simulations were embedded in commercial ANSYS Fluent software and in open-source environment openFOAM. The annular gap (1 mm width) contained an inorganic C8 reverse-phase monolith as stationary phase prepared by an in situ sol-gel process. The process temperature generated by Joule heating was determined by thermal camera system. The local hydrodynamics in the prototype was detected by a gravimetric contact-free measurement method and experimental and simulated values matched quite well. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Equation of state of hard and Weeks-Chandler-Anderson hyperspheres in four and five dimensions

NASA Astrophysics Data System (ADS)

Bishop, Marvin; Masters, Andrew; Clarke, Julian H. R.

1999-06-01

The fifth and sixth virial coefficient for hard hyperspheres in four and five dimensions has been computed using Monte Carlo techniques. It is found that B5/B24 has values 0.035 63±0.000 07 and 0.012 87±0.000 06 and that B6/B25 has values 0.007 691±0.000 028 and 0.000 942±0.000 027 in four and five dimensions, respectively. These values are used to investigate the equation of state of hard and Weeks-Chandler-Anderson (WCA) hyperspheres in four and five dimensions. Molecular dynamics simulations are performed for WCA hyperspheres. When compared to the molecular dynamics calculations, it is found that both the hard hypersphere and WCA equations of state are well described by a variety of theoretical approaches as long as the density is in the low-to-moderate regime. At the highest fluid densities studied, the Luban-Michels procedure provides the best accuracy for hard hyperspheres. The WCA prescription for the scaling of the reference system to a hard hypersphere one is a very good approximation in the fluid region.

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

NASA Astrophysics Data System (ADS)

Foti, Daniel; Duraisamy, Karthik

2017-11-01

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riggs, J.B.

An experimental test model, which is dynamically similar to an actual UCC (Underground Coal Conversion) system, has been used to determine fluid flow patterns and local heat transfer that occur in the UCC burn cavity. This study was designed to provide insight into the little understood mechanisms (i.e., heat transfer and oxygen transport to the cavity walls) which control maximum cavity width, and therefore resource recovery during UCC. The dynamically similar flow model has been designed by equating the Grashof and Reynolds number of the UCC system and the flow model, which employs water as its fluid. Equating the Grashofmore » number results in a scale factor of 0.13 while equating the Reynolds number yields a volumetric flow rate of water for the model of 30 gallons per minute. Qualitative studies were conducted with the flow model for both a void cavity and a cavity partially filled with simulated rubble. These studies provided insight into the combined effects of forced and free convection in a UCC cavity. In addition, dimensionless correlations were developed for the heat transfer to side walls for the case of a void cavity and these results can be used to predict oxygen transport to the side wall in a UCC cavity.« less

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

NASA Technical Reports Server (NTRS)

Kassab, A. J.; Kapat, J. S.

2001-01-01

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

A similarity solution of time dependent MHD liquid film flow over stretching sheet with variable physical properties

NASA Astrophysics Data System (ADS)

Idrees, M.; Rehman, Sajid; Shah, Rehan Ali; Ullah, M.; Abbas, Tariq

2018-03-01

An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM) while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″ (0) , Nusselt number (heat flux) -θ‧ (0) and free surface temperature θ (1) are presented graphically and in tabular form.

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

Sloshing dynamics on rotating helium dewar tank

NASA Technical Reports Server (NTRS)

Hung, R. J.

1993-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

Fundamentals of Geophysical Fluid Dynamics

NASA Astrophysics Data System (ADS)

McWilliams, James C.

2006-07-01

Earth's atmosphere and oceans exhibit complex patterns of fluid motion over a vast range of space and time scales. These patterns combine to establish the climate in response to solar radiation that is inhomogeneously absorbed by the materials comprising air, water, and land. Spontaneous, energetic variability arises from instabilities in the planetary-scale circulations, appearing in many different forms such as waves, jets, vortices, boundary layers, and turbulence. Geophysical fluid dynamics (GFD) is the science of all these types of fluid motion. This textbook is a concise and accessible introduction to GFD for intermediate to advanced students of the physics, chemistry, and/or biology of Earth's fluid environment. The book was developed from the author's many years of teaching a first-year graduate course at the University of California, Los Angeles. Readers are expected to be familiar with physics and mathematics at the level of general dynamics (mechanics) and partial differential equations. Covers the essential GFD required for atmospheric science and oceanography courses Mathematically rigorous, concise coverage of basic theory and applications to both oceans and atmospheres Author is a world expert; this book is based on the course he has taught for many years Exercises are included, with solutions available to instructors from solutions@cambridge.org

Influence of Non-Maxwellian Particles on Dust Acoustic Waves in a Dusty Magnetized Plasma

NASA Astrophysics Data System (ADS)

M. Nouri, Kadijani; Zareamoghaddam, H.

2013-11-01

In this paper an investigation into dust acoustic solitary waves (DASWs) in the presence of superthermal electrons and ions in a magnetized plasma with cold dust grains and trapped electrons is discussed. The dynamic of both electrons and ions is simulated by the generalized Lorentzian (κ) distribution function (DF). The dust grains are cold and their dynamics are studied by hydrodynamic equations. The basic set of fluid equations is reduced to modified Korteweg-de Vries (mKdV) equation using Reductive Perturbation Theory (RPT). Two types of solitary waves, fast and slow dust acoustic soliton (DAS) exist in this plasma. Calculations reveal that compressive solitary structures are possibly propagated in the plasma where dust grains are negatively (or positively) charged. The properties of DASs are also investigated numerically.

The attenuation of sound by turbulence in internal flows.

PubMed

Weng, Chenyang; Boij, Susann; Hanifi, Ardeshir

2013-06-01

The attenuation of sound waves due to interaction with low Mach number turbulent boundary layers in internal flows (channel or pipe flow) is examined. Dynamic equations for the turbulent Reynolds stress on the sound wave are derived, and the analytical solution to the equation provides a frequency dependent eddy viscosity model. This model is used to predict the attenuation of sound propagating in fully developed turbulent pipe flow. The predictions are shown to compare well with the experimental data. The proposed dynamic equation shows that the turbulence behaves like a viscoelastic fluid in the interaction process, and that the ratio of turbulent relaxation time near the wall and the sound wave period is the parameter that controls the characteristics of the attenuation induced by the turbulent flow.

Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

PubMed

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Swimming Behavior and Flow Geometry: A Fluid Mechanical Study of the Feeding Currents in Calanoid Copepods

NASA Astrophysics Data System (ADS)

Jiang, Houshuo; Meneveau, Charles; Osborn, Thomas R.

2003-11-01

Copepods are small crustaceans living in oceans and fresh waters and play an important role in the marine and freshwater food webs. As they are the biggest biomass in the oceans some call them "the insects of the sea". Previous laboratory observations have shown that the fluid mechanical phenomena occurring at copepod body scale are crucial for the survival of copepods. One of the interesting phenomena is that many calanoid copepods display various behaviors to create the feeding currents for the purpose of capturing food particles. We have developed a fluid mechanical model to study the feeding currents. The model is a self-propelled body model in that the Navier-Stokes equations are properly coupled with the dynamic equations for the copepod's body. The model has been solved both analytically using the Stokes approximation with a spherical body shape and numerically using CFD with a realistic body shape.

Black hole event horizons — Teleology and predictivity

NASA Astrophysics Data System (ADS)

Bhattacharya, Swastik; Shankaranarayanan, S.

2017-11-01

General Relativity predicts the existence of black holes. Access to the complete spacetime manifold is required to describe the black hole. This feature necessitates that black hole dynamics is specified by future or teleological boundary condition. Here, we demonstrate that the statistical mechanical description of black holes, the raison d’être behind the existence of black hole thermodynamics, requires teleological boundary condition. Within the fluid-gravity paradigm — Einstein’s equations when projected on spacetime horizons resemble Navier-Stokes equation of a fluid — we show that the specific heat and the coefficient of bulk viscosity of the horizon fluid are negative only if the teleological boundary condition is taken into account. We argue that in a quantum theory of gravity, the future boundary condition plays a crucial role. We briefly discuss the possible implications of this at late stages of black hole evaporation.

Helicity and singular structures in fluid dynamics

PubMed Central

Moffatt, H. Keith

2014-01-01

Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described. PMID:24520175

An efficient passive planar micromixer with ellipse-like micropillars for continuous mixing of human blood.

PubMed

Tran-Minh, Nhut; Dong, Tao; Karlsen, Frank

2014-10-01

In this paper, a passive planar micromixer with ellipse-like micropillars is proposed to operate in the laminar flow regime for high mixing efficiency. With a splitting and recombination (SAR) concept, the diffusion distance of the fluids in a micromixer with ellipse-like micropillars was decreased. Thus, space usage for micromixer of an automatic sample collection system is also minimized. Numerical simulation was conducted to evaluate the performance of proposed micromixer by solving the governing Navier-Stokes equation and convection-diffusion equation. With software (COMSOL 4.3) for computational fluid dynamics (CFD) we simulated the mixing of fluids in a micromixer with ellipse-like micropillars and basic T-type mixer in a laminar flow regime. The efficiency of the proposed micromixer is shown in numerical results and is verified by measurement results. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

A field theory approach to the evolution of canonical helicity and energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

You, S.

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems.more » For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.« less

DYNAMIC MODELING STRATEGY FOR FLOW REGIME TRANSITION IN GAS-LIQUID TWO-PHASE FLOWS

DOE Office of Scientific and Technical Information (OSTI.GOV)

X. Wang; X. Sun; H. Zhao

In modeling gas-liquid two-phase flows, the concept of flow regime has been used to characterize the global interfacial structure of the flows. Nearly all constitutive relations that provide closures to the interfacial transfers in two-phase flow models, such as the two-fluid model, are often flow regime dependent. Currently, the determination of the flow regimes is primarily based on flow regime maps or transition criteria, which are developed for steady-state, fully-developed flows and widely applied in nuclear reactor system safety analysis codes, such as RELAP5. As two-phase flows are observed to be dynamic in nature (fully-developed two-phase flows generally do notmore » exist in real applications), it is of importance to model the flow regime transition dynamically for more accurate predictions of two-phase flows. The present work aims to develop a dynamic modeling strategy for determining flow regimes in gas-liquid two-phase flows through the introduction of interfacial area transport equations (IATEs) within the framework of a two-fluid model. The IATE is a transport equation that models the interfacial area concentration by considering the creation and destruction of the interfacial area, such as the fluid particle (bubble or liquid droplet) disintegration, boiling and evaporation; and fluid particle coalescence and condensation, respectively. For the flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and shape (which are correlated), namely small bubbles and large bubbles. A preliminary approach to dynamically identifying the flow regimes is provided, in which discriminators are based on the predicted information, such as the void fraction and interfacial area concentration of small bubble and large bubble groups. This method is expected to be applied to computer codes to improve their predictive capabilities of gas-liquid two-phase flows, in particular for the applications in which flow regime transition occurs.« less

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

NASA Technical Reports Server (NTRS)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Jeans self gravitational instability of strongly coupled quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Prerana, E-mail: preranaiitd@rediffmail.com; Chhajlani, R. K.

2014-07-15

The Jeans self-gravitational instability is studied for quantum plasma composed of weakly coupled degenerate electron fluid and non-degenerate strongly coupled ion fluid. The formulation for such system is done on the basis of two fluid theory. The dynamics of weakly coupled degenerate electron fluid is governed by inertialess momentum equation. The quantum forces associated with the quantum diffraction effects and the quantum statistical effects act on the degenerate electron fluid. The strong correlation effects of ion are embedded in generalized viscoelastic momentum equation including the viscoelasticity and shear viscosities of ion fluid. The general dispersion relation is obtained using themore » normal mode analysis technique for the two regimes of propagation, i.e., hydrodynamic and kinetic regimes. The Jeans condition of self-gravitational instability is also obtained for both regimes, in the hydrodynamic regime it is observed to be affected by the ion plasma oscillations and quantum parameter while in the kinetic regime in addition to ion plasma oscillations and quantum parameter, it is also affected by the ion velocity which is modified by the viscosity generated compressional effects. The Jeans critical wave number and corresponding critical mass are also obtained for strongly coupled quantum plasma for both regimes.« less

Investigation on Stability in Roll of Square Section Missile at High Angle of Attack

NASA Astrophysics Data System (ADS)

Tao, Yang; Fan, Zhaolin; Wu, Jifei; Wu, Wenhua

An experimental investigation of the stability in roll of a square section missile at high incidence was conducted in FL-23 wind tunnel. Dynamic motions were obtained on a square section missile that is free to rotate about its longitudinal axis. Different dynamic rolling motions were observed depending on the incidence of the model sting. These dynamic regimes include damped oscillations, quasi-limit-cycle wing-rock motion, and constant rolling. A coupling numerical method was established by solving the fluid dynamics equations and the rigid-body dynamics equations synchronously in order to predict the onset and the development of uncommented motions and then explore the unsteady movement characteristics of the aircraft. The study indicates that the aircraft loss stability at high incidence is caused by the asymmetric vertex on the level fin tip liftoff and attach alternately. The computation results are in line with the experiment results.

COMPRESSIBLE FLOW, ENTRAINMENT, AND MEGAPLUME

EPA Science Inventory

It is generally believed that low Mach number, i.e., low-velocity, flow may be assumed to be incompressible flow. Under steady-state conditions, an exact equation of continuity may then be used to show that such flow is non-divergent. However, a rigorous, compressible fluid-dynam...

A mixed method Poisson solver for three-dimensional self-gravitating astrophysical fluid dynamical systems

NASA Technical Reports Server (NTRS)

Duncan, Comer; Jones, Jim

1993-01-01

A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.

Infrared imaging - A validation technique for computational fluid dynamics codes used in STOVL applications

NASA Technical Reports Server (NTRS)

Hardman, R. R.; Mahan, J. R.; Smith, M. H.; Gelhausen, P. A.; Van Dalsem, W. R.

1991-01-01

The need for a validation technique for computational fluid dynamics (CFD) codes in STOVL applications has led to research efforts to apply infrared thermal imaging techniques to visualize gaseous flow fields. Specifically, a heated, free-jet test facility was constructed. The gaseous flow field of the jet exhaust was characterized using an infrared imaging technique in the 2 to 5.6 micron wavelength band as well as conventional pitot tube and thermocouple methods. These infrared images are compared to computer-generated images using the equations of radiative exchange based on the temperature distribution in the jet exhaust measured with the thermocouple traverses. Temperature and velocity measurement techniques, infrared imaging, and the computer model of the infrared imaging technique are presented and discussed. From the study, it is concluded that infrared imaging techniques coupled with the radiative exchange equations applied to CFD models are a valid method to qualitatively verify CFD codes used in STOVL applications.

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Cryogenic Propellant Tanks

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff

2016-01-01

Propellant slosh is a potential source of disturbance critical to the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. A Volume-Of-Fluid (VOF) based Computational Fluid Dynamics (CFD) program developed at MSFC was applied to extract slosh damping in the baffled tank from the first principle. First the experimental data using water with sub-scale smooth wall tank were used as the baseline validation. It is demonstrated that CFD can indeed accurately predict low damping values from the smooth wall at different fill levels. The damping due to a ring baffles at different depths from the free surface was then simulated, and fairly good agreement with experimental measurement was observed. Comparison with an empirical correlation of Miles equation is also made.

A simple scaling law for the equation of state and the radial distribution functions calculated by density-functional theory molecular dynamics

NASA Astrophysics Data System (ADS)

Danel, J.-F.; Kazandjian, L.

2018-06-01

It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.

Performance of a parallel code for the Euler equations on hypercube computers

NASA Technical Reports Server (NTRS)

Barszcz, Eric; Chan, Tony F.; Jesperson, Dennis C.; Tuminaro, Raymond S.

1990-01-01

The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.

Electrokinetically induced alterations in dynamic response of viscoelastic fluids in narrow confinements.

PubMed

Bandopadhyay, Aditya; Chakraborty, Suman

2012-05-01

We investigate a dynamical interplay between interfacial electrokinetics and a combined dissipative and elastic behavior of flow through narrow confinements, in analogy with spatiotemporal hydrodynamics of porous media. In particular, we investigate the effects of streaming potential on the pertinent dynamic responses, by choosing a Maxwell fluid model for representing the consequent electro-hydrodynamic characteristics. We transform the pertinent governing equation to the frequency domain, so that a dynamic generalization of Darcy's law in the presence of streaming potential effects can be effectively realized. We show that the frequencies corresponding to local maxima in the dynamic permeability also correspond to local maxima in the induced streaming potential. We also bring out the effects of Stern layer conductivity on the dynamic permeability. Our analytical estimates do reveal that serious overestimations in the commonly portrayed notion of massive amplifications of dynamic permeability at resonating frequencies may be possible, if interactions between spontaneous electrochemical interfacial phenomena and pulsating pressure-gradient-driven viscoelastic transport are trivially ignored.

Dynamical system analysis for DBI dark energy interacting with dark matter

NASA Astrophysics Data System (ADS)

Mahata, Nilanjana; Chakraborty, Subenoy

2015-01-01

A dynamical system analysis related to Dirac-Born-Infeld (DBI) cosmological model has been investigated in this present work. For spatially flat FRW spacetime, the Einstein field equation for DBI scenario has been used to study the dynamics of DBI dark energy interacting with dark matter. The DBI dark energy model is considered as a scalar field with a nonstandard kinetic energy term. An interaction between the DBI dark energy and dark matter is considered through a phenomenological interaction between DBI scalar field and the dark matter fluid. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables. The potential of the DBI scalar field is assumed to be exponential. Finally, critical points are determined, their nature have been analyzed and corresponding cosmological scenario has been discussed.

Helicity in dynamic atmospheric processes

NASA Astrophysics Data System (ADS)

Kurgansky, M. V.

2017-03-01

An overview on the helicity of the velocity field and the role played by this concept in modern research in the field of geophysical fluid dynamics and dynamic meteorology is given. Different (both previously known in the literature and first presented) formulations of the equation of helicity balance in atmospheric motions (including those with allowance for effects of air compressibility and Earth's rotation) are brought together. Equations and relationships are given which are valid in different approximations accepted in dynamic meteorology: Boussinesq approximation, quasi-static approximation, and quasi-geostrophic approximation. Emphasis is placed on the analysis of helicity budget in large-scale quasi-geostrophic systems of motion; a formula for the helicity flux across the upper boundary of the nonlinear Ekman boundary layer is given, and this flux is shown to be exactly compensated for by the helicity destruction inside the Ekman boundary layer.

Scaling effects in spiral capsule robots.

PubMed

Liang, Liang; Hu, Rong; Chen, Bai; Tang, Yong; Xu, Yan

2017-04-01

Spiral capsule robots can be applied to human gastrointestinal tracts and blood vessels. Because of significant variations in the sizes of the inner diameters of the intestines as well as blood vessels, this research has been unable to meet the requirements for medical applications. By applying the fluid dynamic equations, using the computational fluid dynamics method, to a robot axial length ranging from 10 -5 to 10 -2  m, the operational performance indicators (axial driving force, load torque, and maximum fluid pressure on the pipe wall) of the spiral capsule robot and the fluid turbulent intensity around the robot spiral surfaces was numerically calculated in a straight rigid pipe filled with fluid. The reasonableness and validity of the calculation method adopted in this study were verified by the consistency of the calculated values by the computational fluid dynamics method and the experimental values from a relevant literature. The results show that the greater the fluid turbulent intensity, the greater the impact of the fluid turbulence on the driving performance of the spiral capsule robot and the higher the energy consumption of the robot. For the same level of size of the robot, the axial driving force, the load torque, and the maximum fluid pressure on the pipe wall of the outer spiral robot were larger than those of the inner spiral robot. For different requirements of the operating environment, we can choose a certain kind of spiral capsule robot. This study provides a theoretical foundation for spiral capsule robots.

Relaxation and self-organization in two-dimensional plasma and neutral fluid flow systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, Amita

Extensive numerical studies in the framework of a simplified two-dimensional model for neutral and plasma fluid for a variety of initial configurations and for both decaying and driven cases are carried out to illustrate relaxation toward a self-organized state. The dynamical model equation constitutes a simple choice for this purpose, e.g., the vorticity equation of the Navier-Stokes dynamics for the incompressible neutral fluids and the Hasegawa-Mima equation for plasma fluid flow system. Scatter plots are employed to observe a development of functional relationship, if any, amidst the generalized vorticity and its Laplacian. It is seen that they do not satisfymore » a linear relationship as the well known variational approach of enstrophy minimization subject to constancy of the energy integral for the two-dimensional (2D) system suggests. The observed nonlinear functional relationship is understood by separating the contribution to the scatter plot from spatial regions with intense vorticity patches and those of the background flow region where the background vorticity is weak or absent altogether. It is shown that such a separation has close connection with the known exact analytical solutions of the system. The analytical solutions are typically obtained by assuming a finite source of vorticity for the inner core of the localized structure, which is then matched with the solution in the outer region where vorticity is chosen to be zero. The work also demonstrates that the seemingly ad hoc choice of the linear vorticity source function for the inner region is in fact consistent with the self-organization paradigm of the 2D systems.« less

The onset of fluid-dynamical behavior in relativistic kinetic theory

NASA Astrophysics Data System (ADS)

Noronha, Jorge; Denicol, Gabriel S.

2017-11-01

In this proceedings we discuss recent findings regarding the large order behavior of the Chapman-Enskog expansion in relativistic kinetic theory. It is shown that this series in powers of the Knudsen number has zero radius of convergence in the case of a Bjorken expanding fluid described by the Boltzmann equation in the relaxation time approximation. This divergence stems from the presence of non-hydrodynamic modes, which give non-perturbative contributions to the Knudsen series.

Canonical structures for dispersive waves in shallow water

NASA Astrophysics Data System (ADS)

Neyzi, Fahrünisa; Nutku, Yavuz

1987-07-01

The canonical Hamiltonian structure of the equations of fluid dynamics obtained in the Boussinesq approximation are considered. New variational formulations of these equations are proposed and it is found that, as in the case of the KdV equation and the equations governing long waves in shallow water, they are degenerate Lagrangian systems. Therefore, in order to cast these equations into canonical form it is again necessary to use Dirac's theory of constraints. It is found that there are primary and secondary constraints which are second class and it is possible to construct the Hamiltonian in terms of canonical variables. Among the examples of Boussinesq equations that are discussed are the equations of Whitham-Broer-Kaup which Kupershmidt has recently expressed in symmetric form and shown to admit tri-Hamiltonian structure.

A Dynamic Analysis of Hydrodynamic Wave Journal Bearings

NASA Technical Reports Server (NTRS)

Ene, Nicoleta M.; Dimofte, Florin; Keith, Theo G.

2008-01-01

The purpose of this paper is to study the dynamic behavior of a three-wave journal bearing using a transient approach. The transient analysis permits the determination of the rotor behavior after the fractional frequency whirl appears. The journal trajectory is determined by solving a set of nonlinear equations of motion using the Runge-Katta method. The fluid film forces are computed by integrating the transient Reynolds equation at each time step location of the shaft with respect to the bearing. Because of the large values of the rotational speeds, turbulent effects were included in the computations. The influence of the temperature on the viscosity was also considered. Numerical results were compared to experimenta1 results obtained at the NASA Glenn Research Center. Comparisons of the theoretical results with experimental data were found to be in good agreement. The numerical and experimental results showed that the fluid film of a three-wave journal bearing having a diameter of 30 mm, a length of 27 mm, and a wave amplitude ratio greater than 0.15 is stable even at rotational speeds of 60,000 RPM. For lower wave amplitude ratios, the threshold speed at which the fluid film becomes unstable depends on the wave amplitude and on the supply pocket pressure. Even if the fluid film is unstable, the wave bearing maintains the whirl orbit inside the bearing clearance.

Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models

NASA Astrophysics Data System (ADS)

Wang, L.; Jiang, T. L.; Dai, H. L.; Ni, Q.

2018-05-01

The present study develops a new three-dimensional nonlinear model for investigating vortex-induced vibrations (VIV) of flexible pipes conveying internal fluid flow. The unsteady hydrodynamic forces associated with the wake dynamics are modeled by two distributed van der Pol wake oscillators. In particular, the nonlinear partial differential equations of motion of the pipe and the wake are derived, taking into account the coupling between the structure and the fluid. The nonlinear equations of motion for the coupled system are then discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. It is shown that the natural frequencies for in-plane and out-of-plane motions of the pipe may be different at high internal flow velocities beyond the threshold of buckling instability. The orientation angle of the postbuckling configuration is time-varying due to the disturbance of hydrodynamic forces, thus yielding sometimes unexpected results. For a buckled pipe with relatively low cross-flow velocity, interestingly, examining the nonlinear dynamics of the pipe indicates that the combined effects of the cross-flow-induced resonance of the in-plane first mode and the internal-flow-induced buckling on the IL and CF oscillation amplitudes may be significant. For higher cross-flow velocities, however, the effect of internal fluid flow on the nonlinear VIV responses of the pipe is not pronounced.

Evolution of an electron plasma vortex in a strain flow

NASA Astrophysics Data System (ADS)

Danielson, J. R.

2016-10-01

Coherent vortex structures are ubiquitous in fluids and plasmas and are examples of self-organized structures in nonlinear dynamical systems. The fate of these structures in strain and shear flows is an important issue in many physical systems, including geophysical fluids and shear suppression of turbulence in plasmas. In two-dimensions, an inviscid, incompressible, ideal fluid can be modeled with the Euler equations, which is perhaps the simplest system that supports vortices. The Drift-Poisson equations for pure electron plasmas in a strong, uniform magnetic field are isomorphic to the Euler equations, and so electron plasmas are an excellent test bed for the study of 2D vortex dynamics. This talk will describe results from a new experiment using pure electron plasmas in a specially designed Penning-Malmberg (PM) trap to study the evolution of an initially axisymmetric 2D vortex subject to externally imposed strains. Complementary vortex-in-cell simulations are conducted to validate the 2D nature of the experimental results and to extend the parameter range of these studies. Data for vortex destruction using both instantaneously applied and time dependent strains with flat (constant vorticity) and extended radial profiles will be presented. The role of vortex self-organization will be discussed. A simple 2D model works well for flat vorticity profiles. However, extended profiles exhibit more complicated behavior, such as filamentation and stripping; and these effects and their consequences will be discussed. Work done in collaboration with N. C. Hurst, D. H. E. Dubin, and C. M. Surko.

Modeling fluid transport in 2d paper networks

NASA Astrophysics Data System (ADS)

Tirapu Azpiroz, Jaione; Fereira Silva, Ademir; Esteves Ferreira, Matheus; Lopez Candela, William Fernando; Bryant, Peter William; Ohta, Ricardo Luis; Engel, Michael; Steiner, Mathias Bernhard

2018-02-01

Paper-based microfluidic devices offer great potential as a low-cost platform to perform chemical and biochemical tests. Commercially available formats such as dipsticks and lateral-flow test devices are widely popular as they are easy to handle and produce fast and unambiguous results. While these simple devices lack precise control over the flow to enable integration of complex functionality for multi-step processes or the ability to multiplex several tests, intense research in this area is rapidly expanding the possibilities. Modeling and simulation is increasingly more instrumental in gaining insight into the underlying physics driving the processes inside the channels, however simulation of flow in paper-based microfluidic devices has barely been explored to aid in the optimum design and prototyping of these devices for precise control of the flow. In this paper, we implement a multiphase fluid flow model through porous media for the simulation of paper imbibition of an incompressible, Newtonian fluid such as when water, urine or serum is employed. The formulation incorporates mass and momentum conservation equations under Stokes flow conditions and results in two coupled Darcy's law equations for the pressures and saturations of the wetting and non-wetting phases, further simplified to the Richard's equation for the saturation of the wetting fluid, which is then solved using a Finite Element solver. The model tracks the wetting fluid front as it displaces the non-wetting fluid by computing the time-dependent saturation of the wetting fluid. We apply this to the study of liquid transport in two-dimensional paper networks and validate against experimental data concerning the wetting dynamics of paper layouts of varying geometries.

Existence of Corotating and Counter-Rotating Vortex Pairs for Active Scalar Equations

NASA Astrophysics Data System (ADS)

Hmidi, Taoufik; Mateu, Joan

2017-03-01

In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the {(SQG)_{α}} equations with {α in (0,1)}. From the numerical experiments implemented for Euler equations in Deem and Zabusky (Phys Rev Lett 40(13):859-862, 1978), Pierrehumbert (J Fluid Mech 99:129-144, 1980), Saffman and Szeto (Phys Fluids 23(12):2339-2342, 1980) it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle (Keady in J Aust Math Soc Ser B 26:487-502, 1985; Turkington in Nonlinear Anal Theory Methods Appl 9(4):351-369, 1985); however, they do not give enough information about the pairs, such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments and extend these results for the {(SQG)_{α}} equation when {α in (0,1)}. The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem.

Coiling, Entrainment, and Hydrodynamic Coupling of Decelerated Fluid Jets

NASA Astrophysics Data System (ADS)

Dombrowski, Christopher; Lewellyn, Braddon; Pesci, Adriana I.; Restrepo, Juan M.; Kessler, John O.; Goldstein, Raymond E.

2005-10-01

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system—a saline jet descending through a salinity gradient—which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines

NASA Technical Reports Server (NTRS)

Trudell, J. J.; Mehmed, O.; Stefko, G. L.; Bakhle, M. A.; Reddy, T. S. R.; Montgomery, M.; Verdon, J.

2006-01-01

The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.

A fictitious domain finite element method for simulations of fluid-structure interactions: The Navier-Stokes equations coupled with a moving solid

NASA Astrophysics Data System (ADS)

Court, Sébastien; Fournié, Michel

2015-05-01

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal approximation of the normal stress tensor at the interface. The dynamics of the solid is governed by the Newton's laws and the interface between the fluid and the structure is materialized by a level-set which cuts the elements of the mesh. An algorithm is proposed in order to treat the time evolution of the geometry and numerical results are presented on a classical benchmark of the motion of a disk falling in a channel.

Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Kapral, Raymond

2018-04-01

The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions at the interface between the fluid and the particle. These equations are consistent with microreversibility and the Onsager-Casimir reciprocal relations between affinities and currents and provide a thermodynamically consistent basis for the investigation of the dynamics of active particles propelled by diffusiophoretic mechanisms.

Computational Fluid Dynamics Modeling of Nickel Hydrogen Batteries

NASA Technical Reports Server (NTRS)

Cullion, R.; Gu, W. B.; Wang, C. Y.; Timmerman, P.

2000-01-01

An electrochemical Ni-H2 battery model has been expanded to include thermal effects. A thermal energy conservation equation was derived from first principles. An electrochemical and thermal coupled model was created by the addition of this equation to an existing multiphase, electrochemical model. Charging at various rates was investigated and the results validated against experimental data. Reaction currents, pressure changes, temperature profiles, and concentration variations within the cell are predicted numerically and compared with available data and theory.

Nonlinear Oscillators in Space Physics

NASA Technical Reports Server (NTRS)

Lester,Daniel; Thronson, Harley

2011-01-01

We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.

Thermally driven mass flows in the convection zone of the sun

NASA Technical Reports Server (NTRS)

Dijkhuis, G. C.

1973-01-01

A formulation of the fluid dynamics of convective regions is developed which leads to an analytical description of the solar rotation, the Evershed flow, and the supergranulation. The starting point of the present formulation is the mixing length picture of convective equilibrium, but the earlier point mass model for convective molecules is replaced here by a model with both inertia and intrinsic moment of inertia. This extension introduces three rotational degrees of freedom into the dynamics of individual convective molecules, which enter into the dynamical equations for a mixing length fluid in the form of a separate vector field which we term the spin field. It is shown that for convective molecules having a spherically symmetric mass distribution, the spin field is proportional to the local vorticity.

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

NASA Astrophysics Data System (ADS)

Farid, T.; Shukla, P. K.; Sakanaka, P. H.; Mirza, A. M.

2000-12-01

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.

Spectral collocation methods

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T.

1987-01-01

This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions. Some stability and convergence results are presented for simple elliptic, parabolic, and hyperbolic equations. Applications of these methods to fluid dynamics problems are discussed in Section 2.

Lattice Boltzmann simulations of multiple-droplet interaction dynamics.

PubMed

Zhou, Wenchao; Loney, Drew; Fedorov, Andrei G; Degertekin, F Levent; Rosen, David W

2014-03-01

A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface phenomena.

A weak-coupling immersed boundary method for fluid-structure interaction with low density ratio of solid to fluid

NASA Astrophysics Data System (ADS)

Kim, Woojin; Lee, Injae; Choi, Haecheon

2018-04-01

We present a weak-coupling approach for fluid-structure interaction with low density ratio (ρ) of solid to fluid. For accurate and stable solutions, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid-structure interface at each time step, respectively. The incompressible Navier-Stokes equations, together with these provisional velocity and position at the fluid-structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid-structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate, respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 (ρmin = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling.

Harvesting liquid from unsaturated vapor - nanoflows induced by capillary condensation

NASA Astrophysics Data System (ADS)

Vincent, Olivier; Marguet, Bastien; Stroock, Abraham

2016-11-01

A vapor, even subsaturated, can spontaneously form liquid in nanoscale spaces. This process, known as capillary condensation, plays a fundamental role in various contexts, such as the formation of clouds or the dynamics of hydrocarbons in the geological subsurface. However, large uncertainties remain on the thermodynamics and fluid mechanics of the phenomenon, due to experimental challenges as well as outstanding questions about the validity of macroscale physics at the nanometer scale. We studied experimentally the spatio-temporal dynamics of water condensation in a model nanoporous medium (pore radius 2 nm), taking advantage of the color change of the material upon hydration. We found that at low relative humidities (< 60 % RH), capillary condensation progressed in a diffusive fashion, while it occurred through a well-defined capillary-viscous imbibition front at > 60 % RH, driven by a balance between the pore capillary pressure and the condensation stress given by Kelvin equation. Further analyzing the imbibition dynamics as a function of saturation allowed us to extract detailed information about the physics of nano-confined fluids. Our results suggest excellent extension of macroscale fluid dynamics and thermodynamics even in pores 10 molecules in diameter.

Fluid-acoustic interactions and their impact on pathological voiced speech

NASA Astrophysics Data System (ADS)

Erath, Byron D.; Zanartu, Matias; Peterson, Sean D.; Plesniak, Michael W.

2011-11-01

Voiced speech is produced by vibration of the vocal fold structures. Vocal fold dynamics arise from aerodynamic pressure loadings, tissue properties, and acoustic modulation of the driving pressures. Recent speech science advancements have produced a physiologically-realistic fluid flow solver (BLEAP) capable of prescribing asymmetric intraglottal flow attachment that can be easily assimilated into reduced order models of speech. The BLEAP flow solver is extended to incorporate acoustic loading and sound propagation in the vocal tract by implementing a wave reflection analog approach for sound propagation based on the governing BLEAP equations. This enhanced physiological description of the physics of voiced speech is implemented into a two-mass model of speech. The impact of fluid-acoustic interactions on vocal fold dynamics is elucidated for both normal and pathological speech through linear and nonlinear analysis techniques. Supported by NSF Grant CBET-1036280.

Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background

DOE PAGES

Floerchinger, Stefan; Martinez, Mauricio

2015-12-11

Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity, and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane, and rapidity. Here, we examine how the time evolution of linear perturbations depends on the equation of statemore » as well as on shear viscosity, bulk viscosity, and heat conductivity for modes with different azimuthal, radial, and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.« less

Molecular dynamics equation of state for nonpolar geochemical fluids

NASA Astrophysics Data System (ADS)

Duan, Zhenhao; Møller, Nancy; Wears, John H.

1995-04-01

Remarkable agreement between molecular dynamics simulations and experimental measurements has been obtained for methane for a large range of intensive variables, including those corresponding to liquid/vapor coexistence. Using a simple Lennard-Jones potential the simulations not only predict the PVT properties up to 2000°C and 20,000 bar with errors less than 1.5%, but also reproduce phase equilibria well below 0°C with accuracy close to experiment. This two-parameter molecular dynamics equation of state (SOS) is accurate for a much larger range of temperatures and pressures than our previously published EOS with a total fifteen parameters or that of Angus et al. (1978) with thirty-three parameters. By simple scaling, it is possible to predict PVT and phase equilibria of other nonpolar and weakly polar species.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garifullin, R. N., E-mail: rustem@matem.anrb.ru; Suleimanov, B. I., E-mail: bisul@mail.r

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

Preconditioning and the limit to the incompressible flow equations

NASA Technical Reports Server (NTRS)

Turkel, E.; Fiterman, A.; Vanleer, B.

1993-01-01

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

An Analysis of the Oil-Whirl Instability

NASA Astrophysics Data System (ADS)

Schultz, William W.; Han, Heng-Chu; Boyd, John P.; Schumack, Mark

1997-11-01

We investigate the hydrodynamic stability of a rotating journal translating inside a stationary bearing. A long (two-dimensional) journal bearing separated by a Newtonian non-cavitating lubricant is studied for shaft stability. Spectral element methods, perturbation methods, and linear stability analyses are used. The influences of fluid inertia, eccentricity, ellipticity, shaft mass, and finite gap on hydrodynamic stability are explored. Lubrication theory using Reynolds equation ignoring fluid inertia leads to erroneous conclusions. Without fluid inertia, the shaft is always unstable. However, the journal is conditionally stable even in the limit Rearrow 0 if fluid inertia is included. Increasing eccentricity helps stabilize a whirling shaft. Non-circular shaft bearings, for example elliptical bearings, are observed to have better dynamic stability.

Temperature-dependent poroelastic and viscoelastic effects on microscale-modelling of seismic reflections in heavy oil reservoirs

NASA Astrophysics Data System (ADS)

Ciz, Radim; Saenger, Erik H.; Gurevich, Boris; Shapiro, Serge A.

2009-03-01

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rocks.

A numerical simulation of magma motion, crustal deformation, and seismic radiation associated with volcanic eruptions

USGS Publications Warehouse

Nishimura, T.; Chouet, B.

2003-01-01

The finite difference method is used to calculate the magma dynamics, seismic radiation, and crustal deformation associated with a volcanic eruption. The model geometry consists of a cylindrical reservoir and narrow cylindrical conduit embedded in a homogeneous crust. We consider two models of eruption. In the first model, a lid caps the vent and the magma is overpressurized prior to the eruption. The eruption is triggered by the instantaneous removal of the lid, at which point the exit pressure becomes equal to the atmospheric pressure. In the second model, a plug at the reservoir outlet allows pressurization of only the magmatic fluid in the reservoir before the eruption. Magma transfer between the reservoir and conduit is triggered by the instantaneous removal of the plug, and the eruption occurs when the pressure at the conduit orifice exceeds the material strength of the lid capping the vent. In both models, magma dynamics are expressed by the equations of mass and momentum conservation in a compressible fluid, in which fluid expansion associated with depressurization is accounted for by a constitutive law relating pressure and density. Crustal motions are calculated from the equations of elastodynamics. The fluid and solid are dynamically coupled by applying the continuity of wall velocities and normal stresses across the conduit and reservoir boundaries. Free slip is allowed at the fluid-solid boundary. Both models predict the gradual depletion of the magma reservoir, which causes crustal deformation observed as a long-duration dilatational signal. Superimposed on this very-long-period (VLP) signal generated by mass transport are long-period (LP) oscillations of the magma reservoir and conduit excited by the acoustic resonance of the reservoir-conduit system during the eruption. The volume of the reservoir, vent size, and magma properties control the duration of VLP waves and dominant periods of LP oscillations. The second model predicts that when the magmatic fluid reaches the vent, a high-pressure pulse occurs at this location in accordance with the basic theory of compressible fluid dynamics. This abrupt pressure increase just beneath the vent is consistent with observed seismograms in which pulse-like Rayleigh waves excited by a shallow source are dominant. The strength of the lid plays an important role in the character of the seismograms and in defining the type of eruption observed.

ISCFD Nagoya 1989 - International Symposium on Computational Fluid Dynamics, 3rd, Nagoya, Japan, Aug. 28-31, 1989, Technical Papers

NASA Astrophysics Data System (ADS)

Recent advances in computational fluid dynamics are discussed in reviews and reports. Topics addressed include large-scale LESs for turbulent pipe and channel flows, numerical solutions of the Euler and Navier-Stokes equations on parallel computers, multigrid methods for steady high-Reynolds-number flow past sudden expansions, finite-volume methods on unstructured grids, supersonic wake flow on a blunt body, a grid-characteristic method for multidimensional gas dynamics, and CIC numerical simulation of a wave boundary layer. Consideration is given to vortex simulations of confined two-dimensional jets, supersonic viscous shear layers, spectral methods for compressible flows, shock-wave refraction at air/water interfaces, oscillatory flow in a two-dimensional collapsible channel, the growth of randomness in a spatially developing wake, and an efficient simplex algorithm for the finite-difference and dynamic linear-programming method in optimal potential control.

Simulating the flow of entangled polymers.

PubMed

Masubuchi, Yuichi

2014-01-01

To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.

Non-minimally coupled scalar field cosmology with torsion

NASA Astrophysics Data System (ADS)

Cid, Antonella; Izaurieta, Fernando; Leon, Genly; Medina, Perla; Narbona, Daniela

2018-04-01

In this work we present a generalized Brans-Dicke lagrangian including a non-minimally coupled Gauss-Bonnet term without imposing the vanishing torsion condition. In the resulting field equations, the torsion is closely related to the dynamics of the scalar field, i.e., if non-minimally coupled terms are present in the theory, then the torsion must be present. For the studied lagrangian we analyze the cosmological consequences of an effective torsional fluid and we show that this fluid can be responsible for the current acceleration of the universe. Finally, we perform a detailed dynamical system analysis to describe the qualitative features of the model, we find that accelerated stages are a generic feature of this scenario.

Dynamic analysis of liquid-lubricated hydrostatic journal bearings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kocur, J.A. Jr.

1990-01-01

A hybrid bearing reduces the dependency of its behavior on the lubricant viscosity, bearing clearance, bearing surface area by combining the hydrostatic and hydrodynamic effects. The combination permits the hybrid bearing to be incorporated into rotor designs, where the working fluids of the rotor may be used in place of externally supplied lubricants. An effective and practical method to predict the static and dynamic behavior of hybrid bearings is developed. The model includes the three major fluid effects in the bearing; the orifice restriction, inertia losses at the pocket edges, and hydrodynamic effects on the bearing land regions. Lubrication ismore » modeled and calculated using a finite element solution of Reynolds equation with turbulence corrections.« less

Domain decomposition methods in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gropp, William D.; Keyes, David E.

1991-01-01

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Instability of multi-layer fluid configurations in the presence of time-dependent accelerations in a microgravity environment

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Roh, Michael

1991-01-01

The increasing number of research opportunities in a microgravity environment will benefit not only fundamental studies in fluid dynamics, but also technological applications such as those involving materials processing. In particular, fluid configurations which involve fluid-fluid interfaces would occur in a variety of experimental investigations. This work investigates the stability of a configuration involving fluid-fluid interfaces in the presence of a time-dependent forcing. Both periodic (g-jitter) and nonperiodic accelerations are considered. The fluid configuration is multilayered, and infinite in extent. The analysis is linear and inviscid, and the acceleration vector is oriented perpendicular to each interface. A Floquet analysis is employed in the case of the periodic forcing. In the problem of nonperiodic forcing, the resulting system of equations are integrated in time. Specific nondimensional parameters appear in each problem. The configuration behavior is investigated for a range of parameter values.

Cell-model prediction of the melting of a Lennard-Jones solid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holian, B.L.

The classical free energy of the Lennard-Jones 6-12 solid is computed from a single-particle anharmonic cell model with a correction to the entropy given by the classical correlational entropy of quasiharmonic lattice dynamics. The free energy of the fluid is obtained from the Hansen-Ree analytic fit to Monte Carlo equation-of-state calculations. The resulting predictions of the solid-fluid coexistence curves by this corrected cell model of the solid are in excellent agreement with the computer experiments.

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

Zak, Michail

2006-01-01

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Towards a mulitphase equation of state of Carbon from first principles

NASA Astrophysics Data System (ADS)

Correa, Alfredo; Benedict, Lorin; Schwegler, Eric

2007-03-01

Ab initio molecular dynamics and electronic structure calculation had become one of the most useful tools to investigate properties of materials. Unfortunately these atomistic detailed results are rarely reused in calculations at a higher level of description, such as fluid dynamics and finite elements calculations. In this talk we present a concrete example showing the way that first principles results can be expressed in a way that is useful for hydrodynamics calculations, in particular we show how to build a analytic equation of state for Carbon that involves solid (diamond and BC8) and liquid phases. Applications of this newly obtained equation of state will be presented. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.

PAGOSA physics manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weseloh, Wayne N.; Clancy, Sean P.; Painter, James W.

2010-08-01

PAGOSA is a computational fluid dynamics computer program developed at Los Alamos National Laboratory (LANL) for the study of high-speed compressible flow and high-rate material deformation. PAGOSA is a three-dimensional Eulerian finite difference code, solving problems with a wide variety of equations of state (EOSs), material strength, and explosive modeling options.

NMR Study of Viscoelastic Fluids and Elastomers Under Extreme Conditions of Temperature and Pressure

DTIC Science & Technology

1980-09-30

of alkali metal carboxylates ; and (3) selected polymer systems. The results obtained carried us towards our long term goal of better understanding...applicability of hydrodynamic equations at the molecular level. In the studies of alkali metal carboxylates , our research efforts have focused on the dynamic

Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation.

PubMed

Fach, S; Sitzenfrei, R; Rauch, W

2009-01-01

It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

Fluid and hybrid models for streamers

NASA Astrophysics Data System (ADS)

Bonaventura, Zdeněk

2016-09-01

Streamers are contracted ionizing waves with self-generated field enhancement that propagate into a low-ionized medium exposed to high electric field leaving filamentary trails of plasma behind. The widely used model to study streamer dynamics is based on drift-diffusion equations for electrons and ions, assuming local field approximation, coupled with Poisson's equation. For problems where presence of energetic electrons become important a fluid approach needs to be extended by a particle model, accompanied also with Monte Carlo Collision technique, that takes care of motion of these electrons. A combined fluid-particle approach is used to study an influence of surface emission processes on a fast-pulsed dielectric barrier discharge in air at atmospheric pressure. It is found that fluid-only model predicts substantially faster reignition dynamics compared to coupled fluid-particle model. Furthermore, a hybrid model can be created in which the population of electrons is divided in the energy space into two distinct groups: (1) low energy `bulk' electrons that are treated with fluid model, and (2) high energy `beam' electrons, followed as particles. The hybrid model is then capable not only to deal with streamer discharges in laboratory conditions, but also allows us to study electron acceleration in streamer zone of lighting leaders. There, the production of fast electrons from streamers is investigated, since these (runaway) electrons act as seeds for the relativistic runaway electron avalanche (RREA) mechanism, important for high-energy atmospheric physics phenomena. Results suggest that high energy electrons effect the streamer propagation, namely the velocity, the peak electric field, and thus also the production rate of runaway electrons. This work has been supported by the Czech Science Foundation research project 15-04023S.

The application of the constants of motion to nonlinear stationary waves in complex plasmas: a unified fluid dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Dubinin, E.; Sauer, K.; Doyle, T. B.

2004-08-01

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall magnetohydrodynamic and ion cyclotron acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

Simulation of swimming strings immersed in a viscous fluid flow

NASA Astrophysics Data System (ADS)

Huang, Wei-Xi; Sung, Hyung Jin

2006-11-01

In nature, many phenomena involve interactions between flexible bodies and their surrounding viscous fluid, such as a swimming fish or a flapping flag. The intrinsic dynamics is complicate and not well understood. A flexible string can be regarded as a one-dimensional flag model. Many similarities can be found between the flapping string and swimming fish, although different wake speed results in a drag force for the flapping string and a propulsion force for the swimming fish. In the present study, we propose a mathematical formulation for swimming strings immersed in a viscous fluid flow. Fluid motion is governed by the Navier-Stokes equations and a momentum forcing is added in order to bring the fluid to move at the same velocity with the immersed surface. A flexible inextensible string model is described by another set of equations with an additional momentum forcing which is a result of the fluid viscosity and the pressure difference across the string. The momentum forcing is calculated by a feedback loop. Simulations of several numerical examples are carried out, including a hanging string which starts moving under gravity without ambient fluid, a swinging string immersed in a quiescent viscous fluid, a string swimming within a uniform surrounding flow, and flow over two side-by-side strings. The numerical results agree well with the theoretical analysis and previous experimental observations. Further simulation of a swimming fish is under consideration.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Dynamics of viscous cosmologies in the full Israel-Stewart formalism

NASA Astrophysics Data System (ADS)

Lepe, Samuel; Otalora, Giovanni; Saavedra, Joel

2017-07-01

A detailed dynamical analysis for a bulk viscosity model in the full Israel-Stewart formalism for a spatially flat Friedmann-Robertson-Walker universe is performed. In our study we have considered the total cosmic fluid constituted by radiation, dark matter, and dark energy. The dark matter fluid is treated as an imperfect fluid which has a bulk viscosity that depends on its energy density in the usual form ξ (ρm)=ξ0ρm1 /2, whereas the other components are assumed to behave as perfect fluids with constant equation of state parameter. We show that the thermal history of the Universe is reproduced provided that the viscous coefficient satisfies the condition ξ0≪1 , either for a zero or a suitable nonzero coupling between dark energy and viscous dark matter. In this case, the final attractor is a dark-energy-dominated, accelerating universe, with an effective equation of state parameter in the quintessence-like, cosmological constant-like, or phantom-like regime, in agreement with observations. As our main result, we show that in order to obtain a viable cosmological evolution and at the same time alleviating the cosmological coincidence problem via the mechanism of scaling solution, an explicit interaction between dark energy and viscous dark matter seems inevitable. This result is consistent with the well-known fact that models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. Furthermore, by insisting on above, we show that in the present context a phantom nature of this interacting dark energy fluid is also favored.

Integration of Extended MHD and Kinetic Effects in Global Magnetosphere Models

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Wang, L.; Maynard, K. R. M.; Raeder, J.; Bhattacharjee, A.

2015-12-01

Computational models of Earth's geospace environment are an important tool to investigate the science of the coupled solar-wind -- magnetosphere -- ionosphere system, complementing satellite and ground observations with a global perspective. They are also crucial in understanding and predicting space weather, in particular under extreme conditions. Traditionally, global models have employed the one-fluid MHD approximation, which captures large-scale dynamics quite well. However, in Earth's nearly collisionless plasma environment it breaks down on small scales, where ion and electron dynamics and kinetic effects become important, and greatly change the reconnection dynamics. A number of approaches have recently been taken to advance global modeling, e.g., including multiple ion species, adding Hall physics in a Generalized Ohm's Law, embedding local PIC simulations into a larger fluid domain and also some work on simulating the entire system with hybrid or fully kinetic models, the latter however being to computationally expensive to be run at realistic parameters. We will present an alternate approach, ie., a multi-fluid moment model that is derived rigorously from the Vlasov-Maxwell system. The advantage is that the computational cost remains managable, as we are still solving fluid equations. While the evolution equation for each moment is exact, it depends on the next higher-order moment, so that truncating the hiearchy and closing the system to capture the essential kinetic physics is crucial. We implement 5-moment (density, momentum, scalar pressure) and 10-moment (includes pressure tensor) versions of the model, and use local approximations for the heat flux to close the system. We test these closures by local simulations where we can compare directly to PIC / hybrid codes, and employ them in global simulations using the next-generation OpenGGCM to contrast them to MHD / Hall-MHD results and compare with observations.

A three-dimensional computational fluid dynamics model of shear stress distribution during neotissue growth in a perfusion bioreactor.

PubMed

Guyot, Y; Luyten, F P; Schrooten, J; Papantoniou, I; Geris, L

2015-12-01

Bone tissue engineering strategies use flow through perfusion bioreactors to apply mechanical stimuli to cells seeded on porous scaffolds. Cells grow on the scaffold surface but also by bridging the scaffold pores leading a fully filled scaffold following the scaffold's geometric characteristics. Current computational fluid dynamic approaches for tissue engineering bioreactor systems have been mostly carried out for empty scaffolds. The effect of 3D cell growth and extracellular matrix formation (termed in this study as neotissue growth), on its surrounding fluid flow field is a challenge yet to be tackled. In this work a combined approach was followed linking curvature driven cell growth to fluid dynamics modeling. The level-set method (LSM) was employed to capture neotissue growth driven by curvature, while the Stokes and Darcy equations, combined in the Brinkman equation, provided information regarding the distribution of the shear stress profile at the neotissue/medium interface and within the neotissue itself during growth. The neotissue was assumed to be micro-porous allowing flow through its structure while at the same time allowing the simulation of complete scaffold filling without numerical convergence issues. The results show a significant difference in the amplitude of shear stress for cells located within the micro-porous neo-tissue or at the neotissue/medium interface, demonstrating the importance of taking along the neotissue in the calculation of the mechanical stimulation of cells during culture.The presented computational framework is used on different scaffold pore geometries demonstrating its potential to be used a design as tool for scaffold architecture taking into account the growing neotissue. Biotechnol. Bioeng. 2015;112: 2591-2600. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Numerical studies of the surface tension effect of cryogenic liquid helium

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time- and length-scales

NASA Astrophysics Data System (ADS)

Gat, Amir; Friedman, Yonathan

2017-11-01

The characteristic time of low-Reynolds number fluid-structure interaction scales linearly with the ratio of fluid viscosity to solid Young's modulus. For sufficiently large values of Young's modulus, both time- and length-scales of the viscous-elastic dynamics may be similar to acoustic time- and length-scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time- and length-scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel meta-materials with unique acoustic properties. ISF 818/13.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zubarev, N. M., E-mail: nick@iep.uran.ru; Zubareva, O. V.

The dynamics of a bubble in a dielectric liquid under the influence of a uniform external electric field is considered. It is shown that in the situation where the boundary motion is determined only by electrostatic forces, the special regime of fluid motion can be realized for which the velocity and electric field potentials are linearly related. In the two-dimensional case, the corresponding equations are reduced to an equation similar in structure to the well-known Laplacian growth equation, which, in turn, can be reduced to a finite number of ordinary differential equations. This allows us to obtain exact solutions formore » asymmetric bubble deformations resulting in the formation of a finite-time singularity (cusp)« less

Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagmeijer, R.

1994-11-01

A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of themore » computational coordinates.« less

KdV-like equations for fluid dynamics

NASA Astrophysics Data System (ADS)

Ruggieri, M.; Speciale, M. P.

2014-12-01

Main goal of the authors is to consider the generalized system of KdV equations ut+uxxx+2uux+2e1vvx+e2(uxv+uvx)+e3vxxx = 0 c1vt+vxxx+2vvx+c2vx+c3(e1(uxv+uvx)+2e2uux+e3uxxx) = 0 (1), and to construct the optimal system of one dimensional subalgebras. The reduction of the above system to ODEs through the optimal systems is performed and finally an application is shown.

Research in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Modeling quantum fluid dynamics at nonzero temperatures

PubMed Central

Berloff, Natalia G.; Brachet, Marc; Proukakis, Nick P.

2014-01-01

The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures. PMID:24704874

Modeling and Bio molecular Self-assembly via Molecular Dynamics and Dissipative Particle Dynamics

NASA Astrophysics Data System (ADS)

Rakesh, L.

2009-09-01

Surfactants like materials can be used to increase the solubility of poorly soluble drugs in water and to increase drug bioavailability. A typical case study will be demonstrated using DPD simulation to model the distribution of anti-inflammatory drug molecules. Computer simulation is a convenient approach to understand drug distribution and solubility concepts without much wastage and costly experiments in the laboratory. Often in molecular dynamics (MD) the atoms are represented explicitly and the equation of motion as described by Newtonian dynamics is integrated explicitly. MD has been used to study spontaneous formation of micelles by hydrophobic molecules with amphiphilic head groups in bulk water, as well as stability of pre-configured micelles and membranes. DPD is a state-of the- art mesoscale simulation, it is a more recent molecular dynamics technique, originally developed for simulating complex fluids but lately also applied to membrane dynamics, hemodynamic in biomedical applications. Such fluids pervade industrial research from paints to pharmaceuticals and from cosmetics to the controlled release of drugs. Dissipative particle dynamics (DPD) can provide structural and dynamic properties of fluids in equilibrium, under shear or confined to narrow cavities, at length- and time-scales beyond the scope of traditional atomistic molecular dynamics simulation methods. Mesoscopic particles are used to represent clusters of molecules. The interaction conserves mass and momentum and as a consequence the dynamics is consistent with Navier-Stokes equations. In addition to the conservative forces, stochastic drive and dissipation is introduced to represent internal degrees of freedom in the mesoscopic particles. In this research, an initial study is being conducted using the aqueous solubilization of the nonsteroidal, anti-inflammatory drug is studied theoretically in micellar solution of nonionic (dodecyl hexa(ethylene oxide), C12E6) surfactants possessing the hydrocarbon "tail" and their hydrophilic head groups. We find that, for the surfactants, the aqueous solubility of anti-inflammatory molecules increases linearly with increasing surfactant concentration. In particular, we observed a 10-fold increase in the solubility of anti-inflammatory drugs relative to that in the aqueous buffer upon the addition of 100 mM dodecyltrimethyl ammonium bromide -DTAB.

Numerical analysis on interactions between fluid flow and structure deformation in plate-fin heat exchanger by Galerkin method

NASA Astrophysics Data System (ADS)

Liu, Jing-cheng; Wei, Xiu-ting; Zhou, Zhi-yong; Wei, Zhen-wen

2018-03-01

The fluid-structure interaction performance of plate-fin heat exchanger (PFHE) with serrated fins in large scale air-separation equipment was investigated in this paper. The stress and deformation of fins were analyzed, besides, the interaction equations were deduced by Galerkin method. The governing equations of fluid flow and heat transfer in PFHE were deduced by finite volume method (FVM). The distribution of strain and stress were calculated in large scale air separation equipment and the coupling situation of serrated fins under laminar situation was analyzed. The results indicated that the interactions between fins and fluid flow in the exchanger have significant impacts on heat transfer enhancement, meanwhile, the strain and stress of fins includes dynamic pressure of the sealing head and flow impact with the increase of flow velocity. The impacts are especially significant at the conjunction of two fins because of the non-alignment fins. It can be concluded that the soldering process and channel width led to structure deformation of fins in the exchanger, and degraded heat transfer efficiency.

Far-Field Noise Induced by Bubble near Free Surface

NASA Astrophysics Data System (ADS)

Ye, Xi; Li, Jiang-tao; Liu, Jian-hua; Chen, Hai-long

2018-03-01

The motion of a bubble near the free surface is solved by the boundary element method based on the linear wave equation, and the influence of fluid compressibility on bubble dynamics is analyzed. Based on the solution of the bubble motion, the far-field radiation noise induced by the bubble is calculated using Kirchhoff moving boundary integral equation, and the influence of free surface on far-field noise is researched. As the results, the oscillation amplitude of the bubble is weakened in compressible fluid compared with that in incompressible fluid, and the free surface amplifies the effect of fluid compressibility. When the distance between the bubble and an observer is much larger than that between the bubble and free surface, the sharp wave trough of the sound pressure at the observer occurs. With the increment of the distance between the bubble and free surface, the time of the wave trough appearing is delayed and the value of the wave trough increase. When the distance between the observer and the bubble is reduced, the sharp wave trough at the observer disappears.

On axial temperature gradients due to large pressure drops in dense fluid chromatography.

PubMed

Colgate, Sam O; Berger, Terry A

2015-03-13

The effect of energy degradation (Degradation is the creation of net entropy resulting from irreversibility.) accompanying pressure drops across chromatographic columns is examined with regard to explaining axial temperature gradients in both high performance liquid chromatography (HPLC) and supercritical fluid chromatography (SFC). The observed effects of warming and cooling can be explained equally well in the language of thermodynamics or fluid dynamics. The necessary equivalence of these treatments is reviewed here to show the legitimacy of using whichever one supports the simpler determination of features of interest. The determination of temperature profiles in columns by direct application of the laws of thermodynamics is somewhat simpler than applying them indirectly by solving the Navier-Stokes (NS) equations. Both disciplines show that the preferred strategy for minimizing the reduction in peak quality caused by temperature gradients is to operate columns as nearly adiabatically as possible (i.e. as Joule-Thomson expansions). This useful fact, however, is not widely familiar or appreciated in the chromatography community due to some misunderstanding of the meaning of certain terms and expressions used in these disciplines. In fluid dynamics, the terms "resistive heating" or "frictional heating" have been widely used as synonyms for the dissipation function, Φ, in the NS energy equation. These terms have been widely used by chromatographers as well, but often misinterpreted as due to friction between the mobile phase and the column packing, when in fact Φ describes the increase in entropy of the system (dissipation, ∫TdSuniv>0) due to the irreversible decompression of the mobile phase. Two distinctly different contributions to the irreversibility are identified; (1) ΔSext, viscous dissipation of work done by the external surroundings driving the flow (the pump) contributing to its warming, and (2) ΔSint, entropy change accompanying decompression of fluid in the column, contributing either to warming or cooling depending on local density and temperature. The molecular basis for this variation is described. Sample calculations of dissipation and temperature profiles of several model fluids including carbon dioxide-methanol mixtures are presented, based on the NIST REFPROP program including select equations of state and property calculation software. Copyright © 2015 Elsevier B.V. All rights reserved.

Two-fluid description of wave-particle interactions in strong Buneman turbulence

NASA Astrophysics Data System (ADS)

Che, H.

2014-06-01

To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation while a plasma is unstable to the Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. We show that both energy dissipation and momentum transport along electric current in the current layer are locally quasi-static, but globally dynamic and irreversible. Turbulent drag dissipates both the streaming energy of the current sheet and the associated magnetic energy. The net loss of streaming energy is converted into the electron component heat conduction parallel to the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that relates the turbulence-induced convective momentum transport and thermal momentum transport. Electron trapping and de-trapping drive local momentum transports, while phase mixing converts convective momentum into thermal momentum. The drag acts like a micro-macro link in the anomalous heating processes. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons, but most of the magnetic energy is dissipated and converted into the component heat of electrons perpendicular to the magnetic field. This heating process is decoupled from the heating of Buneman instability in the current sheets. Ion heating is weak but ions play an important role in assisting energy exchanges between waves and electrons. Cold ion fluid equations together with our electron fluid equations form a complete set of equations that describes the occurrence, growth, saturation and decay of the Buneman instability.

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Methodological inaccuracies in clinical aortic valve severity assessment: insights from computational fluid dynamic modeling of CT-derived aortic valve anatomy

NASA Astrophysics Data System (ADS)

Traeger, Brad; Srivatsa, Sanjay S.; Beussman, Kevin M.; Wang, Yechun; Suzen, Yildirim B.; Rybicki, Frank J.; Mazur, Wojciech; Miszalski-Jamka, Tomasz

2016-04-01

Aortic stenosis is the most common valvular heart disease. Assessing the contribution of the valve as a portion to total ventricular load is essential for the aging population. A CT scan for one patient was used to create one in vivo tricuspid aortic valve geometry and assessed with computational fluid dynamics (CFD). CFD simulated the pressure, velocity, and flow rate, which were used to assess the Gorlin formula and continuity equation, current clinical diagnostic standards. The results demonstrate an underestimation of the anatomic orifice area (AOA) by Gorlin formula and overestimation of AOA by the continuity equation, using peak velocities, as would be measured clinically by Doppler echocardiography. As a result, we suggest that the Gorlin formula is unable to achieve the intended estimation of AOA and largely underestimates AOA at the critical low-flow states present in heart failure. The disparity in the use of echocardiography with the continuity equation is due to the variation in velocity profile between the outflow tract and the valve orifice. Comparison of time-averaged orifice areas by Gorlin and continuity with instantaneous orifice areas by planimetry can mask the errors of these methods, which is a result of the assumption that the blood flow is inviscid.

The impact of CFD on development test facilities - A National Research Council projection. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Korkegi, R. H.

1983-01-01

The results of a National Research Council study on the effect that advances in computational fluid dynamics (CFD) will have on conventional aeronautical ground testing are reported. Current CFD capabilities include the depiction of linearized inviscid flows and a boundary layer, initial use of Euler coordinates using supercomputers to automatically generate a grid, research and development on Reynolds-averaged Navier-Stokes (N-S) equations, and preliminary research on solutions to the full N-S equations. Improvements in the range of CFD usage is dependent on the development of more powerful supercomputers, exceeding even the projected abilities of the NASA Numerical Aerodynamic Simulator (1 BFLOP/sec). Full representation of the Re-averaged N-S equations will require over one million grid points, a computing level predicted to be available in 15 yr. Present capabilities allow identification of data anomalies, confirmation of data accuracy, and adequateness of model design in wind tunnel trials. Account can be taken of the wall effects and the Re in any flight regime during simulation. CFD can actually be more accurate than instrumented tests, since all points in a flow can be modeled with CFD, while they cannot all be monitored with instrumentation in a wind tunnel.

Dynamics of contracting surfactant-covered filaments

NASA Astrophysics Data System (ADS)

Kamat, Pritish; Thete, Sumeet; Xu, Qi; Basaran, Osman

2013-11-01

When drops are produced from a nozzle, a thin liquid thread connects the primary drop that is about to form to the rest of the liquid in the nozzle. Often, the thread becomes disconnected from both the primary drop and the remnant liquid mass hanging from the nozzle and thereby gives rise to a free filament. Due to surface tension, the free filament then contracts or recoils. During recoil, the filament can either contract into a single satellite droplet or break up into several small satellites. Such satellite droplets are undesirable in applications where they can, for example, cause misting in a manufacturing environment and mar product quality in ink-jet printing. In many applications, the filaments are coated with a monolayer of surfactant. In this work, we study the dynamics of contraction of slender filaments of a Newtonian fluid that are covered with a monolayer of surfactant when the surrounding fluid is a passive gas. Taking advantage of the fact that the filaments are long and slender, we use a 1D-slender-jet approximation of the governing system of equations consisting of the Navier-Stokes system and the convection-diffusion equation for surfactant transport. We solve the 1D system of equations by a finite element based numerical method.

Natural frequency and stability analysis of a pipe conveying fluid with axially moving supports immersed in fluid

NASA Astrophysics Data System (ADS)

Ni, Qiao; Luo, Yangyang; Li, Mingwu; Yan, Hao

2017-09-01

Structural model for a slender and uniform pipe conveying fluid, with axially moving supports on both ends, immersed in an incompressible fluid, is formulated. Free vibration and stability of the system are studied through numerical calculation. First, the equations of motion of the system are derived in an absolute coordinate system. An "axial added mass coefficient" is adopted to amend the forces caused by the external fluid. Boundary conditions are fixed by using coordinated conversion. Then, numerical results of the natural frequency are obtained via the Galerkin method, both for pinned-pinned and clamped-clamped supports. The critical speeds of supports and several instability types are discussed. Last, the effects of the system parameters on the dynamics and instability of the system are investigated.

Kinetic theory of Lennard-Jones fluids

NASA Astrophysics Data System (ADS)

Leegwater, Jan A.

1991-12-01

A kinetic theory that describes the time evolution of a fluid consisting of Lennard-Jones particles at all densities is proposed. The kinetic equation assumes binary collisions, but takes into account the finite time duration of a collision. Furthermore, it is an extension of a kinetic equation for the square well fluid as well as the hard sphere Enskog theory. In the low density limit, the Boltzmann theory is obtained. It is shown that the proposed theory obeys all the conservation laws. The exchange of potential and kinetic energies is studied and it is shown that at high density this is a fast process. The dominant mechanism for energy exchange is found to be collisions at the strongly repulsive part of the potential that are disturbed by third particles. The kinetic equation is also used to calculate the Green-Kubo integrands for shear viscosity and heat conductivity. The major structures found in molecular dynamics simulations are reproduced at intermediate densities quantitatively and at high density semiquantitatively. It is found that at high density, not only correlated collisions have to be taken into account, but that even the concept of collisions in the sense of sudden changes in the velocity is no longer useful.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

PubMed Central

Li, Qiang; He, Guo-Wei

2009-01-01

Recent experiments have found that slip length could be as large as on the order of 1 μm for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper, an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces, in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths, which cannot be obtained by molecular dynamics simulation alone. PMID:19693344

Stable Eigenmodes and Energy Dynamics in a Model of LAPD Turbulence

NASA Astrophysics Data System (ADS)

Friedman, Brett; Carter, T. A.; Umansky, M. V.

2011-10-01

A three field Braginskii fluid model that semi-quantitatively predicts turbulent statistics in the Large Plasma Device (LAPD) at UCLA is analyzed. A 3D simulation of turbulence in LAPD using the BOUT++ fluid code is shown to reproduce experimental turbulent properties such as the frequency spectrum and correlation length with semi-qualitative and semi-quantitative accuracy. In an attempt to explain turbulent saturation in the simulation, equations for the energy dynamics are derived and applied to the results. The degree to which stable linear drift wave eigenmodes draw energy from the system and the affect that zonal flows have on transferring energy to stable eigenmode branches is explored. It is also shown that zonal flows drive Kelvin-Helmholtz flute modes, which come to dominate the energy dynamics in the quasi steady state regime.

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Strongly Coupled Fluid-Body Dynamics in the Immersed Boundary Projection Method

NASA Astrophysics Data System (ADS)

Wang, Chengjie; Eldredge, Jeff D.

2014-11-01

A computational algorithm is developed to simulate dynamically coupled interaction between fluid and rigid bodies. The basic computational framework is built upon a multi-domain immersed boundary method library, whirl, developed in previous work. In this library, the Navier-Stokes equations for incompressible flow are solved on a uniform Cartesian grid by the vorticity-based immersed boundary projection method of Colonius and Taira. A solver for the dynamics of rigid-body systems is also included. The fluid and rigid-body solvers are strongly coupled with an iterative approach based on the block Gauss-Seidel method. Interfacial force, with its intimate connection with the Lagrange multipliers used in the fluid solver, is used as the primary iteration variable. Relaxation, developed from a stability analysis of the iterative scheme, is used to achieve convergence in only 2-4 iterations per time step. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including flapping of flexible wings, self-excited oscillations of a system of linked plates and three-dimensional propulsion of flexible fluked tail. This work has been supported by AFOSR, under Award FA9550-11-1-0098.

Applied Computational Fluid Dynamics at NASA Ames Research Center

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Kwak, Dochan (Technical Monitor)

1994-01-01

The field of Computational Fluid Dynamics (CFD) has advanced to the point where it can now be used for many applications in fluid mechanics research and aerospace vehicle design. A few applications being explored at NASA Ames Research Center will be presented and discussed. The examples presented will range in speed from hypersonic to low speed incompressible flow applications. Most of the results will be from numerical solutions of the Navier-Stokes or Euler equations in three space dimensions for general geometry applications. Computational results will be used to highlight the presentation as appropriate. Advances in computational facilities including those associated with NASA's CAS (Computational Aerosciences) Project of the Federal HPCC (High Performance Computing and Communications) Program will be discussed. Finally, opportunities for future research will be presented and discussed. All material will be taken from non-sensitive, previously-published and widely-disseminated work.

Computational fluid dynamics in a marine environment

NASA Technical Reports Server (NTRS)

Carlson, Arthur D.

1987-01-01

The introduction of the supercomputer and recent advances in both Reynolds averaged, and large eddy simulation fluid flow approximation techniques to the Navier-Stokes equations, have created a robust environment for the exploration of problems of interest to the Navy in general, and the Naval Underwater Systems Center in particular. The nature of problems that are of interest, and the type of resources needed for their solution are addressed. The goal is to achieve a good engineering solution to the fluid-structure interaction problem. It is appropriate to indicate that a paper by D. Champman played a major role in developing the interest in the approach discussed.

Turbulence coefficients and stability studies for the coaxial flow or dissimiliar fluids. [gaseous core nuclear reactors

NASA Technical Reports Server (NTRS)

Weinstein, H.; Lavan, Z.

1975-01-01

Analytical investigations of fluid dynamics problems of relevance to the gaseous core nuclear reactor program are presented. The vortex type flow which appears in the nuclear light bulb concept is analyzed along with the fluid flow in the fuel inlet region for the coaxial flow gaseous core nuclear reactor concept. The development of numerical methods for the solution of the Navier-Stokes equations for appropriate geometries is extended to the case of rotating flows and almost completes the gas core program requirements in this area. The investigations demonstrate that the conceptual design of the coaxial flow reactor needs further development.

Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

2017-12-01

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

Results of Microgravity Fluid Dynamics Captured With the Spheres-Slosh Experiment

NASA Technical Reports Server (NTRS)

Lapilli, Gabriel; Kirk, Daniel; Gutierrez, Hector; Schallhorn, Paul; Marsell, Brandon; Roth, Jacob; Moder, Jeffrey

2015-01-01

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

Result of Microgravity Fluid Dynamics Captured with the SPHERES-Slosh Experiment

NASA Technical Reports Server (NTRS)

Lapilli, Gabriel; Kirk, Daniel; Gutierrez, Hector; Schallhorn, Paul; Marsell, Brandon; Roth, Jacob; Moder, Jeffrey

2015-01-01

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

Results of Microgravity Fluid Dynamics Captured with the Spheres-Slosh Experiment

NASA Technical Reports Server (NTRS)

Lapilli, Gabriel; Kirk, Daniel Robert; Gutierrez, Hector; Schallhorn, Paul; Marsell, Brandon; Roth, Jacob; Jeffrey Moder

2015-01-01

This paper provides an overview of the SPHERES-Slosh Experiment (SSE) aboard the International Space Station (ISS) and presents on-orbit results with data analysis. In order to predict the location of the liquid propellant during all times of a spacecraft mission, engineers and mission analysts utilize Computational Fluid Dynamics (CFD). These state-of-the-art computer programs numerically solve the fluid flow equations to predict the location of the fluid at any point in time during different spacecraft maneuvers. The models and equations used by these programs have been extensively validated on the ground, but long duration data has never been acquired in a microgravity environment. The SSE aboard the ISS is designed to acquire this type of data, used by engineers on earth to validate and improve the CFD prediction models, improving the design of the next generation of space vehicles as well as the safety of current missions. The experiment makes use of two Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES) connected by a frame. In the center of the frame there is a plastic, pill shaped tank that is partially filled with green-colored water. A pair of high resolution cameras records the movement of the liquid inside the tank as the experiment maneuvers within the Japanese Experimental Module test volume. Inertial measurement units record the accelerations and rotations of the tank, making the combination of stereo imaging and inertial data the inputs for CFD model validation.

Two-Fluid Models and Interfacial Area Transport in Microgravity Condition

NASA Technical Reports Server (NTRS)

Ishii, Mamoru; Sun, Xiao-Dong; Vasavada, Shilp

2004-01-01

The objective of the present study is to develop a two-fluid model formulation with interfacial area transport equation applicable for microgravity conditions. The new model is expected to make a leapfrog improvement by furnishing the constitutive relations for the interfacial interaction terms with the interfacial area transport equation, which can dynamically model the changes of the interfacial structures. In the first year of this three-year project supported by the U.S. NASA, Office of Biological and Physics Research, the primary focus is to design and construct a ground-based, microgravity two-phase flow simulation facility, in which two immiscible fluids with close density will be used. In predicting the two-phase flow behaviors in any two-phase flow system, the interfacial transfer terms are among the most essential factors in the modeling. These interfacial transfer terms in a two-fluid model specify the rate of phase change, momentum exchange, and energy transfer at the interface between the two phases. For the two-phase flow under the microgravity condition, the stability of the fluid particle interface and the interfacial structures are quite different from those under normal gravity condition. The flow structure may not reach an equilibrium condition and the two fluids may be loosely coupled such that the inertia terms of each fluid should be considered separately by use of the two-fluid model. Previous studies indicated that, unless phase-interaction terms are accurately modeled in the two-fluid model, the complex modeling does not necessarily warrant an accurate solution.

Study of effect of magnetohydrodynamics and couple stress on steady and dynamic characteristics of porous exponential slider bearings

NASA Astrophysics Data System (ADS)

Hanumagowda, B. N.; Gonchigara, Thippeswamy; Santhosh Kumar, J.; MShiva Kumar, H.

2018-04-01

Exponential slider bearings with porous facing is analysed in this article. The modified Reynolds equation is derived for the Exponential porous slider bearing with MHD and couple stress fluid. Computed values of Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient are presented in graphical form. The Steady film pressure, Steady load capacity, Dynamic stiffness and Damping coefficient decreases with increasing values of permeability parameter and increases with increasing values of couplestress parameter and Hartmann number.

Physically-Based Modelling and Real-Time Simulation of Fluids.

NASA Astrophysics Data System (ADS)

Chen, Jim Xiong

1995-01-01

Simulating physically realistic complex fluid behaviors presents an extremely challenging problem for computer graphics researchers. Such behaviors include the effects of driving boats through water, blending differently colored fluids, rain falling and flowing on a terrain, fluids interacting in a Distributed Interactive Simulation (DIS), etc. Such capabilities are useful in computer art, advertising, education, entertainment, and training. We present a new method for physically-based modeling and real-time simulation of fluids in computer graphics and dynamic virtual environments. By solving the 2D Navier -Stokes equations using a CFD method, we map the surface into 3D using the corresponding pressures in the fluid flow field. This achieves realistic real-time fluid surface behaviors by employing the physical governing laws of fluids but avoiding extensive 3D fluid dynamics computations. To complement the surface behaviors, we calculate fluid volume and external boundary changes separately to achieve full 3D general fluid flow. To simulate physical activities in a DIS, we introduce a mechanism which uses a uniform time scale proportional to the clock-time and variable time-slicing to synchronize physical models such as fluids in the networked environment. Our approach can simulate many different fluid behaviors by changing the internal or external boundary conditions. It can model different kinds of fluids by varying the Reynolds number. It can simulate objects moving or floating in fluids. It can also produce synchronized general fluid flows in a DIS. Our model can serve as a testbed to simulate many other fluid phenomena which have never been successfully modeled previously.

New Perspectives: Wave Mechanical Interpretations of Dark Matter, Baryon and Dark Energy

NASA Astrophysics Data System (ADS)

Russell, Esra

We model the cosmic components: dark matter, dark energy and baryon distributions in the Cosmic Web by means of highly nonlinear Schrodinger type and reaction diffusion type wave mechanical descriptions. The construction of these wave mechanical models of the structure formation is achieved by introducing the Fisher information measure and its comparison with highly nonlinear term which has dynamical analogy to infamous quantum potential in the wave equations. Strikingly, the comparison of this nonlinear term and the Fisher information measure provides a dynamical distinction between lack of self-organization and self-organization in the dynamical evolution of the cosmic components. Mathematically equivalent to the standard cosmic fluid equations, these approaches make it possible to follow the evolution of the matter distribution even into the highly nonlinear regime by circumventing singularities. Also, numerical realizations of the emerging web-like patterns are presented from the nonlinear dynamics of the baryon component while dark energy component shows Gaussian type dynamics corresponding to soliton-like solutions.

VISCOPLASTIC FLUID MODEL FOR DEBRIS FLOW ROUTING.

USGS Publications Warehouse

Chen, Cheng-lung

1986-01-01

This paper describes how a generalized viscoplastic fluid model, which was developed based on non-Newtonian fluid mechanics, can be successfully applied to routing a debris flow down a channel. The one-dimensional dynamic equations developed for unsteady clear-water flow can be used for debris flow routing if the flow parameters, such as the momentum (or energy) correction factor and the resistance coefficient, can be accurately evaluated. The writer's generalized viscoplastic fluid model can be used to express such flow parameters in terms of the rheological parameters for debris flow in wide channels. A preliminary analysis of the theoretical solutions reveals the importance of the flow behavior index and the so-called modified Froude number for uniformly progressive flow in snout profile modeling.

Fluid-structure interactions of photo-responsive polymer cantilevers

NASA Astrophysics Data System (ADS)

Bin, Jonghoon; Oates, William S.; Yousuff Hussaini, M.

2013-02-01

A new class of photomechanical liquid crystal networks (LCNs) has emerged, which generate large bending deformation and fast response times that scale with the resonance of the polymer films. Here, a numerical study is presented that describes the photomechanical structural dynamic behavior of an LCN in a fluid medium; however, the methodology is also applicable to fluid-structure interactions of a broader range of adaptive structures. Here, we simulate the oscillation of photomechanical cantilevers excited by light while simultaneously modeling the effect of the surrounding fluid at different ambient pressures. The photoactuated LCN is modeled as an elastic thin cantilever plate, and gradients in photostrain from the external light are computed from the assumptions of light absorption and photoisomerization through the film thickness. Numerical approximations of the equations governing the plate are based on cubic B-spline shape functions and a second order implicit Newmark central scheme for time integration. For the fluid, three dimensional unsteady incompressible Navier-Stokes equations are solved using the arbitrary Lagrangian-Eulerian (ALE) method, which employs a structured body-fitted curvilinear coordinate system where the solid-fluid interface is a mesh line of the system, and the complicated interface boundary conditions are accommodated in a conventional finite-volume formulation. Numerical examples are given which provide new insight into material behavior in a fluid medium as a function of ambient pressure.

Rational rates of uniform decay for strong solutions to a fluid-structure PDE system

NASA Astrophysics Data System (ADS)

Avalos, George; Bucci, Francesca

2015-06-01

In this work we investigate the uniform stability properties of solutions to a well-established partial differential equation (PDE) model for a fluid-structure interaction. The PDE system under consideration comprises a Stokes flow which evolves within a three-dimensional cavity; moreover, a Kirchhoff plate equation is invoked to describe the displacements along a (fixed) portion - say, Ω - of the cavity wall. Contact between the respective fluid and structure dynamics occurs on the boundary interface Ω. The main result in the paper is as follows: the solutions to the composite PDE system, corresponding to smooth initial data, decay at the rate of O (1 / t). Our method of proof hinges upon the appropriate invocation of a relatively recent resolvent criterion for polynomial decays of C0-semigroups. While the characterization provided by said criterion originates in the context of operator theory and functional analysis, the work entailed here is wholly within the realm of PDE.

Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity φ and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian H=|φ|dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in [1].

The fluid-dynamic paradigm of the dust-acoustic soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-06-01

In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the wave, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech2-type solitons associated with the Korteweg de Vries equation, and indicates the parameter regimes in which solitons may exist.

Comprehensive representation of the Lennard-Jones equation of state based on molecular dynamics simulation data

NASA Astrophysics Data System (ADS)

Pieprzyk, S.; Brańka, A. C.; Maćkowiak, Sz.; Heyes, D. M.

2018-03-01

The equation of state (EoS) of the Lennard-Jones fluid is calculated using a new set of molecular dynamics data which extends to higher temperature than in previous studies. The modified Benedict-Webb-Rubin (MBWR) equation, which goes up to ca. T ˜ 6, is reparametrized with new simulation data. A new analytic form for the EoS, which breaks the fluid range into two regions with different analytic forms and goes up to ca. T ≃ 35, is also proposed. The accuracy of the new formulas is at least as good as the MBWR fit and goes to much higher temperature allowing it to now encompass the Amagat line. The fitted formula extends into the high temperature range where the system can be well represented by inverse power potential scaling, which means that our specification of the equation of state covers the entire (ρ, T) plane. Accurate analytic fit formulas for the Boyle, Amagat, and inversion curves are presented. Parametrizations of the extrema loci of the isochoric, CV, and isobaric, CP, heat capacities are given. As found by others, a line maxima of CP terminates in the critical point region, and a line of minima of CP terminates on the freezing line. The line of maxima of CV terminates close to or at the critical point, and a line of minima of CV terminates to the right of the critical point. No evidence for a divergence in CV in the critical region is found.

CFD modeling of space-time evolution of fast pyrolysis products in a bench-scale fluidized-bed reactor

USDA-ARS?s Scientific Manuscript database

A model for the evolution of pyrolysis products in a fluidized bed has been developed. In this study the unsteady constitutive transport equations for inert gas flow and decomposition kinetics were modeled using the commercial computational fluid dynamics (CFD) software FLUENT-12. The model system d...

Design and Analysis of Turbomachinery for Space Applications

NASA Technical Reports Server (NTRS)

Dorney, D.; Garcia, Roberto (Technical Monitor)

2002-01-01

This presentation provides an overview of CORSAIR, a three dimensional computational fluid dynamics software code for the analysis of turbomachinery components available from NASA, and discusses its potential use in the design of these parts. Topics covered include: time-dependent equations of motion, grid topology, turbulence models, boundary conditions, parallel simulations and miscellaneous capabilities.

Future Computer Requirements for Computational Aerodynamics

NASA Technical Reports Server (NTRS)

1978-01-01

Recent advances in computational aerodynamics are discussed as well as motivations for and potential benefits of a National Aerodynamic Simulation Facility having the capability to solve fluid dynamic equations at speeds two to three orders of magnitude faster than presently possible with general computers. Two contracted efforts to define processor architectures for such a facility are summarized.

Tree Hydraulics: How Sap Rises

ERIC Educational Resources Information Center

Denny, Mark

2012-01-01

Trees transport water from roots to crown--a height that can exceed 100 m. The physics of tree hydraulics can be conveyed with simple fluid dynamics based upon the Hagen-Poiseuille equation and Murray's law. Here the conduit structure is modelled as conical pipes and as branching pipes. The force required to lift sap is generated mostly by…

Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes

NASA Astrophysics Data System (ADS)

Gnedin, Nickolay Y.; Semenov, Vadim A.; Kravtsov, Andrey V.

2018-04-01

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally constrained time steps. However, such a scheme can result in violation of the Courant-Friedrichs-Lewy (CFL) condition, which is manifestly non-local. Although the violations can be considered to be "weak" in a certain sense and the corresponding numerical solution may be stable, such calculation does not guarantee the correct propagation speed for arbitrary waves. We use an experimental fluid dynamics code that allows cubic "patches" of grid cells to step with independent, locally constrained time steps to demonstrate how the CFL condition can be enforced by imposing a constraint on the time steps of neighboring patches. We perform several numerical tests that illustrate errors introduced in the numerical solutions by weak CFL condition violations and show how strict enforcement of the CFL condition eliminates these errors. In all our tests the strict enforcement of the CFL condition does not impose a significant performance penalty.

Accuracy of the lattice Boltzmann method for describing the behavior of a gas in the continuum limit.

PubMed

Kataoka, Takeshi; Tsutahara, Michihisa

2010-11-01

The accuracy of the lattice Boltzmann method (LBM) for describing the behavior of a gas in the continuum limit is systematically investigated. The asymptotic analysis for small Knudsen numbers is carried out to derive the corresponding fluid-dynamics-type equations, and the errors of the LBM are estimated by comparing them with the correct fluid-dynamics-type equations. We discuss the following three important cases: (I) the Mach number of the flow is much smaller than the Knudsen number, (II) the Mach number is of the same order as the Knudsen number, and (III) the Mach number is finite. From the von Karman relation, the above three cases correspond to the flows of (I) small Reynolds number, (II) finite Reynolds number, and (III) large Reynolds number, respectively. The analysis is made with the information only of the fundamental properties of the lattice Boltzmann models without stepping into their detailed form. The results are therefore applicable to various lattice Boltzmann models that satisfy the fundamental properties used in the analysis.

Two- and three-dimensional natural and mixed convection simulation using modular zonal models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wurtz, E.; Nataf, J.M.; Winkelmann, F.

We demonstrate the use of the zonal model approach, which is a simplified method for calculating natural and mixed convection in rooms. Zonal models use a coarse grid and use balance equations, state equations, hydrostatic pressure drop equations and power law equations of the form {ital m} = {ital C}{Delta}{sup {ital n}}. The advantage of the zonal approach and its modular implementation are discussed. The zonal model resolution of nonlinear equation systems is demonstrated for three cases: a 2-D room, a 3-D room and a pair of 3-D rooms separated by a partition with an opening. A sensitivity analysis withmore » respect to physical parameters and grid coarseness is presented. Results are compared to computational fluid dynamics (CFD) calculations and experimental data.« less

Small data global solutions for the Camassa–Choi equations

NASA Astrophysics Data System (ADS)

Harrop-Griffiths, Benjamin; Marzuola, Jeremy L.

2018-05-01

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa–Choi (1996 J. Fluid Mech. 313 83–103). This model is a natural generalization of the Benjamin–Ono and intermediate long wave equations for weak transverse effects as in the case of the Kadomtsev–Petviashvili equations for the Korteweg-de Vries equation. For that reason they are often referred to as the KP-ILW or the KP–Benjamin–Ono equations regarding finite or infinite depth respectively. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on . The techniques applied here involve testing by wave packet techniques developed by Ifrim and Tataru in (2015 Nonlinearity 28 2661–75 2016 Bull. Soc. Math. France 144 369–94).

Stationary spiral flow in polytropic stellar models

PubMed Central

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

Lump Solutions for the (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Liu, De-Yin; Tian, Bo; Xie, Xi-Yang

2016-12-01

In this article, we investigate the lump solutions for the Kadomtsev-Petviashvili equation in (3+1) dimensions that describe the dynamics of plasmas or fluids. Via the symbolic computation, lump solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are derived based on the bilinear forms. The conditions to guarantee analyticity and rational localisation of the lump solutions are presented. The lump solutions contain eight parameters, two of which are totally free, and the other six of which need to satisfy the presented conditions. Plots with particular choices of the involved parameters are made to show the lump solutions and their energy distributions.

Modeling Solar Wind Flow with the Multi-Scale Fluid-Kinetic Simulation Suite

DOE PAGES

Pogorelov, N.V.; Borovikov, S. N.; Bedford, M. C.; ...

2013-04-01

Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) is a package of numerical codes capable of performing adaptive mesh refinement simulations of complex plasma flows in the presence of discontinuities and charge exchange between ions and neutral atoms. The flow of the ionized component is described with the ideal MHD equations, while the transport of atoms is governed either by the Boltzmann equation or multiple Euler gas dynamics equations. We have enhanced the code with additional physical treatments for the transport of turbulence and acceleration of pickup ions in the interplanetary space and at the termination shock. In this article, we present themore » results of our numerical simulation of the solar wind (SW) interaction with the local interstellar medium (LISM) in different time-dependent and stationary formulations. Numerical results are compared with the Ulysses, Voyager, and OMNI observations. Finally, the SW boundary conditions are derived from in-situ spacecraft measurements and remote observations.« less

Perturbation of Large Anti-deSitter Black Holes and AdS/CFT Correspondence

NASA Astrophysics Data System (ADS)

Ahmadzadegan, Aida

As the main goal of this thesis, the canonical form of the perturbation metric of anti-de Sitter black holes in four dimensions is derived by choosing the Regge-Wheeler gauge in the standard Schwarzschild coordinates (t, r, theta, ϕ). By assuming the perturbations to be small, the differential equations governing the perturbations are obtained from the equations deltaRmunu(h ) = 0. Then, by taking the limit of m > > R where R is the radius of AdS space, the perturbation metric and field equations of large AdS black holes are found. Finally, under the shadow of AdS/CFT correspondence, these perturbations can be compared to their corresponding three-dimensional theory of fluid dynamics on the dual space, R x S2. Furthermore, by using the definitions of stress-energy tensor and its perturbation, we can find energy density, pressure and shear viscosity which are the quantities we need to describe the behavior of the fluid on the boundary of the AdS space.

Non-invasive pressure difference estimation from PC-MRI using the work-energy equation

PubMed Central

Donati, Fabrizio; Figueroa, C. Alberto; Smith, Nicolas P.; Lamata, Pablo; Nordsletten, David A.

2015-01-01

Pressure difference is an accepted clinical biomarker for cardiovascular disease conditions such as aortic coarctation. Currently, measurements of pressure differences in the clinic rely on invasive techniques (catheterization), prompting development of non-invasive estimates based on blood flow. In this work, we propose a non-invasive estimation procedure deriving pressure difference from the work-energy equation for a Newtonian fluid. Spatial and temporal convergence is demonstrated on in silico Phase Contrast Magnetic Resonance Image (PC-MRI) phantoms with steady and transient flow fields. The method is also tested on an image dataset generated in silico from a 3D patient-specific Computational Fluid Dynamics (CFD) simulation and finally evaluated on a cohort of 9 subjects. The performance is compared to existing approaches based on steady and unsteady Bernoulli formulations as well as the pressure Poisson equation. The new technique shows good accuracy, robustness to noise, and robustness to the image segmentation process, illustrating the potential of this approach for non-invasive pressure difference estimation. PMID:26409245

Computational manipulation of a radiative MHD flow with Hall current and chemical reaction in the presence of rotating fluid

NASA Astrophysics Data System (ADS)

Alias Suba, Subbu; Muthucumaraswamy, R.

2018-04-01

A numerical analysis of transient radiative MHD(MagnetoHydroDynamic) natural convective flow of a viscous, incompressible, electrically conducting and rotating fluid along a semi-infinite isothermal vertical plate is carried out taking into consideration Hall current, rotation and first order chemical reaction.The coupled non-linear partial differential equations are expressed in difference form using implicit finite difference scheme. The difference equations are then reduced to a system of linear algebraic equations with a tri-diagonal structure which is solved by Thomas Algorithm. The primary and secondary velocity profiles, temperature profile, concentration profile, skin friction, Nusselt number and Sherwood Number are depicted graphically for a range of values of rotation parameter, Hall parameter,magnetic parameter, chemical reaction parameter, radiation parameter, Prandtl number and Schmidt number.It is recognized that rate of heat transfer and rate of mass transfer decrease with increase in time but they increase with increasing values of radiation parameter and Schmidt number respectively.

Control volume analyses of glottal flow using a fully-coupled numerical fluid-structure interaction model

NASA Astrophysics Data System (ADS)

Yang, Jubiao; Krane, Michael; Zhang, Lucy

2013-11-01

Vocal fold vibrations and the glottal jet are successfully simulated using the modified Immersed Finite Element method (mIFEM), a fully coupled dynamics approach to model fluid-structure interactions. A self-sustained and steady vocal fold vibration is captured given a constant pressure input at the glottal entrance. The flow rates at different axial locations in the glottis are calculated, showing small variations among them due to the vocal fold motion and deformation. To further facilitate the understanding of the phonation process, two control volume analyses, specifically with Bernoulli's equation and Newton's 2nd law, are carried out for the glottal flow based on the simulation results. A generalized Bernoulli's equation is derived to interpret the correlations between the velocity and pressure temporally and spatially along the center line which is a streamline using a half-space model with symmetry boundary condition. A specialized Newton's 2nd law equation is developed and divided into terms to help understand the driving mechanism of the glottal flow.

Navier-Stokes-Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

NASA Astrophysics Data System (ADS)

Di Plinio, Francesco; Giorgini, Andrea; Pata, Vittorino; Temam, Roger

2018-04-01

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. Unlike the classical Navier-Stokes-Voigt system, the energy balance involves the spatial gradient of the past history of the velocity rather than providing an instantaneous control on the high modes. In spite of this difficulty, we show that our system is dissipative in the dynamical systems sense and even possesses regular global and exponential attractors of finite fractal dimension. Such features of asymptotic well-posedness in absence of instantaneous high modes dissipation appear to be unique within the realm of dynamical systems arising from fluid models.

Fluid and particle transport of a hairy structure

NASA Astrophysics Data System (ADS)

Lee, Hongki; Lahooti, Mohsen; Kim, Daegyoum; Jung, Seyeong

2017-11-01

Hairy appendages of animals are used to capture particles, sense surrounding flow, and generate propulsive force. Due to the small size of the hairy structures, their hydrodynamics have been studied mostly in very low Reynolds number. In this work, in a broad range of Reynolds number, O(1) - O(100), flow structure and inertial particle dynamics around an array of two-dimensional cylinders are investigated numerically by using an immersed boundary method. Given flow fields, Maxey-Riley equation is adopted to examine particle dynamics. Here, we discuss the effects of Reynolds number, density ratio of inertial particles and fluid, and distance between cylinders on particle behaviors around a moving structure. In addition, drift volume of inertial particles is correlated with the model parameters.

van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

NASA Astrophysics Data System (ADS)

Wang, Xian-Zhi

2004-04-01

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.

Smoothed dissipative particle dynamics with angular momentum conservation

NASA Astrophysics Data System (ADS)

Müller, Kathrin; Fedosov, Dmitry A.; Gompper, Gerhard

2015-01-01

Smoothed dissipative particle dynamics (SDPD) combines two popular mesoscopic techniques, the smoothed particle hydrodynamics and dissipative particle dynamics (DPD) methods, and can be considered as an improved dissipative particle dynamics approach. Despite several advantages of the SDPD method over the conventional DPD model, the original formulation of SDPD by Español and Revenga (2003) [9], lacks angular momentum conservation, leading to unphysical results for problems where the conservation of angular momentum is essential. To overcome this limitation, we extend the SDPD method by introducing a particle spin variable such that local and global angular momentum conservation is restored. The new SDPD formulation (SDPD+a) is directly derived from the Navier-Stokes equation for fluids with spin, while thermal fluctuations are incorporated similarly to the DPD method. We test the new SDPD method and demonstrate that it properly reproduces fluid transport coefficients. Also, SDPD with angular momentum conservation is validated using two problems: (i) the Taylor-Couette flow with two immiscible fluids and (ii) a tank-treading vesicle in shear flow with a viscosity contrast between inner and outer fluids. For both problems, the new SDPD method leads to simulation predictions in agreement with the corresponding analytical theories, while the original SDPD method fails to capture properly physical characteristics of the systems due to violation of angular momentum conservation. In conclusion, the extended SDPD method with angular momentum conservation provides a new approach to tackle fluid problems such as multiphase flows and vesicle/cell suspensions, where the conservation of angular momentum is essential.

Time scales of relaxation dynamics during transient conditions in two-phase flow: RELAXATION DYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schlüter, Steffen; Berg, Steffen; Li, Tianyi

2017-06-01

The relaxation dynamics toward a hydrostatic equilibrium after a change in phase saturation in porous media is governed by fluid reconfiguration at the pore scale. Little is known whether a hydrostatic equilibrium in which all interfaces come to rest is ever reached and which microscopic processes govern the time scales of relaxation. Here we apply fast synchrotron-based X-ray tomography (X-ray CT) to measure the slow relaxation dynamics of fluid interfaces in a glass bead pack after fast drainage of the sample. The relaxation of interfaces triggers internal redistribution of fluids, reduces the surface energy stored in the fluid interfaces, andmore » relaxes the contact angle toward the equilibrium value while the fluid topology remains unchanged. The equilibration of capillary pressures occurs in two stages: (i) a quick relaxation within seconds in which most of the pressure drop that built up during drainage is dissipated, a process that is to fast to be captured with fast X-ray CT, and (ii) a slow relaxation with characteristic time scales of 1–4 h which manifests itself as a spontaneous imbibition process that is well described by the Washburn equation for capillary rise in porous media. The slow relaxation implies that a hydrostatic equilibrium is hardly ever attained in practice when conducting two-phase experiments in which a flux boundary condition is changed from flow to no-flow. Implications for experiments with pressure boundary conditions are discussed.« less

PREFACE: Special section on vortex rings Special section on vortex rings

NASA Astrophysics Data System (ADS)

Fukumoto, Yasuhide

2009-10-01

This special section of Fluid Dynamics Research includes five articles on vortex rings in both classical and quantum fluids. The leading scientists of the field describe the trends in and the state-of-the-art development of experiments, theories and numerical simulations of vortex rings. The year 2008 was the 150th anniversary of 'vortex motion' since Hermann von Helmholtz opened up this field. In 1858, Helmholtz published a paper in Crelle's Journal which put forward the concept of 'vorticity' and made the first analysis of vortex motion. Fluid mechanics before that was limited to irrotational motion. In the absence of vorticity, the motion of an incompressible homogeneous fluid is virtually equivalent to a rigid-body motion in the sense that the fluid motion is determined once the boundary configuration is specified. Helmholtz proved, among other things, that, without viscosity, a vortex line is frozen into the fluid. This Helmholtz's law immediately implies the preservation of knots and links of vortex lines and its implication is enormous. One of the major trends of fluid mechanics since the latter half of the 20th century is to clarify the topological meaning of Helmholtz's law and to exploit it to develop theoretical and numerical methods to find the solutions of the Euler equations and to develop experimental techniques to gain an insight into fluid motion. Vortex rings are prominent coherent structures in a variety of fluid motions from the microscopic scale, through human and mesoscale to astrophysical scales, and have attracted people's interest. The late professor Philip G Saffman (1981) emphasized the significance of studies on vortex rings. One particular motion exemplifies the whole range of problems of vortex motion and is also a commonly known phenomenon, namely the vortex ring or smoke ring. Vortex rings are easily produced by dropping drops of one liquid into another, or by puffing fluid out of a hole, or by exhaling smoke if one has the skill. Their formation is a problem of vortex sheet dynamics, the steady state is a problem of existence, their duration is a problem of stability, and if there are several we have the problem of vortex interactions. Helmholtz himself, in the same paper (1858), devoted a few pages to an analysis of the motion of a vortex ring, and made substantial contributions. Since then, theoretical, experimental and numerical treatments of vortex rings have been developing continuously, yet we encounter mysteries and novel phenomena, with which vortex rings find new applications in, say, bio-fluid mechanics. Recently vortex rings have enlarged their scope beyond classical fluids to encompass super-fluids and Bose-Einstein condensates. On the occasion of the 150th anniversary of Helmholtz's theory on a vortex ring, it is worthwhile to bring together, in one issue, the latest understandings of and open problems in vortex rings from various aspects. The topics in this issue include development of theories and experiments for motion of vortex rings and their interaction with other vortex rings, flows and boundaries, with application to vortex-ring manipulation for flow control, original experiments on collision of vortex rings with a porous boundary, a novel numerical technique to simulate three-dimensional motion of vortex rings and new theories of dynamics of quantum vortex rings governed by nonlinear Schrödinger equations. I hope that this special section gives a sketch, in some proportion, of the current frontier of the field and provides a means to tackle future problems. References Saffman P G 1981 Dynamics of vorticity J. Fluid Mech. 106 49-58 von Helmholtz H 1858 Über Integrale der hydrodynamischen Gleichungen welche den Wirbelbewegungen entsprechen J. Reine Angew. Math. 55 25-55 (Engl. transl.: Tait P G 1867 On the integrals of the hydrodynamical equations which express vortex-motion Phil. Mag. 33 (4) 485-512)

Turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow: A priori assessment of gradient-diffusion and similarity modeling

NASA Astrophysics Data System (ADS)

Schilling, Oleg; Mueschke, Nicholas J.

2017-12-01

Data from a 1152 ×760 ×1280 direct numerical simulation [N. J. Mueschke and O. Schilling, Phys. Fluids 21, 014106 (2009), 10.1063/1.3064120] of a Rayleigh-Taylor mixing layer modeled after a small-Atwood-number water-channel experiment is used to investigate the validity of gradient diffusion and similarity closures a priori. The budgets of the mean flow, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate transport equations across the mixing layer were previously analyzed [O. Schilling and N. J. Mueschke, Phys. Fluids 22, 105102 (2010), 10.1063/1.3484247] at different evolution times to identify the most important transport and mixing mechanisms. Here a methodology is introduced to systematically estimate model coefficients as a function of time in the closures of the dynamically significant terms in the transport equations by minimizing the L2 norm of the difference between the model and correlations constructed using the simulation data. It is shown that gradient-diffusion and similarity closures used for the turbulent kinetic energy K , turbulent kinetic energy dissipation rate ɛ , heavy-fluid mass fraction variance S , and heavy-fluid mass fraction variance dissipation rate χ equations capture the shape of the exact, unclosed profiles well over the nonlinear and turbulent evolution regimes. Using order-of-magnitude estimates [O. Schilling and N. J. Mueschke, Phys. Fluids 22, 105102 (2010), 10.1063/1.3484247] for the terms in the exact transport equations and their closure models, it is shown that several of the standard closures for the turbulent production and dissipation (destruction) must be modified to include Reynolds-number scalings appropriate for Rayleigh-Taylor flow at small to intermediate Reynolds numbers. The late-time, large Reynolds number coefficients are determined to be different from those used in shear flow applications and largely adopted in two-equation Reynolds-averaged Navier-Stokes (RANS) models of Rayleigh-Taylor turbulent mixing. In addition, it is shown that the predictions of the Boussinesq model for the Reynolds stress agree better with the data when additional buoyancy-related terms are included. It is shown that an unsteady RANS paradigm is needed to predict the transitional flow dynamics from early evolution times, analogous to the small Reynolds number modifications in RANS models of wall-bounded flows in which the production-to-dissipation ratio is far from equilibrium. Although the present study is specific to one particular flow and one set of initial conditions, the methodology could be applied to calibrations of other Rayleigh-Taylor flows with different initial conditions (which may give different results during the early-time, transitional flow stages, and perhaps asymptotic stage). The implications of these findings for developing high-fidelity eddy viscosity-based turbulent transport and mixing models of Rayleigh-Taylor turbulence are discussed.

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

NASA Astrophysics Data System (ADS)

Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar

2018-05-01

Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.

Self-Assembled Magnetic Surface Swimmers: Theoretical Model

NASA Astrophysics Data System (ADS)

Aranson, Igor; Belkin, Maxim; Snezhko, Alexey

2009-03-01

The mechanisms of self-propulsion of living microorganisms are a fascinating phenomenon attracting enormous attention in the physics community. A new type of self-assembled micro-swimmers, magnetic snakes, is an excellent tool to model locomotion in a simple table-top experiment. The snakes self-assemble from a dispersion of magnetic microparticles suspended on the liquid-air interface and subjected to an alternating magnetic field. Formation and dynamics of these swimmers are captured in the framework of theoretical model coupling paradigm equation for the amplitude of surface waves, conservation law for the density of particles, and the Navier-Stokes equation for hydrodynamic flows. The results of continuum modeling are supported by hybrid molecular dynamics simulations of magnetic particles floating on the surface of fluid.

A loosely-coupled scheme for the interaction between a fluid, elastic structure and poroelastic material

NASA Astrophysics Data System (ADS)

Bukač, M.

2016-05-01

We model the interaction between an incompressible, viscous fluid, thin elastic structure and a poroelastic material. The poroelastic material is modeled using the Biot's equations of dynamic poroelasticity. The fluid, elastic structure and the poroelastic material are fully coupled, giving rise to a nonlinear, moving boundary problem with novel energy estimates. We present a modular, loosely coupled scheme where the original problem is split into the fluid sub-problem, elastic structure sub-problem and poroelasticity sub-problem. An energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters, β, is equal to zero. We present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow. Our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid-structure interaction only.