Global Well-Posedness for the Heat-conductive Incompressible Viscous Fluids
NASA Astrophysics Data System (ADS)
Ye, Xia; Zhu, Mingxuan
2016-09-01
This paper is concerned with the Cauchy problem derived from the non-stationary motion of heat-conducting incompressible viscous fluids in three-dimensional whole space, where the viscosity and heat-conductivity coefficient vary with the temperature. We establish blow-up criteria and existence of global strong solution provided that the initial data is small enough.
Incompressible Viscous Fluid Dynamics
1992-02-13
NACHOS2 is a finite element program designed for the analysis of two-dimensional, incompressible viscous fluid flow problems. The basic flows considered may be isothermal, nonisothermal, or may involve other physical processes, such as mass transport. Both steady and transient flows may be analyzed. The class of problems treated are those described by the two-dimensional (plane or axisymmetric) incompressible form of the Navier-Stokes equations. An energy transport equation is included in the formulation for problems inmore » which heat transfer effects are important. Two auxiliary transport equations can be added to describe other physical processes,e.g. mass transfer, chemical reactions. Among the specific types of flow problems treated are: isothermal flow; forced, free, or mixed convection; conjugate heat transfer; flow in saturated porous media with or without heat transfer; and inelastic, non-Newtonian flows with or without heat transfer. Other problem classes are possible depending on the specific definitions applied to the auxiliary transport equations.« less
Interfacial gauge methods for incompressible fluid dynamics.
Saye, Robert
2016-06-01
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
Interfacial gauge methods for incompressible fluid dynamics
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
The Hamiltonian description of incompressible fluid ellipsoids
Morrison, P.J. Lebovitz, Norman R.; Biello, Joseph A.
2009-08-15
We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler's equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie-Poisson form.
NACHOS2. Incompressible Viscous Fluid Dynamics
Gartling, D.K.
1992-02-21
NACHOS2 is a finite element program designed for the analysis of two-dimensional, incompressible viscous fluid flow problems. The basic flows considered may be isothermal, nonisothermal, or may involve other physical processes, such as mass transport. Both steady and transient flows may be analyzed. The class of problems treated are those described by the two-dimensional (plane or axisymmetric) incompressible form of the Navier-Stokes equations. An energy transport equation is included in the formulation for problems in which heat transfer effects are important. Two auxiliary transport equations can be added to describe other physical processes,e.g. mass transfer, chemical reactions. Among the specific types of flow problems treated are: isothermal flow; forced, free, or mixed convection; conjugate heat transfer; flow in saturated porous media with or without heat transfer; and inelastic, non-Newtonian flows with or without heat transfer. Other problem classes are possible depending on the specific definitions applied to the auxiliary transport equations.
Triangular spectral elements for incompressible fluid flow
NASA Technical Reports Server (NTRS)
Mavriplis, C.; Vanrosendale, John
1993-01-01
We discuss the use of triangular elements in the spectral element method for direct simulation of incompressible flow. Triangles provide much greater geometric flexibility than quadrilateral elements and are better conditioned and more accurate when small angles arise. We employ a family of tensor product algorithms for triangles, allowing triangular elements to be handled with comparable arithmetic complexity to quadrilateral elements. The triangular discretizations are applied and validated on the Poisson equation. These discretizations are then applied to the incompressible Navier-Stokes equations and a laminar channel flow solution is given. These new triangular spectral elements can be combined with standard quadrilateral elements, yielding a general and flexible high order method for complex geometries in two dimensions.
Calculation of incompressible fluid flow through cambered blades
NASA Technical Reports Server (NTRS)
Hsu, C. C.
1970-01-01
Conformal mapping technique yields linear, approximate solutions for calculating flow of an incompressible fluid through staggered array of cambered blades for the cases of flow with partial cavitation and supercavitation. Lift and drag coefficients, cavitation number, cavity shape, and exit flow conditions can be determined.
Stability of axisymmetric swirl flows of viscous incompressible fluid
NASA Astrophysics Data System (ADS)
Aktershev, S. P.; Kuibin, P. A.
2013-09-01
A new method of solution to the problem of stability of the swirl flow of viscous incompressible fluid is developed. The method based on expansion of the required function into power series of radial coordinate allows an avoidance of difficulties related to numerical integration of the system of differential equations with a singular point. Stability of the Poiseuille flow in a rotating pipe is considered as an example.
Local mesh refinement for incompressible fluid flow with free surfaces
Terasaka, H.; Kajiwara, H.; Ogura, K.
1995-09-01
A new local mesh refinement (LMR) technique has been developed and applied to incompressible fluid flows with free surface boundaries. The LMR method embeds patches of fine grid in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. This method is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By using this technique, one can place finer grids only near the surfaces, and therefore greatly reduce the total number of cells and computational costs. This paper introduces LMR3D, a three-dimensional incompressible flow analysis code. Numerical examples calculated with the code demonstrate well the advantages of the LMR method.
AN INCOMPRESSIBLE ALE METHOD FOR FLUID-STRUCTURE INTERACTION
Dunn, T A
2004-12-01
Multi-disciplinary analysis is becoming more and more important to tackle todays complex engineering problems. Therefore, computational tools must be able to handle the complex multi-physics requirements of these problems. A computer code may need to handle the physics associated with fluid dynamics, structural mechanics, heat transfer, chemistry, electro-magnetics, or a variety of other disciplines--all coupled in a highly non-linear system. The objective of this project was to couple an incompressible fluid dynamics package to a solid mechanics code. The code uses finite-element methods and is useful for three-dimensional transient problems with fluid-structure interaction. The code is designed for efficient performance on large multi-processor machines. An ALE finite element method was developed to investigate fluid-structure interaction. The write-up contains information about the method, the problem formulation, and some results from example test problems.
Experimental realization of an incompressible Newtonian fluid in two dimensions.
Qi, Zhiyuan; Park, Cheol Soo; Glaser, Matthew A; Maclennan, Joseph E; Clark, Noel A
2016-01-01
The Brownian diffusion of micron-scale inclusions in freely suspended smectic-A liquid crystal films a few nanometers thick and several millimeters in diameter depends strongly on the air surrounding the film. Near atmospheric pressure, the three-dimensionally coupled film-gas system is well described by Hughes-Pailthorpe-White hydrodynamic theory but at lower pressure (p≲70 torr), the diffusion coefficient increases substantially, tending in high vacuum toward the two-dimensional limit where it is determined by film size. In the absence of air, the films are found to be a nearly ideal physical realization of a two-dimensional, incompressible Newtonian fluid.
Magnetic reconnection in incompressible fluids. [of solar atmosphere and interior
NASA Technical Reports Server (NTRS)
Deluca, Edward E.; Craig, Ian J.
1992-01-01
The paper investigates the dynamical relaxation of a disturbed X-type magnetic neutral point in a periodic geometry, with an ignorable coordinate, for an incompressible fluid. It is found that the properties of the current sheet cannot be understood in terms of steady state reconnection theory or more recent linear dynamical solutions. Accordingly, a new scaling law for magnetic reconnection is presented, consistent with fast energy dissipation (i.e., the dissipation rate at current maximum is approximately independent of magnetic diffusivity (eta)). The flux annihilation rate, however, scales at eta exp 1/4, faster than the Sweet-Parker rate of sq rt eta but asymptotically much slower than the dissipation rate. These results suggest a flux pile-up regime in which the bulk of the free magnetic energy is released as heat rather than as kinetic energy of mass motion. The implications of our results for reconnection in the solar atmosphere and interior are discussed.
Global Regularity for Several Incompressible Fluid Models with Partial Dissipation
NASA Astrophysics Data System (ADS)
Wu, Jiahong; Xu, Xiaojing; Ye, Zhuan
2016-09-01
This paper examines the global regularity problem on several 2D incompressible fluid models with partial dissipation. They are the surface quasi-geostrophic (SQG) equation, the 2D Euler equation and the 2D Boussinesq equations. These are well-known models in fluid mechanics and geophysics. The fundamental issue of whether or not they are globally well-posed has attracted enormous attention. The corresponding models with partial dissipation may arise in physical circumstances when the dissipation varies in different directions. We show that the SQG equation with either horizontal or vertical dissipation always has global solutions. This is in sharp contrast with the inviscid SQG equation for which the global regularity problem remains outstandingly open. Although the 2D Euler is globally well-posed for sufficiently smooth data, the associated equations with partial dissipation no longer conserve the vorticity and the global regularity is not trivial. We are able to prove the global regularity for two partially dissipated Euler equations. Several global bounds are also obtained for a partially dissipated Boussinesq system.
Instantaneous Point Explosion in Incompressible Fluid-like Media
NASA Astrophysics Data System (ADS)
Grinfeld, Michael; Segletes, Steven
The problem of point explosion is one of the most famous and extensively developed in in the sense of corresponding physics, mechanics, and applied mathematics. There are many reasons for that based on its practical importance and theoretical beauty. We refer interested readers to the publications of Sedov, Taylor, Laudau and Lifshitz, and Lavrent'ev and Shabat. In the paper, we discuss this classical program from the standpoint of terminal ballistics and present our novel results relating to the special situation when the media can be treated as an ``effective'' incompressible liquid. Sedov, L.I., Similarity and Dimensional Methods in Mechanics, CRC Press, 1993. Taylor, J., Explosion. II. The Atomic Explosion of 1945. Proc. Roy. Soc. London, A201, ¹ 1065, 1950, p. 175. Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, Pergamon Press, 1959. Zeldovich Ya. B. and Raizer, Yu.P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena,Dover, New York, 2002. Lavrent'ev, M.A. and Shabat, B.V., Hydrodynamic Phenomena and Their Mathematical Models. Hauka, 1973 (in Russian).
An upwind nodal integral method for incompressible fluid flow
Esser, P.D. ); Witt, R.J. )
1993-05-01
An upwind nodal solution method is developed for the steady, two-dimensional flow of an incompressible fluid. The formulation is based on the nodal integral method, which uses transverse integrations, analytical solutions of the one-dimensional averaged equations, and node-averaged uniqueness constraints to derive the discretized nodal equations. The derivation introduces an exponential upwind bias by retaining the streamwise convection term in the homogeneous part of the transverse-integrated convection-diffusion equation. The method is adapted to the stream function-vorticity form of the Navier-Stokes equations, which are solved over a nonstaggered nodal mesh. A special nodal scheme is used for the Poisson stream function equation to properly account for the exponentially varying vorticity source. Rigorous expressions for the velocity components and the no-slip vorticity boundary condition are derived from the stream function formulation. The method is validated with several benchmark problems. An idealized purely convective flow of a scalar step function indicates that the nodal approximation errors are primarily dispersive, not dissipative, in nature. Results for idealized and actual recirculating driven-cavity flows reveal a significant reduction in false diffusion compared with conventional finite difference techniques.
MHD Couette flow of viscous incompressible fluid with Hall current and suction
NASA Astrophysics Data System (ADS)
Parvin, Afroja; Dola, Tanni Alam; Alam, Md. Mahmud
2016-07-01
An electrically conducting viscous incompressible fluid bounded by two parallel non-conducting plates has been investigated in the presence of Hall current. The fluid motion is uniform at the upper plate and the uniform magnetic field is applied perpendicular to the plate. The lower plate is stationary while upper plate moves with a constant velocity. The governing equations have been non-dimensionalzed by using usual transformations. The obtained governing non-linear coupled partial differential equations have been solved by using implicit finite difference technique. The numerical solutions are obtained for momentum and energy equations. The influence of various interesting parameters on the flow has been analyzed and discussed through graph in details. The values of Nusselt number and Skin-Friction for different physical parameters are also elucidated in the form of graph.
Nearly incompressible fluids: hydrodynamics and large scale inhomogeneity.
Hunana, P; Zank, G P; Shaikh, D
2006-08-01
A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as "nearly incompressible hydrodynamics," is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term "locally incompressible" to describe the equations. This term should be distinguished from the term "nearly incompressible," which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly
Experiments on the Richtmyer-Meshkov Instability of Incompressible Fluids
NASA Technical Reports Server (NTRS)
Jacobs, J.; Niederhaus, C.
2000-01-01
Richtmyer-Meshkov (R-M) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and possibly become turbulent given the proper initial conditions. R-M instability is similar to the Rayleigh-Taylor (R-T) instability, which is generated when the two fluids undergo a constant acceleration. R-M instability is a fundamental fluid instability that is important to fields ranging from astrophysics to high-speed combustion. For example, R-M instability is currently the limiting factor in achieving a net positive yield with inertial confinement fusion. The experiments described here utilize a novel technique that circumvents many of the experimental difficulties previously limiting the study of the R-M instability. A Plexiglas tank contains two unequal density liquids and is gently oscillated horizontally to produce a controlled initial fluid interface shape. The tank is mounted to a sled on a high speed, low friction linear rail system, constraining the main motion to the vertical direction. The sled is released from an initial height and falls vertically until it bounces off of a movable spring, imparting an impulsive acceleration in the upward direction. As the sled travels up and down the rails, the spring retracts out of the way, allowing the instability to evolve in free-fall until impacting a shock absorber at the end of the rails. The impulsive acceleration provided to the system is measured by a piezoelectric accelerometer mounted on the tank, and a capacitive accelerometer measures the low-level drag of the bearings. Planar Laser-Induced Fluorescence is used for flow visualization, which uses an Argon ion laser to illuminate the flow and a CCD camera, mounted to the sled, to capture images of the interface. This experimental study investigates the instability of an interface between incompressible, miscible liquids
NASA Technical Reports Server (NTRS)
Krolik, J. H.
1977-01-01
The paper examines the behavior of linear perturbations in an incompressible fluid undergoing acceleration by radiation pressure, with reference to processes occurring in quasars, supernovae, and planetary nebulae. It is shown that, contrary to prior expectation, fluids accelerated by radiation pressure, are not always unstable to Rayleigh-Taylor modes. Some are, in fact, unstable, but the nature of the instability is qualitatively different.
Incompressible Limit for Compressible Fluids with Stochastic Forcing
NASA Astrophysics Data System (ADS)
Breit, Dominic; Feireisl, Eduard; Hofmanová, Martina
2016-11-01
We study the asymptotic behavior of the isentropic Navier-Stokes system driven by a multiplicative stochastic forcing in the compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of a weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic incompressible Navier-Stokes system is identified as the limit problem.
NASA Astrophysics Data System (ADS)
Zhu, Minjie; Scott, Michael H.
2016-07-01
Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.
The incompressible Rindler fluid versus the Schwarzschild-AdS fluid
NASA Astrophysics Data System (ADS)
Matsuo, Yoshinori; Natsuume, Makoto; Ohta, Masahiro; Okamura, Takashi
2013-02-01
We study the proposal by Bredberg et al. [J. High Energy Phys. 1103, 141 (2011)], where the fluid is defined by the Brown-York tensor on a timelike surface at r = rc in black hole backgrounds. We consider both Rindler space and the Schwarzschild-AdS (SAdS) black hole. The former describes an incompressible fluid, whereas the latter describes the vanishing bulk viscosity at arbitrary rc. Although the near-horizon limit of the SAdS black hole is Rindler space, these two results do not contradict each other. We also find an interesting "coincidence" with the black hole membrane paradigm that gives a negative bulk viscosity. In order to show these results, we rewrite the hydrodynamic stress tensor via metric perturbations using the conservation equation. The resulting expressions are suitable to compare with the Brown-York tensor.
A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems
NASA Astrophysics Data System (ADS)
Geissert, Matthias; Hieber, Matthias; Nguyen, Thieu Huy
2016-06-01
This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier-Stokes-Oseen flow, the Navier-Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein-Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.
Pesch, L. Vegt, J.J.W. van der
2008-05-10
Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The well-defined incompressible limit relies on using pressure primitive or entropy variables. In particular entropy variables can provide numerical methods with attractive properties, e.g. fulfillment of the second law of thermodynamics. We show how a discontinuous Galerkin finite element discretization previously used for compressible flow with an ideal gas equation of state can be extended for general fluids. We also examine which components of the numerical method have to be changed or adapted. Especially, we investigate different possibilities of solving the nonlinear algebraic system with a pseudo-time iteration. Numerical results highlight the applicability of the method for various fluids.
An Improved Lattice Kinetic Scheme for Incompressible Viscous Fluid Flows
NASA Astrophysics Data System (ADS)
Suzuki, Kosuke; Inamuro, Takaji
2014-01-01
The lattice Boltzmann method (LBM) is an explicit numerical scheme for the incompressible Navier-Stokes equations (INSE) without integrating the Poisson equation for the pressure. In spite of its merit, the LBM has some drawbacks in accuracy. First, we review drawbacks for three numerical methods based on the LBM. The three methods are the LBM with the Bhatnagar-Gross-Krook model (LBGK), the lattice kinetic scheme (LKS) and the link-wise artificial compressibility method (LWACM). Second, in order to remedy the drawbacks, we propose an improved LKS. The present method incorporates (i) the scheme used in the LWACM for determining the kinematic viscosity, (ii) an iterative calculation of the pressure and (iii) a semi-implicit algorithm, while preserving the simplicity of the algorithm of the original LKS. Finally, in simulations of test problems, we find that the improved LKS eliminates the drawbacks and gives more accurate and stable results than LBGK, LKS and LWACM.
Grigoryan, L.S.
1985-03-01
Models of superdense incompressible-fluid stellar configurations are calculated under the assumption that a special gravitational vacuum exists. In the case of superdense celestial bodies, vacuum effects are important. The most important result is the conclusion that equilibrium superdense celestial bodies with masses much greater than the Sun's can exist.
ERIC Educational Resources Information Center
Vollmer, Michael; Mollmann, Klaus-Peter
2012-01-01
We present fascinating simple demonstration experiments recorded with high-speed cameras in the field of fluid dynamics. Examples include oscillations of falling droplets, effects happening upon impact of a liquid droplet into a liquid, the disintegration of extremely large droplets in free fall and the consequences of incompressibility. (Contains…
Dynamics of the two-dimensional ideal incompressible fluid and Casimirs
NASA Astrophysics Data System (ADS)
Dymnikov, V. P.
2016-07-01
Problems are considered in which the role of Casimirs in forming dynamics of the two-dimensional ideal incompressible fluid is basically studied; in particular, the conditions are formulated which arise in the stability problem of two-dimensional flows in the presence of Casimirs. Some general approaches to the construction of difference schemes for solving equations of two-dimensional fluid which possess the given Casimirs are considered.
Laminar motion of the incompressible fluids in self-acting thrust bearings with spiral grooves.
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
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
NASA Astrophysics Data System (ADS)
Imai, Yohsuke; Aoki, Takayuki; Takizawa, Kenji
2008-02-01
The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.
Direct pore-level modeling of incompressible fluid flow in porous media
Ovaysi, Saeed; Piri, Mohammad
2010-09-20
We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier-Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid-solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 {mu}m resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.
Multi-material incompressible flow simulation using the moment-of-fluid method
Garimella, R V; Schofield, S P; Lowrie, R B; Swartz, B K; Christon, M A; Dyadechko, V
2009-01-01
The Moment-of-Fluid interface reconstruction technique is implemented in a second order accurate, unstructured finite element variable density incompressible Navier-Stokes solver. For flows with multiple materials, MOF significantly outperforms existing first and second order interface reconstruction techniques. For two material flows, the performance of MOF is similar to other interface reconstruction techniques. For strongly driven bouyant flows, the errors in the flow solution dominate and all the interface reconstruction techniques perform similarly.
A p-version finite element method for steady incompressible fluid flow and convective heat transfer
NASA Technical Reports Server (NTRS)
Winterscheidt, Daniel L.
1993-01-01
A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.
Optimum step design for centering of pistons moving in an incompressible fluid
NASA Technical Reports Server (NTRS)
Etsion, I.; Hamrock, B. J.
1976-01-01
Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Hydrostatic effects are analyzed and a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water-filled tube are presented.
Incompressible two-phase flows with an inextensible Newtonian fluid interface
NASA Astrophysics Data System (ADS)
Reuther, Sebastian; Voigt, Axel
2016-10-01
We introduce a diffuse interface approximation for an incompressible two-phase flow problem with an inextensible Newtonian fluid interface. This approach allows to model lipid membranes as viscous fluids. In the present setting the membranes are assumed to be stationary. We validate the model and the numerical approach, which is based on a stream function formulation for the surface flow problem, an operator splitting approach and a semi-implicit adaptive finite element discretization, against observed flow patterns in vesicles, which are adhered to a solid surface and are subjected to shear flow. The influence of the Gaussian curvature on the surface flow pattern is discussed.
The numerical calculation of the viscous incompressible fluid transfer between contacting surfaces
NASA Astrophysics Data System (ADS)
Varepo, L. G.; Panichkin, A. V.; Trapeznikova, O. V.
2016-04-01
The movement of the thin layer of the viscous incompressible fluid (VTF) between two cylinders is analysed. The numerical calculations results of VTF transfer from the engaged zone of two cylinders to porous substrates are presented. The VTF (ink) is moved along the rubberized top blanket of the first cylinder. The surface of the second cylinder contacts the substrate with some part of the VTF layer transferred from the first cylinder. The fluid is double bounded by the free surface. Images of cylinders boundary deformation and VTF flow areas are shown.
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
Incompressible SPH Model for Simulating Violent Free-Surface Fluid Flows
NASA Astrophysics Data System (ADS)
Staroszczyk, Ryszard
2014-06-01
In this paper the problem of transient gravitational wave propagation in a viscous incompressible fluid is considered, with a focus on flows with fast-moving free surfaces. The governing equations of the problem are solved by the smoothed particle hydrodynamics method (SPH). In order to impose the incompressibility constraint on the fluid motion, the so-called projection method is applied in which the discrete SPH equations are integrated in time by using a fractional-step technique. Numerical performance of the proposed model has been assessed by comparing its results with experimental data and with results obtained by a standard (weakly compressible) version of the SPH approach. For this purpose, a plane dam-break flow problem is simulated, in order to investigate the formation and propagation of a wave generated by a sudden collapse of a water column initially contained in a rectangular tank, as well as the impact of such a wave on a rigid vertical wall. The results of simulations show the evolution of the free surface of water, the variation of velocity and pressure fields in the fluid, and the time history of pressures exerted by an impacting wave on a wall.
TEMPEST/N33.5. Computational Fluid Dynamics Package For Incompressible, 3D, Time Dependent Pro
Trent, Dr.D.S.; Eyler, Dr.L.L.
1991-04-01
TEMPESTN33.5 provides numerical solutions to general incompressible flow problems with coupled heat transfer in fluids and solids. Turbulence is created with a k-e model and gas, liquid or solid constituents may be included with the bulk flow. Problems may be modeled in Cartesian or cylindrical coordinates. Limitations include incompressible flow, Boussinesq approximation, and passive constituents. No direct steady state solution is available; steady state is obtained as the limit of a transient.
NASA Astrophysics Data System (ADS)
Yang, Kang; Guo, Zhaoli
2016-04-01
In this paper, a lattice Boltzmann equation (LBE) model is proposed for binary fluids based on a quasi-incompressible phase-field model [J. Shen et al., Commun. Comput. Phys. 13, 1045 (2013), 10.4208/cicp.300711.160212a]. Compared with the other incompressible LBE models based on the incompressible phase-field theory, the quasi-incompressible model conserves mass locally. A series of numerical simulations are performed to validate the proposed model, and comparisons with an incompressible LBE model [H. Liang et al., Phys. Rev. E 89, 053320 (2014), 10.1103/PhysRevE.89.053320] are also carried out. It is shown that the proposed model can track the interface accurately. As the stationary droplet and rising bubble problems, the quasi-incompressible LBE gives nearly the same predictions as the incompressible model, but the compressible effect in the present model plays a significant role in the phase separation problem. Therefore, in general cases the present mass-conserving model should be adopted.
User's manual for PELE3D: a computer code for three-dimensional incompressible fluid dynamics
McMaster, W H
1982-05-07
The PELE3D code is a three-dimensional semi-implicit Eulerian hydrodynamics computer program for the solution of incompressible fluid flow coupled to a structure. The fluid and coupling algorithms have been adapted from the previously developed two-dimensional code PELE-IC. The PELE3D code is written in both plane and cylindrical coordinates. The coupling algorithm is general enough to handle a variety of structural shapes. The free surface algorithm is able to accommodate a top surface and several independent bubbles. The code is in a developmental status since all the intended options have not been fully implemented and tested. Development of this code ended in 1980 upon termination of the contract with the Nuclear Regulatory Commission.
Swimming of a deformable slab in a viscous incompressible fluid with inertia.
Felderhof, B U
2015-12-01
The swimming of a deformable planar slab in a viscous incompressible fluid is studied on the basis of the Navier-Stokes equations. A continuum of plane wave displacements, symmetric on both sides of the slab and characterized by a polarization angle, allows optimization of the swimming efficiency with respect to polarization. The mean swimming velocity and mean rate of dissipation are calculated to second order in the amplitude of the stroke. The optimum efficiency depends on the ratio of viscosity and mass density of the fluid. For high viscosity a stroke is found with significantly higher efficiency than Taylor's solution for a waving sheet. For low viscosity the efficiency is optimal for a nearly irrotational flow pattern. PMID:26764811
NASA Astrophysics Data System (ADS)
Agrawal, H. L.; Nath, R.; Singh, R. P.
1987-01-01
An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (1) suction velocity normal to the plate is constant, (2) the second plate oscillates in time about a constant nonzero mean, (3) fluid is subjected to a constant heat source of absorption type. Approximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated.
Weak Dual Pairs and Jetlet Methods for Ideal Incompressible Fluid Models in n ≥ 2 Dimensions
NASA Astrophysics Data System (ADS)
Cotter, C. J.; Eldering, J.; Holm, D. D.; Jacobs, H. O.; Meier, D. M.
2016-07-01
We review the role of dual pairs in mechanics and use them to derive particle-like solutions to regularized incompressible fluid systems. In our case we have a dual pair resulting from the action of diffeomorphisms on point particles (essentially by moving the points). We then augment our dual pair by considering the action of diffeomorphisms on Taylor series, also known as jets. The augmented weak dual pairs induce a hierarchy of particle-like solutions and conservation laws with particles carrying a copy of a jet group. We call these augmented particles jetlets. The jet groups serve as finite-dimensional models of the diffeomorphism group itself, and so the jetlet particles serve as a finite-dimensional model of the self-similarity exhibited by ideal incompressible fluids. The conservation law associated to jetlet solutions is shown to be a shadow of Kelvin's circulation theorem. Finally, we study the dynamics of infinite time particle mergers. We prove that two merging particles at the zeroth level in the hierarchy yield dynamics which asymptotically approach that of a single particle in the first level in the hierarchy. This merging behavior is then verified numerically as well as the exchange of angular momentum which must occur during a near collision of two particles. The resulting particle-like solutions suggest a new class of meshless methods which work in dimensions n ≥ 2 and which exhibit a shadow of Kelvin's circulation theorem. More broadly, this provides one of the first finite-dimensional models of self-similarity in ideal fluids.
NASA Technical Reports Server (NTRS)
Mhuiris, N. M. G.
1986-01-01
For incompressible fluids the law of mass conservation reduces to a constraint on the velocity vector, namely that it be divergence free. This constraint has long been a source of great difficulty to the numericist seeking to discretize the Navier-Stokes and Euler equations. A spectral method is discussed which overcomes this difficulty. Its efficacy is demonstrated on some simple problems. The velocity is approximated by a finite sum of divergence free vectors, each of which satisfies the same boundary conditions as the velocity. Projecting the governing equation onto the space of inviscid vector fields eliminates the pressure term and produces a set of ordinary differential equations that must be solved for the coefficents in the velocity. The pressure can then be recovered if it is needed.
Gagliardi, J.C.
1987-01-01
The equations of motion for a viscous incompressible fluid in a rotating spherical annulus, subject to case study boundary conditions were developed. The specific boundary conditions studied were: (1) one or both spheres rotates with prescribed constant angular velocities, and (2) one sphere rotates under the action of an applied constant or impulsive torque. The solution of the stream and circumferential functions were obtained in the form of a series in powers of the Reynolds number. The number of independent variables in the perturbation equations were reduced (from three to two) by specifying the meridional dependence with Gegenbauer functions and then employing the concept of orthogonality. The zeroth-order perturbation solution for the resulting partial differential equation subject to nonhomogeneous boundary conditions were obtained by employing the Laplace Transform in conjunction with Cauchy's Residual Theorem. The higher-order perturbation solutions were obtained by applying the method of Separation of Variables. Results were obtained for a fifth-order solution.
An incompressible smoothed particle hydrodynamics method for the motion of rigid bodies in fluids
NASA Astrophysics Data System (ADS)
Tofighi, N.; Ozbulut, M.; Rahmat, A.; Feng, J. J.; Yildiz, M.
2015-09-01
A two-dimensional incompressible smoothed particle hydrodynamics scheme is presented for simulation of rigid bodies moving through Newtonian fluids. The scheme relies on combined usage of the rigidity constraints and the viscous penalty method to simulate rigid body motion. Different viscosity ratios and interpolation schemes are tested by simulating a rigid disc descending in quiescent medium. A viscosity ratio of 100 coupled with weighted harmonic averaging scheme has been found to provide satisfactory results. The performance of the resulting scheme is systematically tested for cases with linear motion, rotational motion and their combination. The test cases include sedimentation of a single and a pair of circular discs, sedimentation of an elliptic disc and migration and rotation of a circular disc in linear shear flow. Comparison with previous results at various Reynolds numbers indicates that the proposed method captures the motion of rigid bodies driven by flow or external body forces accurately.
Inexact Uzawa conjugate gradient method for the Stokes problem for incompressible fluid
NASA Astrophysics Data System (ADS)
Dementyeva, E.; Karepova, E.; Kireev, I.
2016-10-01
In this paper, the two-dimensional Stokes equations are considered for a viscous incompressible fluid in a channel. To construct a discrete problem, the Taylor-Hood finite elements are used. The obtained system of linear algebraic equations is of the saddle point type and is solved by a modified inexact Uzawa conjugate gradient method. Usually the Uzawa methods are considered for velocity-pressure unknowns. In our version, the problem is formulated in terms of velocity-pressure deviations from the desired saddle point of the discrete problem. This allows one to improve considerably the numerical efficiency of the method. The convergence of the method is studied numerically as well as theoretically.
Velocity relaxation of an ellipsoid immersed in a viscous incompressible fluid
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2013-01-01
The motion of an ellipsoid in a viscous incompressible fluid, caused by a small time-dependent applied force, is studied on the basis of the linearized Navier-Stokes equations in terms of the frequency-dependence of the friction tensor. The asymptotic behavior of the hydrodynamic force at high frequency contains a term linear in frequency, with an added mass coefficient, and a term proportional to the square root of frequency, with a Basset coefficient. The latter is calculated from an expression derived by Batchelor [An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967)]. A simple approximate three-pole expression is proposed for the frequency-dependent admittance for each principal direction, embodying added mass, particle mass, the steady state friction coefficient, and the Basset coefficient. It is suggested that a remaining unknown coefficient in the expression be determined by experiment, computer simulation, or numerical solution of an integral equation derived by Pozrikidis ["A study of linearized oscillatory flow past particles by the boundary-integral method," J. Fluid Mech. 202, 17 (1989), 10.1017/S0022112089001084].
Williams, P.T.
1993-09-01
As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H{sup 1} Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.
Advanced computational techniques for incompressible/compressible fluid-structure interactions
NASA Astrophysics Data System (ADS)
Kumar, Vinod
2005-07-01
Fluid-Structure Interaction (FSI) problems are of great importance to many fields of engineering and pose tremendous challenges to numerical analyst. This thesis addresses some of the hurdles faced for both 2D and 3D real life time-dependent FSI problems with particular emphasis on parachute systems. The techniques developed here would help improve the design of parachutes and are of direct relevance to several other FSI problems. The fluid system is solved using the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation for the Navier-Stokes equations of incompressible and compressible flows. The structural dynamics solver is based on a total Lagrangian finite element formulation. Newton-Raphson method is employed to linearize the otherwise nonlinear system resulting from the fluid and structure formulations. The fluid and structural systems are solved in decoupled fashion at each nonlinear iteration. While rigorous coupling methods are desirable for FSI simulations, the decoupled solution techniques provide sufficient convergence in the time-dependent problems considered here. In this thesis, common problems in the FSI simulations of parachutes are discussed and possible remedies for a few of them are presented. Further, the effects of the porosity model on the aerodynamic forces of round parachutes are analyzed. Techniques for solving compressible FSI problems are also discussed. Subsequently, a better stabilization technique is proposed to efficiently capture and accurately predict the shocks in supersonic flows. The numerical examples simulated here require high performance computing. Therefore, numerical tools using distributed memory supercomputers with message passing interface (MPI) libraries were developed.
NASA Astrophysics Data System (ADS)
Dong, S.
2015-02-01
We present a family of physical formulations, and a numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N ⩾ 2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N - 1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicit fashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N - 1) strongly-coupled phase field equations for general order parameters into 2 (N - 1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir-de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases.
Dong, S.
2015-02-15
We present a family of physical formulations, and a numerical algorithm, based on a class of general order parameters for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids with given densities, dynamic viscosities, and pairwise surface tensions. The N-phase formulations stem from a phase field model we developed in a recent work based on the conservations of mass/momentum, and the second law of thermodynamics. The introduction of general order parameters leads to an extremely strongly-coupled system of (N−1) phase field equations. On the other hand, the general form enables one to compute the N-phase mixing energy density coefficients in an explicit fashion in terms of the pairwise surface tensions. We show that the increased complexity in the form of the phase field equations associated with general order parameters in actuality does not cause essential computational difficulties. Our numerical algorithm reformulates the (N−1) strongly-coupled phase field equations for general order parameters into 2(N−1) Helmholtz-type equations that are completely de-coupled from one another. This leads to a computational complexity comparable to that for the simplified phase field equations associated with certain special choice of the order parameters. We demonstrate the capabilities of the method developed herein using several test problems involving multiple fluid phases and large contrasts in densities and viscosities among the multitude of fluids. In particular, by comparing simulation results with the Langmuir–de Gennes theory of floating liquid lenses we show that the method using general order parameters produces physically accurate results for multiple fluid phases.
NASA Astrophysics Data System (ADS)
Prabhakar Reddy, B.
2016-02-01
In this paper, a numerical solution of mass transfer effects on an unsteady free convection flow of an incompressible electrically conducting viscous dissipative fluid past an infinite vertical porous plate under the influence of a uniform magnetic field considered normal to the plate has been obtained. The non-dimensional governing equations for this investigation are solved numerically by using the Ritz finite element method. The effects of flow parameters on the velocity, temperature and concentration fields are presented through the graphs and numerical data for the skin-friction, Nusselt and Sherwood numbers are presented in tables and then discussed.
Axial Couette Flow of AN Electrically Conducting Fluid in AN Annulus
NASA Astrophysics Data System (ADS)
Hayat, T.; Momoniat, E.; Mahomed, F. M.
The unsteady flow in an annulus due to a velocity applied to one of the boundaries is addressed. The fluid considered is non-Newtonian, incompressible and electrically conducting. The strength of the applied magnetic field is time-dependent. Both analytical and numerical approaches are presented and compared. The nonlinear effects on the velocity profile are shown.
NASA Astrophysics Data System (ADS)
Mahulikar, S. P.; Herwig, H.
2008-03-01
The Reynolds' analogy between the Stanton number (St) and the skin friction coefficient (cf) is popularly believed to hold when St increases with increasing cf, for simple situations. In this investigation, the validity of Reynolds' analogy between St and cf for micro-convection of liquids with variations in fluid properties is re-examined. It is found that the Sieder-Tate's property-ratio method for obtaining Nusselt number corrections is theoretically based on the validity of Reynolds' analogy. The inverse dependence of Reynolds number and skin friction coefficient is the basis for validity of the Reynolds' analogy, in convective flows with fluid property variations. This leads to the unexpected outcome that Reynolds' analogy now results in St increasing with decreasing cf. These results and their analyses indicate that the validity of Reynolds' analogy is based on deeper foundations, and the well-known validity criterion is a special case.
NASA Astrophysics Data System (ADS)
Rivera, Christian A.; Heniche, Mourad; Glowinski, Roland; Tanguy, Philippe A.
2010-07-01
A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.
A GPU-accelerated flow solver for incompressible two-phase fluid flows
NASA Astrophysics Data System (ADS)
Codyer, Stephen; Raessi, Mehdi; Khanna, Gaurav
2011-11-01
We present a numerical solver for incompressible, immiscible, two-phase fluid flows that is accelerated by using Graphics Processing Units (GPUs). The Navier-Stokes equations are solved by the projection method, which involves solving a pressure Poisson problem at each time step. A second-order discretization of the Poisson problem leads to a sparse matrix with five and seven diagonals for two- and three-dimensional simulations, respectively. Running a serial linear algebra solver on a single CPU can take 50-99.9% of the total simulation time to solve the above system for pressure. To remove this bottleneck, we utilized the large parallelization capabilities of GPUs; we developed a linear algebra solver based on the conjugate gradient iterative method (CGIM) by using CUDA 4.0 libraries and compared its performance with CUSP, an open-source, GPU library for linear algebra. Compared to running the CGIM solver on a single CPU core, for a 2D case, our GPU solver yields speedups of up to 88x in solver time and 81x overall time on a single GPU card. In 3D cases, the speedups are up to 81x (solver) and 15x (overall). Speedup is faster at higher grid resolutions and our GPU solver outperforms CUSP. Current work examines the acceleration versus a parallel CGIM CPU solver.
NASA Technical Reports Server (NTRS)
Zahm, A. F.
1979-01-01
The pressure distribution and resistance found by theory and experiment for simple quadrics fixed in an infinite uniform stream of practically incompressible fluid are calculated. The experimental values pertain to air and some liquids, especially water; the theoretical refer sometimes to perfect, again to viscid fluids. Formulas for the velocity at all points of the flow field are given. Pressure and pressure drag are discussed for a sphere, a round cylinder, the elliptic cylinder, the prolate and oblate spheroid, and the circular disk. The velocity and pressure in an oblique flow are examined.
Cochran, R.J.
1992-01-01
A study of the finite element method applied to two-dimensional incompressible fluid flow analysis with heat transfer is performed using a mixed Galerkin finite element method with the primitive variable form of the model equations. Four biquadratic, quadrilateral elements are compared in this study--the serendipity biquadratic element with bilinear continuous pressure interpolation (Q2(8)-Q1) and the Lagrangian biquadratic element with bilinear continuous pressure interpolation (Q2-Q1) of the Taylor-Hood form. A modified form of the Q2-Q1 element is also studied. The pressure interpolation is augmented by a discontinuous constant shape function for pressure (Q2-Q1+). The discontinuous pressure element formulation makes use of biquadratic shape functions and a discontinuous linear interpolation of the pressure (Q2-P1(3)). Laminar flow solutions, with heat transfer, are compared to analytical and computational benchmarks for flat channel, backward-facing step and buoyancy driven flow in a square cavity. It is shown that the discontinuous pressure elements provide superior solution characteristics over the continuous pressure elements. Highly accurate heat transfer solutions are obtained and the Q2-P1(3) element is chosen for extension to turbulent flow simulations. Turbulent flow solutions are presented for both low turbulence Reynolds number and high Reynolds number formulations of two-equation turbulence models. The following three forms of the length scale transport equation are studied; the turbulence energy dissipation rate ([var epsilon]), the turbulence frequency ([omega]) and the turbulence time scale (tau). It is shown that the low turbulence Reynolds number model consisting of the K - [tau] transport equations, coupled with the damping functions of Shih and Hsu, provides an optimal combination of numerical stability and solution accuracy for the flat channel flow.
Thermal conductivity of nanoparticle-fluid mixture.
Wang, X.; Xu, X.; Choi, S. U.-S.; Energy Technology; Purdue Univ.
1999-10-01
Effective thermal conductivity of mixtures of fluids and nanometer-size particles is measured by a steady-state parallel-plate method. The tested fluids contain two types of nanoparticles, Al{sub 2}O{sub 3} and CuO, dispersed in water, vacuum pump fluid, engine oil, and ethylene glycol. Experimental results show that the thermal conductivities of nanoparticle-fluid mixtures are higher than those of the base fluids. Using theoretical models of effective thermal conductivity of a mixture, we have demonstrated that the predicted thermal conductivities of nanoparticle-fluid mixtures are much lower than our measured data, indicating the deficiency in the existing models when used for nanoparticle-fluid mixtures. Possible mechanisms contributing to enhancement of the thermal conductivity of the mixtures are discussed. A more comprehensive theory is needed to fully explain the behavior of nanoparticle-fluid mixtures.
NASA Astrophysics Data System (ADS)
Ovaysi, S.; Piri, M.
2009-12-01
We present a three-dimensional fully dynamic parallel particle-based model for direct pore-level simulation of incompressible viscous fluid flow in disordered porous media. The model was developed from scratch and is capable of simulating flow directly in three-dimensional high-resolution microtomography images of naturally occurring or man-made porous systems. It reads the images as input where the position of the solid walls are given. The entire medium, i.e., solid and fluid, is then discretized using particles. The model is based on Moving Particle Semi-implicit (MPS) technique. We modify this technique in order to improve its stability. The model handles highly irregular fluid-solid boundaries effectively. It takes into account viscous pressure drop in addition to the gravity forces. It conserves mass and can automatically detect any false connectivity with fluid particles in the neighboring pores and throats. It includes a sophisticated algorithm to automatically split and merge particles to maintain hydraulic connectivity of extremely narrow conduits. Furthermore, it uses novel methods to handle particle inconsistencies and open boundaries. To handle the computational load, we present a fully parallel version of the model that runs on distributed memory computer clusters and exhibits excellent scalability. The model is used to simulate unsteady-state flow problems under different conditions starting from straight noncircular capillary tubes with different cross-sectional shapes, i.e., circular/elliptical, square/rectangular and triangular cross-sections. We compare the predicted dimensionless hydraulic conductances with the data available in the literature and observe an excellent agreement. We then test the scalability of our parallel model with two samples of an artificial sandstone, samples A and B, with different volumes and different distributions (non-uniform and uniform) of solid particles among the processors. An excellent linear scalability is
NASA Astrophysics Data System (ADS)
Sohn, Jeong L.
1988-08-01
The purpose of the study is the evaluation of the numerical accuracy of FIDAP (Fluid Dynamics Analysis Package). Accordingly, four test problems in laminar and turbulent incompressible flows are selected and the computational results of these problems compared with other numerical solutions and/or experimental data. These problems include: (1) 2-D laminar flow inside a wall-driven cavity; (2) 2-D laminar flow over a backward-facing step; (3) 2-D turbulent flow over a backward-facing step; and (4) 2-D turbulent flow through a turn-around duct.
Hydrodynamic focusing of conducting fluids for conductivity-based biosensors.
Nasir, Mansoor; Ateya, Daniel A; Burk, Diana; Golden, Joel P; Ligler, Frances S
2010-02-15
Hydrodynamic focusing of a conducting fluid by a non-conducting fluid to form a constricted current path between two sensing electrodes is implemented in order to enhance the sensitivity of a 4-electrode conductance-based biosensor. The sensor has a simple two-inlet T-junction design and performs four-point conductivity measurements to detect particles immobilized between the sensing electrode pair. Computational simulations conducted in conjunction with experimental flow studies using confocal microscopy show that a flat profile for the focused layer is dependent on the Reynolds number for the chosen flow parameters. The results also indicate that a flat focused layer is desirable for both increased sensitivity as well as surface-binding efficiency. Proof of concept for conductance measurements in a hydrodynamically focused conducting fluid was demonstrated with entrapped magnetic beads. PMID:19932019
Abrous, A.; Emery, A.F.
1995-12-31
The steady-state, buoyancy-driven flow of an incompressible fluid with temperature dependent viscosity within a square enclosure is solved numerically and the results are presented. The benchmark problem`s geometrical and mathematical descriptions adopted herein are those specified by the AdHoc Committee of Computational Heat Transfer which is compiling different solutions for this benchmark problem in heat transfer analysis. The objective is to compare solutions computed with several different algorithmic approaches for a problem having a large variation in fluid viscosity, characteristic of modeling turbulent flows with eddy diffusivity concepts. The results of the present analysis are submitted as a contribution to this comparison exercise that has for objective the assessment of the numerical accuracy of modeling the diffusion terms in the conservation equations with variable property.
Enhancing thermal conductivity of fluids with nanoparticles
Choi, S.U.S.; Eastman, J.A.
1995-10-01
Low thermal conductivity is a primary limitation in the development of energy-efficient heat transfer fluids that are required in many industrial applications. In this paper we propose that an innovative new class of heat transfer fluids can be engineered by suspending metallic nanoparticles in conventional heat transfer fluids. The resulting {open_quotes}nanofluids{close_quotes} are expected to exhibit high thermal conductivities compared to those of currently used heat transfer fluids, and they represent the best hope for enhancement of heat transfer. The results of a theoretical study of the thermal conductivity of nanofluids with copper nanophase materials are presented, the potential benefits of the fluids are estimated, and it is shown that one of the benefits of nanofluids will be dramatic reductions in heat exchanger pumping power.
NASA Astrophysics Data System (ADS)
Hatanaka, K.; Hayashi, M.; Kawahara, M.
A novel FEM scheme that is based on the fractional-step method for solving time-dependent, incompressible viscous flow is presented and employed in the solution of a free-surface flow. The equations are given in indicial notation, as well as in the summation convention for repeated indices. The numerical results obtained exhibit good stability without the specification of Neumann conditions, and are compared in tabular form with the solutions given by Laitone's (1960) approximation. The method is also applicable to problems with artificial, open boundaries.
Felderhof, B U
2015-01-01
A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.
Felderhof, B U
2015-01-01
A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied. PMID:26651783
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2015-11-01
A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.
Baer, T.A.; Cairncross, R.A.; Rao, R.R.; Sackinger, P.A.; Schunk, P.R.
1999-01-29
To date, few researchers have solved three-dimensional free-surface problems with dynamic wetting lines. This paper extends the free-surface finite element method described in a companion paper [Cairncross, R.A., P.R. Schunk, T.A. Baer, P.A. Sackinger, R.R. Rao, "A finite element method for free surface flows of incompressible fluid in three dimensions, Part I: Boundary-Fitted mesh motion.", to be published (1998)] to handle dynamic wetting. A generalization of the technique used in two dimensional modeling to circumvent double-valued velocities at the wetting line, the so-called kinematic paradox, is presented for a wetting line in three dimensions. This approach requires the fluid velocity normal to the contact line to be zero, the fluid velocity tangent to the contact line to be equal to the tangential component of web velocity, and the fluid velocity into the web to be zero. In addition, slip is allowed in a narrow strip along the substrate surface near the dynamic contact line. For realistic wetting-line motion, a contact angle which varies with wetting speed is required because contact lines in three dimensions typically advance or recede a different rates depending upon location and/or have both advancing and receding portions. The theory is applied to capillary rise of static fluid in a corner, the initial motion of a Newtonian droplet down an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving substrate. The extrusion results are compared to experimental visualization. Subject Categories
Peristaltic Motion of an Incompressible Generalized Newtonian Fluid in a Planar Channel
NASA Astrophysics Data System (ADS)
Misery, A.; Elshehawey, Elsayed; Hakeem, A.
1996-11-01
Peristaltic flow in a two-dimensional channel with a sinusoidal wave is analyzed. Under the assumption of creeping motion, the problem is formulated using a perturbation expansion in terms of a variant of the Weissenberg number. To determine the characteristics of the peristaltic motion of shear thinning non-Newtonian fluids, the motion of a Carreau fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and neglecting wave number. We found the pumping rate of a Carreau fluid is less than that for a Newtonian having a shear viscosity the same as zero-shear-rate viscosity of the non-Newtonian fluid. The peristaltic pumping and the augmented pumping are discussed for various values of the physical parameters of interest.
NASA Astrophysics Data System (ADS)
Muha, Boris; Canić, Suncica
2013-03-01
We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid-structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916-6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk-Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.
NASA Astrophysics Data System (ADS)
Lalanne, Benjamin; Villegas, Lucia Rueda; Tanguy, Sébastien; Risso, Frédéric
2015-11-01
In this paper, we present a detailed analysis of the computation of the viscous terms for the simulation of incompressible two-phase flows in the framework of Level Set/Ghost Fluid Method when viscosity is discontinuous across the interface. Two pioneering papers on the topic, Kang et al. [10] and Sussman et al. [26], proposed two different approaches to deal with viscous terms. However, a definitive assessment of their respective efficiency is currently not available. In this paper, we demonstrate from theoretical arguments and confirm from numerical simulations that these two approaches are equivalent from a continuous point of view and we compare their accuracies in relevant test-cases. We also propose a new intermediate method which uses the properties of the two previous methods. This new method enables a simple implementation for an implicit temporal discretization of the viscous terms. In addition, the efficiency of the Delta Function method [24] is also assessed and compared to the three previous ones, which allow us to propose a general overview of the accuracy of all available methods. The selected test-cases involve configurations wherein viscosity plays a major role and for which either theoretical results or experimental data are available as reference solutions: simulations of spherical rising bubbles, shape-oscillating bubbles and deformed rising bubbles at low Reynolds numbers.
On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe
NASA Technical Reports Server (NTRS)
Shortis, Trudi A.; Hall, Philip
1995-01-01
The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.
Film Flow Dominated Simultaneous Flow of Two Viscous Incompressible Fluids Through a Porous Medium
NASA Astrophysics Data System (ADS)
Aursjø, Olav; Erpelding, Marion; Tallakstad, Ken; Flekkøy, Eirik; Hansen, Alex; Måløy, Knut Jørgen
2014-11-01
We present an experimental study of two-phase flow in a quasi-two-dimensional porous medium. The two phases, a water-glycerol solution and a commercial food grade rapeseed/canola oil, having an oil to water-glycerol viscosity ratio of 1.3, are injected simultaneously into a Hele-Shaw cell with a mono-layer of randomly distributed glass beads. The two liquids are injected into the model from alternating point inlets. Initially, the porous model is filled with the water-glycerol solution. We observe that after an initial transient state, an overall static cluster configuration is obtained. While the oil is found to create a connected system spanning cluster, a large part of the water-glycerol clusters left behind the initial invasion front is observed to remain immobile throughout the rest of the experiment. This could suggest that the water-glycerol flow-dynamics is largely dominated by film flow. The flow pathways are thus given through the dynamics of the initial invasion. This behavior is quite different from that observed in systems with large viscosity differences between the two fluids, and where compressibility plays an important part of the process.
NASA Astrophysics Data System (ADS)
Attia, H. A.; Abdeen, M. A. M.; Elbarawy, M. T. M. M.
2014-09-01
In this paper, a steady magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting Oldroyd 8-constant fluid through a circular pipe is examined with considering the ion slip effect. A constant pressure gradient in the axial direction and an external uniform magnetic field in the perpendicular direction are applied. A numerical solution is obtained for the governing nonlinear momentum equations by using finite differences. The effect of the ion slip, the non-Newtonian fluid characteristics, and the particle-phase viscosity on the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is reported.
Experimental Study of the Richtmyer-Meshkov Instability of Incompressible Fluids
NASA Technical Reports Server (NTRS)
Niederhaus, Charles; Jacobs, Jeffrey W.
2002-01-01
The Richtmyer-Meshkov instability of a low Atwood number, miscible, two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted to a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent freefall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined, sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, a(sub 0), for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a nondimensional time ka(sub 0)t = 0.7, where k is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations up until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to ka(sub 0)t = 3, while published nonlinear single-mode models provide good agreement up to ka(sub 0)t = 30. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed.
Flow rate measurement in aggressive conductive fluids
NASA Astrophysics Data System (ADS)
Dubovikova, Nataliia; Kolesnikov, Yuri; Karcher, Christian
2014-03-01
Two non-contact experimental methods of flow rate measurements for aggressive conductive liquids are described. The techniques are based on electromagnetic forces and Faraday's law: Lorentz force is induced inside moving conductive liquid under influence of variable magnetic field of permanent magnets. They are mounted along a liquid metal channel or (in case of the second method) inserted into rotated metal wheels. The force acts in the opposite of fluids' velocity direction and hence it is possible to measure reaction force of it that takes place according to Newton's law on magnetic field source - permanent magnets. And by knowing the force, which linearly depends on velocity, one can calculate mean flow rate of liquid. In addition experimental "dry" calibration and its results are described for one of the measurements' techniques.
McHugh, P.R.
1995-10-01
Fully coupled, Newton-Krylov algorithms are investigated for solving strongly coupled, nonlinear systems of partial differential equations arising in the field of computational fluid dynamics. Primitive variable forms of the steady incompressible and compressible Navier-Stokes and energy equations that describe the flow of a laminar Newtonian fluid in two-dimensions are specifically considered. Numerical solutions are obtained by first integrating over discrete finite volumes that compose the computational mesh. The resulting system of nonlinear algebraic equations are linearized using Newton`s method. Preconditioned Krylov subspace based iterative algorithms then solve these linear systems on each Newton iteration. Selected Krylov algorithms include the Arnoldi-based Generalized Minimal RESidual (GMRES) algorithm, and the Lanczos-based Conjugate Gradients Squared (CGS), Bi-CGSTAB, and Transpose-Free Quasi-Minimal Residual (TFQMR) algorithms. Both Incomplete Lower-Upper (ILU) factorization and domain-based additive and multiplicative Schwarz preconditioning strategies are studied. Numerical techniques such as mesh sequencing, adaptive damping, pseudo-transient relaxation, and parameter continuation are used to improve the solution efficiency, while algorithm implementation is simplified using a numerical Jacobian evaluation. The capabilities of standard Newton-Krylov algorithms are demonstrated via solutions to both incompressible and compressible flow problems. Incompressible flow problems include natural convection in an enclosed cavity, and mixed/forced convection past a backward facing step.
NASA Astrophysics Data System (ADS)
Attia, H. A.
2007-04-01
It has come to the attention of the Institute of Physics that this article should not have been submitted for publication owing to its plagiarism of an earlier paper (Hossain A, Hossain M A and Wilson M 2001 Unsteady flow of viscous incompressible fluid with temperature-dependent viscosity due to a rotating disc in presence of transverse magnetic field and heat transfer Int. J. Therm. Sci. 40 11-20). Therefore this article has been retracted by the Institute of Physics and by the author, Hazem Ali Attia.
Magnetic field effect on waves in a centrifuged layer of a rotating conducting viscous fluid
NASA Astrophysics Data System (ADS)
Klueva, N. V.; Sandalov, V. M.; Tkach, M. E.; Soldatov, I. N.
2015-05-01
This paper considers wave processes in a centrifuged layer of an incompressible viscous conducting fluid in an axial magnetic field in the cavity of a rapidly rotating infinite cylinder with insulating walls. Inertial modes (solutions of the linearized boundary-value problem of magnetohydrodynamics) are represented as a superposition of helical fields. Expressions for the vorticity parameters of the helical flows forming the inertial mode at a small Stewart number are given. Dispersion curves of inertial waves are constructed, and the influence of the magnetic field on the flow field is analyzed. The critical frequencies at which the lowest (surface) mode arises are determined. The spatial and temporal stability of the modes are investigated.
Interfacial phase transitions in conducting fluids.
Freyland, Werner
2008-02-21
We present a review, largely based on recent experimental work of our group, on phase transitions at interfaces of fluid metals, alloys and ionic liquids. After a brief analysis of possible experimental errors and limitations of surface sensitive methods, we first deal with first-order wetting transitions at the liquid/vapour and liquid/wall interface in systems such as Ga-based alloys, K-KCl melts, and fluid Hg. The following chapter refers to surface freezing or surface induced crystallization in different metal alloys. The respective surface phase diagrams are discussed in comparison with their bulk counterpart. In the last part we present very recent investigations of ionic liquid interfaces, including order-disorder transitions at the liquid/vapour interface and examples of two-dimensional phase transitions at the electrified ionic liquid/metal interface. Finally, a simple electrowetting experiment with an ionic liquid droplet under vacuum is described which gives new insight into the contact angle saturation problem. The article ends up with a few perspective remarks on open problems and potential impact of interfacial phenomena on applied research. PMID:18259631
NASA Technical Reports Server (NTRS)
Rossow, Vernon J
1958-01-01
The use of a magnetic field to control the motion of electrically conducting fluids is studied. The incompressible boundary-layer solutions are found for flow over a flat plate when the magnetic field is fixed relative to the plate or to the fluid. The equations are integrated numerically for the effect of the transverse magnetic field on the velocity and temperature profiles, and hence, the skin friction and rate of heat transfer. It is concluded that the skin friction and the heat-transfer rate are reduced when the transverse magnetic field is fixed relative to the plate and increased when fixed relative to the fluid. The total drag is increased in all of the areas.
Incompressible Flows Free Surfaces
1992-02-01
NASA-VOF3D is a three-dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slipmore » wall, continuative, periodic, and specified pressure outflow boundary.« less
NASA Astrophysics Data System (ADS)
Raju, T. Linga; Nagavalli, M.
2013-08-01
The unsteady magnetohydrodynamic flow of two immiscible fluids in a horizontal channel bounded by two parallel porous isothermal plates in the presence of an applied magnetic and electric field is investigated. The flow is driven by a constant uniform pressure gradient in the channel bounded by two parallel insulating plates, one being stationary and the other oscillating, when both fluids are considered as electrically conducting. Also, both fluids are assumed to be incompressible with variable properties, viz. different viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperatures. The governing equations are partial in nature, which are then reduced to the ordinary linear differential equations using two-term series. Closed form solutions for velocity and temperature distributions are obtained in both fluid regions of the channel. Profiles of these solutions are plotted to discuss the effect on the flow and heat transfer characteristics, and their dependence on the governing parameters involved, such as the Hartmann number, porous parameter, ratios of the viscosities, heights, electrical and thermal conductivities
System and method for determining velocity of electrically conductive fluid
NASA Technical Reports Server (NTRS)
Polzin, Kurt A. (Inventor); Korman, Valentin (Inventor); Markusic, Thomas E. (Inventor); Stanojev, Boris Johann (Inventor)
2008-01-01
A flowing electrically-conductive fluid is controlled between an upstream and downstream location thereof to insure that a convection timescale of the flowing fluid is less than a thermal diffusion timescale of the flowing fluid. First and second nodes of a current-carrying circuit are coupled to the fluid at the upstream location. A current pulse is applied to the current-carrying circuit so that the current pulse travels through the flowing fluid to thereby generate a thermal feature therein at the upstream location. The thermal feature is convected to the downstream location where it is monitored to detect a peak associated with the thermal feature so-convected. The velocity of the fluid flow is determined using a time-of-flight analysis.
Computational Challenges of Viscous Incompressible Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin; Kim, Chang Sung
2004-01-01
Over the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to the rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low-speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient CFD took become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews some of the successes made possible by advances in computational technologies during the same period, and discusses some of the current challenges faced in computing incompressible flows.
Hybrid fluid/kinetic model for parallel heat conduction
Callen, J.D.; Hegna, C.C.; Held, E.D.
1998-12-31
It is argued that in order to use fluid-like equations to model low frequency ({omega} < {nu}) phenomena such as neoclassical tearing modes in low collisionality ({nu} < {omega}{sub b}) tokamak plasmas, a Chapman-Enskog-like approach is most appropriate for developing an equation for the kinetic distortion (F) of the distribution function whose velocity-space moments lead to the needed fluid moment closure relations. Further, parallel heat conduction in a long collision mean free path regime can be described through a combination of a reduced phase space Chapman-Enskog-like approach for the kinetics and a multiple-time-scale analysis for the fluid and kinetic equations.
NASA Technical Reports Server (NTRS)
Childs, D. W.
1991-01-01
An algorithm is developed for calculating complex eigenvalues and eigenvectors associated with the fluid resonances and is used to analyze the perturbed flow in the leakage path between a shrouded-pump impeller and its housing. The eigenvalues obtained are consistent with the forced-response curves. First- and second-natural-frequency eigensolutions are presented for mode shapes corresponding to lateral excitations, and first-natural-frequency eigensolutions are presented for mode shapes corresponding to axial excitation.
Probe for measurements of density/conductivity in flows of conducting fluids
NASA Astrophysics Data System (ADS)
Fan, Xuejun; Brown, Garry L.
2006-04-01
A probe utilizing the bipolar pulse method to measure the density of a conducting fluid has been developed. The probe is specially designed such that the concentration of a stream tube can be sampled continuously. The density was determined indirectly from the measurement of solution conductivity. The probe was calibrated using standard NaCl solutions of varying molarity and was able to rapidly determine the density of a fluid with continuously varying conductance. Measurements of the conductivity profiles, corresponding density profiles, and their fluctuation levels are demonstrated in a channel flow with an electrolyte injected from a slot in one wall.
Role of dielectric constant in electrohydrodynamics of conducting fluids
NASA Technical Reports Server (NTRS)
Rhodes, Percy H.; Snyder, Robert S.; Roberts, Glyn O.
1992-01-01
Electrohydrodynamic (EHD) flows are driven by the interaction of an electric field with variations in electric conductivity or dielectric constant. In reported EHD experiments on the deformation of drops of immiscible dielectric fluids, the role of conductivity has tended to overshadow the role of dielectric constant. Often, large conductivity contrasts were convenient because the conductivities of the dielectric fluid were relatively uncertain. As a result, the observed effects were always qualitatively the same as if there had been no contrast in dielectric constant. Our early experiments studying the EHC deformations of cylindrical streams readily showed the conductivity effect but the dielectric constant effect was not discernible. We have modified our flow chamber and improved our method of observation and can now see an unequivocal dielectric constant effect which is in agreement with the prior theory. In this paper we first give a brief description of the physics of charge buildup at the interface of an immersed spherical drop or flowing cylindrical sample stream and then show how these charge distributions lead to interface distortions and accompanying viscous flows which constitute EHD. We next review theory and experiment describing the deformation of spherical drops. We show that in the reported drop deformation experiments, the contrast in dielectric constant was never sufficient to reverse the deformation due to the conductivity contrast. We review our work describing the deformation of a cylindrical stream of one fluid flowing in a parallel flow of another, and we compare the deformation equations with those for spherical drops. Finally, we show a definite experimental dielectric constant effect for cylindrical stream of aqueous polystyrene latex suspension. The dielectric constant varies with the frequency of the imposed electric field, and the associated EHD flow change is very apparent.
Role of dielectric constant in electrohydrodynamics of conducting fluids
NASA Astrophysics Data System (ADS)
Rhodes, Percy H.; Snyder, Robert S.; Roberts, Glyn O.
Electrohydrodynamic (EHD) flows are driven by the interaction of an electric field with variations in electric conductivity or dielectric constant. In reported EHD experiments on the deformation of drops of immiscible dielectric fluids, the role of conductivity has tended to overshadow the role of dielectric constant. Often, large conductivity contrasts were convenient because the conductivities of the dielectric fluid were relatively uncertain. As a result, the observed effects were always qualitatively the same as if there had been no contrast in dielectric constant. Our early experiments studying the EHC deformations of cylindrical streams readily showed the conductivity effect but the dielectric constant effect was not discernible. We have modified our flow chamber and improved our method of observation and can now see an unequivocal dielectric constant effect which is in agreement with the prior theory. In this paper we first give a brief description of the physics of charge buildup at the interface of an immersed spherical drop or flowing cylindrical sample stream and then show how these charge distributions lead to interface distortions and accompanying viscous flows which constitute EHD. We next review theory and experiment describing the deformation of spherical drops. We show that in the reported drop deformation experiments, the contrast in dielectric constant was never sufficient to reverse the deformation due to the conductivity contrast. We review our work describing the deformation of a cylindrical stream of one fluid flowing in a parallel flow of another, and we compare the deformation equations with those for spherical drops. Finally, we show a definite experimental dielectric constant effect for cylindrical stream of aqueous polystyrene latex suspension. The dielectric constant varies with the frequency of the imposed electric field, and the associated EHD flow change is very apparent.
An incompressible state of a photo-excited electron gas
Chepelianskii, Alexei D.; Watanabe, Masamitsu; Nasyedkin, Kostyantyn; Kono, Kimitoshi; Konstantinov, Denis
2015-01-01
Two-dimensional electrons in a magnetic field can form new states of matter characterized by topological properties and strong electronic correlations as displayed in the integer and fractional quantum Hall states. In these states, the electron liquid displays several spectacular characteristics, which manifest themselves in transport experiments with the quantization of the Hall resistance and a vanishing longitudinal conductivity or in thermodynamic equilibrium when the electron fluid becomes incompressible. Several experiments have reported that dissipationless transport can be achieved even at weak, non-quantizing magnetic fields when the electrons absorb photons at specific energies related to their cyclotron frequency. Here we perform compressibility measurements on electrons on liquid helium demonstrating the formation of an incompressible electronic state under these resonant excitation conditions. This new state provides a striking example of irradiation-induced self-organization in a quantum system. PMID:26007282
Successes and Challenges of Incompressible Flow Simulation
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin
2003-01-01
During the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of CFD discipline. Even though incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient, CFD tools become indispensable in fluid engineering for incompressible and low speed flow. This paper is intended to review some of the successes made possible by advances in computational technologies during the same period, and discuss some of the current challenges.
Optimal time step for incompressible SPH
NASA Astrophysics Data System (ADS)
Violeau, Damien; Leroy, Agnès
2015-05-01
A classical incompressible algorithm for Smoothed Particle Hydrodynamics (ISPH) is analyzed in terms of critical time step for numerical stability. For this purpose, a theoretical linear stability analysis is conducted for unbounded homogeneous flows, leading to an analytical formula for the maximum CFL (Courant-Friedrichs-Lewy) number as a function of the Fourier number. This gives the maximum time step as a function of the fluid viscosity, the flow velocity scale and the SPH discretization size (kernel standard deviation). Importantly, the maximum CFL number at large Reynolds number appears twice smaller than with the traditional Weakly Compressible (WCSPH) approach. As a consequence, the optimal time step for ISPH is only five times larger than with WCSPH. The theory agrees very well with numerical data for two usual kernels in a 2-D periodic flow. On the other hand, numerical experiments in a plane Poiseuille flow show that the theory overestimates the maximum allowed time step for small Reynolds numbers.
NASA Astrophysics Data System (ADS)
Linga Raju, T.; Neela Rao, B.
2016-05-01
An unsteady MHD two-layered fluid flow of electrically conducting fluids in a horizontal channel bounded by two parallel porous plates under the influence of a transversely applied uniform strong magnetic field in a rotating system is analyzed. The flow is driven by a common constant pressure gradient in a channel bounded by two parallel porous plates, one being stationary and the other oscillatory. The two fluids are assumed to be incompressible, electrically conducting with different viscosities and electrical conductivities. The governing partial differential equations are reduced to the linear ordinary differential equations using two-term series. The resulting equations are solved analytically to obtain exact solutions for the velocity distributions (primary and secondary) in the two regions respectively, by assuming their solutions as a combination of both the steady state and time dependent components of the solutions. Numerical values of the velocity distributions are computed for different sets of values of the governing parameters involved in the study and their corresponding profiles are also plotted. The details of the flow characteristics and their dependence on the governing parameters involved, such as the Hartmann number, Taylor number, porous parameter, ratio of the viscosities, electrical conductivities and heights are discussed. Also an observation is made how the velocity distributions vary with the rotating hydromagnetic interaction in the case of steady and unsteady flow motions. The primary velocity distributions in the two regions are seen to decrease with an increase in the Taylor number, but an increase in the Taylor number causes a rise in secondary velocity distributions. It is found that an increase in the porous parameter decreases both the primary and secondary velocity distributions in the two regions.
NASA Technical Reports Server (NTRS)
Liang, Anita D. (Technical Monitor); Artiles, Antonio
2004-01-01
The objectives of the program were to develop computational fluid dynamics (CFD) codes and simpler industrial codes for analyzing and designing advanced seals for air-breathing and space propulsion engines. The CFD code SCISEAL is capable of producing full three-dimensional flow field information for a variety of cylindrical configurations. An implicit multidomain capability allow the division of complex flow domains to allow optimum use of computational cells. SCISEAL also has the unique capability to produce cross-coupled stiffness and damping coefficients for rotordynamic computations. The industrial codes consist of a series of separate stand-alone modules designed for expeditious parametric analyses and optimization of a wide variety of cylindrical and face seals. Coupled through a Knowledge-Based System (KBS) that provides a user-friendly Graphical User Interface (GUI), the industrial codes are PC based using an OS/2 operating system. These codes were designed to treat film seals where a clearance exists between the rotating and stationary components. Leakage is inhibited by surface roughness, small but stiff clearance films, and viscous pumping devices. The codes have demonstrated to be a valuable resource for seal development of future air-breathing and space propulsion engines.
The magnetic-distortion probe: Velocimetry in conducting fluids
NASA Astrophysics Data System (ADS)
Miralles, Sophie; Verhille, Gautier; Plihon, Nicolas; Pinton, Jean-François
2011-09-01
A new type of velocimeter, capable of local velocity measurements in conducting fluids, is introduced. The principle of the "magnetic-distortion probe" is based on the measurement of the induced magnetic field by the flow of a conducting fluid in the vicinity of a localized magnetic field. The new velocimeter has no moving parts, and can be enclosed in a sealed cap, easing the implementation in harsh environments, such as liquid metals. The proposed method allows one to probe both the continuous part and fluctuations of the velocity, the temporal and spatial resolution being linked to the actual geometric configuration of the probe. A prototype probe has been tested in a gallinstan pipe flow and in a fully turbulent flow of liquid gallium generated by the counter rotation of two coaxial impellers in a cylinder. The signals have been compared to a reference potential probe and show very good agreement both for time-averaged velocities and turbulent fluctuations. The prototype is shown to detect motion from a few cm s-1 to a few m s-1. Moreover, the use of the magnetic-distortion probe with large-scale applied magnetic field is discussed.
Metastable Lennard-Jones fluids. II. Thermal conductivity.
Baidakov, Vladimir G; Protsenko, Sergey P
2014-06-01
The method of equilibrium molecular dynamics with the use of the Green-Kubo formalism has been used to calculate the thermal conductivity λ in stable and metastable regions of a Lennard-Jones fluid. Calculations have been made in the range of reduced temperatures 0.4 ≤ T* = k(b)T/ε ≤ 2.0 and densities 0.01 ≤ ρ* = ρσ³ ≤ 1.2 on 15 isotherms for 234 states, 130 of which refer to metastable regions: superheated and supercooled liquids, supersaturated vapor. Equations have been built up which describe the dependence of the regular part of the thermal conductivity on temperature and density, and also on temperature and pressure. It has been found that in (p, T) variables in the region of a liquid-gas phase transition a family of lines of constant value of excess thermal conductivity Δλ = λ - λ0, where λ0 is the thermal conductivity of a dilute gas, has an envelope which coincides with the spinodal. Thus, at the approach to the spinodal of a superheated liquid and supersaturated vapor (∂Δλ/∂p)T → ∞, (∂Δλ/∂T)p → ∞. PMID:24908025
Instability of nanometric fluid films on a thermally conductive substrate
NASA Astrophysics Data System (ADS)
Dong, N.; Kondic, L.
2016-10-01
We consider thin fluid films placed on thermally conductive substrates and exposed to a time-dependent spatially uniform heat source. The evolution of the films is considered within the long-wave framework in the regime such that both fluid-substrate interaction, modeled via disjoining pressure, and Marangoni forces are relevant. We analyze the problem by the means of linear stability analysis as well as time-dependent nonlinear simulations. The main finding is that when self-consistent computation of the temperature field is performed, a complex interplay of different instability mechanisms results. This includes either monotonous or oscillatory dynamics of the free surface. This oscillatory behavior is absent if the film temperature is assumed to be slaved to the current value of the film thickness. The results are discussed within the context of liquid metal films but are of relevance to dynamics of any thin film involving variable temperature of the free surface, such that the temperature and the film interface itself evolve on comparable time scales.
Miniatuization of the flowing fluid electric conductivity loggingtec hnique
Su, Grace W.; Quinn, Nigel W.T.; Cook, Paul J.; Shipp, William
2005-10-19
An understanding of both the hydraulic properties of the aquifer and the depth distribution of salts is critical for evaluating the potential of groundwater for conjunctive water use and for maintaining suitable groundwater quality in agricultural regions where groundwater is used extensively for irrigation and drinking water. The electrical conductivity profiles recorded in a well using the flowing fluid electric conductivity logging (FEC logging) method can be analyzed to estimate interval specific hydraulic conductivity and estimates of the salinity concentration with depth. However, irrigation wells that are common in agricultural regions have limited access into them because these wells are still in operation, and the traditional equipment used for FEC logging cannot fit through the small access pipe intersecting the well. A modified, miniaturized FEC logging technique was developed such that this logging method could be used in wells with limited access. In addition, a new method for injecting water over the entire screened interval of the well was developed to reduce the time required to perform FEC logging. Results of FEC logging using the new methodology and miniaturized system in two irrigation wells are also summarized.
Ray A. Berry; Richard C. Martineau
2007-04-01
The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods – the strictly incompressible limit, the nearly incompressible limit, and the f ully compressible limit. The PCICE method’s behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the f ully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow.
NASA Astrophysics Data System (ADS)
Linga Raju, T.; Neela Rao, B.
2016-08-01
The paper aims to analyze the heat transfer aspects of a two-layered fluid flow in a horizontal channel under the action of an applied magnetic and electric fields, when the whole system is rotated about an axis perpendicular to the flow. The flow is driven by a common constant pressure gradient in the channel bounded by two parallel porous insulating plates, one being stationary and the other one oscillatory. The fluids in the two regions are considered electrically conducting, and are assumed to be incompressible with variable properties, namely, different densities, viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperature. The governing partial differential equations are then reduced to the ordinary linear differential equations by using a two-term series. The temperature distributions in both fluid regions of the channel are derived analytically. The results are presented graphically to discuss the effect on the heat transfer characteristics and their dependence on the governing parameters, i.e., the Hartmann number, Taylor number, porous parameter, and ratios of the viscosities, heights, electrical and thermal conductivities. It is observed that, as the Coriolis forces become stronger, i.e., as the Taylor number increases, the temperature decreases in the two fluid regions. It is also seen that an increase in porous parameter diminishes the temperature distribution in both the regions.
Self-gravitational instability in magnetized finitely conducting viscoelastic fluid
NASA Astrophysics Data System (ADS)
Prajapati, R. P.; Chhajlani, R. K.
2013-04-01
The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability.
Astronaut Mike Fincke Conducts Fluid Merging Viscosity Measurement (FMVM) Experiment
NASA Technical Reports Server (NTRS)
2004-01-01
Astronaut Mike Fincke places droplets of honey onto the strings for the Fluid Merging Viscosity Measurement (FMVM) investigation onboard the International Space Station (ISS). The FMVM experiment measures the time it takes for two individual highly viscous fluid droplets to coalesce or merge into one droplet. Different fluids and droplet size combinations were tested in the series of experiments. By using the microgravity environment, researchers can measure the viscosity or 'thickness' of fluids without the influence of containers and gravity using this new technique. Understanding viscosity could help scientists understand industrially important materials such as paints, emulsions, polymer melts and even foams used to produce pharmaceutical, food, and cosmetic products.
Zhou, Yijie; Lim, Hyun-Kyung; de Almeida, Valmor F; Navamita, Ray; Wang, Shuqiang; Glimm, James G; Li, Xiao-lin; Jiao, Xiangmin
2012-06-01
This progress report describes the development of a front tracking method for the solution of the governing equations of motion for two-phase micromixing of incompressible, viscous, liquid-liquid solvent extraction processes. The ability to compute the detailed local interfacial structure of the mixture allows characterization of the statistical properties of the two-phase mixture in terms of droplets, filaments, and other structures which emerge as a dispersed phase embedded into a continuous phase. Such a statistical picture provides the information needed for building a consistent coarsened model applicable to the entire mixing device. Coarsening is an undertaking for a future mathematical development and is outside the scope of the present work. We present here a method for accurate simulation of the micromixing dynamics of an aqueous and an organic phase exposed to intense centrifugal force and shearing stress. The onset of mixing is the result of the combination of the classical Rayleigh- Taylor and Kelvin-Helmholtz instabilities. A mixing environment that emulates a sector of the annular mixing zone of a centrifugal contactor is used for the mathematical domain. The domain is small enough to allow for resolution of the individual interfacial structures and large enough to allow for an analysis of their statistical distribution of sizes and shapes. A set of accurate algorithms for this application requires an advanced front tracking approach constrained by the incompressibility condition. This research is aimed at designing and implementing these algorithms. We demonstrate verification and convergence results for one-phase and unmixed, two-phase flows. In addition we report on preliminary results for mixed, two-phase flow for realistic operating flow parameters.
Electrical conductivity of fluid-bearing quartzite under lower crustal conditions
NASA Astrophysics Data System (ADS)
Shimojuku, Akira; Yoshino, Takashi; Yamazaki, Daisuke; Okudaira, Takamoto
2012-05-01
The electrical conductivity of fluid-bearing quartzite was determined as function of temperature and fluid fraction at 1 GPa in order to assess the origin of the high conductivity anomalies observed in the middle to lower crustal levels. Dihedral angles of quartz-fluid-quartz determined from recovered samples were below 60°, suggesting that fluid forms an interconnected network through the quartz aggregate. The electrical conductivity of quartzite increases with increasing temperature, which can be approximately expressed by Arrhenius equation. The apparent activation enthalpy decreases from 0.70 to 0.25 eV with increasing fluid fraction in volume from 0.00043 to 0.32. The electrical conductivity (σ) of the fluid-bearing quartzite increased with fluid fraction (ϕ) proportionally to a power law (σ ∝ ϕ0.56-0.71) within the temperature range of 900-1000 K. The electrical conductivity of the aqueous fluid-bearing quartzite with the maximum fluid fraction (0.32) was found to be about three orders of magnitude higher than that of dry quartzite at 1000 K. However, its electrical conductivity was definitely lower than the geophysically observed values of high-conductivity anomalies, even if the quartzite contained large fluid fractions (0.32). The present results suggest that fluid-bearing quartzite is unable to account for the high-conductivity anomalies in terms of fluid fraction. A significant amount of other ionic species, such as Na, Cl, and Al in aqueous fluid, in addition to silica phases dissolved in fluid, is required to increase conductivity.
Incompressible limit of solutions of multidimensional steady compressible Euler equations
NASA Astrophysics Data System (ADS)
Chen, Gui-Qiang G.; Huang, Feimin; Wang, Tian-Yi; Xiang, Wei
2016-06-01
A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass conservation and the vorticity. Another observation is that the incompressibility of the limit for the homentropic Euler flow is directly from the continuity equation, while the incompressibility of the limit for the full Euler flow is from a combination of all the Euler equations. As direct applications of the compactness framework, we establish two incompressible limit theorems for multidimensional steady Euler flows through infinitely long nozzles, which lead to two new existence theorems for the corresponding problems for multidimensional steady incompressible Euler equations.
A two-fluid model for relativistic heat conduction
López-Monsalvo, César S.
2014-01-14
Three years ago it was presented in these proceedings the relativistic dynamics of a multi-fluid system together with various applications to a set of topical problems [1]. In this talk, I will start from such dynamics and present a covariant formulation of relativistic thermodynamics which provides us with a causal constitutive equation for the propagation of heat in a relativistic setting.
Scaling the Incompressible Richtmyer-Meshkov Instability
Cotrell, D; Cook, A
2007-01-09
We derive a scaling relation for Richtmyer-Meshkov instability of incompressible fluids. The relation is tested using both numerical simulations and experimental data. We obtain collapse of growth rates for a wide range of initial conditions by using vorticity and velocity scales associated with the interfacial perturbations and the acceleration impulse. A curve fit to the collapsed growth rates yields a fairly universal model for the mixing layer thickness versus time.
High-End Computing for Incompressible Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kiris, Cetin
2001-01-01
The objective of the First MIT Conference on Computational Fluid and Solid Mechanics (June 12-14, 2001) is to bring together industry and academia (and government) to nurture the next generation in computational mechanics. The objective of the current talk, 'High-End Computing for Incompressible Flows', is to discuss some of the current issues in large scale computing for mission-oriented tasks.
Conducting fluid dynamics experiments with vertically falling soap films
NASA Astrophysics Data System (ADS)
Rutgers, M. A.; Wu, X. L.; Daniel, W. B.
2001-07-01
This article gives a detailed description of an apparatus in which flowing soap films are used to perform two dimensional fluid dynamics experiments. We have previously reported scientific findings made with the apparatus, but never carefully described the technique, or its full potential. A brief introduction is given on the nature of soap films as fluids and then all the details necessary for creating robust flowing films are listed. Typical parameters for the system are: flow speeds from 0.5 to 4 m/s, film thickness between 1 and 10 μm, and typical film sizes are 3 m tall and 10 cm wide although films of 20 m tall and 4 m wide have also been made. A vacuum apparatus is also described in which the air drag on the film can be reduced by a factor of 5-10. Finally, a large number of techniques for measuring flow and thickness are outlined and referenced.
The effect of Fe3O4 nanoparticles on the thermal conductivities of various base fluids.
Altan, Cem L; Bucak, Seyda
2011-07-15
Conventional heat transfer fluids have intrinsically poor heat transfer properties compared to solids. Enhancing the efficiency of heat transfer is of great interest for various industrial applications. Suspending solid particles in a fluid increases the thermal conductivity of the resulting suspension and enhances the heat transfer properties. In this work, changes in thermal conductivities of fluids upon the addition of magnetic nanoparticles have been investigated. Fe(3)O(4) nanoparticles are synthesized using different synthesis methods and are suspended in various oils. The effect of the base fluid and the type of magnetic particle on the thermal conductivity is investigated in detail. Up to 28% increase in the thermal conductivity is obtained with 2.5 wt% magnetic particles in hexane. The thermal conductivity enhancement is found to depend on the particle concentration, method of preparation and base fluid. The enhancements obtained are higher than those estimated using any theoretical model present in the literature. PMID:21659690
The effect of Fe3O4 nanoparticles on the thermal conductivities of various base fluids
NASA Astrophysics Data System (ADS)
Altan, Cem L.; Bucak, Seyda
2011-07-01
Conventional heat transfer fluids have intrinsically poor heat transfer properties compared to solids. Enhancing the efficiency of heat transfer is of great interest for various industrial applications. Suspending solid particles in a fluid increases the thermal conductivity of the resulting suspension and enhances the heat transfer properties. In this work, changes in thermal conductivities of fluids upon the addition of magnetic nanoparticles have been investigated. Fe3O4 nanoparticles are synthesized using different synthesis methods and are suspended in various oils. The effect of the base fluid and the type of magnetic particle on the thermal conductivity is investigated in detail. Up to 28% increase in the thermal conductivity is obtained with 2.5 wt% magnetic particles in hexane. The thermal conductivity enhancement is found to depend on the particle concentration, method of preparation and base fluid. The enhancements obtained are higher than those estimated using any theoretical model present in the literature.
Role of dielectric constant in electrohydrodynamics of conducting fluids
NASA Technical Reports Server (NTRS)
Rhodes, Percy H.; Snyder, Robert S.; Roberts, Glyn O.
1994-01-01
Electrohydrodynamic sample distortion during continuous flow electrophoresis is an experiment to be conducted during the second International Microgravity Laboratory (IML-2) in July 1994. The specific objective of this experiment is the distortion caused by the difference in dielectric constant between the sample and surrounding buffer. Although the role of sample conductivity in electrohydrodynamic has been the subject of both flight and ground experiments, the separate role of dielectric constant, independent of sample conductivity, has not been measured. This paper describes some of the laboratory research and model development that will support the flight experiment on IML-2.
Enhancing thermal conductivity of fluids with graphite nanoparticles and carbon nanotube
Zhang, Zhiqiang; Lockwood, Frances E.
2008-03-25
A fluid media such as oil or water, and a selected effective amount of carbon nanomaterials necessary to enhance the thermal conductivity of the fluid. One of the preferred carbon nanomaterials is a high thermal conductivity graphite, exceeding that of the neat fluid to be dispersed therein in thermal conductivity, and ground, milled, or naturally prepared with mean particle size less than 500 nm, and preferably less than 200 nm, and most preferably less than 100 nm. The graphite is dispersed in the fluid by one or more of various methods, including ultrasonication, milling, and chemical dispersion. Carbon nanotubes with graphitic structure is another preferred source of carbon nanomaterial, although other carbon nanomaterials are acceptable. To confer long term stability, the use of one or more chemical dispersants is preferred. The thermal conductivity enhancement, compared to the fluid without carbon nanomaterial, is proportional to the amount of carbon nanomaterials (carbon nanotubes and/or graphite) added.
Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2009-01-01
This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of
Lattice Boltzmann modeling of three-phase incompressible flows
NASA Astrophysics Data System (ADS)
Liang, H.; Shi, B. C.; Chai, Z. H.
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
Lattice Boltzmann modeling of three-phase incompressible flows.
Liang, H; Shi, B C; Chai, Z H
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
The existence of a magnetic dynamo for the dynamically possible motion of a conducting fluid
NASA Astrophysics Data System (ADS)
Solovev, A. A.
The problem of the existence of a magnetic dynamo is analyzed for the case of the Couette-Poiseuille flow, i.e., a dynamically possible velocity field of a conducting fluid. The analysis is carried out without assuming the absence of friction. It is shown that, in principle, the excitation of a magnetic field by the laminar axisymmetric motion of a conducting fluid is possible. However, since the flow remains laminar only for sufficiently low Reynolds numbers, the result is physically meaningful only for fluids with a sufficiently low ratio of the magnetic viscosity to the kinematic viscosity.
Fluid stimulation elicits hearing in the absence of air and bone conduction--An animal study.
Perez, Ronen; Adelman, Cahtia; Sohmer, Haim
2016-01-01
Conclusion Cochlea can be directly excited by fluid (soft-tissue) stimulation. Objective To determine whether there is no difference in auditory-nerve-brainstem evoked response (ABR) thresholds to fluid stimulation between normal and animal models of post radical-mastoidectomy, as seen in a previous human study. Background It has been shown in humans that hearing can be elicited with stimulation to fluid in the external auditory meatus (EAM), and radical-mastoidectomy cavity. These groups differed in age, initial hearing, and drilling exposure. To overcome this difference, experiments were conducted in sand-rats, first intact, and after inducing a radical-mastoidectomy. Methods The EAM of five sand-rats was filled with 0.3 ml saline. ABR thresholds were determined in response to vibratory stimulation by a clinical bone-vibrator with a plastic rod, applied to the saline in the EAM. Then the tympanic membrane was removed, and malleus dislocated (radical-mastoidectomy model). The cavity was filled with 0.45 ml saline and the ABR threshold was determined in response to vibratory stimulation to the cavity fluid. Results There was no difference in ABR fluid thresholds to EAM and mastoidectomy cavity stimulation. Air-conduction stimulation from the bone-vibrator was not involved (conductive loss due to fluid). Bone-conduction stimulation was not involved (large difference in acoustic impedance between fluid and bone).
Growth and Morphology of Supercritical Fluids, a Fluid Physics Experiment Conducted on Mir, Complete
NASA Technical Reports Server (NTRS)
Wilkinson, R. Allen
2001-01-01
The Growth and Morphology of Supercritical Fluids (GMSF) is an international experiment facilitated by the NASA Glenn Research Center and under the guidance of U.S. principal investor Professor Hegseth of the University of New Orleans and three French coinvestigators: Daniel Beysens, Yves Garrabos, and Carole Chabot. The GMSF experiments were concluded in early 1999 on the Russian space station Mir. The experiments spanned the three science themes of near-critical phase separation rates, interface dynamics in near-critical boiling, and measurement of the spectrum of density fluctuation length scales very close to the critical point. The fluids used were pure CO2 or SF6. Three of the five thermostats used could adjust the sample volume with the scheduled crew time. Such a volume adjustment enabled variable sample densities around the critical density as well as pressure steps (as distinct from the usual temperature steps) applied to the sample. The French-built ALICE II facility was used for these experiments. It allows tightly thermostated (left photograph) samples (right photograph) to be controlled and viewed/measured. Its diagnostics include interferometry, shadowgraph, high-speed pressure measurements, and microscopy. Data were logged on DAT tapes, and PCMCIA cards and were returned to Earth only after the mission was over. The ground-breaking near critical boiling experiment has yielded the most results with a paper published in Physical Review Letters (ref. 1). The boiling work also received press in Science Magazine (ref. 2). This work showed that, in very compressible near-critical two-phase pure fluids, a vapor bubble was induced to temporarily overheat during a rapid heating of the sample wall. The temperature rise in the vapor was 23-percent higher than the rise in the driving container wall. The effect is due to adiabatic compression of the vapor bubble by the rapid expansion of fluid near the boundary during heatup. Thermal diffusivity is low near the
Method for electrically producing dispersions of a nonconductive fluid in a conductive medium
DePaoli, D.W.; Tsouris, C.; Feng, J.Q.
1998-06-09
A method is described for use in electrically forming dispersions of a nonconducting fluid in a conductive medium that minimizes power consumption, gas generation, and sparking between the electrode of the nozzle and the conductive medium. The method utilizes a nozzle having a passageway, the wall of which serves as the nozzle electrode, for the transport of the nonconducting fluid into the conductive medium. A second passageway provides for the transport of a flowing low conductivity buffer fluid which results in a region of the low conductivity buffer fluid immediately adjacent the outlet from the first passageway to create the necessary protection from high current drain and sparking. An electrical potential difference applied between the nozzle electrode and an electrode in contact with the conductive medium causes formation of small droplets or bubbles of the nonconducting fluid within the conductive medium. A preferred embodiment has the first and second passageways arranged in a concentric configuration, with the outlet tip of the first passageway withdrawn into the second passageway. 4 figs.
Method for electrically producing dispersions of a nonconductive fluid in a conductive medium
DePaoli, David W.; Tsouris, Constantinos; Feng, James Q.
1998-01-01
A method for use in electrically forming dispersions of a nonconducting fluid in a conductive medium that minimizes power consumption, gas generation, and sparking between the electrode of the nozzle and the conductive medium. The method utilizes a nozzle having a passageway, the wall of which serves as the nozzle electrode, for the transport of the nonconducting fluid into the conductive medium. A second passageway provides for the transport of a flowing low conductivity buffer fluid which results in a region of the low conductivity buffer fluid immediately adjacent the outlet from the first passageway to create the necessary protection from high current drain and sparking. An electrical potential difference applied between the nozzle electrode and an electrode in contact with the conductive medium causes formation of small droplets or bubbles of the nonconducting fluid within the conductive medium. A preferred embodiment has the first and second passageways arranged in a concentric configuration, with the outlet tip of the first passageway withdrawn into the second passageway.
Ni, Huaiwei; Chen, Qi; Keppler, Hans
2014-11-01
Electrical conductivity data of aqueous fluids under pressure can be used to derive the dissociation constants of electrolytes, to assess the effect of ionic dissociation on mineral solubility, and to interpret magnetotelluric data of earth's interior where a free fluid phase is present. Due to limitation on the tensile strength of the alloy material of hydrothermal autoclaves, previous measurements of fluid conductivity were mostly restricted to less than 0.4 GPa and 800 °C. By adapting a Bassett-type hydrothermal diamond anvil cell, we have developed a new method for acquiring electrical conductivity of aqueous fluids under pressure. Our preliminary results for KCl solutions using the new method are consistent with literature data acquired with the conventional method, but the new method has great potential for working in a much broader pressure range.
Ni, Huaiwei; Chen, Qi; Keppler, Hans
2014-11-01
Electrical conductivity data of aqueous fluids under pressure can be used to derive the dissociation constants of electrolytes, to assess the effect of ionic dissociation on mineral solubility, and to interpret magnetotelluric data of earth's interior where a free fluid phase is present. Due to limitation on the tensile strength of the alloy material of hydrothermal autoclaves, previous measurements of fluid conductivity were mostly restricted to less than 0.4 GPa and 800 °C. By adapting a Bassett-type hydrothermal diamond anvil cell, we have developed a new method for acquiring electrical conductivity of aqueous fluids under pressure. Our preliminary results for KCl solutions using the new method are consistent with literature data acquired with the conventional method, but the new method has great potential for working in a much broader pressure range. PMID:25430149
Taylor Instability of Incompressible Liquids
DOE R&D Accomplishments Database
Fermi, E.; von Neumann, J.
1955-11-01
A discussion is presented in simplified form of the problem of the growth of an initial ripple on the surface of an incompressible liquid in the presence of an acceleration, g, directed from the outside into the liquid. The model is that of a heavy liquid occupying at t = 0 the half space above the plane z = 0, and a rectangular wave profile is assumed. The theory is found to represent correctly one feature of experimental results, namely the fact that the half wave of the heavy liquid into the vacuum becomes rapidly narrower while the half wave pushing into the heavy liquid becomes more and more blunt. The theory fails to account for the experimental results according to which the front of the wave pushing into the heavy liquid moves with constant velocity. The case of instability at the boundary of 2 fluids of different densities is also explored. Similar results are obtained except that the acceleration of the heavy liquid into the light liquid is reduced.
Conductivity measurements on H2O-bearing CO2-rich fluids
Capobianco, Ryan M.; Miroslaw S. Gruszkiewicz; Bodnar, Robert J.; Rimstidt, J. Donald
2014-09-10
Recent studies report rapid corrosion of metals and carbonation of minerals in contact with carbon dioxide containing trace amounts of dissolved water. One explanation for this behavior is that addition of small amounts of H2O to CO2 leads to significant ionization within the fluid, thus promoting reactions at the fluid-solid interface analogous to corrosion associated with aqueous fluids. The extent of ionization in the bulk CO2 fluid was determined using a flow-through conductivity cell capable of detecting very low conductivities. Experiments were conducted from 298 to 473 K and 7.39 to 20 MPa with H2O concentrations up to ~1600 ppmwmore » (xH2O ≈ 3.9 x 10-3), corresponding to the H2O solubility limit in liquid CO2 at ambient temperature. All solutions showed conductivities <10 nS/cm, indicating that the solutions were essentially ion-free. Furthermore, this observation suggests that the observed corrosion and carbonation reactions are not the result of ionization in CO2-rich bulk phase, but does not preclude ionization in the fluid at the fluid-solid interface.« less
Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence
NASA Technical Reports Server (NTRS)
Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor
2010-01-01
We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.
Parametric electroconvection in a weakly conducting fluid in a horizontal parallel-plate capacitor
NASA Astrophysics Data System (ADS)
Kartavykh, N. N.; Smorodin, B. L.; Il'in, V. A.
2015-07-01
We study the flows of a nonuniformly heated weakly conducting fluid in an ac electric field of a horizontal parallel-plate capacitor. Analysis is carried out for fluids in which the charge formation is governed by electroconductive mechanism associated with the temperature dependence of the electrical conductivity of the medium. Periodic and chaotic regimes of fluid flow are investigated in the limiting case of instantaneous charge relaxation and for a finite relaxation time. Bifurcation diagrams and electroconvective regimes charts are constructed. The regions where fluid oscillations synchronize with the frequency of the external field are determined. Hysteretic transitions between electroconvection regimes are studied. The scenarios of transition to chaotic oscillations are analyzed. Depending on the natural frequency of electroconvective system and the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.
Parametric electroconvection in a weakly conducting fluid in a horizontal parallel-plate capacitor
Kartavykh, N. N.; Smorodin, B. L. Il’in, V. A.
2015-07-15
We study the flows of a nonuniformly heated weakly conducting fluid in an ac electric field of a horizontal parallel-plate capacitor. Analysis is carried out for fluids in which the charge formation is governed by electroconductive mechanism associated with the temperature dependence of the electrical conductivity of the medium. Periodic and chaotic regimes of fluid flow are investigated in the limiting case of instantaneous charge relaxation and for a finite relaxation time. Bifurcation diagrams and electroconvective regimes charts are constructed. The regions where fluid oscillations synchronize with the frequency of the external field are determined. Hysteretic transitions between electroconvection regimes are studied. The scenarios of transition to chaotic oscillations are analyzed. Depending on the natural frequency of electroconvective system and the external field frequency, the transition from periodic to chaotic oscillations can occur via quasiperiodicity, a subharmonic cascade, or intermittence.
Numerical studies of incompressible viscous flow in a driven cavity
NASA Technical Reports Server (NTRS)
1975-01-01
A series of project papers is presented in computational fluid dynamics. The work was performed during the 1973-74 academic year at Old Dominion University. Each paper briefly examines a numerical method(s) that can be applied to the Navier-Stokes equations governing incompressible flow in a driven cavity. Solutions obtained with a cubic spline procedure are also included.
Liu, L J; Schlesinger, M
2015-09-01
A correct description of the hydraulic conductivity is essential for determining the actual tumor interstitial fluid pressure (TIFP) distribution. Traditionally, it has been assumed that the hydraulic conductivities both in a tumor and normal tissue are constant, and that a tumor has a much larger interstitial hydraulic conductivity than normal tissue. The abrupt transition of the hydraulic conductivity at the tumor surface leads to non-physical results (the hydraulic conductivity and the slope of the TIFP are not continuous at tumor surface). For the sake of simplicity and the need to represent reality, we focus our analysis on avascular or poorly vascularized tumors, which have a necrosis that is mostly in the center and vascularization that is mostly on the periphery. We suggest that there is an intermediary region between the tumor surface and normal tissue. Through this region, the interstitium (including the structure and composition of solid components and interstitial fluid) transitions from tumor to normal tissue. This process also causes the hydraulic conductivity to do the same. We introduce a continuous variation of the hydraulic conductivity, and show that the interstitial hydraulic conductivity in the intermediary region should be monotonically increasing up to the value of hydraulic conductivity in the normal tissue in order for the model to correspond to the actual TIFP distribution. The value of the hydraulic conductivity at the tumor surface should be the lowest in value.
NASA Astrophysics Data System (ADS)
Cheng, Haibin; Zhang, Xiaopeng; Liu, Guizhen; Ma, Wentao; Wereley, Norman M.
2016-05-01
Measuring sedimentation rate of magnetorheological fluids (MRFs) is of great importance when designing and synthesizing MRFs for engineering applications. A method of characterizing sedimentation rate in an MRF column is proposed utilizing thermal conductivity correlated with particle concentration. A series of MRF samples composed of carbonyl iron particles suspended in silicone oil were prepared, and their concentrations (measured as volume fraction, ∅) and thermal conductivities, k, were tested. A calibration curve was developed to relate particle concentration, ∅, to thermal conductivity, k, using this set of MRF samples with known concentration. The particle concentration, ∅, in the MRF column was then monitored by measuring thermal conductivities (k) at a fixed location and using this calibration relationship. Finally, sedimentation rate in the MRF column was determined by examining how particle concentration varied with time. The sedimentation rate measured in the MRF column was validated using visual observation of mudline (boundary between the topmost clarified fluid zone and MRF below).
Volume conservation issues in incompressible smoothed particle hydrodynamics
NASA Astrophysics Data System (ADS)
Nair, Prapanch; Tomar, Gaurav
2015-09-01
A divergence-free velocity field is usually sought in numerical simulations of incompressible fluids. We show that the particle methods that compute a divergence-free velocity field to achieve incompressibility suffer from a volume conservation issue when a finite time-step position update scheme is used. Further, we propose a deformation gradient based approach to arrive at a velocity field that reduces the volume conservation issues in free surface flows and maintains density uniformity in internal flows while retaining the simplicity of first order time updates.
Hamilton, D.C.; Nellis, W.J.; Holmes, N.C.; Radousky, H.B.; Ree, F.H.; Nicol, M.
1987-07-01
Hugoniot equation-of-state, shock temperature, and electrical conductivity measurements are reported for fluids believed to be the primary constituents of the planets Uranus and Neptune. The equation-of-state results are compared with calculations performed using a statistical mechanical, chemical equilibrium computer code and electrical conductivities are discussed in terms of the recently measured magnetic field of Uranus. 4 refs., 2 figs., 1 tab.
CUDA Simulation of Homogeneous, Incompressible Turbulence
NASA Technical Reports Server (NTRS)
Morin, Lee; Shebalin, John V.; Shum, Victor; Fu, Terry
2011-01-01
We discuss very fast Compute Unified Device Architecture (CUDA) simulations of ideal homogeneous incompressible turbulence based on Fourier models. These models have associated statistical theories that predict that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. Prior numerical simulations have shown that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We review the theoretical basis of this "broken ergodicity" as applied to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence. Our new simulations examine the phenomenon of broken ergodicity through very long time and large grid size runs performed on a state-of-the-art CUDA platform. Results comparing various CUDA hardware configurations and grid sizes are discussed. NS and MHD results are compared.
Performance of WPA Conductivity Sensor during Two-Phase Fluid Flow in Microgravity
NASA Technical Reports Server (NTRS)
Carter, Layne; O'Connor, Edward W.; Snowdon, Doug
2003-01-01
The Conductivity Sensor designed for use in the Node 3 Water Processor Assembly (WPA) was based on the existing Space Shuttle application for the fuel cell water system. However, engineering analysis has determined that this sensor design is potentially sensitive to two-phase fluid flow (gadliquid) in microgravity. The source for this sensitivity is the fact that gas bubbles will become lodged between the sensor probe and the wall of the housing without the aid of buoyancy in l-g. Once gas becomes lodged in the housing, the measured conductivity will be offset based on the volume of occluded gas. A development conductivity sensor was flown on the NASA Microgravity Plan to measure the offset, which was determined to range between 0 and 50%. Based on these findings, a development program was initiated at the sensor s manufacturer to develop a sensor design fully compatible with two-phase fluid flow in microgravity.
3ω slope comparative method for fluid and powder thermal conductivity measurements
NASA Astrophysics Data System (ADS)
Zheng, X. H.; Qiu, L.; Yue, P.; Wang, G.; Tang, D. W.
2016-09-01
By analyzing the relationship among the heat penetration depth, measurement frequency and detector characteristic parameters, a simple and practical 3ω slope comparative method has been proposed. The corresponding measurement system for measuring the thermal properties of fluids and powder materials was established and verified using several specimens with known thermophysical parameters, such as alcohol, distilled water, and air. Compared to the two-dimensional model, the data processing of the method is relatively simple and quick. Due to the elimination of errors introduced by the detector parameter measurement, the measurement accuracy of the method is higher than the conventional one-dimensional model. By using an appropriate frequency range, the new method is time saving and convenient for measuring the thermal conductivity of fluids and powders with low thermal conductivity. Based on the analysis, the effective thermal conductivity of nano-SiO2 powder is accurately determined.
NASA Astrophysics Data System (ADS)
Alekseev, Gennady
2016-09-01
We consider the boundary value problem for stationary magnetohydrodynamic equations of electrically and heat conducting fluid under inhomogeneous mixed boundary conditions for electromagnetic field and temperature and Dirichlet condition for the velocity. The problem describes the thermoelectromagnetic flow of a viscous fluid in 3D bounded domain with the boundary consisting of several parts with different thermo- and electrophysical properties. The global solvability of the boundary value problem is proved and the apriori estimates of the solution are derived. The sufficient conditions on the data are established which provide a local uniqueness of the solution.
NASA Astrophysics Data System (ADS)
Alekseev, Gennady
2016-04-01
We consider the boundary value problem for stationary magnetohydrodynamic equations of electrically and heat conducting fluid under inhomogeneous mixed boundary conditions for electromagnetic field and temperature and Dirichlet condition for the velocity. The problem describes the thermoelectromagnetic flow of a viscous fluid in 3D bounded domain with the boundary consisting of several parts with different thermo- and electrophysical properties. The global solvability of the boundary value problem is proved and the apriori estimates of the solution are derived. The sufficient conditions on the data are established which provide a local uniqueness of the solution.
NASA Astrophysics Data System (ADS)
Voorhies, Goerte V.; Nishihama, Masahiro
1994-04-01
The effects of laterally homogeneous mantle electrical conductivity have been included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary and the subadjacent fluid motion; it also features Gauss' method for solving the nonlinear inverse problem associated with steady motional induction. The trade-off between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and fluid flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
Computation of viscous incompressible flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan
1989-01-01
Incompressible Navier-Stokes solution methods and their applications to three-dimensional flows are discussed. A brief review of existing methods is given followed by a detailed description of recent progress on development of three-dimensional generalized flow solvers. Emphasis is placed on primitive variable formulations which are most promising and flexible for general three-dimensional computations of viscous incompressible flows. Both steady- and unsteady-solution algorithms and their salient features are discussed. Finally, examples of real world applications of these flow solvers are given.
NASA Astrophysics Data System (ADS)
Doughty, Christine; Tsang, Chin-Fu; Yabuuchi, Satoshi; Kunimaru, Takanori
2013-03-01
SummaryThe flowing fluid electric conductivity (FFEC) logging method is a well-logging technique that may be used to estimate flow rate, salinity, transmissivity, and hydraulic head of individual fractures or high-permeability zones intersected by a wellbore. Wellbore fluid is first replaced with fluid of a contrasting electric conductivity, then repeated FEC logging is done while the well is pumped. Zones where fluid flows into the wellbore show peaks in the FEC logs, which may be analyzed to infer inflow rate and salinity of the individual fractures. Conducting the procedure with two or more pumping rates (multi-rate FFEC logging) enables individual fracture transmissivity and hydraulic head to be determined. Here we describe the first application of the multi-rate FFEC logging method to an artesian well, using a 500-m well in fractured rock at Horonobe, Japan. An additional new factor at the site is the presence of regional groundwater flow, which heretofore has only been studied with synthetic data. FFEC logging was conducted for two different pumping rates. Several analysis techniques had to be adapted to account for the artesian nature of the well. The results were subsequently compared with independent salinity measurements and transmissivity and hydraulic head values obtained from packer tests in the same well. Despite non-ideal operating conditions, multi-rate FFEC logging successfully determined flow rate, salinity, and transmissivity of 17 conducting fractures intercepted by the logged section of the borehole, including two fractures with regional groundwater flow. Predictions of hydraulic head were less accurate, a not unexpected result in light of operational problems and the form of the equation for hydraulic head, which involves the difference between two uncertain quantities. This study illustrates the strengths and weaknesses of the multi-rate FFEC logging method applied to artesian wells. In conjunction with previous studies, it demonstrates the
NASA Astrophysics Data System (ADS)
Mele, M.; Giudici, M.; Inzoli, S.; Cavalli, E.; Bersezio, R.
2012-04-01
The estimate of hydraulic conductivity from Direct Current methods represents a powerful tool in aquifer characterization as both electrical and hydraulic conductivities depend on connected pore volumes and connected pore surface areas. A crucial, intermediate stage of this process is the assessment of sediments' textures and lithology from DC electrical conductivity as the electrical response of the aquifers' basic building blocks (i.e., hydrofacies) is controlled by the prevailing process of electrical conduction, electrolytic (σEL; pore-volume dominated) vs. "shale" (σSH; pore-surface dominated), determined by pore-space structure, clay distribution and electrical properties of pore fluids (σW). In this work laboratory experiments were conducted and the results were interpreted through the analysis i) of a volume-averaged, macroscopic litho-textural property of alluvial hydrofacies', the coarse-to-fine ratio (C/F), as a "proxy" of the process of electrical conduction within each samples on the basis of the volume proportion between nonconductive, coarse-grained and conductive, shaly textures and ii) of the surface conduction component, produced in fresh-to-salt water environment by clay materials. 8 hydrofacies' samples were collected with an hand-auger within the outcropping alluvial aquifers of the Quaternary meander river belt of the southernmost Lodi plain (northern Italy), represented by loose gravelly-sands to sands (6 samples), fine and sandy-silty clays (2 samples). As a first step, laboratory measurements of the bulk electrical conductivity (σB) of representative sub-samples, totally saturated with water with different salinity (σW from 125 to 1100 μs/cm), were performed. The experimental apparatus was made up by a series of polycarbonate, cylindrical cells (9cm x 12cm) equipped with external, copper plates as current electrodes and internal, copper squared-grids as potential electrodes. Electrical conductivity of each sample was obtained
Evaluation of Fluid Conduction and Mixing within a Subassembly of the Actinide Burner Test Reactor
Cliff B. Davis
2007-09-01
The RELAP5-3D code is being considered as a thermal-hydraulic system code to support the development of the sodium-cooled Actinide Burner Test Reactor as part of the Global Nuclear Energy Partnership. An evaluation was performed to determine whether the control system could be used to simulate the effects of non-convective mechanisms of heat transport in the fluid, including axial and radial heat conduction and subchannel mixing, that are not currently represented with internal code models. The evaluation also determined the relative importance of axial and radial heat conduction and fluid mixing on peak cladding temperature for a wide range of steady conditions and during a representative loss-of-flow transient. The evaluation was performed using a RELAP5-3D model of a subassembly in the Experimental Breeder Reactor-II, which was used as a surrogate for the Actinide Burner Test Reactor.
A monolithic mass tracking formulation for bubbles in incompressible flow
Aanjaneya, Mridul Patkar, Saket Fedkiw, Ronald
2013-08-15
We devise a novel method for treating bubbles in incompressible flow that relies on the conservative advection of bubble mass and an associated equation of state in order to determine pressure boundary conditions inside each bubble. We show that executing this algorithm in a traditional manner leads to stability issues similar to those seen for partitioned methods for solid–fluid coupling. Therefore, we reformulate the problem monolithically. This is accomplished by first proposing a new fully monolithic approach to coupling incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions, and then subsequently making a number of simplifying assumptions on the air flow removing not only the nonlinearities but also the spatial variations of both the density and the pressure. The resulting algorithm is quite robust, has been shown to converge to known solutions for test problems, and has been shown to be quite effective on more realistic problems including those with multiple bubbles, merging and pinching, etc. Notably, this approach departs from a standard two-phase incompressible flow model where the air flow preserves its volume despite potentially large forces and pressure differentials in the surrounding incompressible fluid that should change its volume. Our bubbles readily change volume according to an isothermal equation of state.
Assessing Redox Potential and Fluid Conductivity of a Contaminant Plume from Geoelectric Methods
NASA Astrophysics Data System (ADS)
Naudet, V.; Revil, A.; Rizzo, E.; Bottero, J.; Begassat, P.
2003-12-01
The redox potential and the fluid conductivity of a contaminant plume are two key-parameter to evaluate the plume development and to propose appropriate remediation technologies. we applied geo-electrical methods (self-potential, SP, and electrical resistivity tomography, ERT) to the Entressen landfill site (South-eastern France). From the knowledge of the piezometric head variation of the groundwater, the electrokinetic source is removed from the SP signals measured on the field. Then, a correlation (Rý=0.85) is obtained between the residual SP due to redox effect and the redox potential values measured in monitoring wells. The first-order linear relationship derived from this correlation is finally used to obtain a redox potential map of the overall contaminated site. A correlation (Rý=0.70) is observed between the electrical conductivities determined from the 3D ERT image and the conductivity of the groundwater measured in boreholes. From this correlation a map of the fluid conductivity is obtained. The maps of the redox potential and conductivity of the groundwater are both indicative of the presence of contaminants. The first one is more sensitive to the presence of organic matter and biodegradation. The second one gives information on the mineralization of the groundwater. Both maps can therefore be used to optimise the position of pumping wells for remediation.
Turning waves and breakdown for incompressible flows
Castro, Angel; Córdoba, Diego; Fefferman, Charles L.; Gancedo, Francisco; López-Fernández, María
2011-01-01
We consider the evolution of an interface generated between two immiscible, incompressible, and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (α,f0(α)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time t∗ where the solution of the free boundary problem parameterized as (α,f(α,t)) blows up: ‖∂αf‖L∞(t∗) = ∞. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh–Taylor condition changes sign and the solution breaks down.
Incompressible magnetohydrodynamic surface waves - Nonlinear aspects
NASA Technical Reports Server (NTRS)
Hollweg, Joseph V.
1987-01-01
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
Fluid flow volume measurements using a capacitance/conductance probe system
NASA Technical Reports Server (NTRS)
Nguyen, T. X.; Arndt, G. D.; Carl, J. R.
1995-01-01
A probe system has been developed to measure the flow volume of a single fluid passing through an orifice or flow line. The system employs both capacitance and a conductance probe at the orifice, together with phase detection and data acquisition circuitry to measure flow volume and salinity under low or zero gravity conditions. A wide variety of frequencies can be used for the radio frequency (RF) signal source which is chosen primarily by the capacitance of the orifice probe and the fluid passing through the orifice. Rapid measurements are made using the reflected signal from the orifice probe to determine the 'instantaneous' permittivity of the fluid/gas mixture passing through. The 'instantaneous' measurements are integrated over time to determine flow volume. Analysis reveals that a narrow orifice helps to reduce non-linearities caused by differing flow rates. The geometry of 'deflectors' and 'directors' for the flowing fluid are important in obtaining linearity. Measured data shows that a volume measurement accuracy of approximately four percent can be consistently achieved. The prototype hardware system and associated software have been optimized and are available for further applications. The system has immediate application in low or zero gravity environments for measurements of urine or other liquid volumes.
Fuel cell assembly unit for promoting fluid service and electrical conductivity
Jones, D.O.
1999-12-28
Fluid service and/or electrical conductivity for a fuel cell assembly is promoted. Open-faced flow channel(s) are formed in a flow field plate face, and extend in the flow field plate face between entry and exit fluid manifolds. A resilient gas diffusion layer is located between the flow field plate face and a membrane electrode assembly, fluidly serviced with the open-faced flow channel(s). The resilient gas diffusion layer is restrained against entering the open-faced flow channel(s) under a compressive force applied to the fuel cell assembly. In particular, a first side of a support member abuts the flow field plate face, and a second side of the support member abuts the resilient gas diffusion layer. The support member is formed with a plurality of openings extending between the first and second sides of the support member. In addition, a clamping pressure is maintained for an interface between the resilient gas diffusion layer and a portion of the membrane electrode assembly. Preferably, the support member is spikeless and/or substantially flat. Further, the support member is formed with an electrical path for conducting current between the resilient gas diffusion layer and position(s) on the flow field plate face.
Fuel cell assembly unit for promoting fluid service and electrical conductivity
Jones, Daniel O.
1999-01-01
Fluid service and/or electrical conductivity for a fuel cell assembly is promoted. Open-faced flow channel(s) are formed in a flow field plate face, and extend in the flow field plate face between entry and exit fluid manifolds. A resilient gas diffusion layer is located between the flow field plate face and a membrane electrode assembly, fluidly serviced with the open-faced flow channel(s). The resilient gas diffusion layer is restrained against entering the open-faced flow channel(s) under a compressive force applied to the fuel cell assembly. In particular, a first side of a support member abuts the flow field plate face, and a second side of the support member abuts the resilient gas diffusion layer. The support member is formed with a plurality of openings extending between the first and second sides of the support member. In addition, a clamping pressure is maintained for an interface between the resilient gas diffusion layer and a portion of the membrane electrode assembly. Preferably, the support member is spikeless and/or substantially flat. Further, the support member is formed with an electrical path for conducting current between the resilient gas diffusion layer and position(s) on the flow field plate face.
Optimal magnet configurations for Lorentz force velocimetry in low conductivity fluids
NASA Astrophysics Data System (ADS)
Alferenok, A.; Pothérat, A.; Luedtke, U.
2013-06-01
We show that the performances of flowmeters based on the measurement of Lorentz force in duct flows can be sufficiently optimized to be applied to fluids of low electrical conductivity. The main technological challenge is to design a system with permanent magnets generating a strong enough field for the Lorentz force generated when a fluid of low conductivity passes through it to be reliably measured. To achieve this, we optimize the design of a magnet system based on Halbach arrays placed on either side of the duct. In the process, we show that the fluid flow can be approximated as a moving solid bar with practically no impact on the optimization result and devise a rather general iterative optimization procedure, which incurs drastically less computational cost than a direct procedure of equivalent precision. We show that both the Lorentz force and the efficiency of the system (defined as the ratio of the Lorentz force to the weight of the system) can be increased several fold by using Halbach arrays made of three, five, seven or nine magnets on either side of the duct but that this improvement comes at a cost in terms of the precision required to position the system.
Linden, D.S.
1993-05-01
The traditional two-fluid model of superconducting conductivity was modified to make it accurate, while remaining fast, for designing and simulating microwave devices. The modification reflects the BCS coherence effects in the conductivity of a superconductor, and is incorporated through the ratio of normal to superconducting electrons. This modified ratio is a simple analytical expression which depends on frequency, temperature and material parameters. This modified two-fluid model allows accurate and rapid calculation of the microwave surface impedance of a superconductor in the clean and dirty limits and in the weak- and strong-coupled regimes. The model compares well with surface resistance data for Nb and provides insight into Nb3Sn and Y1Ba2Cu3O(7-delta). Numerical calculations with the modified two-fluid model are an order of magnitude faster than the quasi-classical program by Zimmermann (1), and two to five orders of magnitude faster than Halbritter's BCS program (2) for surface resistance.
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.; Nishihama, Masahiro
1993-01-01
The effects of laterally homogeneous mantle electrical conductivity were included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary (CMB) and the sub-adjacent fluid motion; it also features Gauss' method for solving the non-linear inverse problem associated with steady motional induction. The tradeoff between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models (DGRF's) is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition, a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.
Dynamic permeability of electrically conducting fluids under magnetic fields in annular ducts.
Cuevas, S; del Río, J A
2001-07-01
The dynamic response of an electrically conducting fluid (either Newtonian or Maxwellian) flowing between straight concentric circular cylinders under a constant radial magnetic field, is analyzed. The isothermal flow is studied using the time Fourier transform, so that the dynamic generalization of Darcy's law in the frequency domain is obtained and analytical expressions for the dynamic permeability are derived. For the Newtonian case, the range of frequencies where the dynamic permeability approaches the static value is enlarged the smaller the gap between the cylinders and the higher the magnetic-field strength. For the Maxwell fluid, the presence of the inner cylinder shifts the frequencies that lead to the enhancement of the real part of the dynamic permeability to larger values and increases its maximum values relative to the case where the inner cylinder is absent. In addition, the Ohmic dissipation causes the damping of the amplitude of the response. PMID:11461397
NASA Astrophysics Data System (ADS)
Holotescu, S.; Stoian, F. D.; Marinica, O.; Kubicar, L.; Kopcansky, P.; Timko, M.
2011-05-01
In this study, the semi-empirical equation for the effective thermal conductivity of the Holotescu-Stoian model was applied to a set of four dilutions of a transformer oil based magnetic fluid with magnetite nanoparticles as magnetic phase, using the results obtained for the size distributions from the magnetogranulometry analysis, followed by a comparison with the measured values of the effective thermal conductivity obtained by the hot ball method. The link between the size distribution by number and by volume used in the magnetogranulometry analysis and the Holotescu-Stoian model adaptation to the lognormal distribution were presented. The comparison between the results given by the model and the corresponding experimental data showed that by using the approximated size distribution to calculate the effective thermal conductivity the analytical results much closer to the experimental ones are obtained, compared to those given by the Maxwell classical model.
NASA Astrophysics Data System (ADS)
Watanabe, T.; Kitano, M.
2011-12-01
Intercrystalline fluid can significantly affect rheological and transport properties of rocks. Its influences are strongly dependent on its distribution. The dihedral angle between solid and liquid phases has been widely accepted as a key parameter that controls solid-liquid textures. The liquid phase is not expected to be interconnected if the dihedral angle is larger than 60 degree. However, observations contradictory to dihedral angle values have been reported. Watanabe (2010) suggested the coexistence of grain boundary fluid with a positive dihedral angle. For good understanding of fluid distribution, it is thus critical to study the nature of grain boundary fluid. We have developed a high pressure and temperature apparatus for study of intercrystalline fluid distribution. It was specially designed for measurements of elastic wave velocities and electrical conductivity. The apparatus mainly consists of a conventional cold-seal vessel with an external heater. The pressure medium is silicon oil of the viscosity of 0.1 Pa s. The pressure and temperature can be controlled from 0 to 200 MPa and from 20 to 200 C, respectively. Dimensions of a sample are 9 mm in diameter, and 15 mm in length. Halite-water system is used as an analog for crustal rocks. The dihedral angle has been studied systematically at various pressure and temperature conditions [Lewis and Holness, 1996]. The dihedral angle is larger than 60 degree at lower pressure and temperature. It decreases to be smaller than 60 degree with increasing pressure and temperature. A sample is prepared by cold-pressing and annealing of wet NaCl powder. Optical examination has shown that synthesized samples are microstructurally homogeneous. Grains are polygonal and equidimensional with a mean diameter of 100 micrometer. Grain boundaries vary from straight to bowed and 120 degree triple junctions are common. Gas and fluid bearing inclusions are visible on the grain boundaries. There are spherical inclusions or
Bartlett, Philip N; Cook, David C; George, Michael W; Ke, Jie; Levason, William; Reid, Gillian; Su, Wenta; Zhang, Wenjian
2010-01-14
Electrochemistry in supercritical CO(2) (scCO(2)) is difficult because the very low dielectric constant of the fluid restricts the solubility of ionic species and the conductivity of dissolved electrolytes. To overcome this problem to allow us to carry out electrodeposition at macroelectrodes from scCO(2) we have investigated the use of co-solvents and modified electrolyte salts chosen to increase their solubility and dissociation in the supercritical fluid. Here we report results of phase behaviour studies for mixtures of CO(2) with [NBu(n)(4)][BF(4)] and either methanol (CH(3)OH) or acetonitrile (CH(3)CN) as the co-solvent. These show that the solubility of [NBu(n)(4)][BF(4)] is approximately 5 times larger when CH(3)CN is the co-solvent rather than CH(3)OH. Consequently the phase behaviour of the ternary of CO(2)-[NBu(n)(4)][BF(4)]-CH(3)CN was studied in greater detail over a range of compositions. To enhance the conductivity of scCO(2)-CH(3)CN a range of electrolyte salts was synthesised in which the [NBu(n)(4)](+) and/or [BF(4)](-) ion were replaced by different derivatives. Results for the phase behaviour and conductivity of these modified electrolyte salts in scCO(2)-CH(3)CN are reported for several different compositions. We find that increasing the degree of fluorination and size of the ions increases the solubility of the electrolyte salt in scCO(2)-CH(3)CN. Of the 11 electrolytes investigated [NBu(n)(4)][B{3,5-C(6)H(3)(CF(3))(2)}(4)] appears the most suitable for use in scCO(2)-CH(3)CN with a molar conductivity of 22-26 S cm(2) mol(-1) and a maximum measured conductivity of approximately 3 mS cm(-1) for 0.07 M [NBu(n)(4)][B{3,5-C(6)H(3)(CF(3))(2)}(4)] dissolved in scCO(2)-CH(3)CN (molar ratio CH(3)CN : CO(2) approximately 0.12) at 20 MPa and 328.15 K. This is an order of magnitude improvement over similar results for the [NBu(n)(4)][BF(4)] parent. Studies of the conductance as a function of the electrolyte concentration suggest that triple ions make an
Instabilities of thin layers of conducting fluids produced by time dependent magnetic fields
NASA Astrophysics Data System (ADS)
Burguete, Javier
2011-11-01
We present the recent results of an experiment where thin layers of conducting fluids are forced by time-dependent magnetic fields perpendicular to their surface. We use as conducting fluid an In-Ga-Sn alloy, immersed in a 5% hydrocloric acid solution to prevent oxidation. The conducting layers have a circular shape, and are placed inside a set-up that produces the vertical magnetic field. Due to MHD effects, the competition between the Lorentz force and gravity triggers an instability of the free surface. The shape of this surface can adopt many different configurations, with a very rich dynamics, presenting azimuthal wave numbers between 3 and 8 for the explored parameters. The magnetic field evolves harmonically with a frequency up to 10Hz, small enough to not to observe skin depth effects and with a magnitude up to 0.1 T. Different resonant regions have been observed, for narrow windows of the forcing frequency. We have analysed the existence of thresholds for these instabilities, depending on the wave number and experimental parameters. These results are compared with others present in the literature.
Viscous Incompressible Flow Computations for 3-D Steady and Unsteady Flows
NASA Technical Reports Server (NTRS)
Kwak, Dochan
2001-01-01
This viewgraph presentation gives an overview of viscous incompressible flow computations for three-dimensional steady and unsteady flows. Details are given on the use of computational fluid dynamics (CFD) as an engineering tool, solution methods for incompressible Navier-Stokes equations, numerical and physical characteristics of the primitive variable approach, and the role of CFD in the past and in current engineering and research applications.
Video of Miscible Fluid Experiment Conducted on NASA Low Gravity Airplane
NASA Technical Reports Server (NTRS)
2003-01-01
This is a video of dyed water being injected into glycerin in a 2.2 centimeter (cm) diameter test tube. The experiment was conducted on the KC-135 aircraft, a NASA plane that creates microgravity and 2g conditions as it maneuvers through multiple parabolas. The water is less dense and so it rises to the top of the glycerin. The goal of the experiment was to determine if a blob of a miscible fluid would spontaneously become spherical in a microgravity environment.
NASA Astrophysics Data System (ADS)
Alekseev, G. V.
2015-12-01
The boundary value problem for the stationary magnetohydrodynamics model of a viscous heatconducting fluid considered under inhomogeneous mixed boundary conditions for an electromagnetic field and the temperature and Dirichlet condition for the velocity is investigated. This problem describes the flow of an electricaland heat-conducting liquid in a bounded three-dimensional domain the boundary of which consists of several parts with different thermoand electrophysical properties. Sufficient conditions imposed on the initial data to provide for global solvability of the problem and local uniqueness of its solution are established.
Internally supported flexible duct joint. [device for conducting fluids in high pressure systems
NASA Technical Reports Server (NTRS)
Kuhn, R. F., Jr. (Inventor)
1975-01-01
An internally supported, flexible duct joint for use in conducting fluids under relatively high pressures in systems where relatively large deflection angles must be accommodated is presented. The joint includes a flexible tubular bellows and an elongated base disposed within the bellows. The base is connected through radiating struts to the bellows near mid-portion and to each of the opposite end portions of the bellows through a pivotal connecting body. A motion-controlling linkage is provided for linking the connecting bodies, whereby angular displacement of the joint is controlled and uniformity in the instantaneous bend radius of the duct is achieved as deflection is imposed.
Il’in, V. A. Mordvinov, A. N.; Petrov, D. A.
2015-01-15
We study the stability of equilibrium and nonlinear regimes of a nonuniformly heated poorly conducting fluid in a horizontal capacitor in the gravity field and in a dc electric field under a unipolar charge injection. A model in which the density of charges injected from the cathode is proportional to the electric field strength in the capacitor is considered. The dependences of critical parameters on the degree of heating and charge injection are determined. The effect of the Prandtl number on the equilibrium instability boundary and on the frequency of neutral vibrations is analyzed. Nonlinear regimes of electroconvection are studied for heating from below.
Fuel cell assembly fluid flow plate having conductive fibers and rigidizing material therein
Walsh, Michael M.
2000-01-01
A fluid flow plate is preferably formed with three initial sections, for instance, two layers of conductive (e.g., metal) fibers and a barrier material (e.g., metal foil) which is interposed between the two layers. For example, sintering of these three sections can provide electrical path(s) between outer faces of the two layers. Then, the sintered sections can be, for instance, placed in a mold for forming of flow channel(s) into one or more of the outer faces. Next, rigidizing material (e.g., resin) can be injected into the mold, for example, to fill and/or seal space(s) about a conductive matrix of the electrical path(s). Preferably, abrading of surface(s) of the outer face(s) serves to expose electrical contact(s) to the electrical path(s).
Supercomputing Aspects for Simulating Incompressible Flow
NASA Technical Reports Server (NTRS)
Kwak, Dochan; Kris, Cetin C.
2000-01-01
The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier
NASA Astrophysics Data System (ADS)
Lesmes, David P.; Frye, Kevin M.
2001-01-01
The spectral induced-polarization (IP) response of rocks and soils is a complex function of pore solution chemistry, sample microgeometry, and surface chemical properties. We measure the complex conductivity and the time domain IP responses of Berea sandstone as a function of pore fluid ionic strength and pH. Complex conductivity is measured over the frequency range 10-3 to 106 Hz, and chargeability is computed using a time window of 0.16 to 1.74 s. The field IP parameters: phase, percent frequency effect, and chargeability are functions of both the surface and bulk electrical properties of the sample and are observed to decrease with increasing solution conductivity. Dividing these parameters by the sample resistivity yields normalized IP parameters (quadrature conductivity, metal factor, normalized chargeability) that are proportional to the imaginary component of the complex surface conductivity. Normalized IP parameters increase with ionic strength up to concentrations of 10-1 M NaCl and show a reduced response at pH 3, the point of zero charge for quartz-dominated systems. For concentrations >10-1 M NaCl, the normalized parameters decrease with increasing concentration. This decrease in surface polarization may indicate a decrease in the effective mobility of polarizing charges at high solution concentration. Our data indicate that normalized IP parameters are directly related to the physiochemical parameters that control the surface conductivity responses of rocks and soils. Normalization of IP measurements in environmental investigations should increase the effectiveness of IP surveys, especially in high-conductivity environments.
Two-fluid nature of phonon heat conduction in a monatomic lattice
NASA Astrophysics Data System (ADS)
Evteev, Alexander V.; Levchenko, Elena V.; Belova, Irina V.; Murch, Graeme E.
2015-08-01
The thermal resistance of a crystal lattice with a monatomic unit cell due to three-phonon scattering processes is investigated in detail theoretically. A general expression for the lattice thermal conductivity is derived from a combined analysis based on: (i) the Boltzmann equation and (ii) data on the heat current autocorrelation function obtained via molecular dynamics simulations in conjunction with the Green-Kubo formalism. It is argued that the phonon gas in a monatomic lattice conducts heat as if it consisted of two distinct parts (two 'thermal fluids'), so that the lattice thermal conductivity can be decomposed into contributions from these two parts. The origin of the behaviour of the phonon gas, which is explored in the present work, is due to an intrinsic interplay between Umklapp and normal three-phonon scattering processes. New insight into the nature of the lattice thermal conductivity is demonstrated and the results of the present work are in agreement with previous studies in this area.
Novel residual-based large eddy simulation turbulence models for incompressible magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Sondak, David
The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting
Decoupling ion conductivity and fluid permeation through optimizing hydrophilic channel morphology
NASA Astrophysics Data System (ADS)
Chu, Peter Po-Jen; Fang, Yu-Shin; Tseng, Yu-Chen
2016-05-01
Approaches to improve membrane ion conductivity usually leads to higher degree of swelling, more serious fuel cross-over and often sacrificed membrane mechanical strength. Preserving all three main membrane properties is a tough challenge in searching high ion conducting fuel cell membrane. The long standing dilemma is resolved by decoupling ion conduction and fluid permeation property by creating optimized channel morphology using external electric field poling. Success of this approach is demonstrated in the proton conducting membrane composed of poly(ether sulfones) (PES) and sulfonated poly(ether ether ketone) (sPEEK, degree of sulfonation=50%) composites prepared under electric field poling condition. The external field enhanced the aromatic chain ordering from both sPEEK and PES and improved the miscibility. This induced interaction is conducive to the formation of more densely packed amorphous domains that eventually leads to preferentially ordered hydrophilic proton conducting channels having a average dimension (3 nm) smaller than that in generic sPEEK or Nafion. The narrower but more ordered channel displayed much lower methanol permeability (3.17×10-7 cm2/s), and lower swelling ratio (31.20%), while the conductivity (~10-1 S/cm) is higher than that of Nafion, or sPEEK at higher (64%) degree of sulfonation. The composite is chemically stable and highly durable with improved membrane mechanical strength. Nearly 50% increase of DMFC power output is observed using this membrane, and the best power density is recorded at 155 mA/cm2 (80 °C, 1M Methanol).
The application of moment methods to the analysis of fluid electrical conductivity logs in boreholes
Loew, S. ); Tsang, Chin-Fu; Hale, F.V. ); Hufschmied, P. , Baden )
1990-08-01
This report is one of a series documenting the results of the Nagra-DOE Cooperative (NDC-I) research program in which the cooperating scientists explore the geological, geophysical, hydrological, geochemical, and structural effects anticipated from the use of a rock mass as a geologic repository for nuclear waste. Previous reports have presented a procedure for analyzing a time sequence of wellbore electric conductivity logs in order to obtain outflow parameters of fractures intercepted by the borehole, and a code, called BORE, used to simulate borehole fluid conductivity profiles given these parameters. The present report describes three new direct (not iterative) methods for analyzing a short time series of electric conductivity logs based on moment quantities of the individual outflow peaks and applies them to synthetic as well as to field data. The results of the methods discussed show promising results and are discussed in terms of their respective advantages and limitations. In particular it is shown that one of these methods, the so-called Partial Moment Method,'' is capable of reproducing packer test results from field experiments in the Leuggern deep well within a factor of three, which is below the range of what is recognized as the precision of packer tests themselves. Furthermore the new method is much quicker than the previously used iterative fitting procedure and is even capable of handling transient fracture outflow conditions. 20 refs., 11 figs., 10 tabs.
Instability in Three-Dimensional Magnetohydrodynamic Flows of an Electrically Conducting Fluid
NASA Astrophysics Data System (ADS)
Zakir, Hussain; Liu, Chan; Zhang, Nianmei; Ni, Mingjiu
2013-12-01
The three-dimensional instability of an electrically conducting fluid between two parallel plates affected by an imposed transversal magnetic field is numerically investigated by a Chebyshev collocation method. The QZ method is utilized to obtain neutral curves of the linear instability. The details of instability are analyzed by solving the generalized Orr-Sommerfeld equation. The critical Reynolds number Rec, the stream-wise and span-wise critical wave numbers αc and βc are obtained for a wide range of Hartmann number Ha. The effects of Lorentz force and span-wise perturbation on three-dimensional instability are investigated. The results show that magnetic field would suppress the instability and critical Reynolds number tends to be larger than that for two-dimensional instability.
A Simple Demonstration of Lorentz Force in Electrically-Conductive Fluid
NASA Astrophysics Data System (ADS)
Ribeiro, A.; Aurnou, J.
2013-12-01
Flows driven by electromagnetic Lorentz forces are ubiquitous in the universe. Lorentz forces are essential, for example, in the dynamics of planetary cores and astrophysical plasmas. In an electrically-conducting fluid, this force is defined as the vector cross product of the magnetic field with the electric current density. We have built an easily-replicated desktop device to demonstrate the effects of Lorentz forces in a copper sulfate solution. The electric current is controlled by a DC power supply, and the magnetic field is imposed using neodymium magnets. By varying the electric current, it is possible to tune the Lorentz forces and, thus, the resulting drive motions in the copper sulfate solution. Experiments will be carried out onsite, along with real time measurements of electric potential, magnetic field strength and local flow velocities.
Three-Dimensional Printing of Highly Conductive Carbon Nanotube Microarchitectures with Fluid Ink.
Kim, Jung Hyun; Lee, Sanghyeon; Wajahat, Muhammad; Jeong, Hwakyung; Chang, Won Suk; Jeong, Hee Jin; Yang, Jong-Ryul; Kim, Ji Tae; Seol, Seung Kwon
2016-09-27
Moving printed electronics to three dimensions essentially requires advanced additive manufacturing techniques yielding multifunctionality materials and high spatial resolution. Here, we report the meniscus-guided 3D printing of highly conductive multiwall carbon nanotube (MWNT) microarchitectures that exploit rapid solidification of a fluid ink meniscus formed by pulling a micronozzle. To achieve high-quality printing with continuous ink flow through a confined nozzle geometry, that is, without agglomeration and nozzle clogging, we design a polyvinylpyrrolidone-wrapped MWNT ink with uniform dispersion and appropriate rheological properties. The developed technique can produce various desired 3D microstructures, with a high MWNT concentration of up to 75 wt % being obtained via post-thermal treatment. Successful demonstrations of electronic components such as sensing transducers, emitters, and radio frequency inductors are also described herein. We expect that the technique presented in this study will facilitate selection of diverse materials in 3D printing and enhance the freedom of integration for advanced conceptual devices.
NASA Astrophysics Data System (ADS)
Ranganayakulu, Ch.; Seetharamu, K. N.
An analysis of a crossflow plate-fin compact heat exchanger, accounting for the combined effect of two-dimensional longitudinal heat conduction through the exchanger wall and nonuniform inlet fluid flow distribution on both hot and cold fluid sides is carried out using a finite element method. Using the fluid flow maldistribution models, the exchanger effectiveness and its deterioration due to the combined effects of longitudinal heat conduction and flow nonuniformity are calculated for various design and operating conditions of the exchanger. It was found that the performance deteriorations are quite significant in some typical applications due to the combined effects of wall longitudinal heat conduction and inlet fluid flow nonuniformity on crossflow plate-fin heat exchanger.
10 CFR 26.97 - Conducting an initial test for alcohol using a specimen of oral fluids.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 10 Energy 1 2010-01-01 2010-01-01 false Conducting an initial test for alcohol using a specimen of oral fluids. 26.97 Section 26.97 Energy NUCLEAR REGULATORY COMMISSION FITNESS FOR DUTY PROGRAMS Collecting Specimens for Testing § 26.97 Conducting an initial test for alcohol using a specimen of...
Khine, Soe Minn; Houra, Tomoya; Tagawa, Masato
2013-04-01
In temperature measurement of non-isothermal fluid flows by a contact-type temperature sensor, heat conduction along the sensor body can cause significant measurement error which is called "heat-conduction error." The conventional formula for estimating the heat-conduction error was derived under the condition that the fluid temperature to be measured is uniform. Thus, if we apply the conventional formula to a thermal field with temperature gradient, the heat-conduction error will be underestimated. In the present study, we have newly introduced a universal physical model of a temperature-measurement system to estimate accurately the heat-conduction error even if a temperature gradient exists in non-isothermal fluid flows. Accordingly, we have been able to successfully derive a widely applicable estimation and/or evaluation formula of the heat-conduction error. Then, we have verified experimentally the effectiveness of the proposed formula using the two non-isothermal fields-a wake flow formed behind a heated cylinder and a candle flame-whose fluid-dynamical characteristics should be quite different. As a result, it is confirmed that the proposed formula can represent accurately the experimental behaviors of the heat-conduction error which cannot be explained appropriately by the existing formula. In addition, we have analyzed theoretically the effects of the heat-conduction error on the fluctuating temperature measurement of a non-isothermal unsteady fluid flow to derive the frequency response of the temperature sensor to be used. The analysis result shows that the heat-conduction error in temperature-fluctuation measurement appears only in a low-frequency range. Therefore, if the power-spectrum distribution of temperature fluctuations to be measured is sufficiently away from the low-frequency range, the heat-conduction error has virtually no effect on the temperature-fluctuation measurements even by the temperature sensor accompanying the heat-conduction error in
NASA Astrophysics Data System (ADS)
Minn Khine, Soe; Houra, Tomoya; Tagawa, Masato
2013-04-01
In temperature measurement of non-isothermal fluid flows by a contact-type temperature sensor, heat conduction along the sensor body can cause significant measurement error which is called "heat-conduction error." The conventional formula for estimating the heat-conduction error was derived under the condition that the fluid temperature to be measured is uniform. Thus, if we apply the conventional formula to a thermal field with temperature gradient, the heat-conduction error will be underestimated. In the present study, we have newly introduced a universal physical model of a temperature-measurement system to estimate accurately the heat-conduction error even if a temperature gradient exists in non-isothermal fluid flows. Accordingly, we have been able to successfully derive a widely applicable estimation and/or evaluation formula of the heat-conduction error. Then, we have verified experimentally the effectiveness of the proposed formula using the two non-isothermal fields—a wake flow formed behind a heated cylinder and a candle flame—whose fluid-dynamical characteristics should be quite different. As a result, it is confirmed that the proposed formula can represent accurately the experimental behaviors of the heat-conduction error which cannot be explained appropriately by the existing formula. In addition, we have analyzed theoretically the effects of the heat-conduction error on the fluctuating temperature measurement of a non-isothermal unsteady fluid flow to derive the frequency response of the temperature sensor to be used. The analysis result shows that the heat-conduction error in temperature-fluctuation measurement appears only in a low-frequency range. Therefore, if the power-spectrum distribution of temperature fluctuations to be measured is sufficiently away from the low-frequency range, the heat-conduction error has virtually no effect on the temperature-fluctuation measurements even by the temperature sensor accompanying the heat-conduction
Tree-Shaped Fluid Flow and Heat Storage in a Conducting Solid
Combelles, L.; Lorente, S.; Anderson, R.; Bejan, A.
2012-01-01
This paper documents the time-dependent thermal interaction between a fluid stream configured as a plane tree of varying complexity embedded in a conducting solid with finite volume and insulated boundaries. The time scales of the convection-conduction phenomenon are identified. Two-dimensional and three-dimensional configurations are simulated numerically. The number of length scales of the tree architecture varies from one to four. The results show that the heat transfer density increases, and the time of approach to equilibrium decreases as the complexity of the tree designs increases. These results are then formulated in the classical notation of energy storage by sensible heating, which shows that the effective number of heat transfer units increases as the complexity of the tree design increases. The complexity of heat transfer designs in many applications is constrained by first cost and operating cost considerations. This work provides a fundamental basis for objective evaluation of cost and performance tradeoffs in thermal design of energy systems with complexity as an unconstrained parameter that can be actively varied over a broad range to determine the optimum system design.
Conductivity measurements on H_{2}O-bearing CO_{2}-rich fluids
Capobianco, Ryan M.; Miroslaw S. Gruszkiewicz; Bodnar, Robert J.; Rimstidt, J. Donald
2014-09-10
Recent studies report rapid corrosion of metals and carbonation of minerals in contact with carbon dioxide containing trace amounts of dissolved water. One explanation for this behavior is that addition of small amounts of H_{2}O to CO_{2} leads to significant ionization within the fluid, thus promoting reactions at the fluid-solid interface analogous to corrosion associated with aqueous fluids. The extent of ionization in the bulk CO_{2} fluid was determined using a flow-through conductivity cell capable of detecting very low conductivities. Experiments were conducted from 298 to 473 K and 7.39 to 20 MPa with H_{2}O concentrations up to ~1600 ppmw (xH_{2}O ≈ 3.9 x 10^{-3}), corresponding to the H_{2}O solubility limit in liquid CO_{2} at ambient temperature. All solutions showed conductivities <10 nS/cm, indicating that the solutions were essentially ion-free. Furthermore, this observation suggests that the observed corrosion and carbonation reactions are not the result of ionization in CO_{2}-rich bulk phase, but does not preclude ionization in the fluid at the fluid-solid interface.
Bandopadhyay, Aditya; Chakraborty, Suman
2015-03-21
By considering an ion moving inside an imaginary sphere filled with a power-law fluid, we bring out the implications of the fluid rheology and the influence of the proximity of the other ions towards evaluating the conduction current in an ionic solution. We show that the variation of the conductivity as a function of the ionic concentration is both qualitatively and quantitatively similar to that predicted by the Kohlrausch law. We then utilize this consideration for estimating streaming potentials developed across narrow fluidic confinements as a consequence of the transport of ions in a convective medium constituting a power-law fluid. These estimates turn out to be in sharp contrast to the classical estimates of streaming potential for non-Newtonian fluids, in which the effect of rheology of the solvent is merely considered to affect the advection current, disregarding its contributions to the conduction current. Our results have potential implications of devising a new paradigm of consistent estimation of streaming potentials for non-Newtonian fluids, with combined considerations of the confinement effect and fluid rheology in the theoretical calculations.
Piyush Sabharwall; Qiao Wu; James J. Sienicki
2012-06-01
The effect of fluid axial thermal conduction on one-dimensional liquid metal natural circulation and its linear stability was performed through nondimensional analysis, steady-state assessment, and linear perturbation evaluation. The Nyquist criterion and a root-search method were employed to find the linear stability boundary of both forward and backward circulations. The study provided a relatively complete analysis method for one-dimensional natural circulation problems with the consideration of fluid axial heat conduction. The results suggest that fluid axial heat conduction in a natural circulation loop should be considered only when the modified Peclet number is {approx}1 or less, which is significantly smaller than the practical value of a lead liquid metal-cooled reactor.
Three-Dimensional Printing of Highly Conductive Carbon Nanotube Microarchitectures with Fluid Ink.
Kim, Jung Hyun; Lee, Sanghyeon; Wajahat, Muhammad; Jeong, Hwakyung; Chang, Won Suk; Jeong, Hee Jin; Yang, Jong-Ryul; Kim, Ji Tae; Seol, Seung Kwon
2016-09-27
Moving printed electronics to three dimensions essentially requires advanced additive manufacturing techniques yielding multifunctionality materials and high spatial resolution. Here, we report the meniscus-guided 3D printing of highly conductive multiwall carbon nanotube (MWNT) microarchitectures that exploit rapid solidification of a fluid ink meniscus formed by pulling a micronozzle. To achieve high-quality printing with continuous ink flow through a confined nozzle geometry, that is, without agglomeration and nozzle clogging, we design a polyvinylpyrrolidone-wrapped MWNT ink with uniform dispersion and appropriate rheological properties. The developed technique can produce various desired 3D microstructures, with a high MWNT concentration of up to 75 wt % being obtained via post-thermal treatment. Successful demonstrations of electronic components such as sensing transducers, emitters, and radio frequency inductors are also described herein. We expect that the technique presented in this study will facilitate selection of diverse materials in 3D printing and enhance the freedom of integration for advanced conceptual devices. PMID:27564233
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.
Numerical Simulation of Incompressible Flows with Moving Interfaces
NASA Astrophysics Data System (ADS)
Medale, Marc; Jaeger, Marc
1997-03-01
A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model.
Electro-response of MoS2 Nanosheets-Based Smart Fluid with Tailorable Electrical Conductivity.
Lee, Seungae; Kim, Yun Ki; Hong, Jin-Yong; Jang, Jyongsik
2016-09-14
The correlation between electrical conductivity and electro-responsive behavior is identified by introducing few-layer molybdenum disulfide (MoS2) nanosheets to electrorheological (ER) fluid. Few-layer MoS2 nanosheets are successfully fabricated, with a high yield of above 60%, using a straightforward method, and applied to an electro-responsive smart fluid. The electrical conductivity of MoS2 is easily tunable by adjusting the annealing temperature because of its semiconducting behavior. From an in-depth study on the conductivity-dependent ER behavior of few-layer MoS2 nanosheets, it can be verified that an optimum value of the electrical conductivity exists for the electro-responsive material, corresponding to the Wagner model. To the best of our knowledge, this is the first report on the potential of a transition-metal dichalcogenide as a candidate material for an ER fluid. This study may provide promising approaches for the performance improvement of electro-responsive smart fluids. PMID:27552369
Electro-response of MoS2 Nanosheets-Based Smart Fluid with Tailorable Electrical Conductivity.
Lee, Seungae; Kim, Yun Ki; Hong, Jin-Yong; Jang, Jyongsik
2016-09-14
The correlation between electrical conductivity and electro-responsive behavior is identified by introducing few-layer molybdenum disulfide (MoS2) nanosheets to electrorheological (ER) fluid. Few-layer MoS2 nanosheets are successfully fabricated, with a high yield of above 60%, using a straightforward method, and applied to an electro-responsive smart fluid. The electrical conductivity of MoS2 is easily tunable by adjusting the annealing temperature because of its semiconducting behavior. From an in-depth study on the conductivity-dependent ER behavior of few-layer MoS2 nanosheets, it can be verified that an optimum value of the electrical conductivity exists for the electro-responsive material, corresponding to the Wagner model. To the best of our knowledge, this is the first report on the potential of a transition-metal dichalcogenide as a candidate material for an ER fluid. This study may provide promising approaches for the performance improvement of electro-responsive smart fluids.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Statistical theory of turbulent incompressible multimaterial flow
Kashiwa, B.
1987-10-01
Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of kappa-epsilon modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy kappa, and the rate of fluctuational energy dissipation epsilon, for each material. Hence a set of kappa and epsilon equations must be solved, together with mean mass and momentum conservation equations, for each material. Both kappa and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe.
Self-similarity in incompressible Navier-Stokes equations.
Ercan, Ali; Kavvas, M Levent
2015-12-01
The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space. PMID:26723165
Fluid Dynamics with Free Surfaces
1992-02-01
RIPPLE is a two-dimensional, transient, free surface incompressible fluid dynamics program. It allows multiple free surfaces with surface tension and wall adhesion forces and has a partial cell treatment which allows curved boundaries and interior obstacles.
NASA Astrophysics Data System (ADS)
Habibi, F.; Pazhouhesh, R.; Shaghaghian, M.
2015-01-01
In this paper, we investigate the time evolution of an accreting magneto-fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one-dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's law; however, the shear viscous stress is neglected, as well as the self-gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto-fluid, we have used a self-similar solution. We introduce two dimensionless variables, S_0 and ɛ_ρ, which represent the size of the electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity, and the rotational velocity are presented analytically. The solutions show that the S_0 and ɛ_ρ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter ɛ_ρ has a more significant effect on the physical quantities for small radii.
Fluid mechanics in fluids at rest.
Brenner, Howard
2012-07-01
Using readily available experimental thermophoretic particle-velocity data it is shown, contrary to current teachings, that for the case of compressible flows independent dye- and particle-tracer velocity measurements of the local fluid velocity at a point in a flowing fluid do not generally result in the same fluid velocity measure. Rather, tracer-velocity equality holds only for incompressible flows. For compressible fluids, each type of tracer is shown to monitor a fundamentally different fluid velocity, with (i) a dye (or any other such molecular-tagging scheme) measuring the fluid's mass velocity v appearing in the continuity equation and (ii) a small, physicochemically and thermally inert, macroscopic (i.e., non-Brownian), solid particle measuring the fluid's volume velocity v(v). The term "compressibility" as used here includes not only pressure effects on density, but also temperature effects thereon. (For example, owing to a liquid's generally nonzero isobaric coefficient of thermal expansion, nonisothermal liquid flows are to be regarded as compressible despite the general perception of liquids as being incompressible.) Recognition of the fact that two independent fluid velocities, mass- and volume-based, are formally required to model continuum fluid behavior impacts on the foundations of contemporary (monovelocity) fluid mechanics. Included therein are the Navier-Stokes-Fourier equations, which are now seen to apply only to incompressible fluids (a fact well-known, empirically, to experimental gas kineticists). The findings of a difference in tracer velocities heralds the introduction into fluid mechanics of a general bipartite theory of fluid mechanics, bivelocity hydrodynamics [Brenner, Int. J. Eng. Sci. 54, 67 (2012)], differing from conventional hydrodynamics in situations entailing compressible flows and reducing to conventional hydrodynamics when the flow is incompressible, while being applicable to both liquids and gases.
Stochastic least-action principle for the incompressible Navier-Stokes equation
NASA Astrophysics Data System (ADS)
Eyink, Gregory L.
2010-07-01
We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton’s principle for the incompressible Euler solutions in the case of zero viscosity. We use this principle to give a new derivation of a stochastic Kelvin Theorem for the Navier-Stokes equation, recently established by Constantin and Iyer, which shows that this stochastic conservation law arises from particle-relabelling symmetry of the action. We discuss issues of irreversibility, energy dissipation, and the inviscid limit of Navier-Stokes solutions in the framework of the stochastic variational principle. In particular, we discuss the connection of the stochastic Kelvin Theorem with our previous “martingale hypothesis” for fluid circulations in turbulent solutions of the incompressible Euler equations.
NASA Astrophysics Data System (ADS)
Thorwart, Martin; Dzierma, Yvonne; Rabbel, Wolfgang; Hensen, Christian
2014-10-01
At the continental margin of north Costa Rica and Nicaragua, the strongly hydrated Cocos Plate subducts beneath the Caribbean Plate. From the downgoing Cocos plate fluids are released through extensional fractures in the overriding plate. At the seafloor, they form fluid seeps, mounds and other types of fluid expulsion. Using an offshore temporary seismic network, we investigated seismicity possibly related to these processes and observed several swarms of earthquakes located on the continental slope trenchward of the seismogenic zone of S Nicaragua. The seismicity occurred within the downgoing plate, near the plate interface and in the overriding plate. We interpret these swarm events as an expression of pore pressure propagation under critical stress conditions driven by fluid release from the downgoing plate. In order to estimate hydraulic diffusivity and permeability values, we applied a theory developed for injection test interpretation to the spatio-temporal development of the swarms. The resulting diffusivity and permeability values are in the ranges of 28-305 m²/s and 3.2 × 10-14 m²-35.1 × 10-14 m², respectively, applying to the continental and oceanic crust near the plate interface. These values are somewhat larger than observed in drill logs on the margin wedge off north Costa Rica, but of comparable magnitude to values estimated for the Antofagasta 1995 earthquake aftershock sequence.
NASA Astrophysics Data System (ADS)
Alsaedi, A.; Hayat, T.; Muhammad, T.; Shehzad, S. A.
2016-09-01
This study models the magnetohydrodynamic (MHD) three-dimensional boundary layer flow of viscoelastic fluid. The flow is due to the exponentially stretching surface. The heat transfer analysis is performed through prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The thermal conductivity is taken temperature dependent. Series solutions of velocities and temperatures are constructed. Graphical results for PST and PHF cases are plotted and analyzed. Numerical values of skin-friction coefficients and Nusselt numbers are presented and discussed.
NASA Astrophysics Data System (ADS)
Coussens, J. P.; Woodman, N. D.; Menzies, C. D.; Teagle, D. A. H.; Sutherland, R.; Capova, L.; Cox, S.; Upton, P.; Townend, J.; Toy, V.
2015-12-01
Fluid flow can play an important role in fault failure, due to the influence of pore pressure on effective confining stress and through chemical and thermal alteration of the fault zone. Rocks of the Alpine Fault Zone, both exposed at the surface and recovered in cores, show evidence for significant alteration by fluids. However, the fluid flow regime in the region is poorly constrained and its relationship with the behaviour of the fault is uncertain. In 2014 the Deep Fault Drilling Project (DFDP) drilled the DFDP-2B borehole, penetrating 893 m into the hanging-wall of the Alpine Fault. Prior to drilling, a set of hydrogeological models for the Whataroa Valley region, encompassing the DFDP-2B drill site, were constructed using the modelling software FEFLOW. Models were constructed for a range of plausible hydraulic conductivity structures for the region. They predicted strongly artesian hydraulic heads of 50-150 m above surface elevation and temperatures exceeding 100 °C within 1 km depth in bedrock beneath the DFDP-2 drill site, with the exact hydraulic and thermal gradients dependent on the hydraulic conductivity structure chosen. During the drilling project hydraulic and thermal data from the borehole was collected. This included 33 slug test datasets, carried out at a range of borehole depths throughout the project. Estimates for hydraulic conductivity were obtained by analysis of slug test data. Steady state hydraulic heads for the borehole, across a range of depths, were estimated from the slug test measurements. Depth profiles of hydraulic head show rapid increases in hydraulic head with depth, in line with model predictions. Results show fluid pressures greatly exceeding hydrostatic pressure in the shallow crust, reflecting significant upward flow of groundwater beneath the Whataroa Valley. Hydraulic conductivity estimates provide constraints on the hydraulic conductivity structure of the region. All hydraulic conductivity structures modelled thus far
NASA Astrophysics Data System (ADS)
Tsang, Chin-Fu; Rosberg, Jan-Erik; Sharma, Prabhakar; Berthet, Theo; Juhlin, Christopher; Niemi, Auli
2016-09-01
Drilling of a deep borehole does not normally allow for hydrologic testing during the drilling period. It is only done when drilling experiences a large loss (or high return) of drilling fluid due to penetration of a large-transmissivity zone. The paper proposes the possibility of conducting flowing fluid electrical conductivity (FFEC) logging during the drilling period, with negligible impact on the drilling schedule, yet providing important information on depth locations of both high- and low-transmissivity zones and their hydraulic properties. The information can be used to guide downhole fluid sampling and post-drilling detailed testing of the borehole. The method has been applied to the drilling of a 2,500-m borehole at Åre, central Sweden, firstly when the drilling reached 1,600 m, and then when the drilling reached the target depth of 2,500 m. Results unveil eight hydraulically active zones from 300 m down to borehole bottom, with depths determined to within the order of a meter. Further, the first set of data allows the estimation of hydraulic transmissivity values of the six hydraulically conductive zones found from 300 to 1,600 m, which are very low and range over one order of magnitude.
NASA Astrophysics Data System (ADS)
Tsang, Chin-Fu; Rosberg, Jan-Erik; Sharma, Prabhakar; Berthet, Theo; Juhlin, Christopher; Niemi, Auli
2016-04-01
Drilling of a deep borehole does not normally allow for hydrologic testing during the drilling period. It is only done when drilling experiences a large loss (or high return) of drilling fluid due to penetration of a large-transmissivity zone. The paper proposes the possibility of conducting flowing fluid electrical conductivity (FFEC) logging during the drilling period, with negligible impact on the drilling schedule, yet providing important information on depth locations of both high- and low-transmissivity zones and their hydraulic properties. The information can be used to guide downhole fluid sampling and post-drilling detailed testing of the borehole. The method has been applied to the drilling of a 2,500-m borehole at Åre, central Sweden, firstly when the drilling reached 1,600 m, and then when the drilling reached the target depth of 2,500 m. Results unveil eight hydraulically active zones from 300 m down to borehole bottom, with depths determined to within the order of a meter. Further, the first set of data allows the estimation of hydraulic transmissivity values of the six hydraulically conductive zones found from 300 to 1,600 m, which are very low and range over one order of magnitude.
Brenner, Howard
2014-04-01
"Diffuse interface" theories for single-component fluids—dating back to van der Waals, Korteweg, Cahn-Hilliard, and many others—are currently based upon an ad hoc combination of thermodynamic principles (built largely upon Helmholtz's free-energy potential) and so-called “nonclassical” continuum-thermomechanical principles (built largely upon Newtonian mechanics), with the latter originating with the pioneering work of Dunn and Serrin [Arch. Ration. Mech. Anal. 88, 95 (1985)]. By introducing into the equation governing the transport of energy the notion of an interstitial work-flux contribution, above and beyond the usual Fourier heat-flux contribution, namely, jq = -k∇T, to the energy flux, Dunn and Serrin provided a rational continuum-thermomechanical basis for the presence of Korteweg stresses in the equation governing the transport of linear momentum in compressible fluids. Nevertheless, by their failing to recognize the existence and fundamental need for an independent volume transport equation [Brenner, Physica A 349, 11 (2005)]—especially for the roles played therein by the diffuse volume flux j v and the rate of production of volume πν at a point of the fluid continuum—we argue that diffuse interface theories for fluids stand today as being both ad hoc and incomplete owing to their failure to recognize the need for an independent volume transport equation for the case of compressible fluids. In contrast, we point out that bivelocity hydrodynamics, as it already exists [Brenner, Phys. Rev. E 86, 016307 (2012)], provides a rational, non-ad hoc, and comprehensive theory of diffuse interfaces, not only for single-component fluids, but also for certain classes of crystalline solids [Danielewski and Wierzba, J. Phase Equilib. Diffus. 26, 573 (2005)]. Furthermore, we provide not only what we believe to be the correct constitutive equation for the Korteweg stress in the class of fluids that are constitutively Newtonian in their rheological response
Massoudi, M.C.; Tran, P.X.
2007-06-15
After providing a brief review of the constitutive modeling of the stress tensor for granular materials using non-Newtonian fluid models, we study the flow between two horizontal flat plates. It is assumed that the granular media behaves as a non-Newtonian fluid (of the Reiner–Rivlin type); we use the constitutive relation derived by Rajagopal and Massoudi [Rajagopal, K. R. and M. Massoudi, “A Method for measuring material moduli of granular materials: flow in an orthogonal rheometer,” Topical Report, DOE/PETC/TR-90/3, 1990] which can predict the normal stress differences. The lower plate is fixed and heated, and the upper plate (which is at a lower temperature than the lower plate) is set into motion with a constant velocity. The steady fully developed flow and the heat transfer equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers and viscous dissipation are discussed.
Feedback control of singular systems with applications to incompressible flows
NASA Astrophysics Data System (ADS)
Gandikota, Ramakrishna V.
2000-10-01
Singular systems of differential equations, also referred to as differential algebraic equation (DAE) systems, arise as models in a variety of engineering applications. In chemical engineering, they typically arise under the quasi-steady state assumptions of phase, reaction or thermal equilibrium in the modeling of processes with fast mass transfer, reaction or heat transfer. They also arise in incompressible fluid flow systems. The control of singular systems has attracted considerable attention in the last two decades. The majority of the developed methods are on the state feedback control of linear and nonlinear singular systems in continuous-time, and they rely on the derivation of standard state space realizations (i.e. ODE descriptions) that can be used as the basis for the controller design. This thesis addresses (i) the derivation of state space realizations for the output feedback control of linear singular systems in continuous time, (ii) the derivation of state space realizations of singular systems of difference equations, which can be used for the state feedback control of nonlinear discrete time singular systems, (iii) a parallel analysis of the continuous in space and discretized in space incompressible Navier Stokes equations, with emphasis on the derivation of standard PDE and ODE descriptions respectively, and (iv) a case study on the numerical simulation and feedback control of the flow pattern in a lid-driven cavity. The performance of the developed controllers is illustrated via numerical simulation studies.
Harris, M.T.; Basaran, O.A.
1995-03-15
The shapes and stability of pendant drops in the presence of an electric field is a classical problem in capillarity. This problem has been studied in great detail by numerous investigators when the drops are either perfect conductors or nonconductors and the surrounding fluid is a nonconductor. In this paper, the axisymmetric equilibrium shapes and stability of a nonconducting drop hanging from a nonconducting nozzle that is immersed in a perfectly conducting ambient fluid, a problem that has heretofore not been considered in the literature, are determined by solving the free boundary problem comprised of the Young-Laplace equation for drop shape and an integral equation for the electric field distribution. Here the free boundary problem is discretized by a hybrid technique in which the Young-Laplace equation is solved by the finite element method and the electrostatic problem solved by the boundary element method.
Cardiac deformation recovery via incompressible transformation decomposition
NASA Astrophysics Data System (ADS)
Skrinjar, Oskar; Bistoque, Arnaud
2005-04-01
This paper presents a method for automated deformation recovery of the left and right ventricular wall from a time sequence of anatomical images of the heart. The deformation is recovered within the heart wall, i.e. it is not limited only to the epicardium and endocardium. Most of the suggested methods either ignore or approximately model incompressibility of the heart wall. This physical property of the cardiac muscle is mathematically guaranteed to be satisfied by the proposed method. A scheme for decomposition of a complex incompressible geometric transformation into simpler components and its application to cardiac deformation recovery is presented. A general case as well as an application specific solution is discussed. Furthermore, the manipulation of the constructed incompressible transformations, including the computation of the inverse transformation, is computationally inexpensive. The presented method is mathematically guaranteed to generate incompressible transformations which are experimentally shown to be a very good approximation of actual cardiac deformations. The transformation representation has a relatively small number of parameters which leads to a fast deformation recovery. The approach was tested on six sequences of two-dimensional short-axis cardiac MR images. The cardiac deformation was recovered with an average error of 1.1 pixel. The method is directly extendable to three dimensions and to the entire heart.
Equilibria with incompressible flows from symmetry analysis
Kuiroukidis, Ap E-mail: gthroum@cc.uoi.gr; Throumoulopoulos, G. N. E-mail: gthroum@cc.uoi.gr
2015-08-15
We identify and study new nonlinear axisymmetric equilibria with incompressible flow of arbitrary direction satisfying a generalized Grad Shafranov equation by extending the symmetry analysis presented by Cicogna and Pegoraro [Phys. Plasmas 22, 022520 (2015)]. In particular, we construct a typical tokamak D-shaped equilibrium with peaked toroidal current density, monotonically varying safety factor, and sheared electric field.
NASA Astrophysics Data System (ADS)
Zubarev, N. M.; Zubareva, O. V.
2016-09-01
We study the two-dimensional magnetic shaping problem for the situation where the free surface of a perfectly conducting fluid is deformed by the magnetic field of a system of linear current-carrying conductors. Equilibrium is achieved due to the balance of capillary and magnetic pressures. We obtain exact solutions of the problem using conformal map techniques. These solutions describe a system of two-dimensional dimples that appear on the initially flat surface of a liquid conductor under the action of a nonuniform magnetic field. We consider the case of two symmetrically located dimples in detail.
Shehzad, Sabir Ali; Alsaedi, Ahmed; Hayat, Tasawar; Alhuthali, M. Shahab
2013-01-01
This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B fluid with variable thermal conductivity is considered. The flow is induced due to stretching of a surface. Analysis has been carried out in the presence of heat generation/absorption. Homotopy analysis is implemented in developing the series solutions to the governing flow and energy equations. Graphs are presented and discussed for various parameters of interest. Comparison of present study with the existing limiting solution is shown and examined. PMID:24223780
Hunter, M; Lee, J
1992-11-01
The change in venous blood density in an in vitro rabbit lung preparation was measured after the osmolarity of the blood was elevated 17 to 50 mosmol/liter by a constant arterial infusion of hypertonic saline. We observed a transient density decrease of the blood flowing from the lung and then a return to the preinfusion density within 10 sec, an indication of the rapid completion of fluid extraction from the interstitia by the elevation in osmotic pressure. By fitting the time course of the density change with the prediction of an extraction model, we obtained the osmotic conductance sigma K (the product of the reflection and filtration coefficient) of the lung due to the increase in NaCl osmotic pressure as 1.33 +/- 0.18 ml/[hr.(mosmol/liter).g wet lung tissue] (mean +/- SEM), the interstitial volume participating in the extraction process as 0.27 +/- 0.04 ml/g of lung tissue, and the volume of fluid extracted as 1.12 +/- 0.16 microliter/g tissue for every mosmol/liter elevation. Since we also found no significant difference between the osmotic extraction parameters determined in blood-perfused lungs and those determined in plasma-perfused lungs, we concluded that the rapid density change is the result of the fluid extraction and not the flow impediment of red blood cells caused by the increase in osmolarity. PMID:1479932
NASA Astrophysics Data System (ADS)
Karlsen, Jonas; Bruus, Henrik
2015-11-01
We present a theoretical analysis (arxiv.org/abs/1507.01043) of the acoustic radiation force on a single small particle, either a thermoviscous fluid droplet or a thermoelastic solid particle, suspended in a viscous and heat-conducting fluid. Our analysis places no restrictions on the viscous and thermal boundary layer thicknesses relative to the particle radius, but it assumes the particle to be small in comparison to the acoustic wavelength. This is the limit relevant to scattering of ultrasound waves from sub-micrometer particles. For particle sizes smaller than the boundary layer widths, our theory leads to profound consequences for the acoustic radiation force. For example, for liquid droplets and solid particles suspended in gasses we predict forces orders of magnitude larger than expected from ideal-fluid theory. Moreover, for certain relevant choices of materials, we find a sign change in the acoustic radiation force on different-sized but otherwise identical particles. These findings lead to the concept of a particle-size-dependent acoustophoretic contrast factor, highly relevant to applications in acoustic levitation or separation of micro-particles in gases, as well as to handling of μm- and nm-sized particles such as bacteria and vira in lab-on-a-chip systems.
Johnson, Alexander; Brace, Christopher
2015-01-01
Interventional oncology procedures such as thermal ablation are becoming widely used for many tumours in the liver, kidney and lung. Thermal ablation refers to the focal destruction of tissue by generating cytotoxic temperatures in the treatment zone. Hydrodissection - separating tissues with fluids - protects healthy tissues adjacent to the ablation treatment zone to improve procedural safety, and facilitate more aggressive power application or applicator placement. However, fluids such as normal saline and 5% dextrose in water (D5W) can migrate into the peritoneum, reducing their protective efficacy. As an alternative, a thermo-gelable poloxamer 407 (P407) solution has been recently developed to facilitate hydrodissection procedures. We hypothesise that the P407 gel material does not provide convective heat dissipation from the ablation site, and therefore may alter the heat transfer dynamics compared to liquid materials during hydrodissection-assisted thermal ablation. The purpose of this study was to investigate the heat dissipation mechanics within D5W, liquid P407 and gel P407 hydrodissection barriers. Overall it was shown that the gel P407 dissipated heat primarily through conduction, whereas the liquid P407 and D5W dissipated heat through convection. Furthermore, the rate of temperature change within the gel P407 was greater than liquid P407 and D5W. Testing to evaluate the in vivo efficacy of the fluids with different modes of heat dissipation seems warranted for further study.
Spatial resolution of the electrical conductance of ionic fluids using a Green-Kubo method.
Jones, R E; Ward, D K; Templeton, J A
2014-11-14
We present a Green-Kubo method to spatially resolve transport coefficients in compositionally heterogeneous mixtures. We develop the underlying theory based on well-known results from mixture theory, Irving-Kirkwood field estimation, and linear response theory. Then, using standard molecular dynamics techniques, we apply the methodology to representative systems. With a homogeneous salt water system, where the expectation of the distribution of conductivity is clear, we demonstrate the sensitivities of the method to system size, and other physical and algorithmic parameters. Then we present a simple model of an electrochemical double layer where we explore the resolution limit of the method. In this system, we observe significant anisotropy in the wall-normal vs. transverse ionic conductances, as well as near wall effects. Finally, we discuss extensions and applications to more realistic systems such as batteries where detailed understanding of the transport properties in the vicinity of the electrodes is of technological importance.
NASA Astrophysics Data System (ADS)
Chen, Guang-Liang; Chen, Shi-Hua; Chen, Wen-Xing; Yang, Si-Ze
2008-12-01
A cold dielectric barrier discharge (DBD) plasma plume with one highly conductive liquid electrode has been developed to treat thermally sensitive materials, and its preliminary discharging characteristics have been studied. The averaged electron temperature and density is estimated to be 0.6eV and 1011/cm3, respectively. The length of plasma plume can reach 5 cm with helium gas (He), and the conductivity of the outer electrode affects the plume length obviously. This plasma plume could be touched by bare hand without causing any burning or painful sensation, which may provide potential application for safe aseptic skin care. Moreover, the oxidative particles (e.g., OH, O*, O3) in the downstream oxygen (O2) gas of the plume have been applied to treat the landfill leachate. The results show that the activated O2 gas can degrade the landfill leachate effectively, and the chemical oxygen demand (COD), conductivity, biochemical oxygen demand (BOD), and suspended solid (SS) can be decreased by 52%, 57%, 76% and 92%, respectively.
A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows
NASA Astrophysics Data System (ADS)
Hao, Chengchun; Luo, Tao
2014-06-01
In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in Christodoulou and Lindblad (Commun Pure Appl Math 53:1536-1602, 2000), and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids.
Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows
NASA Technical Reports Server (NTRS)
Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark
1998-01-01
A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.
NASA Astrophysics Data System (ADS)
Salahuddin, T.; Malik, M. Y.; Hussain, Arif; Bilal, S.; Awais, M.
2015-12-01
The purpose of present analysis is to examine the effects of temperature dependent viscosity and thermal conductivity on MHD stagnation point flow over a stretching cylinder. The momentum and the temperature equations are modeled by using tangent hyperbolic fluid and the effect of viscous dissipation is also considered. The requisite partial differential equations are metamorphosed into ordinary differential equations by using similarity transformations. The succeeding ordinary differential equations are solved by using shooting method. The physical behavior of non-dimensional parameters for momentum and temperature profiles is deliberated through graphs. The numerical values of skin friction coefficient and local Nusselt number are calculated in order to recognize the behavior of fluid near the surface. The comparison with previous literature is completed in order to check the accuracy of the present work. It is found the velocity reduces with increasing power law index, Weissenberg number, Hartmann number and variable viscosity parameter. With the increasing values of curvature parameter, velocity is found to increase. Variable thermal conductivity parameter and Prandtl number shows opposite behavior for temperature profile.
On a modification of GLS stabilized FEM for solving incompressible viscous flows
NASA Astrophysics Data System (ADS)
Burda, P.; Novotný, J.; Ístek, J.
2006-07-01
We deal with 2D flows of incompressible viscous fluids with high Reynolds numbers. Galerkin Least Squares technique of stabilization of the finite element method is studied and its modification is described. We present a number of numerical results obtained by the developed method, showing its contribution to solving flows with high Reynolds numbers. Several recommendations and remarks are included. We are interested in positive as well as negative aspects of stabilization, which cannot be divorced.
On an Inviscid Model for Incompressible Two-Phase Flows with Nonlocal Interaction
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.
2016-03-01
We consider a diffuse interface model which describes the motion of an ideal incompressible mixture of two immiscible fluids with nonlocal interaction in two-dimensional bounded domains. This model consists of the Euler equation coupled with a convective nonlocal Cahn-Hilliard equation. We establish the existence of globally defined weak solutions as well as well-posedness results for strong/classical solutions.
G-300: The first French Getaway Special microgravity measurements of fluid thermal conductivity
NASA Technical Reports Server (NTRS)
Perron, J. C.; Chretien, P.; Garnier, C.; Lecaude, N.
1987-01-01
Thermal conductivity measurements on liquids are difficult to perform on Earth because of thermal motions due to convection. In microgravity, the convection due to buoyancy is evanescent, and a strong reduction of Rayleigh and Nusselt numbers can be expected. Three low viscosity liquids are selected to carry out the measurements; distilled water (standard) and two silicone oils. A modified hot plate method with a simplified guard ring is used; the reduction of convective motions permitted the use in the experimental cells of larger interplate distances and/or temperature differences than in Earth measurements, improving the accuracy. Comparisons between Earth and orbit results may help to understand the convection occurrence in the cells. Thermal, vibrational, and EMI tests have proved that the design satisfies the NASA requirements.
G-300: The first French Getaway Special microgravity measurements of fluid thermal conductivity
NASA Astrophysics Data System (ADS)
Perron, J. C.; Chretien, P.; Garnier, C.; Lecaude, N.
1987-02-01
Thermal conductivity measurements on liquids are difficult to perform on Earth because of thermal motions due to convection. In microgravity, the convection due to buoyancy is evanescent, and a strong reduction of Rayleigh and Nusselt numbers can be expected. Three low viscosity liquids are selected to carry out the measurements; distilled water (standard) and two silicone oils. A modified hot plate method with a simplified guard ring is used; the reduction of convective motions permitted the use in the experimental cells of larger interplate distances and/or temperature differences than in Earth measurements, improving the accuracy. Comparisons between Earth and orbit results may help to understand the convection occurrence in the cells. Thermal, vibrational, and EMI tests have proved that the design satisfies the NASA requirements.
NASA Technical Reports Server (NTRS)
Faghri, Amir; Chen, Ming-Ming; Mahefkey, E. T.
1989-01-01
Numerical solutions are reported for conjugate heat transfer in a porous pipe having an internal flow with blowing or suction at the inner surface of the pipe and constant heat flux at the outer surface. The effect of the simultaneous axial conduction through the wall and the fluid has been studied for the combined hydrodynamic and thermal entry lengths. The results show that the ratio of the thermal conductivities of the pipe wall to the fluid and the thickness of the pipe wall may become significant factors on the heat transfer when the Peclet number is small, especially for the case when fluid is injected into the pipe. It is also shown that the effect of axial wall conduction for the case of constant heat flux at the outer wall surface can be neglected when the wall thickness is small and the ratio of the conductivities of the wall to the fluid approaches unity.
NASA Astrophysics Data System (ADS)
Zhai, Cuili; Zhang, Ting
2016-09-01
In this article, we consider the global existence and uniqueness of the solution to the 2D incompressible non-resistive MHD system with non-equilibrium background magnetic field. Our result implies that a strong enough non-equilibrium background magnetic field will guarantee the stability of the nonlinear MHD system. Beside the classical energy method, the interpolation inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments.
Interface waves in almost incompressible elastic materials
NASA Astrophysics Data System (ADS)
Virta, Kristoffer; Kreiss, Gunilla
2015-12-01
We study the problem of two elastic half-planes in contact and the Stoneley interface wave that may exist at the interface between two different elastic materials, emphasis being put on the case when the half-planes are almost incompressible. We show that numerical simulations involving interface waves require an unexpectedly high number of grid points per wavelength as the materials become more incompressible. Let λ, μ, ρ and λ‧, μ‧, ρ‧ be the Lamé parameters and densities of the first and second half-plane, respectively. A theoretical study shows that if K is a real constant, λ‧ = Kλ, μ‧ = Kμ, ρ‧ = Kρ and μ → 0, then for an accurate solution the required number of grid points per wavelength scales as (μ / λ) - 1 / p, where p is the order of accuracy of the numerical method. This requirement becomes very restrictive close to the incompressible limit μ ≪ λ, especially for lower order methods i.e., a small p. The theoretical findings are supported by numerical experiments that illustrate the demanding resolution requirement as well as the superiority of higher order methods. The scaling is also seen to hold for a more general choice of Lamé parameters. Numerical experiments when one of the half-planes is a vacuum are also presented, where the higher resolution requirement is illustrated in a numerical solution of Lamb's problem.
Coupled energetic models for incompressible nematic elastomers
NASA Astrophysics Data System (ADS)
Rubiano, Andrea C.
We investigate, through methods in the Calculus of Variations, mathematical energetic models for incompressible nematic elastomers. These models are based on the coupling between the neo-classical energy density, developed by Bladon, Warner and Terentjev as an extension of the rubber elasticity theory, with the classical energy density from the Landau-de Gennes theory for uniaxial nematic liquid crystals. A unit-length molecular director of the nematic elastomer and an incompressible deformation are the unknown functions, minimizers of the coupled energy. In contrast to previous mathematical work in this field, the molecular director is not assumed to be constant throughout the domain. After establishing a suitable generalized energetic model for working in Sobolev spaces, we prove lower semi-continuity of the energy. Considering generalized shear deformations motivated by physical experiments on thin film domains, we show the existence of minimizers, and keeping the restriction of incompressibility on the deformation and unit length of the director, we derive weak Euler Lagrange equations satisfied by the minimizers. Additionally, we consider the reduction of the model to a 2-dimensional one and deduce existence results for non-convex energy densities involving terms related to the constraint of volume's preservation . In this case we also find weak Euler-Lagrange equations and prove a partial regularity result.
Energy Conservation in Two-dimensional Incompressible Ideal Fluids
NASA Astrophysics Data System (ADS)
Cheskidov, A.; Filho, M. C. Lopes; Lopes, H. J. Nussenzveig; Shvydkoy, R.
2016-11-01
This note addresses the issue of energy conservation for the 2D Euler system with an L p -control on vorticity. We provide a direct argument, based on a mollification in physical space, to show that the energy of a weak solution is conserved if {ω = nabla × u in L^{3/2}}. An example of a 2D field in the class {ω in L^{3/2 - ɛ}} for any ɛ > 0, and {u in B^{1/3}_{3,∞}} (Onsager critical space, see Shvydkoy in Discr Contin Dyn Syst Ser S 3(3):473-496, 2010) is constructed with non-vanishing energy flux. This demonstrates sharpness of the kinematic argument, which does not differentiate between 2D and 3D, and requires Onsager's regularity control on the solution. Next, we show that for physically realizable solutions there is a mechanism preventing the anomalous dissipation in 2D that does not require such a control. Namely, we prove that any solution to the Euler equations produced via a vanishing viscosity limit from the Navier-Stokes equations, with {ω in L^p}, for p > 1, conserves energy.
Energy Conservation in Two-dimensional Incompressible Ideal Fluids
NASA Astrophysics Data System (ADS)
Cheskidov, A.; Filho, M. C. Lopes; Lopes, H. J. Nussenzveig; Shvydkoy, R.
2016-08-01
This note addresses the issue of energy conservation for the 2D Euler system with an L p -control on vorticity. We provide a direct argument, based on a mollification in physical space, to show that the energy of a weak solution is conserved if {ω = nabla × u in L^{3/2}} . An example of a 2D field in the class {ω in L^{3/2 - ɛ}} for any ɛ > 0 , and {u in B^{1/3}_{3,∞}} (Onsager critical space, see Shvydkoy in Discr Contin Dyn Syst Ser S 3(3):473-496, 2010) is constructed with non-vanishing energy flux. This demonstrates sharpness of the kinematic argument, which does not differentiate between 2D and 3D, and requires Onsager's regularity control on the solution. Next, we show that for physically realizable solutions there is a mechanism preventing the anomalous dissipation in 2D that does not require such a control. Namely, we prove that any solution to the Euler equations produced via a vanishing viscosity limit from the Navier-Stokes equations, with {ω in L^p} , for p > 1, conserves energy.
Mashimo, T; Chau, R; Zhang, Y; Kobayoshi, T; Sekine, T; Fukuoka, K; Syono, Y; Kodama, M; Nellis, W J
2005-09-19
Cubic, single-crystal, transparent Gd{sub 3}Ga{sub 5}O{sub 12} has a density of 7.10 g/cm{sup 3}, a Hugoniot elastic limit (HEL) of 30 GPa, and undergoes a continuous phase transition from 65 GPa to a quasi-incompressible (QI) phase at 120 GPa. Only diamond has a larger HEL. The QI phase of Gd{sub 3}Ga{sub 5}O{sub 12} is more incompressible than diamond from 170 to 260 GPa. Electrical conductivity measurements indicate the QI phase has a bandgap of 3.1 eV. Gd{sub 3}Ga{sub 5}O{sub 12} can be used to obtain substantially higher pressures and lower temperatures in metallic fluid hydrogen than was achieved previously by shock reverberation between Al{sub 2}O{sub 3} disks. Dynamic compression achieves pressures, densities, and temperatures that enable investigation of ultracondensed matter at conditions yet to be achieved by any other technique. The prototypical example is observation of minimum metallic conductivity (MMC) of dense fluid hydrogen at 140 GPa, nine-fold compression of liquid density, and {approx}3000 K [1-3]. The high pressure and density and relatively low temperature are achieved by multiple-shock compression [2]. Temperature T is relatively low in the sense that T/TP{sub F} {approx} 0.01, where T{sub F} is the Fermi temperature. The time scale of compression is sufficiently long to achieve thermal equilibrium and sufficiently short so the process is adiabatic. Similar results are obtained for oxygen [4] and nitrogen [5]. Fluid Cs and Rb undergo the same transition at 2000 K near their liquid-vapor critical points [6]. All five elemental fluids have essentially the same value of MMC and the density dependences of their semiconductivities scale with the quantum-mechanical charge-density distributions of the respective atoms [5]. Liquid H{sub 2} is one of the most compressible of all materials. In this paper, we report that the dielectric crystal Gd{sub 3}Ga{sub 5}O{sub 12} (GGG) transitions to a virtually incompressible phase at 120 GPa shock pressure.
Long-wavelength corrections to Hall conductivity in fractional quantum Hall fluids
NASA Astrophysics Data System (ADS)
Yang, Bo; Haldane, F. D. M.
2013-03-01
Recent work by Hoyos and Son, then Bradlyn et al., has investigated the relation between the long-wavelength (O (q2)) corrections to the Hall conductivity σH (q) and the Hall viscosity of quantum Hall states. These works assume the presence of Galilean and rotational invariance. However, these are not generic symmetries of electrons in condensed matter. We identify translation and (2D) inversion symmetry as the only generic symmetries of an ``ideal'' quantum Hall liquid, as these are needed to guarantee the absence of any dissipationless ground state current density; then σH (q) = σH (- q) characterizes the dissipation less current that flows in response to a spatially-non-uniform electric field. We consider the general problem for fractional quantum Hall (FQH) states without Galilean or rotational invariance, when the guiding-center contribution to the Hall viscosity becomes a non-trivial tensor property related to an emergent geometry of the FQH state, (Bo Yang et,al (PRB 85,165318). Supported by DOE DE-SC0002140 and Agency for Science Technology and Research (A*STAR, Singapore).
G-300, the first French Getaway Special microgravity measurements of fluid thermal conductivity
NASA Astrophysics Data System (ADS)
Perron, J. C.; Chretien, P.; Garnier, C.; Lecaude, N.
On Earth thermal conductivity measurements on liquids are difficult to perform because thermal motions due to convection. In microgravity the convection due to buoyancy is evanescent and we expect a strong lowering of Rayleigh and Nusselt numbers. Three low viscosity liquids are selected to carry out the measurements: distilled water (standard) and two silicone oils. We use a modified "hot plate" method with a simplified guard ring, the lowering of convective motions let us to use in the experimental cells larger interplate distances and/or temperature differences than in earth measurements so the accuracy must be improved. Comparisons between Earth and orbit results may help to understand the convection occurrence in our cells. G-300 payload is cantilevered from the experiment mounting plate (EMP) and it includes: four struts, an intermediate plate, a bottom plate with four bumpers, a battery box, an electronic rack and six experimental cells assembled in twin-packs thermally coupled with the EMP. Thermal, vibration and EMI tests have proved that the design satisfies the Nasa requirements and acceptance is in progress.
NASA Astrophysics Data System (ADS)
Rassoulinejad-Mousavi, S. M.; Abbasbandy, S.; Alsulami, H. H.
2014-08-01
Hydrodynamics of a conducting visco-elastic fluid in a porous medium sandwiched between two parallel plates, under the effect of the Lorentz force, for both moving and stationary wall boundary conditions, is considered in this paper. The non-linear momentum equation is solved analytically using the optimal homotopy analysis method (OHAM) and the effect of existing parameters in the physics of the problem is demonstrated on the dimensionless velocity profile and skin friction coefficient. The robustness of the analytical solution is checked by comparison with numerical results and plotting the residual errors. Results show that there is excellent agreement between numerical and analytical solutions. Furthermore, the error diagrams show that OHAM yields accurate results in all values of the different effective parameters, such as porous medium shape factor, Forchheimer number, visco-elastic parameter, Reynolds number and the parameters related to the Lorentz force.
NASA Technical Reports Server (NTRS)
Farassat, F.; Baty, R. S.
2000-01-01
The study of the shock structure in a viscous heat conducting fluid is an old problem. We study this problem from a novel mathematical point of view. A new class of generalized functions is defined where multiplication of any two functions is allowed with the usual properties. A Heaviside function in this class has the unit jump at occurring on an infinitesimal interval of the nonstandard analysis (NSA) in the halo of . This jump has a smooth microstructure over the infinitesimal interval . From this point of view, we have a new class of Heaviside functions, and their derivatives the Dirac delta functions, which are equivalent when viewed as continuous linear functionals over the test function space of Schwartz. However, they differ in their microstructures which in applications are determined from physics of the problem as shown in our presentation.
NASA Astrophysics Data System (ADS)
Wang, Chengjie; Eldredge, Jeff D.
2015-08-01
A strong coupling algorithm is presented for simulating the dynamic interactions between incompressible viscous flows and rigid-body systems in both two- and three-dimensional problems. In this work, 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. Dynamical equations for arbitrary rigid-body systems are also developed. The proposed coupling method attempts to unify the treatment of constraints in the fluid and structure-the incompressibility of the fluid, the linkages in the rigid-body system, and the conditions at the interface-through the use of Lagrange multipliers. The resulting partitioned system of equations is solved with a simple relaxation scheme, based on an identification of virtual inertia from the fluid. The scheme achieves convergence in only 2 to 5 iterations per time step for a wide variety of mass ratios. The formulation requires that only a subset of the discrete fluid equations be solved in each iteration. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including a falling cylinder, flapping of flexible wings, self-excited oscillations of a system of many linked plates in a free stream, and passive pivoting of a finite aspect ratio plate under the influence of gravity in a free stream. The results from the current method are compared with previous experimental and numerical results and good agreement is achieved.
Winters, W.S.
1984-01-01
An overview of the computer code TOPAZ (Transient-One-Dimensional Pipe Flow Analyzer) is presented. TOPAZ models the flow of compressible and incompressible fluids through complex and arbitrary arrangements of pipes, valves, flow branches and vessels. Heat transfer to and from the fluid containment structures (i.e. vessel and pipe walls) can also be modeled. This document includes discussions of the fluid flow equations and containment heat conduction equations. The modeling philosophy, numerical integration technique, code architecture, and methods for generating the computational mesh are also discussed.
Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves.
Tuerke, F; Sciamarella, D; Pastur, L R; Lusseyran, F; Artana, G
2015-01-01
We present an alternative perspective on nonharmonic mode coexistence, commonly found in the shear layer spectrum of open-cavity flows. Modes obtained by a local linear stability analysis of perturbations to a two-dimensional, incompressible, and inviscid sheared flow over a cavity of finite length and depth were conditioned by a so-called coincidence condition first proposed by Kulikowskii [J. Appl. Math. Mech. 30, 180 (1966)] which takes into account instability wave reflection within the cavity. The analysis yields a set of discrete, nonharmonic frequencies, which compare well with experimental results [Phys. Fluids 20, 114101 (2008); Exp. Fluids 50, 905 (2010)].
Multigrid Approach to Incompressible Viscous Cavity Flows
NASA Technical Reports Server (NTRS)
Wood, William A.
1996-01-01
Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.
10 CFR 26.97 - Conducting an initial test for alcohol using a specimen of oral fluids.
Code of Federal Regulations, 2011 CFR
2011-01-01
... oral fluids. 26.97 Section 26.97 Energy NUCLEAR REGULATORY COMMISSION FITNESS FOR DUTY PROGRAMS... fluids. (a) To perform the initial test, the collector shall— (1) Check the expiration date on the device... fluids in the manner described by the device's manufacturer (wear single-use examination or...
10 CFR 26.97 - Conducting an initial test for alcohol using a specimen of oral fluids.
Code of Federal Regulations, 2014 CFR
2014-01-01
... oral fluids. 26.97 Section 26.97 Energy NUCLEAR REGULATORY COMMISSION FITNESS FOR DUTY PROGRAMS... fluids. (a) To perform the initial test, the collector shall— (1) Check the expiration date on the device... fluids in the manner described by the device's manufacturer (wear single-use examination or...
10 CFR 26.97 - Conducting an initial test for alcohol using a specimen of oral fluids.
Code of Federal Regulations, 2012 CFR
2012-01-01
... oral fluids. 26.97 Section 26.97 Energy NUCLEAR REGULATORY COMMISSION FITNESS FOR DUTY PROGRAMS... fluids. (a) To perform the initial test, the collector shall— (1) Check the expiration date on the device... fluids in the manner described by the device's manufacturer (wear single-use examination or...
10 CFR 26.97 - Conducting an initial test for alcohol using a specimen of oral fluids.
Code of Federal Regulations, 2013 CFR
2013-01-01
... oral fluids. 26.97 Section 26.97 Energy NUCLEAR REGULATORY COMMISSION FITNESS FOR DUTY PROGRAMS... fluids. (a) To perform the initial test, the collector shall— (1) Check the expiration date on the device... fluids in the manner described by the device's manufacturer (wear single-use examination or...
Vajravelu, K.; Kassab, A.; Hadjinicolaou, A.
1996-11-08
The nonlinear partial differential equations for the transient free convective heat transfer in a viscous, electrically conducting, and heat-generating fluid past a vertical porous plate in the presence of free stream oscillations are solved by the boundary element method (BEM). Time-dependent fundamental solutions are employed in a time marching scheme to resolve the field variables. Numerical results are compared with previously reported analytical solutions in order to validate the developed BEM algorithm. These previous studies reported results for simpler versions of the problem, in which the convective effects in the momentum and energy equations were neglected in order to obtain analytical numerical solutions. The BEM results are shown to be in close agreement with the reported data. The effects of convection currents, the temperature-dependent heat sources (or sinks), the magnetic currents, and the viscous dissipation on the flow and heat transfer characteristics are assessed in a parametric study, which considers a variety of the dimensionless parameters Gr, Ec, Pr, M, and {gamma}. It is observed that {gamma} plays an important role in delaying the fluid flow reversal, present in the case of air, and acts to enhance the effect of Gr in augmenting the rate of heat transfer at the wall. The skin friction is observed to be an increasing function of Gr, Ec, and {gamma} and a decreasing function of M and Pr. However, the rate of heat transfer (in an absolute sense) is an increasing function of M, {gamma}, Gr, and Ec and a decreasing function of Pr. Of all the parameters, the Prandtl number has the strongest effect on the flow and heat transfer characteristics.
Gustavsen, Arlid; Kohler, Christian; Dalehaug, Arvid; Arasteh, Dariush
2008-12-01
This paper assesses the accuracy of the simplified frame cavity conduction/convection and radiation models presented in ISO 15099 and used in software for rating and labeling window products. Temperatures and U-factors for typical horizontal window frames with internal cavities are compared; results from Computational Fluid Dynamics (CFD) simulations with detailed radiation modeling are used as a reference. Four different frames were studied. Two were made of polyvinyl chloride (PVC) and two of aluminum. For each frame, six different simulations were performed, two with a CFD code and four with a building-component thermal-simulation tool using the Finite Element Method (FEM). This FEM tool addresses convection using correlations from ISO 15099; it addressed radiation with either correlations from ISO 15099 or with a detailed, view-factor-based radiation model. Calculations were performed using the CFD code with and without fluid flow in the window frame cavities; the calculations without fluid flow were performed to verify that the CFD code and the building-component thermal-simulation tool produced consistent results. With the FEM-code, the practice of subdividing small frame cavities was examined, in some cases not subdividing, in some cases subdividing cavities with interconnections smaller than five millimeters (mm) (ISO 15099) and in some cases subdividing cavities with interconnections smaller than seven mm (a breakpoint that has been suggested in other studies). For the various frames, the calculated U-factors were found to be quite comparable (the maximum difference between the reference CFD simulation and the other simulations was found to be 13.2 percent). A maximum difference of 8.5 percent was found between the CFD simulation and the FEM simulation using ISO 15099 procedures. The ISO 15099 correlation works best for frames with high U-factors. For more efficient frames, the relative differences among various simulations are larger. Temperature was also
NASA Technical Reports Server (NTRS)
Walowit, Jed A.; Shapiro, Wilbur
2005-01-01
The SPIRALI code predicts the performance characteristics of incompressible cylindrical and face seals with or without the inclusion of spiral grooves. Performance characteristics include load capacity (for face seals), leakage flow, power requirements and dynamic characteristics in the form of stiffness, damping and apparent mass coefficients in 4 degrees of freedom for cylindrical seals and 3 degrees of freedom for face seals. These performance characteristics are computed as functions of seal and groove geometry, load or film thickness, running and disturbance speeds, fluid viscosity, and boundary pressures. A derivation of the equations governing the performance of turbulent, incompressible, spiral groove cylindrical and face seals along with a description of their solution is given. The computer codes are described, including an input description, sample cases, and comparisons with results of other codes.
Computational thermo-fluid analysis of a disk brake
NASA Astrophysics Data System (ADS)
Takizawa, Kenji; Tezduyar, Tayfun E.; Kuraishi, Takashi; Tabata, Shinichiro; Takagi, Hirokazu
2016-06-01
We present computational thermo-fluid analysis of a disk brake, including thermo-fluid analysis of the flow around the brake and heat conduction analysis of the disk. The computational challenges include proper representation of the small-scale thermo-fluid behavior, high-resolution representation of the thermo-fluid boundary layers near the spinning solid surfaces, and bringing the heat transfer coefficient (HTC) calculated in the thermo-fluid analysis of the flow to the heat conduction analysis of the spinning disk. The disk brake model used in the analysis closely represents the actual configuration, and this adds to the computational challenges. The components of the method we have developed for computational analysis of the class of problems with these types of challenges include the Space-Time Variational Multiscale method for coupled incompressible flow and thermal transport, ST Slip Interface method for high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces, and a set of projection methods for different parts of the disk to bring the HTC calculated in the thermo-fluid analysis. With the HTC coming from the thermo-fluid analysis of the flow around the brake, we do the heat conduction analysis of the disk, from the start of the breaking until the disk spinning stops, demonstrating how the method developed works in computational analysis of this complex and challenging problem.
NASA Technical Reports Server (NTRS)
Kiris, Cetin
1995-01-01
Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.
Incompressible viscous flow in tubes with occlusions
NASA Astrophysics Data System (ADS)
Huang, Huaxiong
Viscous, incompressible flow in tubes with partial occlusion is investigated using numerical and experimental procedures. The study is related to the problem of atherosclerosis, one of the most common diseases of the circulatory system. One of the computational difficulties in solving the incompressible Navier-Stokes equations is the lack of pressure or vorticity boundary conditions. A finite difference approach, referred to as the interior constraint (IC) method, is proposed to resolve this difficulty. As a general numerical method, it is formulated for both the stream function-vorticity and primitive (physical) variable formulations. The procedure is explained using a one dimensional model with extensive numerical tests presented for two dimensional cases, including flow in a driven cavity and flow over a backward facing step. Results are obtained with second-order accuracy. Next, the IC method is applied to flow in a tube with an occlusion, which is used as the model for blood flow in stenosed arteries in the study of the pathology of atherosclerosis. Numerical results are obtained for both steady and pulsatile flows. Results are compared with those of SIMPLE, one of the commercially available numerical algorithms. The pulsatile flow study revealed several interesting new features. It suggested that the high shear stress is not likely to initiate atherosclerosis lesions. The recirculation region, which is a prominent feature of the unsteady flow, is more likely to cause the initiation and development of the disease. Experimental measurements for steady flow complement the numerical study and show qualitative agreement.
Sahu, Pooja; Ali, Sk. M. Shenoy, K. T.
2015-02-21
Thermodynamic properties of the fluid in the hydrophobic pores of nanotubes are known to be different not only from the bulk phase but also from other conventional confinements. Here, we use a recently developed theoretical scheme of “two phase thermodynamic (2PT)” model to understand the driving forces inclined to spontaneous filling of carbon nanotubes (CNTs) with polar (water) and nonpolar (methane) fluids. The CNT confinement is found to be energetically favorable for both water and methane, leading to their spontaneous filling inside CNT(6,6). For both the systems, the free energy of transfer from bulk to CNT confinement is favored by the increased entropy (TΔS), i.e., increased translational entropy and increased rotational entropy, which were found to be sufficiently high to conquer the unfavorable increase in enthalpy (ΔE) when they are transferred inside CNT. To the best of our knowledge, this is the first time when it has been established that the increase in translational entropy during confinement in CNT(6,6) is not unique to water-like H bonding fluid but is also observed in case of nonpolar fluids such as methane. The thermodynamic results are explained in terms of density, structural rigidity, and transport of fluid molecules inside CNT. The faster diffusion of methane over water in bulk phase is found to be reversed during the confinement in CNT(6,6). Studies reveal that though hydrogen bonding plays an important role in transport of water through CNT, but it is not the solitary driving factor, as the nonpolar fluids, which do not have any hydrogen bond formation capacity can go inside CNT and also can flow through it. The associated driving force for filling and transport of water and methane is enhanced translational and rotational entropies, which are attributed mainly by the strong correlation between confined fluid molecules and availability of more free space for rotation of molecule, i.e., lower density of fluid inside CNT due to their
NASA Astrophysics Data System (ADS)
Sahu, Pooja; Ali, Sk. M.; Shenoy, K. T.
2015-02-01
Thermodynamic properties of the fluid in the hydrophobic pores of nanotubes are known to be different not only from the bulk phase but also from other conventional confinements. Here, we use a recently developed theoretical scheme of "two phase thermodynamic (2PT)" model to understand the driving forces inclined to spontaneous filling of carbon nanotubes (CNTs) with polar (water) and nonpolar (methane) fluids. The CNT confinement is found to be energetically favorable for both water and methane, leading to their spontaneous filling inside CNT(6,6). For both the systems, the free energy of transfer from bulk to CNT confinement is favored by the increased entropy (TΔS), i.e., increased translational entropy and increased rotational entropy, which were found to be sufficiently high to conquer the unfavorable increase in enthalpy (ΔE) when they are transferred inside CNT. To the best of our knowledge, this is the first time when it has been established that the increase in translational entropy during confinement in CNT(6,6) is not unique to water-like H bonding fluid but is also observed in case of nonpolar fluids such as methane. The thermodynamic results are explained in terms of density, structural rigidity, and transport of fluid molecules inside CNT. The faster diffusion of methane over water in bulk phase is found to be reversed during the confinement in CNT(6,6). Studies reveal that though hydrogen bonding plays an important role in transport of water through CNT, but it is not the solitary driving factor, as the nonpolar fluids, which do not have any hydrogen bond formation capacity can go inside CNT and also can flow through it. The associated driving force for filling and transport of water and methane is enhanced translational and rotational entropies, which are attributed mainly by the strong correlation between confined fluid molecules and availability of more free space for rotation of molecule, i.e., lower density of fluid inside CNT due to their
An efficient algorithm for incompressible N-phase flows
Dong, S.
2014-11-01
We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the
AN IMMERSED BOUNDARY METHOD FOR COMPLEX INCOMPRESSIBLE FLOWS
An immersed boundary method for time-dependant, three- dimensional, incompressible flows is presented in this paper. The incompressible Navier-Stokes equations are discretized using a low-diffusion flux splitting method for the inviscid fluxes and a second order central differenc...
NASA Astrophysics Data System (ADS)
Nomeritae; Daly, Edoardo; Grimaldi, Stefania; Bui, Ha Hong
2016-11-01
Several numerical schemes are available to simulate fluid flow with Smoothed Particles Hydrodynamics (SPH). Although commonly experiencing pressure fluctuations, schemes allowing for small changes in fluid density, referred to as weakly compressible (WCSPH and δ-SPH), are often used because of their faster computational time when compared to implicit incompressible schemes (IISPH). Explicit numerical schemes for incompressible fluid flow (EISPH), although more computationally efficient than IISPH, have not been largely used in the literature. To explore advantages and disadvantages of EISPH, this study compared an EISPH scheme with WCSPH and δ-SPH. The three schemes were compared for the case of still water and a wave generated by a dam-break. EISPH and δ-SPH were also compared for the case of a dam-break wave colliding with a vertical wall and a dam-break wave flowing over a wet bed. The three schemes performed similarly in reproducing theoretical and experimental results. EISPH led to results overall similar to WCSPH and δ-SPH, but with smoother pressure dynamics and faster computational times. EISPH presented some errors in the imposition of incompressibility, with the divergence of velocity being different from zero in parts of the fluid flow, especially near the surface. These errors in the divergence of velocity were comparable to the values of velocity divergence obtained with δ-SPH. In an attempt to reduce the velocity divergence in EISPH, an iterative procedure was implemented to calculate the pressure (iterative-EISPH). Although no real improvement was achieved in terms of velocity divergence, the pressure thus calculated was smoother and in some cases was closer to measured experimental values.
NASA Astrophysics Data System (ADS)
Koda, Jun; Shapiro, P. R.
2007-12-01
Self-interacting dark matter (SIDM) has been proposed to solve the cuspy core problem of dark matter halos in standard CDM. There are two ways to investigate the effect of the 2-body, non-gravitational, elastic collisions of SIDM, Monte-Carlo N-body simulation and a conducting fluid model. The former is a gravitational N-body simulation with a Monte Carlo algorithm for the SIDM scattering that changes the direction of N-body particles randomly according to a given scattering cross section. The latter is a system of fluid conservation equations with a thermal conduction that describes the collisional effect, which was originally invented to describe the gravothermal collapse of globular clusters. Our previous work found a significant disagreement as regards the strength of collisionality required to solve cuspy core problem. However the two methods have not been properly tested against each other. Here, we make direct comparisons between Monte Carlo N-body simulations and analytic and numerical solutions of the conducting fluid (gaseous) model, for various isolated self-interacting dark matter halos. The N-body simulations reproduce the analytical self-similar solution of gravothermal collapse in the fluid model when one free parameter, the coefficient of heat conduction C, is chosen to be 0.75. The gravothermal collapse results of the simulations agrees well with our 1D numerical hydro solutions of the fluid model within 20% for other initial conditions, including Plummer model, Hernquist profile and NFW profile. In conclusion the conducting fluid model is in reasonably good agreement with the Monte Carlo simulations for isolated halos. We will pursue the origin of the reported disagreement between two methods in a cosmological environment by comparing new N-body simulations with fully cosmological initial conditions.
Incompressible Polaritons in a Flat Band.
Biondi, Matteo; van Nieuwenburg, Evert P L; Blatter, Gianni; Huber, Sebastian D; Schmidt, Sebastian
2015-10-01
We study the interplay of geometric frustration and interactions in a nonequilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic correlations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor antibunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ.
Efficient solution of turbulent incompressible separated flows
NASA Astrophysics Data System (ADS)
Michelassi, Vittorio; Martelli, Francesco
A computational method for incompressible separated flows based on two-dimensional approximate factorization is presented. Turbulence effects are accounted for by low-Reynolds number forms of the k-epsilon model. Mass conservation is enforced by the artificial compressibility method. Decoupling and coupling of the equations of motions with the turbulence model equations are investigated. Testing of the coupled solver showed no improvement in convergence or accuracy in comparison to the classical decoupled approach. The solver was then applied to several large-recirculation flows using a modified version of the low-Reynolds-number form of the k-epsilon model proposed by Chien and a two-layer version of the k-epsilon model introduced by Rodi. Both versions gave fast convergence rates and good agreement with experiments.
Incompressible Polaritons in a Flat Band.
Biondi, Matteo; van Nieuwenburg, Evert P L; Blatter, Gianni; Huber, Sebastian D; Schmidt, Sebastian
2015-10-01
We study the interplay of geometric frustration and interactions in a nonequilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic correlations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor antibunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ. PMID:26551811
Incompressible Polaritons in a Flat Band
NASA Astrophysics Data System (ADS)
Biondi, Matteo; van Nieuwenburg, Evert P. L.; Blatter, Gianni; Huber, Sebastian D.; Schmidt, Sebastian
2015-10-01
We study the interplay of geometric frustration and interactions in a nonequilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic correlations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor antibunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ.
Incompressible SPH scour model for movable bed dam break flows
NASA Astrophysics Data System (ADS)
Ran, Qihua; Tong, Jian; Shao, Songdong; Fu, Xudong; Xu, Yueping
2015-08-01
In this study an incompressible smoothed particle hydrodynamics (ISPH) approach coupled with the sediment erosion model is developed to investigate the sediment bed scour and grain movement under the dam break flows. Two-phase formulations are used in the ISPH numerical algorithms to examine the free surface and bed evolution profiles, in which the entrained sediments are treated as a different fluid component as compared with the water. The sediment bed erosion model is based on the concept of pick-up flow velocity and the sediment is initiated when the local flow velocity exceeds a critical value. The proposed model is used to reproduce the sediment erosion and follow-on entrainment process under an instantaneous dam break flow and the results are compared with those from the weakly compressible moving particle semi-implicit (WCMPS) method as well as the experimental data. It has been demonstrated that the two-phase ISPH model performed well with the experimental data. The study shows that the ISPH modelling approach can accurately predict the dynamic sediment scouring process without the need to use empirical sediment transport formulas.
Reduced viscosity interpreted for fluid/gas mixtures
NASA Technical Reports Server (NTRS)
Lewis, D. H.
1981-01-01
Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.
NASA Technical Reports Server (NTRS)
Walowit, Jed A.; Shapiro, Wibur
2005-01-01
This is the source listing of the computer code SPIRALI which predicts the performance characteristics of incompressible cylindrical and face seals with or without the inclusion of spiral grooves. Performance characteristics include load capacity (for face seals), leakage flow, power requirements and dynamic characteristics in the form of stiffness, damping and apparent mass coefficients in 4 degrees of freedom for cylindrical seals and 3 degrees of freedom for face seals. These performance characteristics are computed as functions of seal and groove geometry, load or film thickness, running and disturbance speeds, fluid viscosity, and boundary pressures.
Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space
NASA Technical Reports Server (NTRS)
Miles, Jeffrey Hilton
1997-01-01
The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.
Conditions at the downstream boundary for simulations of viscous incompressible flow
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas
1990-01-01
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries
NASA Astrophysics Data System (ADS)
Popinet, Stéphane
2003-09-01
An adaptive mesh projection method for the time-dependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volume-of-fluid approach. Second-order convergence in space and time is demonstrated on regular, statically and dynamically refined grids. The quad/octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features. The source code of the method implementation is freely available.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
NASA Astrophysics Data System (ADS)
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
Extended neoclassical transport theory for incompressible tokamak plasmas
NASA Astrophysics Data System (ADS)
Shaing, K. C.
1997-09-01
Conventional neoclassical transport theory is extended to include the effects of orbit squeezing, and to allow the effective poloidal Mach number UpM=[(V∥/vt)+(VEB/vtBp)] of the order of unity for incompressible tokamak plasmas. Here, V∥ is the parallel mass flow, vt is the ion thermal speed, VE is the poloidal E×B drift speed, B is the magnetic field strength, and Bp is the poloidal magnetic field strength. It is found that ion thermal conductivity is reduced from its conventional neoclassical value in both banana and plateau regimes if UpM>1 and S>1. Here, S=[1+cI2Φ''/(Ω0B0)] is the orbit squeezing factor with c the speed of light, I=RBt, R the major radius, Φ the electrostatic potential, B0 the magnetic field strength on the axis, Ω0=eB0/Mc, M the ion mass, e the ion charge, Φ''=d2Φ/dψ2, and ψ the poloidal flux function. However, there is an irreducible minimum for the ion thermal conductivity in the banana-plateau regime set by the conventional Pfirsch-Schlüter transport.
Robust preconditioners for incompressible MHD models
NASA Astrophysics Data System (ADS)
Ma, Yicong; Hu, Kaibo; Hu, Xiaozhe; Xu, Jinchao
2016-07-01
In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners for them and carry out rigorous analysis on their performance. We prove that such preconditioners are robust with respect to most physical and discretization parameters. In our proof, we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters, which are usually difficult to choose in practice. This new technique is applicable not only to the MHD system, but also to other problems. Moreover, we prove that Krylov iterative methods with our preconditioners preserve the divergence-free condition exactly, which complements the structure-preserving discretization. Another feature is that we can directly generalize this technique to other discretizations of the MHD system. We also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners.
NASA Astrophysics Data System (ADS)
Fernández, Arturo
2008-04-01
Direct numerical simulations of the effects of an electric field on an emulsion of drops are presented. A simple shear flow configuration is adopted where the electric field is applied perpendicular to the sliding plates. Both the drops and the suspending fluid are assumed to behave as leaky dielectric fluids. Here, drops less conductive than the suspending fluid with an electrical conductivity ratio smaller than the dielectric permittivity ratio are considered. This combination of electrical properties leads to a viscous fluid motion from the poles to the equator. The response of an emulsion is governed by the competition between the electrical forces, the fluid shear, and the capillary forces. The Mason number [Mn=(3λ+2)μγ˙/6(λ+1)ɛ0β2E∞2] and the electric capillary number [Ce=ɛ0β2E∞2a/γ] are used to describe the response of the systems. As previously observed in experiments at low shear rates, Mn <0.2, the drops aggregate in chains that tilt under a shear. The competition between the electrical forces and the fluid shear results in shorter chains at intermediate shear rates, 0.2
An Experimental Investigation of Incompressible Richtmyer-Meshkov Instability
NASA Technical Reports Server (NTRS)
Jacobs, J. W.; Niederhaus, C. E.
2002-01-01
Richtmyer-Meshkov (RM) instability occurs when two different density fluids are impulsively accelerated in the direction normal to their nearly planar interface. The instability causes small perturbations on the interface to grow and eventually become a turbulent flow. It is closely related to Rayleigh-Taylor instability, which is the instability of a planar interface undergoing constant acceleration, such as caused by the suspension of a heavy fluid over a lighter one in the earth's gravitational field. Like the well-known Kelvin-Helmholtz instability, RM instability is a fundamental hydrodynamic instability which exhibits many of the nonlinear complexities that transform simple initial conditions into a complex turbulent flow. Furthermore, the simplicity of RM instability (in that it requires very few defining parameters), and the fact that it can be generated in a closed container, makes it an excellent test bed to study nonlinear stability theory as well as turbulent transport in a heterogeneous system. However, the fact that RM instability involves fluids of unequal densities which experience negligible gravitational force, except during the impulsive acceleration, requires RM instability experiments to be carried out under conditions of microgravity. This experimental study investigates the instability of an interface between incompressible, miscible liquids with an initial sinusoidal perturbation. The impulsive acceleration is generated by bouncing a rectangular tank containing two different density liquids off a retractable vertical spring. The initial perturbation is produced prior to release by oscillating the tank in the horizontal direction to produce a standing wave. The instability evolves in microgravity as the tank travels up and then down the vertical rails of a drop tower until hitting a shock absorber at the bottom. Planar Laser Induced Fluorescence (PLIF) is employed to visualize the flow. PLIF images are captured by a video camera that travels
Energy Equation Approximation in Fluid Mechanics
NASA Technical Reports Server (NTRS)
Goldstein, Arthur W.
1959-01-01
There is some confusion in the literature of fluid mechanics in regard to the correct form of the energy equation for the study of the flow of nearly incompressible fluids. Several forms of the energy equation and their use are therefore discussed in this note.
Vibration characteristics of rectangular plate in compressible inviscid fluid
NASA Astrophysics Data System (ADS)
Liao, Chan-Yi; Ma, Chien-Ching
2016-02-01
This paper presents a mathematical derivation of the vibration characteristics of an elastic thin plate placed at the bottom of a three dimensional rectangular container filled with compressible inviscid fluid. A set of beam functions is used as the admissible functions of the plate in a fluid-plate system, and the motion of the fluid induced by the deformation of the plate is obtained from a three-dimensional acoustic equation. Pressure from the fluid over the fluid-plate interface is integrated to form a virtual mass matrix. The frequency equation of the fluid-plate system is derived by combining mass, stiffness, and the virtual mass matrix. Solving the frequency equation makes it possible to obtain the dynamic characteristic of the fluid-plate system, such as resonant frequencies, corresponding mode shapes, and velocity of the fluid. Numerical calculations were performed for plates coupled with fluids with various degrees of compressibility to illustrate the difference between compressible and incompressible fluids in a fluid-plate system. The proposed method could be used to predict resonant frequencies and mode shapes with accuracy compared to that of incompressible fluid theory (IFT). The proposed method can be used to analyze cases involving high value of sound velocity, such as incompressible fluids. When the sound velocity approaches infinity, the results obtained for compressible fluids are similar to those of incompressible fluids. We also examined the influence of fluid compressibility on vibration characteristics in which a decrease in sound velocity was shown to correspond to a decrease in resonant frequency. Additional modes, not observed in incompressible fluids, were obtained in cases of low sound velocity, particularly at higher resonant frequencies. Fluid velocity plots clearly reveal that the additional resonant modes can be attributed to the compressible behavior of the fluid.
Hadjicharalambous, Myrianthi; Lee, Jack; Smith, Nicolas P; Nordsletten, David A
2014-06-01
The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii-Newton-Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics.
Hadjicharalambous, Myrianthi; Lee, Jack; Smith, Nicolas P.; Nordsletten, David A.
2014-01-01
The Lagrange Multiplier (LM) and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics. In this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed Perturbed Lagrangian formulation, which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of LM techniques. A modified Shamanskii–Newton–Raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and, exploiting its equivalence, modifications are developed for the penalty form. Focusing on accuracy, we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics. Our results illustrate the well-known influence of locking phenomena on the penalty approach (particularly for lower order schemes) and its effect on accuracy for whole-cycle mechanics. Additionally, we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable. Combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics, the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics. PMID:25187672
NASA Astrophysics Data System (ADS)
Bouteraa, Mondher; Nouar, Chérif
2015-12-01
Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Rac and the critical wave number kc decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value αc of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that αc increases with decreasing ξ . The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξc, below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015), 10.1017/jfm.2015.64]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξc. The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates.
Bouteraa, Mondher; Nouar, Chérif
2015-12-01
Finite-amplitude thermal convection in a shear-thinning fluid layer between two horizontal plates of finite thermal conductivity is considered. Weakly nonlinear analysis is adopted as a first approach to investigate nonlinear effects. The rheological behavior of the fluid is described by the Carreau model. As a first step, the critical conditions for the onset of convection are computed as a function of the ratio ξ of the thermal conductivity of the plates to the thermal conductivity of the fluid. In agreement with the literature, the critical Rayleigh number Ra(c) and the critical wave number k(c) decrease from 1708 to 720 and from 3.11 to 0, when ξ decreases from infinity to zero. In the second step, the critical value α(c) of the shear-thinning degree above which the bifurcation becomes subcritical is determined. It is shown that α(c) increases with decreasing ξ. The stability of rolls and squares is then investigated as a function of ξ and the rheological parameters. The limit value ξ(c), below which squares are stable, decreases with increasing shear-thinning effects. This is related to the fact that shear-thinning effects increase the nonlinear interactions between sets of rolls that constitute the square patterns [M. Bouteraa et al., J. Fluid Mech. 767, 696 (2015)]. For a significant deviation from the critical conditions, nonlinear convection terms and nonlinear viscous terms become stronger, leading to a further diminution of ξ(c). The dependency of the heat transfer on ξ and the rheological parameters is reported. It is consistent with the maximum heat transfer principle. Finally, the flow structure and the viscosity field are represented for weakly and highly conducting plates. PMID:26764814
Identification of whistling ability of a single hole orifice from an incompressible flow simulation
Lacombe, Romain; Moussou, Pierre
2012-07-01
Pure tone noise from orifices in pipe result from vortex shedding with lock-in. Acoustic amplification at the orifice is coupled to resonant condition to create self-sustained oscillations. One key feature of this phenomenon is hence the ability of an orifice to amplify acoustic waves in a given range of frequencies. Here a numerical investigation of the linear response of an orifice is undertaken, with the support of experimental data for validation. The study deals with a sharp edge orifice. Its diameter equals to 0.015 m and its thickness to 0.005 m. The pipe diameter is 0.030 m. An air flow with a Mach number 0.026 and a Reynolds number 18000 in the main pipe is present. At such a low Mach number; the fluid behavior can reasonably be described as locally incompressible. The incompressible Unsteady Reynolds Averaged Navier-Stokes (URANS) equations are solved with the help of a finite volume fluid mechanics software. The orifice is submitted to an average flow velocity, with superimposed small harmonic perturbations. The harmonic response of the orifice is the difference between the upstream and downstream pressures, and a straightforward calculation brings out the acoustic impedance of the orifice. Comparison with experiments shows that the main physical features of the whistling phenomenon are reasonably reproduced. (authors)
Kumar, Rajneesh; Rajvanshi, S C; Kaur, Mandeep
2014-01-01
The present investigation is concerned with the propagation of waves at an imperfect boundary of heat conducting elastic solid and micropolar fluid media. The amplitude ratios of various reflected and transmitted waves are obtained in a closed form due to incidence of longitudinal wave (P-wave), thermal wave (T-wave), and transverse wave (SV-wave). The variation of various amplitude ratios with angle of incidence is obtained for normal force stiffness, transverse force stiffness, thermal contact conductance, and perfect bonding. Numerical results are shown graphically to depict the effect of stiffness and thermal relaxation times on resulting quantities. Some particular cases are also deduced in the present investigation.
Turner, Mark J; Saint-Criq, Vinciane; Patel, Waseema; Ibrahim, Salam H; Verdon, Bernard; Ward, Christopher; Garnett, James P; Tarran, Robert; Cann, Martin J; Gray, Michael A
2016-03-15
Hypercapnia is clinically defined as an arterial blood partial pressure of CO2 of above 40 mmHg and is a feature of chronic lung disease. In previous studies we have demonstrated that hypercapnia modulates agonist-stimulated cAMP levels through effects on transmembrane adenylyl cyclase activity. In the airways, cAMP is known to regulate cystic fibrosis transmembrane conductance regulator (CFTR)-mediated anion and fluid secretion, which contributes to airway surface liquid homeostasis. The aim of the current work was to investigate if hypercapnia could modulate cAMP-regulated ion and fluid transport in human airway epithelial cells. We found that acute exposure to hypercapnia significantly reduced forskolin-stimulated elevations in intracellular cAMP as well as both adenosine- and forskolin-stimulated increases in CFTR-dependent transepithelial short-circuit current, in polarised cultures of Calu-3 human airway cells. This CO2 -induced reduction in anion secretion was not due to a decrease in HCO3 (-) transport given that neither a change in CFTR-dependent HCO3 (-) efflux nor Na(+) /HCO3 (-) cotransporter-dependent HCO3 (-) influx were CO2 -sensitive. Hypercapnia also reduced the volume of forskolin-stimulated fluid secretion over 24 h, yet had no effect on the HCO3 (-) content of the secreted fluid. Our data reveal that hypercapnia reduces CFTR-dependent, electrogenic Cl(-) and fluid secretion, but not CFTR-dependent HCO3 (-) secretion, which highlights a differential sensitivity of Cl(-) and HCO3 (-) transporters to raised CO2 in Calu-3 cells. Hypercapnia also reduced forskolin-stimulated CFTR-dependent anion secretion in primary human airway epithelia. Based on current models of airways biology, a reduction in fluid secretion, associated with hypercapnia, would be predicted to have important consequences for airways hydration and the innate defence mechanisms of the lungs.
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium
NASA Astrophysics Data System (ADS)
Lyubimova, T. P.; Lyubimov, D. V.; Baydina, D. T.; Kolchanova, E. A.; Tsiberkin, K. B.
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium.
Lyubimova, T P; Lyubimov, D V; Baydina, D T; Kolchanova, E A; Tsiberkin, K B
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed. PMID:27575214
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium.
Lyubimova, T P; Lyubimov, D V; Baydina, D T; Kolchanova, E A; Tsiberkin, K B
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
A Hybrid Nodal Method for Time-Dependent Incompressible Flow in Two-Dimensional Arbitrary Geometries
Toreja, A J; Uddin, R
2002-10-21
A hybrid nodal-integral/finite-analytic method (NI-FAM) is developed for time-dependent, incompressible flow in two-dimensional arbitrary geometries. In this hybrid approach, the computational domain is divided into parallelepiped and wedge-shaped space-time nodes (cells). The conventional nodal integral method (NIM) is applied to the interfaces between adjacent parallelepiped nodes (cells), while a finite analytic approach is applied to the interfaces between parallelepiped and wedge-shaped nodes (cells). In this paper, the hybrid method is formally developed and an application of the NI-FAM to fluid flow in an enclosed cavity is presented. Results are compared with those obtained using a commercial computational fluid dynamics code.
Global regularity for MHD Sisko fluid in annular pipe
NASA Astrophysics Data System (ADS)
Rahman, S.; Hayat, T.; Ahmad, B.
2016-08-01
The flow of Sisko fluid in an annular pipe is considered. The governing nonlinear equation of an incompressible Sisko fluid is modelled. The purpose of present paper is to obtain the global classical solutions for unsteady flow of magnetohydrodynamic Sisko fluid in terms of the bounded mean oscillations norm. Uniqueness of solution is also verified.
Extended neoclassical transport theory for incompressible tokamak plasmas
Shaing, K.C.
1997-09-01
Conventional neoclassical transport theory is extended to include the effects of orbit squeezing, and to allow the effective poloidal Mach number U{sub pM}=[(V{sub {parallel}}/v{sub t})+(V{sub E}B/v{sub t}B{sub p})] of the order of unity for incompressible tokamak plasmas. Here, V{sub {parallel}} is the parallel mass flow, v{sub t} is the ion thermal speed, V{sub E} is the poloidal {bold E{times}B} drift speed, B is the magnetic field strength, and B{sub p} is the poloidal magnetic field strength. It is found that ion thermal conductivity is reduced from its conventional neoclassical value in both banana and plateau regimes if U{sub pM}{gt}1 and S{gt}1. Here, S=[1+cI{sup 2}{Phi}{sup {prime}{prime}}/({Omega}{sub 0}B{sub 0})] is the orbit squeezing factor with c the speed of light, I=RB{sub t}, R the major radius, {Phi} the electrostatic potential, B{sub 0} the magnetic field strength on the axis, {Omega}{sub 0}=eB{sub 0}/Mc, M the ion mass, e the ion charge, {Phi}{sup {prime}{prime}}=d{sup 2}{Phi}/d{psi}{sup 2}, and {psi} the poloidal flux function. However, there is an irreducible minimum for the ion thermal conductivity in the banana-plateau regime set by the conventional Pfirsch{endash}Schl{umlt u}ter transport. {copyright} {ital 1997 American Institute of Physics.}
Aikins, Ross; Hoefinger, Heidi; Guarino, Honoria; Rosenblum, Andrew; Magura, Stephen; Joseph, Herman
2015-01-01
This study piloted the feasibility of rapidly collecting both self-reports of drug use and saliva specimens for drug toxicology in field settings. The use of oral fluid collection devices to supplement self-reports is unproven in street settings and may pose challenges for field research. Sixty adults who identified as recent illicit drug users were recruited in public settings in New York City and were asked to complete a brief drug screening inventory and provided saliva specimens. Descriptive findings are detailed along with critical best research practices and limitations that provide important directions for researchers looking to employ both toxicology and self-report in rapid field recruitment designs.
Hunter, M; Lee, J
1992-11-01
A dispersion and extraction model of the lung is developed to assess how the infusion of hypertonic saline into the pulmonary artery changes the gravimetric density of pulmonary venous blood. The dispersion analysis is built on the indicator dilution curve measured for the pulmonary circulation. The extraction model consists of microvascular and interstitial compartments separated by a permeable pulmonary endothelium. Because the density of fluid extracted by the hypertonic disturbance is lower than the blood density, the extraction leads to a decrease in blood density. Two cases of fluid extraction are analyzed, a hypertonic infusion to elevate the osmotic pressure in the pulmonary arterial blood in the form of a step function and an infusion performed over a period of 1 sec. Both cases show that the dispersion significantly attenuates the changes in osmotic pressure and density as they are transported by the blood along the pulmonary vasculature. Because the model has taken into account the effect of dispersion and pulmonary blood flow, the equations developed here provide the basis to calculate from the density change in pulmonary venous blood the characteristics of osmotic extraction intrinsic to the lung.
NASA Astrophysics Data System (ADS)
RamReddy, Ch.; Surender, O.; Venkata Rao, Ch.
2016-09-01
The significance of Soret, Hall and Ion-slip effects on mixed convection flow of an electrically conducting Casson fluid in a vertical channel in the presence of viscous dissipation is analyzed. The system of flow governing equations are converted into the system of non-dimensional equations using appropriate non-dimensional transformations and hence solved analytically by homotopy analysis method. A quantitative comparison is made between homotopy analysis method and Adomian decomposition method and the results are found to be in good agreement. The dimensionless velocity, temperature and species concentration profiles are illustrated graphically and quantitatively with special focus on the Casson fluid, Soret, viscous dissipation, Hall and Ion-slip parameters.
Chornack, M.P.; French, C.A.
1989-12-31
Horizontal coring using air as the circulating fluid has been conducted in the G Tunnel Underground Facility (GTUF) at the Nevada Test Site. This work is part of the prototype investigations of hydrogeology for the Yucca Mountain Project. The work is being conducted to develop methods and procedures that will be used at the Department of Energy`s Yucca Mountain Site, a candidate site for the nation`s first high-level nuclear waste repository, during the site characterization phase of the investigations. The United States Geological Survey (USGS) is conducting this prototype testing under the guidance of the Los Alamos National Laboratory (LANL) and in conjunction with Reynolds Electrical & Engineering Company (REECo), the drilling contractor. 7 refs., 8 figs., 5 tabs.
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
Fu, S.C.; So, R.M.C.; Leung, W.W.F.
2010-08-20
With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.
Aikins, Ross; Hoefinger, Heidi; Guarino, Honoria; Rosenblum, Andrew; Magura, Stephen; Joseph, Herman
2016-01-01
This study piloted the feasibility of rapidly collecting both self-reports of drug use and saliva specimens for drug toxicology in field settings. The use of oral fluid collection devices to supplement self-reports is unproven in street settings and may pose challenges for field research. Sixty adults who identified as recent illicit drug users were recruited in public settings in New York City and were asked to complete a brief drug screening inventory and provided saliva specimens. Descriptive findings are detailed along with critical best research practices and limitations that provide important directions for researchers looking to employ both toxicology and self-report in rapid field recruitment designs. PMID:26098766
Fogler, H.S.
1993-12-01
The main objectives of this project were to develop new treatment strategies that would improve the efficiency of oil production, and stimulation procedures. Treatment strategies were developed to treat injection well matrix heterogeneities, production well matrix or saturation heterogeneities, and fractured wells. The treatment strategies investigated included a particulate system, and a foamed gel for injection well profile modification, a foam/acid injection strategy for improving acidization of carbonates, an acid reactive gel for controlling acid leak-off into fractures, and a water reactive gel for water shut-off at production wells. The research performed focused on discovering the principles governing the performance of the treatment strategies to provide a fundamental basis for further development of these techniques. Other goals of this project were to demonstrate the use of Neutron Imaging for real time imaging of fluid flow through heterogeneous porous media and develop a kinetic model to simulate the effect of diagenetic processes on reservoir porosity and permeability.
Lower limb arterial incompressibility and obstruction in rheumatoid arthritis
del Rincon, I; Haas, R; Pogosian, S; Escalante, A
2005-01-01
Background: Despite increased cardiovascular morbidity and mortality in rheumatoid arthritis, the peripheral arteries remain understudied. Objective: To examine the lower limb arteries in age and sex matched, non-smoking subjects with and without rheumatoid arthritis. Methods: The ankle-brachial index (ABI) was measured at the posterior tibial and dorsal pedal arteries. Arteries were classified as obstructed with ABI ⩽0.9, normal with ABI >0.9 but ⩽1.3, and incompressible with ABI >1.3. Multinomial logistic regression was used to estimate differences in ABI between patients and controls, adjusting for cardiovascular risk factors, rheumatoid arthritis manifestations, inflammation markers, and glucocorticoid dose. Results: 234 patients with rheumatoid arthritis and 102 controls were studied. Among the rheumatoid patients, 66 of 931 arteries (7%) were incompressible and 30 (3%) were obstructed. Among the controls, three of 408 arteries (0.7%) were incompressible (p = 0.002) and four (1%) were obstructed (p = 0.06). At the person level, one or more abnormal arteries occurred among 45 rheumatoid patients (19%), v five controls (5%, p = 0.001). The greater frequency of arterial incompressibility and obstruction in rheumatoid arthritis was independent of age, sex, and cardiovascular risk factors. Adjustment for inflammation markers, joint damage, rheumatoid factor, and glucocorticoid use reduced rheumatoid arthritis v control differences. Most arterial impairments occurred in rheumatoid patients with 20 or more deformed joints. This subgroup had more incompressible (15%, p⩽0.001) and obstructed arteries (6%, p = 0.005) than the controls, independent of covariates. Conclusions: Peripheral arterial incompressibility and obstruction are increased in rheumatoid arthritis. Their propensity for patients with advanced joint damage suggests shared pathogenic mechanisms. PMID:15271772
NASA Astrophysics Data System (ADS)
Hudoba, A.; Molokov, S.; Aleksandrova, S.; Pedcenko, A.
2016-09-01
Linear stability of buoyant convective flow in a horizontal layer of an electrically conducting fluid is considered with reference to horizontal Bridgman semiconductor crystal growth. The fluid flows owing to the horizontal temperature gradient in the presence of a vertical magnetic field. The main interest here is in the stability of the flow for a sufficiently strong magnetic field, for the Hartmann number Ha > 10, and increasing to high values, of the order of 103-104. The Prandtl number, Pr, has been fixed at Pr = 0.015. It is shown that besides the Hartmann number the instability strongly depends on the type of the thermal boundary conditions at the horizontal walls. For thermally conducting walls the basic temperature profile exhibits zones of unstable thermal stratification, which leads to instabilities owing to the Rayleigh-Bénard mechanism. However, the transitions between various, most unstable modes as Ha increases are not trivial. For sufficiently high values of Ha, the most unstable mode consists of transverse oscillatory rolls located in the region of unstable stratification. For thermally insulating walls, the transitions are simpler, and for sufficiently high Ha, the most unstable mode consists of longitudinal, steady, three-dimensional mode which is concentrated in the Hartmann layers at the horizontal boundaries. This mode has a combined dynamic-thermal origin and is owed to a strong shear in the Hartmann layers. The electrical boundary conditions do not qualitatively affect the picture of transitions between modes for both thermally conducting and thermally insulating walls.
Incompressibility of osmium metal at ultrahigh pressures and temperatures
Armentrout, Matt M.; Kavner, Abby
2010-07-23
Osmium is one of the most incompressible elemental metals, and is used as a matrix material for synthesis of ultrahard materials. To examine the behavior of osmium metal under extreme conditions of high pressure and temperature, we measured the thermal equation of state of osmium metal at pressures up to 50 GPa and temperatures up to 3000 K. X-ray diffraction measurements were conducted in the laser heated diamond anvil cell at GeoSoilEnviroCARS and the High Pressure at the Advanced Photon Source and beamline 12.2.2 at the advanced light source. Ambient temperature data give a zero pressure bulk modulus of 421 (3) GPa with a first pressure derivative fixed at 4. Fitting to a high temperature Birch-Murnaghan equation of state gives a room pressure thermal expansion of 1.51(0.06) x 10{sup -5} K{sup -1} with a first temperature derivative of 4.9(0.7) x 10{sup -9} K{sup -2} and the first temperature derivative of bulk modulus of be dK{sub 0}/dT = -0.055 (0.004). Fitting to a Mie-Grueneisen-Debye equation of state gives a Grueneisen parameter of 2.32 (0.08) with a q of 7.2 (1.4). A comparison of the high pressure, temperature behavior among Re, Pt, Os, shows that Os has the highest bulk modulus and lowest thermal expansion of the three, suggesting that Os-based ultrahard materials may be especially mechanically stable under extreme conditions.
NASA Astrophysics Data System (ADS)
Malik, M. Y.; Bibi, M.; Khan, Farzana; Salahuddin, T.
2016-03-01
In this article, Williamson fluid flow and heat transfer over a stretching cylinder is discussed. The thermal conductivity is assumed to be vary linearly with temperature. Heat generation/absorption effects are also taken into account. Modeled partial differential equations are converted into ordinary differential form by using appropriate transformations. Shooting method in conjunction with Runge-Kutta-Fehlberg method is used to find the solution of the problem. Moreover, the effects of different flow parameters γ, λ, ɛ, β and Pr on velocity and temperature profiles are shown graphically. Local Nusselt number and skin friction coefficient are shown in tabular and graphical form.
NASA Astrophysics Data System (ADS)
Maqsood, Asghari; Anis-ur-Rehman, M.
2013-12-01
Thermal conductivity and thermal diffusivity are two important physical properties for designing any food engineering processes1. The knowledge of thermal properties of the elements, compounds and different materials in many industrial applications is a requirement for their final functionality. Transient plane source (tps) sensors are reported2 to be useful for the simultaneous measurement of thermal conductivity, thermal diffusivity and volumetric heat capacity of insulators, conductor liquids3 and high-TC superconductors4. The tps-sensor consists of a resistive element in the shape of double spiral made of 10 micrometer thick Ni-foils covered on both sides with 25 micrometer thick Kapton. This sensor acts both as a heat source and a resistance thermometer for recording the time dependent temperature increase. From the knowledge of the temperature co-efficient of the metal spiral, the temperature increase of the sensor can be determined precisely by placing the sensor in between two surfaces of the same material under test. This temperature increase is then related to the thermal conductivity, thermal diffusivity and volumetric heat capacity by simple relations2,5. The tps-sensor has been used to measure thermal conductivities from 0.001 Wm-1K-1to 600 Wm-1K-1 and temperature ranges covered from 77K- 1000K. This talk gives the design, advantages and limitations of the tpl-sensor along with its applications to the measurementof thermal properties in a variety of materials.
NASA Astrophysics Data System (ADS)
Chagelishvili, George; Hau, Jan-Niklas; Khujadze, George; Oberlack, Martin
2016-08-01
The linear dynamics of perturbations in smooth shear flows covers the transient exchange of energies between (1) the perturbations and the basic flow and (2) different perturbations modes. Canonically, the linear exchange of energies between the perturbations and the basic flow can be described in terms of the Orr and the lift-up mechanisms, correspondingly for two-dimensional (2D) and three-dimensional (3D) perturbations. In this paper the mechanical basis of the linear transient dynamics is introduced and analyzed for incompressible plane constant shear flows, where we consider the dynamics of virtual fluid particles in the framework of plane perturbations (i.e., perturbations with plane surfaces of constant phase) for the 2D and 3D case. It is shown that (1) the formation of a pressure perturbation field is the result of countermoving neighboring sets of incompressible fluid particles in the flow, (2) the keystone of the energy exchange mechanism between the basic flow and perturbations is the collision of fluid particles with the planes of constant pressure in accordance with the classical theory of elastic collision of particles with a rigid wall, making the pressure field the key player in this process, (3) the interplay of the collision process and the shear flow kinematics describes the transient growth of plane perturbations and captures the physics of the growth, and (4) the proposed mechanical picture allows us to reconstruct the linearized Euler equations in spectral space with a time-dependent shearwise wave number, the linearized Euler equations for Kelvin modes. This confirms the rigor of the presented analysis, which, moreover, yields a natural generalization of the proposed mechanical picture of the transient growth to the well-established linear phenomenon of vortex-wave-mode coupling.
A stable partitioned FSI algorithm for incompressible flow and deforming beams
NASA Astrophysics Data System (ADS)
Li, L.; Henshaw, W. D.; Banks, J. W.; Schwendeman, D. W.; Main, A.
2016-05-01
An added-mass partitioned (AMP) algorithm is described for solving fluid-structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier-Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler-Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet-Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one
Tůma, Petr
2016-05-20
A new electrophoretic stacking method has been developed for the sensitive determination of nitrates in cerebrospinal fluid. 2M acetic acid was used as the BGE; inorganic anions were detected using a contactless conductivity detector and separation was carried out in an INST-coated capillary with inner diameter of 25μm. The sample of cerebrospinal fluid was injected in a large volume into the short end of the separation capillary (15cm) and separation first occurred in the isotachophoretic mode, where a long zone of the majority chloride migrates in the capillary and is followed by a concentrated zone of the unseparated nitrates. The sample zone passes to the end of the capillary where more than 99% of the chlorides are let out. Then the polarity of the voltage is switched and separation occurs in the zone electrophoresis mode, in which the nitrates are separated from the zone of chlorides. The time of switching the polarity is determined by the decrease in the electrophoretic current. Up to 99.95% of the original amount of chlorides present in the cerebrospinal fluid could be let out of the capillary by this technique, thus increasing the signal/noise ratio by up to 60-fold compared to classical electrophoretic separation.
Sondak, David; Oberai, Assad A.
2012-10-15
Novel large eddy simulation (LES) models are developed for incompressible magnetohydrodynamics (MHD). These models include the application of the variational multiscale formulation of LES to the equations of incompressible MHD. Additionally, a new residual-based eddy viscosity model is introduced for MHD. A mixed LES model that combines the strengths of both of these models is also derived. The new models result in a consistent numerical method that is relatively simple to implement. The need for a dynamic procedure in determining model coefficients is no longer required. The new LES models are tested on a decaying Taylor-Green vortex generalized to MHD and benchmarked against classical LES turbulence models. The LES simulations are run in a periodic box of size [-{pi}, {pi}]{sup 3} with 32 modes in each direction and are compared to a direct numerical simulation (DNS) with 512 modes in each direction. The new models are able to account for the essential MHD physics which is demonstrated via comparisons of energy spectra. We also compare the performance of our models to a DNS simulation by Pouquet et al.['The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD,' Geophys. Astrophys. Fluid Dyn. 104, 115-134 (2010)], for which the ratio of DNS modes to LES modes is 262:144.
Computation of incompressible viscous flows through artificial heart devices with moving boundaries
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Rogers, Stuart; Kwak, Dochan; Chang, I.-DEE
1991-01-01
The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.
Towards a segregated time spectral solution method for incompressible viscous flows
NASA Astrophysics Data System (ADS)
Sabine, Baumbach
2016-06-01
Considering the growth of interest in understanding flow phenomena in rotational machines, computational fluid dynamics (CFD) is a powerful tool to reach this goal. Especially unsteady simulations are becoming a focus of interest. Nevertheless, unsteady simulations require huge computational times and ressources, thus it is necessary to investigate other methods to find more appropriate approaches to model time-periodic cases. For time-periodic flows the time spectral method (TSM) presents an interesting alternative to the regular time marching solvers. The TSM is well-known for computation of compressible time-periodic flows, but applications to incompressible cases are limited. This paper presents an extension of the TSM to incompressible flows. While there have been previous implementations using pressure correction method with an explicit treatment of time coupling, here an implicit treatment is chosen. To increase efficiency and employ a more robust coupling of the individual time instances the momentum equations are solved in block-coupled fashion. The pressure correction term is solved segregatedly. To consider cases with dynamic mesh motion an arbitrary lagrange Euler (ALE) formulation is also used in the solver. The efficiency of the method is demonstrated using a basic 2D aerodynamic test case and the results are compared to traditional time-stepping approaches.
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S.; Ingber, M.S.
1995-04-01
formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S.; Ingber, M.S.
1995-03-01
Velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations are presented. Vorticity is created on boundaries to simultaneously satisfy the tangential and normal components of the velocity boundary condition. The newly created vorticity is specified by a kinematical formulation which is a generalization of Helmholtz decomposition of a vector field. Related forms of the decomposition were developed by Bykhovskiy and Smirnov in 1983, and Wu and Thompson in 1973. Though it has not been generally recognized as such, these formulations resolve the over-specification issues associated with determining a velocity field from velocity boundary conditions and a vorticity field. The generalized decomposition has not been widely used, however, apparently due to a general lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition for the normal and tangential velocity boundary conditions is discussed in detail. As an example of the use of this boundary condition, the flow in a lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRE. ALEGRE`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
Turner, Mark J.; Saint‐Criq, Vinciane; Patel, Waseema; Ibrahim, Salam H.; Verdon, Bernard; Ward, Christopher; Garnett, James P.; Tarran, Robert; Cann, Martin J.
2015-01-01
Key points Raised arterial blood CO2 (hypercapnia) is a feature of many lung diseases.CO2 has been shown to act as a cell signalling molecule in human cells, notably by influencing the levels of cell signalling second messengers: cAMP and Ca2+.Hypercapnia reduced cAMP‐stimulated cystic fibrosis transmembrane conductance regulator‐dependent anion and fluid transport in Calu‐3 cells and primary human airway epithelia but did not affect cAMP‐regulated HCO3 − transport via pendrin or Na+/HCO3 − cotransporters.These results further support the role of CO2 as a cell signalling molecule and suggests CO2‐induced reductions in airway anion and fluid transport may impair innate defence mechanisms of the lungs. Abstract Hypercapnia is clinically defined as an arterial blood partial pressure of CO2 of above 40 mmHg and is a feature of chronic lung disease. In previous studies we have demonstrated that hypercapnia modulates agonist‐stimulated cAMP levels through effects on transmembrane adenylyl cyclase activity. In the airways, cAMP is known to regulate cystic fibrosis transmembrane conductance regulator (CFTR)‐mediated anion and fluid secretion, which contributes to airway surface liquid homeostasis. The aim of the current work was to investigate if hypercapnia could modulate cAMP‐regulated ion and fluid transport in human airway epithelial cells. We found that acute exposure to hypercapnia significantly reduced forskolin‐stimulated elevations in intracellular cAMP as well as both adenosine‐ and forskolin‐stimulated increases in CFTR‐dependent transepithelial short‐circuit current, in polarised cultures of Calu‐3 human airway cells. This CO2‐induced reduction in anion secretion was not due to a decrease in HCO3 − transport given that neither a change in CFTR‐dependent HCO3 − efflux nor Na+/HCO3 − cotransporter‐dependent HCO3 − influx were CO2‐sensitive. Hypercapnia also reduced the volume of forskolin‐stimulated fluid
NASA Astrophysics Data System (ADS)
Sharma, Prabhakar; Tsang, Chin-Fu; Kukkonen, Ilmo T.; Niemi, Auli
2016-07-01
Over the last two decades, the flowing fluid electric conductivity (FFEC) logging method has been applied in boreholes in the well-testing mode to evaluate the transmissivity, hydraulic head, and formation water electrical conductivity as a function of depth with a resolution of about 10-20 cm. FFEC profiles along the borehole are obtained under both shut-in and pumping conditions in a logging procedure that lasts only 3 or 4 days. A method for analyzing these FFEC logs has been developed and successfully employed to obtain formation parameters in a number of field studies. The present paper concerns the analysis of a unique set of FFEC logs that were taken from a deep borehole reaching down to 2.5 km at Outokumpu, Finland, over a 6-year time period. The borehole intersects paleoproterozoic metasedimentary, granitoid, and ophiolite-derived rocks. After the well was drilled, completed, and cleaned up, FFEC logs were obtained after 7, 433, 597, 948, and 2036 days. In analyzing these five profiles, we discovered the need to account for salinity diffusion from water in the formation to the borehole. Analysis results include the identification of 15 hydraulically conducting zones along the borehole, the calculation of flow rates associated with these 15 zones, as well as the estimation of the variation of formation water electrical conductivity as a function of depth. The calculated flow rates were used to obtain the tentative hydraulic conductivity values at these 15 depth levels.
Consistent lattice Boltzmann methods for incompressible axisymmetric flows.
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified. PMID:27627407
Consistent lattice Boltzmann methods for incompressible axisymmetric flows
NASA Astrophysics Data System (ADS)
Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Yin, Linmao; Zhao, Ya; Chew, Jia Wei
2016-08-01
In this work, consistent lattice Boltzmann (LB) methods for incompressible axisymmetric flows are developed based on two efficient axisymmetric LB models available in the literature. In accord with their respective original models, the proposed axisymmetric models evolve within the framework of the standard LB method and the source terms contain no gradient calculations. Moreover, the incompressibility conditions are realized with the Hermite expansion, thus the compressibility errors arising in the existing models are expected to be reduced by the proposed incompressible models. In addition, an extra relaxation parameter is added to the Bhatnagar-Gross-Krook collision operator to suppress the effect of the ghost variable and thus the numerical stability of the present models is significantly improved. Theoretical analyses, based on the Chapman-Enskog expansion and the equivalent moment system, are performed to derive the macroscopic equations from the LB models and the resulting truncation terms (i.e., the compressibility errors) are investigated. In addition, numerical validations are carried out based on four well-acknowledged benchmark tests and the accuracy and applicability of the proposed incompressible axisymmetric LB models are verified.
EVIDENCE FOR THE PHOTOSPHERIC EXCITATION OF INCOMPRESSIBLE CHROMOSPHERIC WAVES
Morton, R. J.; Verth, G.; Fedun, V.; Erdelyi, R.; Shelyag, S.
2013-05-01
Observing the excitation mechanisms of incompressible transverse waves is vital for determining how energy propagates through the lower solar atmosphere. We aim to show the connection between convectively driven photospheric flows and incompressible chromospheric waves. The observations presented here show the propagation of incompressible motion through the quiet lower solar atmosphere, from the photosphere to the chromosphere. We determine photospheric flow vectors to search for signatures of vortex motion and compare results to photospheric flows present in convective simulations. Further, we search for the chromospheric response to vortex motions. Evidence is presented that suggests incompressible waves can be excited by the vortex motions of a strong magnetic flux concentration in the photosphere. A chromospheric counterpart to the photospheric vortex motion is also observed, presenting itself as a quasi-periodic torsional motion. Fine-scale, fibril structures that emanate from the chromospheric counterpart support transverse waves that are driven by the observed torsional motion. A new technique for obtaining details of transverse waves from time-distance diagrams is presented and the properties of transverse waves (e.g., amplitudes and periods) excited by the chromospheric torsional motion are measured.
Valdés-Ramírez, Gabriela; Windmiller, Joshua R.; Claussen, Jonathan C.; Martinez, Alexandra G.; Kuralay, Filiz; Zhou, Ming; Zhou, Nandi; Polsky, Ronen; Miller, Philip R.; Narayan, Roger; Wang, Joseph
2013-01-01
We report on the development of a microneedle-based multiplexed drug delivery actuator that enables the controlled delivery of multiple therapeutic agents. Two individually-addressable channels on a single microneedle array, each paired with its own reservoir and conducting polymer nanoactuator, are used to deliver various permutations of two unique chemical species. Upon application of suitable redox potentials to the selected actuator, the conducting polymer is able to undergo reversible volume changes, thereby serving to release a model chemical agent in a controlled fashion through the corresponding microneedle channels. Time-lapse videos offer direct visualization and characterization of the membrane switching capability and, along with calibration investigations, confirm the ability of the device to alternate the delivery of multiple reagents from individual microneedles of the array with higher precision and temporal resolution than conventional drug delivery actuators. Analytical modeling offers prediction of the volumetric flow rate through a single microneedle and accordingly can be used to assist in the design of subsequent microneedle arrays. The robust solid-state design and lack of mechanical components circumvent reliability issues that challenge fragile conventional microelectromechanical drug delivery devices. This proof-of-concept study demonstrates the potential of the drug delivery actuator system to aid in the rapid administration of multiple therapeutic agents and indicates the potential to counteract diverse biomedical conditions. PMID:24174709
Direct numerical simulation of incompressible acceleration-driven variable-density turbulence
NASA Astrophysics Data System (ADS)
Gat, Ilana; Matheou, Georgios; Chung, Daniel; Dimotakis, Paul
2015-11-01
Fully developed turbulence in variable-density flow driven by an externally imposed acceleration field, e.g., gravity, is fundamental in many applications, such as inertial confinement fusion, geophysics, and astrophysics. Aspects of this turbulence regime are poorly understood and are of interest to fluid modeling. We investigate incompressible acceleration-driven variable-density turbulence by a series of direct numerical simulations of high-density fluid in-between slabs of low-density fluid, in a triply-periodic domain. A pseudo-spectral numerical method with a Helmholtz-Hodge decomposition of the pressure field, which ensures mass conservation, is employed, as documented in Chung & Pullin (2010). A uniform dynamic viscosity and local Schmidt number of unity are assumed. This configuration encapsulates a combination of flow phenomena in a temporally evolving variable-density shear flow. Density ratios up to 10 and Reynolds numbers in the fully developed turbulent regime are investigated. The temporal evolution of the vertical velocity difference across the shear layer, shear-layer growth, mean density, and Reynolds number are discussed. Statistics of Lagrangian accelerations of fluid elements and of vorticity as a function of the density ratio are also presented. This material is based upon work supported by the AFOSR, the DOE, the NSF GRFP, and Caltech.
NASA Astrophysics Data System (ADS)
Dong, Suchuan
2015-11-01
This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. We also present an efficient algorithm for numerically simulating the N-phase system. The algorithm has overcome the issues caused by the variable coefficient matrices associated with the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces. Support from NSF and ONR is gratefully acknowledged.
Computational fluid mechanics utilizing the variational principle of modeling damping seals
NASA Technical Reports Server (NTRS)
Abernathy, J. M.; Farmer, R.
1985-01-01
An analysis for modeling damping seals for use in Space Shuttle main engine turbomachinery is being produced. Development of a computational fluid mechanics code for turbulent, incompressible flow is required.
Computational fluid mechanics utilizing the variational principle of modeling damping seals
NASA Technical Reports Server (NTRS)
1984-01-01
The pressure solution for incompressible flow was investigated in support of a computational fluid mechanics model which simulates the damping seals considered for use in the space shuttle main engine turbomachinery. Future work directions are discussed briefly.
NASA Astrophysics Data System (ADS)
Sanderse, B.; Verstappen, R. W. C. P.; Koren, B.
2014-01-01
Harlow and Welch [Phys. Fluids 8 (1965) 2182-2189] introduced a discretization method for the incompressible Navier-Stokes equations conserving the secondary quantities kinetic energy and vorticity, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy by several researchers [25,14,21]. In this paper we propose a new consistent boundary treatment for this method, which is such that continuous integration-by-parts identities (including boundary contributions) are mimicked in a discrete sense. In this way kinetic energy is exactly conserved even in case of non-zero tangential boundary conditions. We show that requiring energy conservation at the boundary conflicts with order of accuracy conditions, and that the global accuracy of the fourth order method is limited to second order in the presence of boundaries. We indicate how non-uniform grids can be employed to obtain full fourth order accuracy.
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries
Dong, S.; Wang, X.
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries.
Dong, S; Wang, X
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909
Amiloride‐sensitive fluid resorption in NCI‐H441 lung epithelia depends on an apical Cl− conductance
Korbmacher, Jonas P.; Michel, Christiane; Neubauer, Daniel; Thompson, Kristin; Mizaikoff, Boris; Frick, Manfred; Dietl, Paul; Wittekindt, Oliver H.
2014-01-01
Abstract Proper apical airway surface hydration is essential to maintain lung function. This hydration depends on well‐balanced water resorption and secretion. The mechanisms involved in resorption are still a matter of debate, especially as the measurement of transepithelial water transport remains challenging. In this study, we combined classical short circuit current (ISC) measurements with a novel D2O dilution method to correlate ion and water transport in order to reveal basic transport mechanisms in lung epithelia. D2O dilution method enabled precise analysis of water resorption with an unprecedented resolution. NCI‐H441 cells cultured at an air–liquid interface resorbed water at a rate of 1.5 ± 0.4 μL/(h cm2). Water resorption and ISC were reduced by almost 80% in the presence of the bulk Cl− channel inhibitor 5‐nitro‐2‐(3‐phenylpropylamino)benzoic acid (NPPB) or amiloride, a specific inhibitor of epithelial sodium channel (ENaC). However, water resorption and ISC were only moderately affected by forskolin or cystic fibrosis transmembrane regulator (CFTR) channel inhibitors (CFTRinh‐172 and glybenclamide). In line with previous studies, we demonstrate that water resorption depends on ENaC, and CFTR channels have only a minor but probably modulating effect on water resorption. However, the major ENaC‐mediated water resorption depends on an apical non‐CFTR Cl− conductance. PMID:24744880
Some Studies on Viscous Fluids
NASA Astrophysics Data System (ADS)
Zang, Aibin
In this thesis, we study several issues involving incompressible viscous fluids with the slip boundary conditions and the motions of fluid-solid interactions. In the first part, we study the issue of the inviscid limit of the incompressible Navier-Stokes equations on the general smooth domains for completely slip boundary conditions. We verify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in the Prantle's theory. We improve the better regularity for the boundary layer and obtain the uniform Lp--estimates (3 < p ≤ 6) of the remainder. Then we improved these estimates to H 1--estimates. It is shown that the viscous solution converges to the solution of Euler equation in C([0, T]; H1(O)) as the viscosity tends to zero. In the second part, we consider the non-stationary problems of a class of non-Newtonian fluid which is a power law fluid with p > 3nn+2 in the half space with slip boundary conditions. We present the local pressure estimate with the Navier's slip boundary conditions. Using these estimates and an Linfinity -- truncation method, we can obtain that this system has at least one required weak solution. Finally, we investigate the motion of a general form rigid body with smooth boundary by an incompressible perfect fluid occupying R3 . Due to the domain occupied by the fluid depending on the time, this problem can be transformed into a new systems of the fluid in a fixed domain by the frame attached with the body. With the aid of Kato-Lai's theory, we construct a sequence of successive solutions to this problem in some unform time interval. Then by a fixed point argument, we have proved that the existence, uniqueness and persistence of the regularity for the solutions of original fluid-structure interaction problem.
The Effective Field Theory Approach to Fluid Dynamics
NASA Astrophysics Data System (ADS)
Endlich, Solomon George Shamsuddin Osman
In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory
NASA Astrophysics Data System (ADS)
Veera Krishna, M.; Swarnalathamma, B. V.
2016-05-01
In this paper, we discussed the peristaltic MHD flow of an incompressible and electrically conducting Williamson fluid in a symmetric planar channel with heat and mass transfer under the effect of inclined magnetic field. Viscous dissipation and Joule heating are also taken into consideration. Mathematical model is presented by using the long wavelength and low Reynolds number approximations. The differential equations governing the flow are highly nonlinear and thus perturbation solution for small Weissenberg number (We < 1) is presented. Effects of the heat and mass transfer on the longitudinal velocity, temperature and concentration are studied in detail. Main observations are presented in the concluding section. The streamlines pattern is also given due attention.
NASA Astrophysics Data System (ADS)
Rauf, A.; Ashraf, M.; Batool, K.; Hussain, M.; Meraj, M. A.
2015-07-01
This article studies the simultaneous impacts of heat and mass transfer of an incompressible electrically conducting micropolar fluid generated by the stretchable disk in presence of porous medium. The thermal radiation effect is accounted via Rosseland's approximation. The governing boundary layer equations are reduced into dimensionless form by employing the suitable similarity transformations. A finite difference base algorithm is utilized to obtain the solution expressions. The impacts of physical parameters on dimensionless axial velocity, radial velocity, micro-rotation, temperature and concentrations profiles are presented and examined carefully. Numerical computation is performed to compute shear stress, couple stress, heat and mass rate at the disk.
Rauf, A. Meraj, M. A.; Ashraf, M.; Batool, K.; Hussain, M.
2015-07-15
This article studies the simultaneous impacts of heat and mass transfer of an incompressible electrically conducting micropolar fluid generated by the stretchable disk in presence of porous medium. The thermal radiation effect is accounted via Rosseland’s approximation. The governing boundary layer equations are reduced into dimensionless form by employing the suitable similarity transformations. A finite difference base algorithm is utilized to obtain the solution expressions. The impacts of physical parameters on dimensionless axial velocity, radial velocity, micro-rotation, temperature and concentrations profiles are presented and examined carefully. Numerical computation is performed to compute shear stress, couple stress, heat and mass rate at the disk.
NASA Technical Reports Server (NTRS)
Deissler, R. G.; Loeffler, A. L., Jr.
1959-01-01
A previous analysis of turbulent heat transfer and flow with variable fluid properties in smooth passages is extended to flow over a flat plate at high Mach numbers, and the results are compared with experimental data. Velocity and temperature distributions are calculated for a boundary layer with appreciative effects of frictional heating and external heat transfer. Viscosity and thermal conductivity are assumed to vary as a power or the temperature, while Prandtl number and specific heat are taken as constant. Skin-friction and heat-transfer coefficients are calculated and compared with the incompressible values. The rate of boundary-layer growth is obtained for various Mach numbers.
Shirzadi, Zahra; Sadeghi-Naini, Ali; Samani, Abbas
2013-05-15
Purpose: A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Estimating lung tissue incompressibility parameter variations resulting from air content variation throughout respiration is critical for computer assisted tumor motion tracking. Continuous tumor motion is a major challenge in lung cancer radiotherapy, especially with external beam radiotherapy. If not accounted for, this motion may lead to areas of radiation overdosage for normal tissue. Given the unavailability of imaging modality that can be used effectively for real-time lung tumor tracking, computer assisted approach based on tissue deformation estimation can be a good alternative. This approach involves lung biomechanical model where its fidelity depends on input tissue properties. This investigation shows that considering variable tissue incompressibility parameter is very important for predicting tumor motion accurately, hence improving the lung radiotherapy outcome. Methods: First, an in silico lung phantom study was conducted to demonstrate the importance of employing variable Poisson's ratio for tumor motion predication. After it was established that modeling this variability is critical for accurate tumor motion prediction, an optimization based technique was developed to estimate lung tissue Poisson's ratio as a function of respiration cycle time. In this technique, the Poisson's ratio and lung pressure value were varied systematically until optimal values were obtained, leading to maximum similarity between acquired and simulated 4D CT lung images. This technique was applied in an ex vivo porcine lung study where simulated images were constructed using the end exhale CT image and deformation fields obtained from the lung's FE modeling of each respiration time increment. To model the tissue, linear elastic and Marlow hyperelastic material models in conjunction with variable Poisson's ratio were used. Results: The phantom study showed that
NASA Astrophysics Data System (ADS)
Vajravelu, K.; Sreenadh, S.; Dhananjaya, S.; Lakshminarayana, P.
2016-08-01
In this paper, the influence of heat transfer on the peristaltic flow of a conducting Phan-Thien-Tanner fluid in an asymmetric channel with porous medium is studied. The coupled nonlinear governing differential equations are solved by a perturbation technique. The expressions for the temperature field, the stream function, the axial velocity, and the pressure gradient are obtained. The effects of the various physical parameters such as the magnetic parameter M, the permeability parameter σ, the Brinkman number Br and the Weissenberg number We on the pumping phenomenon are analyzed through graphs and the results are discussed in detail. It is observed that the velocity and the pressure are decreased with increasing the magnetic parameter M whereas the effect of the parameter M on the temperature field is quite the opposite.
NASA Astrophysics Data System (ADS)
Ye, Xia; Zhang, Jianwen
2016-08-01
This paper concerns the asymptotic behavior of the solution to an initial-boundary value problem of the cylindrically symmetric Navier–Stokes equations with large data for compressible heat-conducting ideal fluids, as the shear viscosity μ goes to zero. A suitable corrector function (the so-called boundary-layer type function) is constructed to eliminate the disparity of boundary values. As by-products, the convergence rates of the derivatives in L 2 are obtained and the boundary-layer thickness (BL-thickness) of the value O≤ft({μα}\\right) with α \\in ≤ft(0,1/2\\right) is shown by an alternative method, compared with the results proved in Jiang and Zhang (2009 SIAM J. Math. Anal. 41 237–68) and Qin et al (2015 Arch. Ration. Mech. Anal. 216 1049–86).
NASA Astrophysics Data System (ADS)
Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo
2016-06-01
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell-Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic-parabolic Navier-Stokes-Fourier theory is established for the first time via a formal asymptotic analysis in the stiff relaxation limit. From a numerical point of view, the governing partial differential equations are very challenging, since they form a large nonlinear hyperbolic PDE system that includes stiff source terms and non-conservative products. We apply the successful family of one-step ADER-WENO finite volume (FV) and ADER discontinuous Galerkin (DG) finite element schemes to the HPR model in the stiff
Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations
NASA Astrophysics Data System (ADS)
Lacave, Christophe; Masmoudi, Nader
2016-09-01
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size {\\varepsilon} separated by distances {d_{\\varepsilon}} and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of {d_{\\varepsilon}}\\varepsilon} when {\\varepsilon} goes to zero. If {frac{d_{\\varepsilon}}\\varepsilon to infty}, then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, {frac{d_{\\varepsilon}}\\varepsilon to 0}, then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of {frac{d_{\\varepsilon}/\\varepsilon^{2+frac1γ}} where {γ in (0,infty]} is related to the geometry of the lateral boundaries of the obstacles. If {d_{\\varepsilon}/\\varepsilon^{2+frac1γ} to infty}, then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to {\\varepsilon3} for balls.
Receptivity of a TVD Scheme in Incompressible Flow Analysis
NASA Astrophysics Data System (ADS)
Shin, Byeong Rog
A TVD upwind scheme originally designed for compressible flow is applied to the SMAC finite-difference method for incompressible flow analysis. The receptivity and validity of this application are investigated by an evaluation of the accuracy, stability and convergence rate for the SMAC method combined with the TVD scheme. Using this method, three-dimensional developing entry flows through a square-curved duct are calculated and compared with available experimental data as well as some computational results obtained by QUICKs and third-order upwind schemes. Such comparisons show that the numerical method applying the TVD scheme has the highest computational efficiency without a sharp loss of accuracy, resulting in confidence in the application this scheme to incompressible flow computations.
Lattice Boltzmann model for incompressible flows through porous media.
Guo, Zhaoli; Zhao, T S
2002-09-01
In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.
Conservative properties of finite difference schemes for incompressible flow
NASA Technical Reports Server (NTRS)
Morinishi, Youhei
1995-01-01
The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.
Mondal, Sabyasachi; Haroun, Nageeb A. H.; Sibanda, Precious
2015-01-01
In this paper, the magnetohydrodynamic (MHD) axisymmetric stagnation-point flow of an unsteady and electrically conducting incompressible viscous fluid in with temperature dependent thermal conductivity, thermal radiation and Navier slip is investigated. The flow is due to a shrinking surface that is shrunk axisymmetrically in its own plane with a linear velocity. The magnetic field is imposed normally to the sheet. The model equations that describe this fluid flow are solved by using the spectral relaxation method. Here, heat transfer processes are discussed for two different types of wall heating; (a) a prescribed surface temperature and (b) a prescribed surface heat flux. We discuss and evaluate how the various parameters affect the fluid flow, heat transfer and the temperature field with the aid of different graphical presentations and tabulated results. PMID:26414006
Doughty, C.; Tsang, C.-F.; Hatanaka, K.; Yabuuchi, S.; Kurikami, H.
2007-08-01
The flowing fluid electric conductivity (FFEC) loggingmethod is an efficient way to provide information on the depths,salinities, and transmissivities of individual conductive featuresintercepted by a borehole, without the use of specialized probes. Usingit in a multiple-flow-rate mode allows, in addition, an estimate of theinherent "far-field" pressure heads in each of the conductive features.The multi-rate method was successfully applied to a 500-m borehole in agranitic formation and reported recently. The present paper presents theapplication of the method to two zones within a 1000-m borehole insedimentary rock, which produced, for each zone, three sets of logs atdifferent pumping rates, each set measured over a period of about oneday. The data sets involve a number of complications, such as variablewell diameter, free water table decline in the well, and effects ofdrilling mud. To analyze data from this borehole, we apply varioustechniques that have been developed for analyzing FFEC logs:direct-fitting, mass-integral, and the multi-rate method mentioned above.In spite of complications associated with the tests, analysis of the datais able to identify 44 hydraulically conducting fractures distributedover the depth interval 150-775 meters below ground surface. Thesalinities (in FEC), and transmissivities and pressure heads (indimensionless form) of these 44 features are obtained and found to varysignificantly among one another. These results are compared with datafrom eight packer tests with packer intervals of 10-80 m, which wereconducted in this borehole over the same depth interval. They are foundto be consistent with these independent packer-test data, thusdemonstrating the robustness of the FFEC logging method under non-idealconditions.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
A Quantitative Comparison of Leading-edge Vortices in Incompressible and Supersonic Flows
NASA Technical Reports Server (NTRS)
Wang, F. Y.; Milanovic, I. M.; Zaman, K. B. M. Q.
2002-01-01
When requiring quantitative data on delta-wing vortices for design purposes, low-speed results have often been extrapolated to configurations intended for supersonic operation. This practice stems from a lack of database owing to difficulties that plague measurement techniques in high-speed flows. In the present paper an attempt is made to examine this practice by comparing quantitative data on the nearwake properties of such vortices in incompressible and supersonic flows. The incompressible flow data are obtained in experiments conducted in a low-speed wind tunnel. Detailed flow-field properties, including vorticity and turbulence characteristics, obtained by hot-wire and pressure probe surveys are documented. These data are compared, wherever possible, with available data from a past work for a Mach 2.49 flow for the same wing geometry and angles-of-attack. The results indicate that quantitative similarities exist in the distributions of total pressure and swirl velocity. However, the streamwise velocity of the core exhibits different trends. The axial flow characteristics of the vortices in the two regimes are examined, and a candidate theory is discussed.
Ren, Aixia; Zhang, Weiqiang; Yarlagadda, Sunitha; Sinha, Chandrima; Arora, Kavisha; Moon, Chang-Suk; Naren, Anjaparavanda P
2013-04-26
The PDZ (postsynaptic density-95/discs large/zona occludens-1) domain-based interactions play important roles in regulating the expression and function of the cystic fibrosis transmembrane conductance regulator (CFTR). Several PDZ domain-containing proteins (PDZ proteins for short) have been identified as directly or indirectly interacting with the C terminus of CFTR. To better understand the regulation of CFTR processing, we conducted a genetic screen and identified MAST205 (a microtubule-associated serine/threonine kinase with a molecular mass of 205 kDa) as a new CFTR regulator. We found that overexpression of MAST205 increased the expression of CFTR and augmented CFTR-mediated fluid transport in a dose-dependent manner. Conversely, knockdown of MAST205 inhibited CFTR function. The PDZ motif of CFTR is required for the regulatory role of MAST205 in CFTR expression and function. We further demonstrated that MAST205 and the CFTR-associated ligand competed for binding to CFTR, which facilitated the processing of CFTR and consequently up-regulated the expression and function of CFTR at the plasma membrane. More importantly, we found that MAST205 could facilitate the processing of F508del-CFTR mutant and augment its quantity and channel function at the plasma membrane. Taken together, our data suggest that MAST205 plays an important role in regulating CFTR expression and function. Our findings have important clinical implications for treating CFTR-associated diseases such as cystic fibrosis and secretory diarrheas.
NASA Astrophysics Data System (ADS)
Roberts, Michael Scott
The Rayleigh-Taylor instability is a buoyancy driven instability that takes place in a stratified fluid system with a constant acceleration directed from the heavy fluid into the light fluid. In this study, both experimental data and numerical simulations are presented. Experiments are performed primarily using a lithium-tungstate aqueous solution as the heavy liquid, but sometimes a calcium nitrate aqueous solution is used for comparison purposes. Experimental data is obtained for both miscible and immiscible fluid combinations. For the miscible experiments the light liquid is either ethanol or isopropanol, and for the immiscible experiments either silicone oil or trans-anethole is used. The resulting Atwood number is either 0.5 when the lithium-tungstate solution is used or 0.2 when the calcium nitrate solution is used. These fluid combinations are either forced or left unforced. The forced experiments have an initial perturbation imposed by vertically oscillating the liquid containing tank to produce Faraday waves at the interface. The unforced experiments rely on random interfacial fluctuations, due to background noise, to seed the instability. The liquid combination is partially enclosed in a test section that is accelerated downward along a vertical rail system causing the Rayleigh-Taylor instability. Accelerations of approximately 1g (with a weight and pulley system) or 10g (with a linear induction motor system) are experienced by the liquids. The tank is backlit and digitally recorded with high speed video cameras. These experiments are then simulated with the incompressible, Navier-Stokes code Miranda. The main focus of this study is the growth parameter (α) of the mixing region produced by the instability after it has become apparently self-similar and turbulent. The measured growth parameters are compared to determine the effects of miscibility and initial perturbations (of the small wavelength, finite bandwidth type used here). It is found that while
NASA Astrophysics Data System (ADS)
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.
2014-07-01
Stable partitioned algorithms for fluid-structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. Importantly, these new added-mass partitioned (AMP) schemes are stable and retain full accuracy with no sub-iterations per time step, even in the presence of strong added-mass effects (e.g. for light solids). The numerical approach described here for bulk compressible solids extends the scheme of Banks et al. [1,2] for inviscid compressible flow, and uses Robin (mixed) boundary conditions with the fluid and solid solvers at the interface. The basic AMP Robin conditions, involving a linear combination of velocity and stress, are determined from the outgoing solid characteristic relation normal to the fluid-solid interface combined with the matching conditions on the velocity and traction. Two alternative forms of the AMP conditions are then derived depending on whether the fluid equations are advanced with a fractional-step method or not. The stability and accuracy of the AMP algorithm is evaluated for linearized FSI model problems; the full nonlinear case being left for future consideration. A normal mode analysis is performed to show that the new AMP algorithm is stable for any ratio of the solid and fluid densities, including the case of very light solids when added-mass effects are large. In contrast, it is shown that a traditional partitioned algorithm involving a Dirichlet-Neumann coupling for the same FSI problem is formally unconditionally unstable for any ratio of densities. Exact traveling wave solutions are derived for the FSI model problems, and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the AMP algorithm for the cases of light, medium and heavy solids.
Performance of journal bearings with semi-compressible fluids
NASA Technical Reports Server (NTRS)
Carpino, M.; Peng, J.-P.
1991-01-01
Cryogenic fluids in isothermal rigid surface and foil type journal bearings can sometimes be treated as semicompressible fluids. In these applications, the fluid density is a function of the pressure. At low pressures, the fluids can change from a liquid to a saturated liquid-vapor phase. The performance of a rigid surface journal bearing with an idealized semicompressible fluid is discussed. Pressure solutions are based upon a Reynolds equation which includes the effects of a compressibility via the bulk modulus of the fluid. Results are contrasted with the performance of isothermal constant property incompressible fluids.
NASA Astrophysics Data System (ADS)
López-Herrera, J. M.; Popinet, S.; Herrada, M. A.
2011-03-01
In the present study we propose a charge-conservative scheme to solve two-phase electrohydrodynamic (EHD) problems using the volume-of-fluid (VOF) method. EHD problems are usually simplified by assuming that the fluids involved are purely dielectric (insulators) or purely conducting. Gases can be considered as perfect insulators but pure dielectric liquids do not exist in nature and insulating liquids have to be approximated using the "Taylor-Melcher leaky dielectric model" [1,2] in which a leakage of charge through the liquid due to ohmic conduction is allowed. It is also a customary assumption to neglect the convection of charge against the ohmic conduction. The scheme proposed in this article can deal with any EHD problem since it does not rely on any of the above simplifications. An unrestricted EHD solver requires not only to incorporate electric forces in the Navier-Stokes equations, but also to consider the charge migration due to both conduction and convection in the electric charge conservation equation [3]. The conducting or insulating nature of the fluids arise on their own as a result of their electric and fluid mechanical properties. The EHD solver has been built as an extension to Gerris, a free software solver for the solution of incompressible fluid motion using an adaptive VOF method on octree meshes developed by Popinet [4,5].
Three-dimensional Oldroyd-B fluid flow with Cattaneo-Christov heat flux model
NASA Astrophysics Data System (ADS)
Shehzad, S. A.; Hayat, T.; Abbasi, F. M.; Javed, Tariq; Kutbi, M. A.
2016-04-01
The impact of Cattaneo-Christov heat flux in three-dimensional flow of an Oldroyd-B fluid over a bidirectional stretching surface is explored in this article. The boundary layer flow of an incompressible fluid is considered. Heat transfer analysis is discussed via the Cattaneo-Christov model of heat flux. Similarity transformations lead to the nonlinear ordinary differential systems. Convergent solutions of dimensionless velocities and temperature have been computed. Convergence analysis is presented graphically and numerically. The influence of physical parameters on the velocities and temperature are plotted and discussed. We observed that the values of temperature gradient are higher for the Cattaneo-Christov heat flux model when we compare it with the values obtained by the simple Fourier's law of heat conduction.
Tzanos, C. P.; Dionne, B.
2011-05-23
To support the analyses related to the conversion of the BR2 core from highly-enriched (HEU) to low-enriched (LEU) fuel, the thermal-hydraulics codes PLTEMP and RELAP-3D are used to evaluate the safety margins during steady-state operation (PLTEMP), as well as after a loss-of-flow, loss-of-pressure, or a loss of coolant event (RELAP). In the 1-D PLTEMP and RELAP simulations, conduction in the azimuthal and axial directions is not accounted. The very good thermal conductivity of the cladding and the fuel meat and significant temperature gradients in the lateral directions (axial and azimuthal directions) could lead to a heat flux distribution that is significantly different than the power distribution. To evaluate the significance of the lateral heat conduction, 3-D computational fluid dynamics (CFD) simulations, using the CFD code STAR-CD, were performed. Safety margin calculations are typically performed for a hot stripe, i.e., an azimuthal region of the fuel plates/coolant channel containing the power peak. In a RELAP model, for example, a channel between two plates could be divided into a number of RELAP channels (stripes) in the azimuthal direction. In a PLTEMP model, the effect of azimuthal power peaking could be taken into account by using engineering factors. However, if the thermal mixing in the azimuthal direction of a coolant channel is significant, a stripping approach could be overly conservative by not taking into account this mixing. STAR-CD simulations were also performed to study the thermal mixing in the coolant. Section II of this document presents the results of the analyses of the lateral heat conduction and azimuthal thermal mixing in a coolant channel. Finally, PLTEMP and RELAP simulations rely on the use of correlations to determine heat transfer coefficients. Previous analyses showed that the Dittus-Boelter correlation gives significantly more conservative (lower) predictions than the correlations of Sieder-Tate and Petukhov. STAR-CD 3-D
NASA Astrophysics Data System (ADS)
Omelyan, Igor P.
The dielectric properties of interaction site models of polar fluids may be investigated in a computer experiment using not only the charge fluctuations but also correlations corresponding to a current of moving charges. This current may be associated with a generalized dynamical polarization or separated into electric and magnetic components. The first approach deals with the dielectric permittivity related to a generalized conductivity, whereas the second leads to the functions describing polarization and magnetization fluctuations separately. The latter functions are only the source for calculating the magnetic susceptibility for a system of interaction sites. The transverse wavevector dependent and frequency dependent dielectric functions and magnetic susceptibility are evaluated for the TIP4P water model over a very wide scale of wavelengths and frequencies using molecular dynamics simulations. The transverse part of the dielectric functions may differ drastically from their longitudinal component. A relationship between the two approaches is discussed and the limiting transition to the static dielectric constant in the infinite-wavelength regime is analysed. The propagation of transverse electromagnetic waves in TIP4P water is considered.
Rotation of a rod system containing inertial fluid flow
NASA Astrophysics Data System (ADS)
Sergeev, A. D.
2012-11-01
This paper considers a rod system for which it is possible to correctly formulate and solve the problem of three-dimensional motion in the physical space of an elastic pipeline area containing inertial incompressible fluid flow. The precession of the axis of an elastic pipeline along which inertial incompressible fluid flows is described, a physical phenomenon which has not been previously studied. With the use of rigid body dynamics, it was theoretically established that a three-dimensional dynamic process is possible in an open (exchanging mass with the environment) elastic-inertial rod system.
NASA Astrophysics Data System (ADS)
Das, Utpal Jyoti
2016-01-01
The purpose of the study is to investigate the steady, two-dimensional, hydromagnetic, mixed convection heat and mass transfer of a conducting, optically thin, incompressible, elastico-viscous fluid (characterized by the Walters' B' model) past a permeable, stationary, vertical, infinite plate in the presence of thermal radiation and chemical reaction with account for an induced magnetic field. The governing equations of the flow are solved by the series method, and expressions for the velocity field, induced magnetic field, temperature field, and the skin friction are obtained.
A multilevel approximate projections for incompressible flow calculations
Howell, L.H.
1994-12-31
An adaptive-mesh projection algorithm for unsteady, variable-density, incompressible flow at high Reynolds number has been developed in the Applied Mathematics Group at LLNL. A grid-based refinement scheme combines the theoretical efficiencies of adaptive methods with the computational advantages of uniform grids, while a second-order Godunov method provides a robust and accurate treatment of advection in the presence of discontinuities without excessive dissipation. This paper focuses on the work of the present author concerning the approximate projection itself, which involves the numerical inversion of the operator {del} {center_dot} (1/{rho}){del} on various subsets of the adaptive grid hierarchy.
Spectral element methods for the incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Maday, Yvon; Patera, Anthony T.
1989-01-01
Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.
Weighted-mean scheme for solving incompressible viscous flow
NASA Technical Reports Server (NTRS)
Huynh, Q. Q.
1981-01-01
The problem of how a boundary layer responds to the motion of a convexed vortex on a porous wall was investigated. The wall velocity is approximately given by Darcy's law. The vorticity-stream function approach was adopted for solving Navier-Stokes equations of two dimensional incompressible viscous flows. The weighted-mean scheme was used for constructing finite difference approximations of spatial derivatives. Several test problems were solved and numerical results demonstrate clearly the accuracy, stability, and efficiency of the scheme. The weighted mean scheme then can be applied to the vortical flow problem.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.
Incompressible viscous flow simulations of the NFAC wind tunnel
NASA Technical Reports Server (NTRS)
Champney, Joelle Milene
1986-01-01
The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
This paper considers several topics arising in the finite element solution of the incompressible Navier-Stokes equations. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. Following this, the role of artificial viscosity in viscous flow calculations is studied, emphasizing recent work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some recent modifications are mentioned.
Analysis of Laminar Incompressible Flow on Semiporous Channels
NASA Technical Reports Server (NTRS)
Donoughe, Patrick L
1956-01-01
Perturbation solutions for laminar incompressible flow in semiporous and fully porous channels are compared. The perturbation parameter measures the amount of suction or blowing at the porous wall. The velocity profile and the wall friction parameter are more affected by suction or blowing for the semiporous channel than for the fully porous channel. For blowing through the wall, the pressure decreases in channel direction for both channels; with sufficiently high suction rates, the analysis showed that the pressure rises in flow direction for the fully porous channel.
Determining the alpha dynamo parameter in incompressible homogeneous magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Goldstein, M. L.; Lantz, S. R.
1983-01-01
Alpha, an important parameter in dynamo theory, is proportional to either the kinetic, current, magnetic, or velocity helicity of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first order smoothed equations that describe the alpha effect. In two cases, when alpha is proportional to either the magnetic helicity or velocity helicity, alpha is determined experimentally from two point measurements of the fluctuating fields in incompressible, homogeneous turbulence having arbitrary symmetry. For the other two possibilities, alpha is determined if the turbulence is isotropic.
Flow Solver for Incompressible 2-D Drive Cavity
NASA Technical Reports Server (NTRS)
Kalb, Virginia L.
2008-01-01
This software solves the Navier-Stokes equations for the incompressible driven cavity flow problem. The code uses second-order finite differencing on a staggered grid using the Chorin projection method. The resulting intermediate Poisson equation is efficiently solved using the fast Fourier transform. Time stepping is done using fourth-order Runge-Kutta for stability at high Reynolds numbers. Features include check-pointing, periodic field snapshots, ongoing reporting of kinetic energy and changes between time steps, time histories at selected points, and optional streakline generation.
Poiseuille equation for steady flow of fractal fluid
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
... fluid imbalance; Hypernatremia - fluid imbalance; Hypokalemia - fluid imbalance; Hyperkalemia - fluid imbalance ... of sodium or potassium is present as well. Medicines can also affect fluid balance. The most common ...
Dominated splitting and zero volume for incompressible three flows
NASA Astrophysics Data System (ADS)
Araujo, Vitor; Bessa, Mário
2008-07-01
We prove that there exists an open and dense subset of the incompressible 3-flows of class C2 such that, if a flow in this set has a positive volume regular invariant subset with dominated splitting for the linear Poincaré flow, then it must be an Anosov flow. With this result we are able to extend the dichotomies of Bochi-Mañé (see Bessa 2007 Ergod. Theory Dyn. Syst. 27 1445-72, Bochi 2002 Ergod. Theory Dyn. Syst. 22 1667-96, Mañé 1996 Int. Conf. on Dynamical Systems (Montevideo, Uruguay, 1995) (Harlow: Longman) pp 110-9) and of Newhouse (see Newhouse 1977 Am. J. Math. 99 1061-87, Bessa and Duarte 2007 Dyn. Syst. Int. J. submitted Preprint 0709.0700) for flows with singularities. That is, we obtain for a residual subset of the C1 incompressible flows on 3-manifolds that: (i) either all Lyapunov exponents are zero or the flow is Anosov and (ii) either the flow is Anosov or else the elliptic periodic points are dense in the manifold.
NASA Astrophysics Data System (ADS)
Esmaili Sikarudi, M. A.; Nikseresht, A. H.
2016-01-01
Smoothed particle hydrodynamics is a robust Lagrangian particle method which is widely used in various applications, from astrophysics to hydrodynamics and heat conduction. It has intrinsic capabilities for simulating large deformation, composites, multiphysics events, and multiphase fluid flows. It is vital to use reliable boundary conditions when boundary value problems like heat conduction or Poisson equation for incompressible flows are solved. Since smoothed particle hydrodynamics is not a boundary fitted grids method, implementation of boundary conditions can be problematic. Many methods have been proposed for enhancing the accuracy of implementation of boundary conditions. In the present study a new approach for facilitating the implementation of Robin and Neumann boundary conditions is proposed and proven to give accurate results. Also there is no need to use complicated preprocessing as in virtual particle method. The new method is compared to an equivalent one dimensional moving least square scheme and it is shown that the present method is less sensitive to particle disorder.
Fluid Physics in a Fluctuating Acceleration Environment
NASA Technical Reports Server (NTRS)
Thomson, J. Ross; Drolet, Francois; Vinals, Jorge
1996-01-01
We summarize several aspects of an ongoing investigation of the effects that stochastic residual accelerations (g-jitter) onboard spacecraft can have on experiments conducted in a microgravity environment. The residual acceleration field is modeled as a narrow band noise, characterized by three independent parameters: intensity (g(exp 2)), dominant angular frequency Omega, and characteristic correlation time tau. Realistic values for these parameters are obtained from an analysis of acceleration data corresponding to the SL-J mission, as recorded by the SAMS instruments. We then use the model to address the random motion of a solid particle suspended in an incompressible fluid subjected to such random accelerations. As an extension, the effect of jitter on coarsening of a solid-liquid mixture is briefly discussed, and corrections to diffusion controlled coarsening evaluated. We conclude that jitter will not be significant in the experiment 'Coarsening of solid-liquid mixtures' to be conducted in microgravity. Finally, modifications to the location of onset of instability in systems driven by a random force are discussed by extending the standard reduction to the center manifold to the stochastic case. Results pertaining to time-modulated oscillatory convection are briefly discussed.
The handbook of fluid dynamics
Johnson, R.W.
1998-07-01
This book provides professionals in the field of fluid dynamics with a comprehensive guide and resource. The book balances three traditional areas of fluid mechanics--theoretical, computational, and experimental--and expounds on basic science and engineering techniques. Each chapter introduces a topic, discusses the primary issues related to this subject, outlines approaches taken by experts, and supplies references for further information. Topics discussed include: (1) basic engineering fluid dynamics; (2) classical fluid dynamics; (3) turbulence modeling; (4) reacting flows; (5) multiphase flows; (6) flow and porous media; (7) high Reynolds number asymptotic theories; (8) finite difference method; (9) finite volume method; (10) finite element methods; (11) spectral element methods for incompressible flows; (12) experimental methods, such as hot-wire anemometry, laser-Doppler velocimetry, and flow visualization; and (13) applications, such as axial-flow compressor and fan aerodynamics, turbomachinery, airfoils and wings, atmospheric flows, and mesoscale oceanic flows.
The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Koh, Youngwoo; Yang, Minsuk
2016-09-01
We study the possible interior singular points of suitable weak solutions to the three dimensional incompressible Navier-Stokes equations. We present an improved parabolic upper Minkowski dimension of the possible singular set, which is bounded by 95/63. The result also continue to hold for the three dimensional incompressible magnetohydrodynamic equations without any difficulty.
NASA Astrophysics Data System (ADS)
Shahzad, F.; Hayat, T.
2012-05-01
The unsteady MHD flow of an incompressible micropolar fluid have been considered. The fluid is filling the semi-infinite space z>0 which is in contact with an infinite porous rotating disk at z = 0. The common angular velocity of the disk and fluid at infinity is Ω. The fluid is electrically conducting in presence of an applied constant magnetic field B0. Initially the disk and the fluid are rotating about the z/-axis and at time t = 0, suddenly the disk starts rotating about the z-axis and moving with uniform acceleration, while the fluid at infinity continue to rotate about z/-axis with same angular velocity Ω. The axes of rotation of both the disk and that of the fluid at infinity are assumed to be in the plane x = 0, and distance between axes is l. The governing problem is solved numerically using Newton's method. Numerical results explaining the effects of various parameters associated with the flow are discussed graphically.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
Microfabrication of hybrid fluid membrane for microengines
NASA Astrophysics Data System (ADS)
Chutani, R.; Formosa, F.; de Labachelerie, M.; Badel, A.; Lanzetta, F.
2015-12-01
This paper describes the microfabrication and dynamic characterization of thick membranes providing a technological solution for microengines. The studied membranes are called hybrid fluid-membrane (HFM) and consist of two thin membranes that encapsulate an incompressible fluid. This work details the microelectromechanical system (MEMS) scalable fabrication and characterization of HFMs. The membranes are composite structures based on Silicon spiral springs embedded in a polymer (RTV silicone). The anodic bonding of multiple stacks of Si/glass structures, the fluid filling and the sealing have been demonstrated. Various HFMs were successfully fabricated and their dynamic characterization demonstrates the agreement between experimental and theoretical results.
Efficient solutions of two-dimensional incompressible steady viscous flows
NASA Technical Reports Server (NTRS)
Morrison, J. H.; Napolitano, M.
1986-01-01
A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.
STREMR: Numerical model for depth-averaged incompressible flow
NASA Astrophysics Data System (ADS)
Roberts, Bernard
1993-09-01
The STREMR computer code is a two-dimensional model for depth-averaged incompressible flow. It accommodates irregular boundaries and nonuniform bathymetry, and it includes empirical corrections for turbulence and secondary flow. Although STREMR uses a rigid-lid surface approximation, the resulting pressure is equivalent to the displacement of a free surface. Thus, the code can be used to model free-surface flow wherever the local Froude number is 0.5 or less. STREMR uses a finite-volume scheme to discretize and solve the governing equations for primary flow, secondary flow, and turbulence energy and dissipation rate. The turbulence equations are taken from the standard k-Epsilon turbulence model, and the equation for secondary flow is developed herein. Appendices to this report summarize the principal equations, as well as the procedures used for their discrete solution.
Linear analysis of incompressible Rayleigh-Taylor instability in solids.
Piriz, A R; Cela, J J López; Tahir, N A
2009-10-01
The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed.
Linear analysis of incompressible Rayleigh-Taylor instability in solids
Piriz, A. R.; Lopez Cela, J. J.; Tahir, N. A.
2009-10-15
The study of the linear stage of the incompressible Rayleigh-Taylor instability in elastic-plastic solids is performed by considering thick plates under a constant acceleration that is also uniform except for a small sinusoidal ripple in the horizontal plane. The analysis is carried out by using an analytical model based on the Newton second law and it is complemented with extensive two-dimensional numerical simulations. The conditions for marginal stability that determine the instability threshold are derived. Besides, the boundary for the transition from the elastic to the plastic regime is obtained and it is demonstrated that such a transition is not a sufficient condition for instability. The model yields complete analytical solutions for the perturbation amplitude evolution and reveals the main physical process that governs the instability. The theory is in general agreement with the numerical simulations and provides useful quantitative results. Implications for high-energy-density-physics experiments are also discussed.
NASA Astrophysics Data System (ADS)
Singh, K. D.
2016-08-01
An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., T^* ( {y^* ,z^* ,t^* } ) = T_1 + ( {T_2} - {T_ 1} ) cos ( {{{π z^* } over d} - ω ^* t^* } ). A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.
2014-01-01
This paper presents an incompressible two-dimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical reaction, Hall and ion slip effects. Let there be periodic injection or suction at the lower and upper plates and the nonuniform temperature and concentration at the plates are varying periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations using similarity transformations and then solved numerically by quasilinearization technique. The profiles of velocity components, microrotation, temperature distribution and concentration are studied for different values of fluid and geometric parameters such as Hartmann number, Hall and ion slip parameters, inverse Darcy parameter, Prandtl number, Schmidt number, and chemical reaction rate and shown in the form of graphs. PMID:27419211
Filter-matrix lattice Boltzmann model for incompressible thermal flows.
Zhuo, Congshan; Zhong, Chengwen; Cao, Jun
2012-04-01
In this study, a new filter-matrix lattice Boltzmann (FMLB) model is proposed and extended to include incompressible thermal flows. A new equilibrium solution is found in the improved FMLB model, which is derived from the Hermite expansion. As a result, the velocity-dependent pressure is removed, which is an inherent defect of Somers's FMLB model. In addition, the improved model is extended to include incompressible thermal flows by introducing a class of temperature-distribution function for evaluating the temperature field. Two different temperature-distribution functions are discussed. The improved FMLB model and the temperature-evaluation equation are combined into one coupled model. Numerical simulations are performed on the two-dimensional (2D) lid-driven square cavity flow and the 2D natural convection flow in a square cavity using the improved FMLB model and the two coupled models, respectively. The numerical results of the 2D lid-driven square cavity flow show that the improved FMLB model is superior to the lattice Bhatnagar-Gross-Krook (LBGK) model in terms of both accuracy and stability. When compared with the multi-relaxation-time (MRT) model, the similar accuracy and slightly enhanced stability can be obtained by the improved model. The advantage of the improved model is that it no longer relies on difficult selection of the free parameters requested by the MRT model; in addition, the force term is already included in the collision operator of the improved model. In the case of 2D natural convection flow, the numerical results of the two present models are almost the same, and both exhibit good agreement with the benchmark solution.
Filter-matrix lattice Boltzmann model for incompressible thermal flows
NASA Astrophysics Data System (ADS)
Zhuo, Congshan; Zhong, Chengwen; Cao, Jun
2012-04-01
In this study, a new filter-matrix lattice Boltzmann (FMLB) model is proposed and extended to include incompressible thermal flows. A new equilibrium solution is found in the improved FMLB model, which is derived from the Hermite expansion. As a result, the velocity-dependent pressure is removed, which is an inherent defect of Somers's FMLB model. In addition, the improved model is extended to include incompressible thermal flows by introducing a class of temperature-distribution function for evaluating the temperature field. Two different temperature-distribution functions are discussed. The improved FMLB model and the temperature-evaluation equation are combined into one coupled model. Numerical simulations are performed on the two-dimensional (2D) lid-driven square cavity flow and the 2D natural convection flow in a square cavity using the improved FMLB model and the two coupled models, respectively. The numerical results of the 2D lid-driven square cavity flow show that the improved FMLB model is superior to the lattice Bhatnagar-Gross-Krook (LBGK) model in terms of both accuracy and stability. When compared with the multi-relaxation-time (MRT) model, the similar accuracy and slightly enhanced stability can be obtained by the improved model. The advantage of the improved model is that it no longer relies on difficult selection of the free parameters requested by the MRT model; in addition, the force term is already included in the collision operator of the improved model. In the case of 2D natural convection flow, the numerical results of the two present models are almost the same, and both exhibit good agreement with the benchmark solution.
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
Flow-Induced Vibration of Flexible Hydrofoils in Incompressible, Turbulent Flows
NASA Astrophysics Data System (ADS)
Chae, Eun Jung; Akcabay, Deniz Tolga; Young, Yin Lu
2014-11-01
Flexible lifting bodies can be used to enhance the energy-efficiency and maneuverability of propulsion devices compared to their rigid counterparts. To take advantage of advances in materials and active/passive control techniques, an improved understanding of the fluid-structure interaction physics is needed. This numerical study focuses on flexible hydrofoil in incompressible, turbulent flows. The spanwise bending and twisting of a rectangular, cantilevered hydrofoil was modeled as 2DOF equations of motion coupled with the unsteady RANS equation. The results, which have been validated with experimental measurements, showed that the natural frequencies are lower in water compared to those in air due to the added mass effect, and the natural frequencies vary slightly with speed and angle of attack due to hydrodynamic bend-twist coupling and viscous effects. Lock-in of the vortex shedding frequencies with the natural frequencies was observed, along with modification of the wake patterns due to hydrodynamic bend-twist coupling. The hydrodynamic damping was found to be much greater than structural damping, and depends on the relative velocity, angle of attack, as well as structural stiffness and density, and can lead to destabilizing condition of structure in particular cases.
Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA
NASA Astrophysics Data System (ADS)
Chakraborty, Souvik; Chowdhury, Rajib
2016-11-01
This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.
An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows
Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.
1997-06-01
A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.
NASA Astrophysics Data System (ADS)
Nellis, W. J.
2014-12-01
Electrical conductivities of metallic fluid H and ionic fluids H2O and Synthetic Uranus (SU) have been measured experimentally under dynamic quasi-isentropic compression up to 180 GPa and several 1000 K. SU is a mixture of H2O, NH3 and C3H8O with composition representative of "Ice". Pressures P and temperatures T of the conductivity experiments were similar to P and T in interiors of Uranus and Neptune (U/N). Fluid H semiconducts at ~90 GPa and becomes a degenerate fluid metal with conductivity 2000/(ohm-cm) at 140 GPa, 0.64 g/cm3 and T/TF~0.01, where TF is Fermi temperature, conditions near the envelope/core boundaries of U/N. Metallization density is within a few% of the insulator-metal transition predicted by Wigner and Huntington in 1935. SU and water have conductivities of ~100/(ohm-cm) at 150 GPa. Podolak et al have shown a mixture of 75% Rock-25% Gas (by mass) behaves similarly to "pure" Ice in region that encompasses most mass of Uranus. The bandgap of water is predicted to close at 300 GPa and ~7000 K by Cavazonni et al. Models of pressure, temperature and density in U/N based on Voyager II gravity data have been developed by Helled et al. Stanley and Bloxham (SB) have developed MHD models that calculate non-dipolar and non-axisymmetric magnetic fields similar to those of U/N. The MHD models of SB assume that materials at planetary radii below the thin-shell dynamos that make the magnetic fields are stably stratified. The purpose of this paper is to develop a common picture for the deep interiors of U/N based on Voyager II gravity and magnetic data, measured electrical conductivities of planetary fluids, theoretical computations of interior conditions and the likely source of unusual magnetic fields, and extrapolation of existing experimental data for materials at 180 GPa to greater planetary depths. Main conclusions are the magnetic fields of U/N are probably made primarily by fluid metallic H at radii out to ~0.8 or more of U/N outer radii. Most of the
MHD Two-Fluid Flow and Heat Transfer between Two Inclined Parallel Plates in a Rotating System
Sri Ramachandra Murty, P.; Balaji Prakash, G.
2014-01-01
Two-phase magnetohydrodynamic convective flow of electrically conducting fluid through an inclined channel is studied under the action of a constant transverse magnetic field in a rotating system. The fluids in the two phases are steady, incompressible, laminar, immiscible, and electrically conducting, having different densities, viscosities, and thermal and electrical conductivities. The transport properties of both the fluids are assumed constant. The bounding infinite inclined parallel plates are maintained at different constant temperatures, making an angle ϕ with the horizontal. Approximate solutions for velocity and temperature distributions are obtained by using a straightforward regular perturbation technique. An in-depth study has been done on the effects of rotation parameter, Hartmann number, inclination angle, the ratio of electrical conductivities, and viscosities of two fluids on the flow. It is observed that the effect of increasing rotation is to decrease the primary velocity. Further it is noticed that as the rotation increases, the secondary velocity increases for smaller rotation, while for larger rotation it decreases. It is also found that the temperature distribution decreases as the rotation increases. PMID:27351017
SOLA-VOF. Transient Fluid Flow Free Boundaries
Nichols, B.D.; Hirt, C.W.; Hotchkiss, R.S.
1992-03-03
SOLA-VOF is a program for the solution of two-dimensional transient fluid flow with free boundaries, based on the concept of a fractional volume of fluid (VOF). Its basic mode of operation is for single fluid calculations having multiple free surfaces. However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface. In either case, the fluids may be treated as incompressible or as having limited compressibility. Surface tension forces with wall adhesion are permitted in both cases. Internal obstacles may be defined by blocking out any desired combination of cells in the mesh, which is composed of rectangular cells of variable size.
Impact of bodies on and their penetration into fluids
NASA Astrophysics Data System (ADS)
Sagomonian, Artur Iakovlevich
Transition phenomena accompanying the impact of solid bodies on fluid surfaces (i.e., high-velocity impact and the subsequent initial period of penetration into the fluid) are examined. Analytical and numerical methods for the investigation of this interaction are examined in a review of examples from the published literature. The case of an ideal incompressible fluid is considered first, with subsequent attention given to the impact of rigid and elastic bodies on ideal compressible fluids. Finally, analytical and numerical solutions are given to the problem of high-velocity impact on a plastically compressible fluid (a soil model).
NASA Technical Reports Server (NTRS)
Macaraeg, M. G.
1985-01-01
A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modelled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.
SANTHANAKRISHNAN, ARVIND; NESTLE, TRENT T.; MOORE, BRIAN L.; YOGANATHAN, AJIT P.; PADEN, MATTHEW L.
2013-01-01
Acute kidney injury is common in critically ill children and renal replacement therapies provide a life saving therapy to a subset of these children. However, there is no Food and Drug Administration approved device to provide pediatric continuous renal replacement therapy (CRRT). Consequently, clinicians adapt approved adult CRRT devices for use in children due to lack of safer alternatives. Complications occur using adult CRRT devices in children due to inaccurate fluid balance (FB) between the volumes of ultrafiltrate (UF) removed and replacement fluid (RF) delivered. We demonstrate the design and validation of a pediatric fluid management system for obtaining accurate instantaneous and cumulative FB. Fluid transport was achieved via multiple novel pulsatile diaphragm pumps. The conservation of volume principle leveraging the physical property of fluid incompressibility along with mechanical coupling via a crankshaft was used for FB. Accuracy testing was conducted in vitro for 8-hour long continuous operation of the coupled UF and RF pumps. The mean cumulative FB error was <1% across filtration flows from 300 mL/hour to 3000 mL/hour. This approach of FB control in a pediatric specific CRRT device would represent a significant accuracy improvement over currently used clinical implementations. PMID:23644618
Santhanakrishnan, Arvind; Nestle, Trent T; Moore, Brian L; Yoganathan, Ajit P; Paden, Matthew L
2013-01-01
Acute kidney injury is common in critically ill children, and renal replacement therapies provide a life-saving therapy to a subset of these children. However, there is no Food and Drug Administration-approved device to provide pediatric continuous renal replacement therapy (CRRT). Consequently, clinicians adapt approved adult CRRT devices for use in children because of lack of safer alternatives. Complications occur using adult CRRT devices in children because of inaccurate fluid balance (FB) between the volumes of ultrafiltrate (UF) removed and replacement fluid (RF) delivered. We demonstrate the design and validation of a pediatric fluid management system for obtaining accurate instantaneous and cumulative FB. Fluid transport was achieved via multiple novel pulsatile diaphragm pumps. The conservation of volume principle leveraging the physical property of fluid incompressibility along with mechanical coupling via a crankshaft was used for FB. Accuracy testing was conducted in vitro for 8 hour long continuous operation of the coupled UF and RF pumps. The mean cumulative FB error was <1% across filtration flows from 300 to 3000 ml/hour. This approach of FB control in a pediatric-specific CRRT device would represent a significant accuracy improvement over currently used clinical implementations. PMID:23644618
Fluid-Structure Interaction Study on a Pre-Buckled Deformable Flat Ribbon
NASA Astrophysics Data System (ADS)
Fovargue, Lauren; Shams, Ehsan; Watterson, Amy; Corson, Dave; Filardo, Benjamin; Zimmerman, Daniel; Shan, Bob; Oberai, Assad
2015-11-01
A Fluid-Structure Interaction study is conducted for the flow over a deformable flat ribbon. This mechanism, which is called ribbon frond, maybe used as a device for pumping water and/or harvesting energy in rivers. We use a lower dimensional mathematical model, which represents the ribbon as a pre-buckled structure. The surface forces from the fluid flow, dictate the deformation of the ribbon, and the ribbon in turn imposes boundary conditions for the incompressible Navier-Stokes equations. The mesh motion is handled using an Arbitrary Lagrangian-Eulerian (ALE) scheme and the fluid-structure coupling is handled by iterating over the staggered governing equations for the structure, the fluid and the mesh. Simulations are conducted at three different free stream velocities. The results, including the frequency of oscillations, show agreement with experimental data. The vortical structures near the surface of the ribbon and its deformation are highly correlated. It is observed that the ribbon motion exhibits deviation from a harmonic motion, especially at lower free stream velocities. The behavior of the ribbon is compared to swimming animals, such as eels, in order to better understand its performance. The authors acknowledge support from ONR SBIR Phase II, contract No. N0001412C0604 and USDA, NIFA SBIR Phase I, contract No. 2013-33610-20836 and NYSERDA PON 2569, contract No. 30364.
NASA Astrophysics Data System (ADS)
Frigeri, Sergio; Grasselli, Maurizio; Rocca, Elisabetta
2015-05-01
We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective non-local Cahn-Hilliard equation with non-constant mobility. We first prove the existence of a global weak solution in the case of non-degenerate mobilities and regular potentials of polynomial growth. Then we extend the result to degenerate mobilities and singular (e.g. logarithmic) potentials. In the latter case we also establish the existence of a global attractor in dimension two. Using a similar technique, we show that there is a global attractor for the convective non-local Cahn-Hilliard equation with degenerate mobility and singular potential in dimension three.
Incompressible laminar flow through hollow fibers: a general study by means of a two-scale approach
NASA Astrophysics Data System (ADS)
Borsi, Iacopo; Farina, Angiolo; Fasano, Antonio
2011-08-01
We study the laminar flow of an incompressible Newtonian fluid in a hollow fiber, whose walls are porous. We write the Navier-Stokes equations for the flow in the inner channel and Darcy's law for the flow in the fiber, coupling them by means of the Beavers-Joseph condition which accounts for the (possible) slip at the membrane surface. Then, we introduce a small parameter {\\varepsilon ≪ 1} (the ratio between the radius and the length of the fiber) and expand all relevant quantities in powers of ɛ. Averaging over the fiber cross section, we find the velocity profiles for the longitudinal flow and for the cross-flow, and eventually, we determine the explicit expression of the permeability of the system. This work is also preliminary to the study of more complex systems comprising a large number of identical fibers (e.g., ultrafiltration modules and dialysis).
Moon, Ji Young; Suh, Dae Chul; Lee, Yong Sang; Kim, Young Woo; Lee, Joon Sang
2014-02-01
Despite recent development of computational fluid dynamics (CFD) research, analysis of computational fluid dynamics of cerebral vessels has several limitations. Although blood is a non-Newtonian fluid, velocity and pressure fields were computed under the assumptions of incompressible, laminar, steady-state flows and Newtonian fluid dynamics. The pulsatile nature of blood flow is not properly applied in inlet and outlet boundaries. Therefore, we present these technical limitations and discuss the possible solution by comparing the theoretical and computational studies. PMID:24642855
NASA Astrophysics Data System (ADS)
Meng, Xuhui; Guo, Zhaoli
2015-10-01
A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.
Saturated hydraulic conductivity and biofilms: A theoretical approach linking pore and pedon scale
NASA Astrophysics Data System (ADS)
Richter, M.; Moenickes, S.; Richter, O.; Schröder, T.
2012-04-01
The fate of active substances in the soil environment is shaped by soil physical properties as well as microbial life. Microorganisms degrading those substances occur in soil pores either in suspension or as biofilms on grain surfaces. At the same scale, i.e. pore scale, the soil physical properties texture, density, porosity, and water content have an impact on transport behaviour of active substances. Macroscopic parameters describe these processes at pedon scale; e.g. hydraulic conductivity summarizes the effect of named pore scale parameters. Narsilio et al. [2009] derived a relationship between the saturated hydraulic conductivity and pore scale water velocity fields based on Navier-Stokes equation for incompressible fluids. However, they did not analyse the influence of heterogeneity and microbial activity, whereas microorganisms, especially biofilms, do have an impact on hydraulic conductivity [Vandevivere and Baveye, 1992]. Biofilms alter the pore geometry while growing. This alteration directly influences the soil water flow field and hence the convective transport of active substances. Here, we present a way to couple the saturated hydraulic conductivity at macro scale to biomass population dynamics and pore space. The hydraulic conductivity will be analysed with regard to heterogeneous soils. The model combining fluid flow, reactive transport, and biofilm dynamics is applied to investigate the degradation and transport behaviour of pesticides in heterogeneous soils.
Compressible and incompressible fluid seals: Influence on rotordynamic response and stability
NASA Technical Reports Server (NTRS)
Thames, Howard D.
1992-01-01
The flow field inside a whirling annular seal operating a Reynolds numbers of 12,000 and 24,000 and a Taylor number of 6,600 was measured. The rotor was mounted eccentric (50 percent) upon the facilities shaft which resulted in a circular orbit at a whirl ratio of 1.0. Three papers which summarize the work were written and are presented. Addition measurements were performed for the annular seal operating at an eccentricity ratio of 10 percent for Re = 24,000 and Ta = 6,600. A labyrinth seal was also installed into the facility and operated at an eccentricity ratio of 50 percent at the same Reynolds and Taylor numbers. These data are currently being reduced and analyzed.
Stokes’ Second Problem for a Micropolar Fluid with Slip
Florea, Olivia Ana; Roşca, Ileana Constanţa
2015-01-01
In this paper is presented the model of an incompressible micropolar fluid flow with slip using the initial and boundary conditions when the wall velocity is considered depending on the frequency of the vibration. Regarding the boundary conditions of the velocity at the wall, we remark that there is a discontinuity of the velocity at the fluid-wall interface. The solutions for velocity and microrotation with the given conditions are obtained using the method of numerical inversion of Laplace transform. PMID:26161780
Bonneville, Alain; Jung, Hun Bok; Shao, Hongbo; Kabilan, Senthil; Um, Wooyong; Carroll, Kenneth C.; Varga, Tamas; Suresh, Niraj; Stephens, Sean A.; Fernandez, Carlos A.
2014-12-14
We have used an environmentally friendly and recyclable hydraulic fracturing fluid - diluted aqueous solutions of polyallylamine or PAA – for reservoir stimulation in Enhanced Geothermal System (EGS). This fluid undergoes a controlled and large volume expansion with a simultaneous increase in viscosity triggered by CO2 at EGS temperatures. We are presenting here the results of laboratory-scale hydraulic fracturing experiment using the fluid on small cylindrical rock cores (1.59 cm in diameter and 5.08 cm in length) from the Coso geothermal field in California. Rock samples consisted of Mesozoic diorite metamorphosed to greenschist facies. The experiments were conducted on 5 samples for realistic ranges of pressures (up to 275 bar) and temperatures (up to 210 °C) for both the rock samples and the injected fluid. After fracturing, cores were subjected to a CO2 leakage test, injection of KI solution, and X-ray microtomography (XMT) scanning to examine the formation and distribution of fractures. The design and conduct of these experiments will be presented and discussed in details. Based on the obtained XMT images, Computational Fluid Dynamics (CFD) simulations were then performed to visualize hydraulic fractures and compute the bulk permeability. OpenFOAM (OpenCFD Ltd., Reading, UK), was used to solve the steady state simulation. The flow predictions, based upon the laminar, 3-D, incompressible Navier-Stokes equations for fluid mass and momentum, show the remarkable stimulation of the permeability in the core samples and demonstrate the efficiency of such a CO2 triggered fluid in EGS.
A massively parallel fractional step solver for incompressible flows
Houzeaux, G. Vazquez, M. Aubry, R. Cela, J.M.
2009-09-20
This paper presents a parallel implementation of fractional solvers for the incompressible Navier-Stokes equations using an algebraic approach. Under this framework, predictor-corrector and incremental projection schemes are seen as sub-classes of the same class, making apparent its differences and similarities. An additional advantage of this approach is to set a common basis for a parallelization strategy, which can be extended to other split techniques or to compressible flows. The predictor-corrector scheme consists in solving the momentum equation and a modified 'continuity' equation (namely a simple iteration for the pressure Schur complement) consecutively in order to converge to the monolithic solution, thus avoiding fractional errors. On the other hand, the incremental projection scheme solves only one iteration of the predictor-corrector per time step and adds a correction equation to fulfill the mass conservation. As shown in the paper, these two schemes are very well suited for massively parallel implementation. In fact, when compared with monolithic schemes, simpler solvers and preconditioners can be used to solve the non-symmetric momentum equations (GMRES, Bi-CGSTAB) and to solve the symmetric continuity equation (CG, Deflated CG). This gives good speedup properties of the algorithm. The implementation of the mesh partitioning technique is presented, as well as the parallel performances and speedups for thousands of processors.
The calculation of incompressible separated turbulent boundary layers
NASA Astrophysics Data System (ADS)
Kogan, A.; Migemi, S.
1990-02-01
The algebraic turbulent model of Baldwin-Lomax was incorporated into the incompressible Navier-Stokes code FIDAP. This model has been extensively tested in the past in finite difference codes. We believe that the incorporation of the model into the finite element code also has resulted in a practical method to compute a variety of separated turbulent two-dimensional flows. Firstly, the model is used to compute the attached flow about an airfoil. Next, the application of the model to separated flows is presented, by computing the flows at high angles of attack up to maximum lift. It is shown that the model is capable of predicting separation, steady stall and C(sub L MAX). As a difficult test of the model, we compute the laminar separation bubble development directly, using the full Navier-Stokes finite elements code. As far as we know, this approach has not been reported previously. The importance of using an appropriate upwinding is discussed. When possible, comparison of computed results with experiments is presented and the agreement is good.
A multilevel adaptive projection method for unsteady incompressible flow
NASA Technical Reports Server (NTRS)
Howell, Louis H.
1993-01-01
There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.
A study of local anisotropy in globally isotropic incompressible MHD
NASA Astrophysics Data System (ADS)
Milano, L. J.; Dmitruk, P.; Matthaeus, W. H.; Montgomery, D.
2000-10-01
It is a well known fact that in presence of a DC applied field, MHD turbulence develops spectral anisotropy from an isotropic initial condition [1]. Typically, the reduced spectrum is steeper in the direction of the magnetic field than it is in any transverse direction. Theoretical insight into the origin of this effect has been derived from simulations in which there is a uniform DC magnetic field, but suggestions of a similar anisotropy is seen in various laboratory devices and also in the solar wind [2,3]. One might expect that a DC field is not essential, and it is the local mean field that is responsible. Here we investigate the occurence of local anisotropy in 3 dimensional MHD, i.e. we search for a local version of the spectral anisotropy effect. We perform 3D MHD pseudo-spectral incompressible relaxation simulations, and compute structure functions accumulated according to whether the separation is parallel to, or transverse to, the local magnetic field. Preliminary results show that correlations decay slower in the locally averaged magnetic field direction. [1] J. Shebalin, W. Matthaeus and D. Montgomery, J. Plasma Phys. 29, 525 (1983) [2] W.H. Matthaeus, M.L. Goldsteon and D.A. Roberts, J. Geophys. Res. 95, 20 673 (1990) [3] J. Armstrong, W. Coles, M. Kojima and B. Rickett, Ap. J. 358, 685 (1990)
High -Pressure Synthesis and Characterization of Incompressible Titanium Pernitride
NASA Astrophysics Data System (ADS)
Bhadram, Venkata; Kim, Duck Young; Strobel, Timothy
We report the discovery of a new transition-metal pernitride, TiN2, which was synthesized by reacting TiN with N2 at 73GPa in a laser-heated diamond anvil cell (DAC). Our in situ pressure dependent x-ray diffraction studies suggest that TiN2 is recoverable at ambient conditions in a crystal structure that contains single bonded nitrogen units (N2 dumbbells) embedded in the metal lattice and exhibits high bulk modulus (in the range 360-385 GPa) which is usually observed in superhard materials. We have performed ab initio calculations to understand the electronic properties and bonding nature in TiN2 and thereby elucidate the origin of incompressible behavior of this material which is rooted in the nearly filled anti-bonding states of the pernitride units. Although, study of transition metal pernitrides has been an active area of research for quite some time, most of the pernitrides synthesized so far are belong to noble metal group. To our knowledge, this is the first experimental report on TiN2 which is the only light metal pernitride exhibiting bonding-mechanical property relation that is usually seen in heavy metal pernitrides. This work was supported by Energy Frontier Research in Extreme Environments (EFree) Center, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science under Award No. DE-SC0001057.
Consistent and conservative framework for incompressible multiphase flow simulations
NASA Astrophysics Data System (ADS)
Owkes, Mark; Desjardins, Olivier
2015-11-01
We present a computational methodology for convection that handles discontinuities with second order accuracy and maintains conservation to machine precision. We use this method in the context of an incompressible gas-liquid flow to transport the phase interface, momentum, and scalars. Using the same methodology for all the variables ensures discretely consistent transport, which is necessary for robust and accurate simulations of turbulent atomizing flows with high-density ratios. The method achieves conservative transport by computing consistent fluxes on a refined mesh, which ensures all conserved quantities are fluxed with the same discretization. Additionally, the method seamlessly couples semi-Lagrangian fluxes used near the interface with finite difference fluxes used away from the interface. The semi-Lagrangian fluxes are three-dimensional, un-split, and conservatively handle discontinuities. Careful construction of the fluxes ensures they are divergence-free and no gaps or overlaps form between neighbors. We have tested and used the scheme for many cases and demonstrate a simulation of an atomizing liquid jet.
The standard upwind compact difference schemes for incompressible flow simulations
NASA Astrophysics Data System (ADS)
Fan, Ping
2016-10-01
Compact difference schemes have been used extensively for solving the incompressible Navier-Stokes equations. However, the earlier formulations of the schemes are of central type (called central compact schemes, CCS), which are dispersive and susceptible to numerical instability. To enhance stability of CCS, the optimal upwind compact schemes (OUCS) are developed recently by adding high order dissipative terms to CCS. In this paper, it is found that OUCS are essentially not of the upwind type because they do not use upwind-biased but central type of stencils. Furthermore, OUCS are not the most optimal since orders of accuracy of OUCS are at least one order lower than the maximum achievable orders. New upwind compact schemes (called standard upwind compact schemes, SUCS) are developed in this paper. In contrast to OUCS, SUCS are constructed based completely on upwind-biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations. Furthermore, SUCS can achieve the maximum achievable orders of accuracy and hence be more compact than OUCS. More importantly, SUCS have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments.
Hall effects on peristaltic flow of a Maxwell fluid in a porous medium
NASA Astrophysics Data System (ADS)
Hayat, T.; Ali, N.; Asghar, S.
2007-04-01
This work is concerned with the peristaltic transport of an incompressible, electrically conducting Maxwell fluid in a planar channel. The flow in the porous space is due to a sinusoidal wave traveling on the channel walls. The Hall effect is taken into account and permeability of porous medium is considered uniform. Modified Darcy's law has been used to model the governing equation. An analytical solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio is small. The present theoretical model may be considered as mathematical representation to the case of gall bladder and bile duct with stones and dynamics of blood flow in living creatures. Finally, the graphical results are reported and discussed for various values of the physical parameters of interest.
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
Fouxon, Itzhak; Oz, Yaron
2008-12-31
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.
NASA Astrophysics Data System (ADS)
Shirzadi, Zahra; Samani, Abbas
2013-03-01
A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Lung tissue incompressibility variation stems from significant air content variation in the tissue throughout respiration. Estimating lung tissue incompressibility and its variation is critical for computer assisted tumor motion tracking. Continuous tumor motion during respiration is a major challenge in lung cancer treatment by external beam radiotherapy. If not accounted for, this motion leads to areas of radiation over dosage for the lung normal tissues. Since no effective imaging modality is available for real-time lung tumor tracking, computer based modeling which has the capability for accurate tissue deformation estimation can be a good alternative. Lung tissue deformation estimation can be made using the lung Finite Element (FE) model where its accuracy depends on input tissue biomechanical properties including incompressibility parameter. In this research, an optimization algorithm is proposed to estimate the incompressibility parameter function in terms of respiration cycle time. In this algorithm, the incompressibility parameter and lung pressure values are varied systematically until optimal values, which result in maximum similarity between acquired and simulated 4D CT images of the lung, are achieved for each respiration time point. The simulated images are constructed using a reference image in conjunction with the deformation field obtained from the lung's FE model in each respiration time increment. We demonstrated that utilizing the calculated function along with respiratory system FE modeling leads to accurate tumor targeting, hence potentially improving lung radiotherapy outcome.
Static fluid cylinders and their fields: global solutions
NASA Astrophysics Data System (ADS)
Bicák, J.; Ledvinka, T.; Schmidt, B. G.; Zofka, M.
2004-03-01
The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of state of the fluid. In the case of a fluid admitting a non-vanishing density for zero pressure, it is shown that the cylinder's radius has to be finite. For incompressible fluid, the field equations are solved analytically for nearly Newtonian cylinders and numerically in fully relativistic situations. Various physical quantities such as proper and circumferential radii, external conicity parameter and masses per unit proper/coordinate length are exhibited graphically.
Computational fluid dynamics - A personal view
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.
1989-01-01
This paper provides a personal view of computational fluid dynamics. The main theme is divided into two categories - one dealing with algorithms and engineering applications and the other with scientific investigations. The former category may be termed computational aerodynamics, with the objective of providing reliable aerodynamic or engineering predictions. The latter category is essentially basic research, where the algorithmic tools are used to unravel and elucidate fluid-dynamic phenomena hard to obtain in a laboratory. A critique of the numerical solution techniques for both compressible and incompressible flows is included. The discussion on scientific investigations deals in particular with transition and turbulence.
Reduced MHD and Astrophysical Fluid Dynamics
NASA Astrophysics Data System (ADS)
Arter, Wayne
2011-08-01
Recent work has shown a relationship between between the equations of Reduced Magnetohydrodynamics (RMHD), used to model magnetic fusion laboratory experiments, and incompressible magnetoconvection (IMC), employed in the simulation of astrophysical fluid dynamics (AFD), which means that the two systems are mathematically equivalent in certain geometries. Limitations on the modelling of RMHD, which were found over twenty years ago, are reviewed for an AFD audience, together with hitherto unpublished material on the role of finite-time singularities in the discrete equations used to model fluid dynamical systems. Possible implications for turbulence modelling are mentioned.
Qiang, Bo; Brigham, John C; Aristizabal, Sara; Greenleaf, James F; Zhang, Xiaoming; Urban, Matthew W
2015-02-01
In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions.
Detached Eddy Simulations of Incompressible Turbulent Flows Using the Finite Element Method
Laskowski, G M
2001-08-01
An explicit Galerkin finite-element formulation of the Spalart-Allmaras (SA) 1 - equation turbulent transport model was implemented into the incompressible flow module of a parallel, multi-domain, Galerkin finite-element, multi-physics code, using both a RANS formulation and a DES formulation. DES is a new technique for simulating/modeling turbulence using a hybrid RANSkES formulation. The turbulent viscosity is constructed from an intermediate viscosity obtained from the transport equation which is spatially discretized using Q1 elements and integrated in time via forward Euler time integration. Three simulations of plane channel flow on a RANS-type grid, using different turbulence models, were conducted in order to validate the implementation of the SA model: SA-RANS, SA-DES and Smagorinksy (without wall correction). Very good agreement was observed between the SA-RANS results and theory, namely the Log Law of the Wall (LLW), especially in the viscous sublayer region and, to a lesser extent, in the log-layer region. The results obtained using the SA-DES model did not agree as well with the LLW, and it is believed that this poor agreement can be attributed to using a DES model on a RANS grid, namely using an incorrect length-scale. It was observed that near the wall, the SA-DES model acted as an RANS model, and away from the wall it acted as an LES model.
Qiang, Bo; Brigham, John C.; Aristizabal, Sara; Greenleaf, James F.; Zhang, Xiaoming; Urban, Matthew W.
2015-01-01
In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions. PMID:25591921
Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; Tuminaro, R. S.; Chacon, L.; Weber, P. D.
2016-02-10
Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method,more » and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.« less
NASA Astrophysics Data System (ADS)
Tura, A.; Sbrignadello, S.; Mambelli, E.; Ravazzani, P.; Santoro, A.; Pacini, G.
2013-09-01
In humans, sodium is essential for the regulation of blood volume and pressure. During hemodialysis, sodium measurement is important to preserve the patient from hypo- or hyper-natremia Usually, sodium measurement is performed through laboratory equipment which is typically expensive, and requires manual intervention. We propose a new method, based on conductivity measurement after treatment of dialysate solution through ion-exchange resin. To test this method, we performed in vitro experiments. We prepared 40 ml sodium chloride (NaCl) samples at 280, 140, 70, 35, 17.5, 8.75, 4.375 mEq/l, and some "mixed samples", i.e., with added potassium chloride (KCl) at different concentrations (4.375-17.5 mEq/l), to simulate the confounding factors in a conductivity-based sodium measurement. We measured the conductivity of all samples. Afterwards, each sample was treated for 1 min with 1 g of Dowex G-26 resin, and conductivity measured again. On average, the difference ɛ in the conductivity between mixed samples and corresponding pure NaCl samples (at the same NaCl concentration) was 20.9%. With treatment with the resin, it was 9.9%, only. We conclude that ion-exchange resin treatment coupled with conductivity measures may be a possible simple approach for continuous and automatic sodium measurement during hemodialysis.
Straight contact lines on a soft, incompressible solid.
Limat, Laurent
2012-12-01
The deformation of a soft substrate by a straight contact line is calculated, and the result applied to a static rivulet between two parallel contact lines. The substrate is supposed to be incompressible (Stokes-like description of elasticity), and having a non-zero surface tension, that eventually differs depending on whether its surface is dry or wet. For a single straight line separating two domains with the same substrate surface tension, the ridge profile is shown to be very close to that of Shanahan and de Gennes, but shifts from the contact line of a distance equal to the elastocapillary length built upon substrate surface tension and shear modulus. As a result, the divergence near contact line disappears and is replaced by a balance of surface tensions at the contact line (Neumann equilibrium), though the profile remains nearly logarithmic. In the rivulet case, using the previous solution as a Green function allows one to calculate analytically the geometry of the distorted substrate, and in particular its slope on each side (wet and dry) of the contact lines. These two slopes are shown to be nearly proportional to the inverse of substrate surface tensions, though the respective weight of each side (wet and dry) in the final expressions is difficult to establish because of the linear nature of standard elasticity. A simple argument combining Neumann and Young equations is however provided to overcome this limitation. The result may have surprising implications for the modelling of hysteresis on systems having both plastic and elastic properties, as initiated long ago by Extrand and Kumagai.
Standardization of Thermo-Fluid Modeling in Modelica.Fluid
Franke, Rudiger; Casella, Francesco; Sielemann, Michael; Proelss, Katrin; Otter, Martin; Wetter, Michael
2009-09-01
This article discusses the Modelica.Fluid library that has been included in the Modelica Standard Library 3.1. Modelica.Fluid provides interfaces and basic components for the device-oriented modeling of onedimensional thermo-fluid flow in networks containing vessels, pipes, fluid machines, valves and fittings. A unique feature of Modelica.Fluid is that the component equations and the media models as well as pressure loss and heat transfer correlations are decoupled from each other. All components are implemented such that they can be used for media from the Modelica.Media library. This means that an incompressible or compressible medium, a single or a multiple substance medium with one or more phases might be used with one and the same model as long as the modeling assumptions made hold. Furthermore, trace substances are supported. Modeling assumptions can be configured globally in an outer System object. This covers in particular the initialization, uni- or bi-directional flow, and dynamic or steady-state formulation of mass, energy, and momentum balance. All assumptions can be locally refined for every component. While Modelica.Fluid contains a reasonable set of component models, the goal of the library is not to provide a comprehensive set of models, but rather to provide interfaces and best practices for the treatment of issues such as connector design and implementation of energy, mass and momentum balances. Applications from various domains are presented.
Kelvin-Helmholtz instability in a rotating ideally conducting inhomogeneous plasma
NASA Astrophysics Data System (ADS)
Kumar, Vinod; Srivastava, K. M.; Kumar, Nagendra; Sikka, Himanshu
2004-04-01
The Kelvin--Helmholtz instability in sheared magnetohydrodynamic flow of an ideally conducting rotating inhomogeneous compressible plasma is investigated. The asymptotic behaviour in x of the Kelvin--Helmholtz eigenfunctions for the case of finite compressibility in the presence of rotation is discussed and instability condition is derived. In the incompressible limit, a dispersion relation is derived which has been solved numerically and discussed in detail. It is found that the inhomogeneous system is unstable in an incompressible plasma.
Computational fluid mechanics utilizing the variational principle of modeling damping seals
NASA Technical Reports Server (NTRS)
Abernathy, J. M.
1986-01-01
A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed.
Simulation of large incompressible flows by the finite element method
NASA Astrophysics Data System (ADS)
Bercovier, M.; Engelman, M.
Super computers together with low cost 32 bit machines with graphics render more actual the challenge of designing a general purpose Fluid Dynamic code. Such an approach was the key to the introduction of computational structural mechanics into the design cycle. There FEM codes have replaced experiments and are evaluation tools at every stage. Except for a very limited domain (low Reynolds numbers for instance) this "black box" concept cannot be aplied in fluid mechanics. Nevertheless the success of the modular approach of FIDAP, the addition of new models and the extension of its pre and post-processing capabilities bring a new bridge between the fluid mechanics engineer and the design floor shop. It is now the task of the scientific community to design acceptable models in domains like turbulent flows,multiphase flows slightly compressible flows and so on. At the same time faster and robust algorithms for highly non linear problems must be devised.
NASA Astrophysics Data System (ADS)
Chen, Mufeng; Niu, Xiaodong
2016-06-01
An improved momentum-exchanged immersed boundary-based lattice Boltzmann method (MEIB-LBM) for incompressible viscous thermal flows is presented here. MEIB-LBM was first proposed by Niu et al, which has been shown later that the non-slip boundary condition is not satisfied. Wang. et al. and Hu. et al overcome this drawback by iterative method. But it needs to give an appropriate relaxation parameter. In this work, we come back to the intrinsic feature of LBM, which uses the density distribution function as a dependent variable to evolve the flow field, and uses the density distribution function correction at the neighboring Euler mesh points to satisfy the non-slip boundary condition on the immersed boundary. The same idea can also be applied to the thermal flows with fluid-structure interference. The merits of present improvements for the original MEIB-LBM are that the intrinsic feature of LBM is kept and the flow penetration across the immersed boundaries is avoided. To validate the present method, examples, including forced convection over a stationary heated circular cylinder for heat flux condition, and natural convection with a suspended circle particle in viscous fluid, are simulated. The streamlines, isothermal contours, the drag coefficients and Nusselt numbers are calculated and compared to the benchmark results to demonstrate the effective of the present method.
NASA Astrophysics Data System (ADS)
Lind, S. J.; Stansby, P. K.; Rogers, B. D.
2016-03-01
A new two-phase incompressible-compressible Smoothed Particle Hydrodynamics (SPH) method has been developed where the interface is discontinuous in density. This is applied to water-air problems with a large density difference. The incompressible phase requires surface pressure from the compressible phase and the compressible phase requires surface velocity from the incompressible phase. Compressible SPH is used for the air phase (with the isothermal stiffened ideal gas equation of state for low Mach numbers) and divergence-free (projection based) incompressible SPH is used for the water phase, with the addition of Fickian shifting to produce sufficiently homogeneous particle distributions to enable stable, accurate, converged solutions without noise in the pressure field. Shifting is a purely numerical particle regularisation device. The interface remains a true material discontinuity at a high density ratio with continuous pressure and velocity at the interface. This approach with the physics of compressibility and incompressibility represented is novel within SPH and is validated against semi-analytical results for a two-phase elongating and oscillating water drop, analytical results for low amplitude inviscid standing waves, the Kelvin-Helmholtz instability, and a dam break problem with high interface distortion and impact on a vertical wall where experimental and other numerical results are available.
NASA Astrophysics Data System (ADS)
Moawad, S. M.; Ibrahim, D. A.
2016-08-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
Front Speed Enhancement by Incompressible Flows in Three or Higher Dimensions
NASA Astrophysics Data System (ADS)
El Smaily, Mohammad; Kirsch, Stéphane
2014-07-01
We study, in dimensions N ≥ 3, the family of first integrals of an incompressible flow: these are functions whose level surfaces are tangential to the streamlines of the advective incompressible field. One main motivation for this study comes from earlier results proving that the existence of nontrivial first integrals of an incompressible flow q is the main key that leads to a "linear speed up" by a large advection of pulsating traveling fronts solving a reaction-advection-diffusion equation in a periodic heterogeneous framework. The family of first integrals is not well understood in dimensions N ≥ 3 due to the randomness of the trajectories of q and this is in contrast with the case N = 2. By looking at the domain of propagation as a union of different components produced by the advective field, we provide more information about first integrals and we give a class of incompressible flows which exhibit "ergodic components" of positive Lebesgue measure (and hence are not shear flows) and which, under certain sharp geometric conditions, speed up the KPP fronts linearly with respect to the large amplitude. In the proofs, we establish a link between incompressibility, ergodicity, first integrals and the dimension to give a sharp condition about the asymptotic behavior of the minimal KPP speed in terms of the configuration of ergodic components.
NASA Astrophysics Data System (ADS)
Hu, S.; Zhang, R.; Zhang, X.
2013-12-01
Recently, we designed a new experimental apparatus, which was used to measure dissolution rates as water-rock interactions, and simultaneously in situ measure the electric conductance of the multi phase (rock - fluid) system. At first, a tubular reactor is put in horizontally. The rock sample was crushed and sieved to 20-40 mesh, and cleaned, then put in a titanium network bag inside of the vessel. The electric conductivity detectors were connected to the two ends of the vessel. Fluid inlet and outlet were also fabricated in the two ends of the vessel. And the furnace, temperature controller, liquid pump, back pressure regulator etc. are involved in the whole experimental system. High temperature (T) and pressure (P) electric conductivity measuring system consists of an electric conductivity detector (ECD limit.), which was reformed by us and connected to the vessel; and a transfer: T23-CDH-UM: 5.67(L)×3.50(W)×5.67(H) (inch).The distance between the two electrode of the sensor is 10cm. The electrode is 5cm of length and its diameter is 5/16 inch. Water-rock interaction experiments were performed using this apparatus. The volume inside of vessel is 10.81 ml, l= 170mm, d=4.5mm and 7.246g rock sample put in the vessel. The fluid velocity was changed from 1.5 to 3.5 ml/min, allowing the water through the sample. As in situ to measure the electric conductance of the rock-fluids in the vessel, continuously record the electric conductance, each record in 5 seconds. Water-basalt interaction experiments were carried out and in situ measured electric conductance at high T up to 450°C and at 22 to 36MPa. Basalt sample was collected from natural outcrop (volcanic area in Yangtze valley, China, which is K-rich trachy-basalt. Rock sample was crushed and sieved to 20-40 mesh, and cleaned. 8.0097g sample was put in the vessel (surface area: 1.37m2/g ). Experiments found dissolution rates (dis.r.) for different metals of the rock vary with T. Usually, dis.r., rSi increase with T
NASA Technical Reports Server (NTRS)
Hirsch, Charles (Editor); Periaux, J. (Editor); Kordulla, W. (Editor)
1992-01-01
A conference was held on Computational Fluid Dynamics (CFD) and produced related papers. Topics included CFD algorithms, transition and turbulent flow, hypersonic reacting flow, incompressible flow, two phase flow and combustion, internal flow, compressible flow, grid generation and adaption, boundary layers, environmental and industrial applications, and non-Newtonian flow.
Lattice Boltzmann methods for viscous fluid flows and for two-phase fluid flows
NASA Astrophysics Data System (ADS)
Inamuro, Takaji
2006-09-01
Lattice Boltzmann methods (LBMs) for viscous fluid flows and for two-phase fluid flows are presented. First, the LBMs for incompressible viscous fluid flows and for temperature fields are described. Then, we derive a lattice kinetic scheme (LKS) which is an improved scheme of the LBM. The LKS does not require any velocity distribution functions and is more stable than the LBMs. In addition, the LBM for two-phase fluid flows is presented. The method can simulate flows with the density ratio up to 1000. Numerical examples of unsteady flows in a three-dimensional porous structure, binary droplet collision and rising bubbles in a square duct are illustrated. It is expected that the LBMs (and LKS) will become promising numerical schemes for simulating complex fluid flows.
Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid
NASA Astrophysics Data System (ADS)
F, M. Abbasi; M, Mustafa; S, A. Shehzad; M, S. Alhuthali; T, Hayat
2016-01-01
We investigate the Cattaneo-Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo-Christov heat flux model than those in the Fourier’s law of heat conduction. Project supported by the Deanship of Scientific Research (DSR) King Abdulaziz University, Jeddah, Saudi Arabia (Grant No. 32-130-36-HiCi).
Phase-field modeling of isothermal quasi-incompressible multicomponent liquids
NASA Astrophysics Data System (ADS)
Tóth, Gyula I.
2016-09-01
In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.
A comparison of two incompressible Navier-Stokes algorithms for unsteady internal flow
NASA Technical Reports Server (NTRS)
Wiltberger, N. Lyn; Rogers, Stuart E.; Kwak, Dochan
1993-01-01
A comparative study of two different incompressible Navier-Stokes algorithms for solving an unsteady, incompressible, internal flow problem is performed. The first algorithm uses an artificial compressibility method coupled with upwind differencing and a line relaxation scheme. The second algorithm uses a fractional step method with a staggered grid, finite volume approach. Unsteady, viscous, incompressible, internal flow through a channel with a constriction is computed using the first algorithm. A grid resolution study and parameter studies on the artificial compressibility coefficient and the maximum allowable residual of the continuity equation are performed. The periodicity of the solution is examined and several periodic data sets are generated using the first algorithm. These computational results are compared with previously published results computed using the second algorithm and experimental data.
Projection methods for incompressible flow problems with WENO finite difference schemes
NASA Astrophysics Data System (ADS)
de Frutos, Javier; John, Volker; Novo, Julia
2016-03-01
Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.
A Non-Incompressible Non-Boussinesq (NINB) framework for studying atmospheric turbulence
NASA Astrophysics Data System (ADS)
Yan, C.; Archer, C. L.; Xie, S.; Ghaisas, N.
2015-12-01
The incompressible assumption is widely used for studying the turbulent atmospheric boundary layer (ABL) and is generally accepted when the Mach number < ~0.3 (velocity < ~100 m/s). Since the tips of modern wind turbine blades can reach and exceed this threshold, neglecting air compressibility will introduce errors. In addition, if air incompressibility does not hold, then the Boussinesq approximation, by which air density is treated as a constant except in the gravity term of the Navier-Stokes equation, is also invalidated. Here, we propose a new theoretical framework, called NINB for Non-Incompressible Non-Boussinesq, in which air is not considered incompressible and air density is treated as a non-turbulent 4D variable. First, the NINB mass, momentum, and energy conservation equations are developed using Reynolds averaging. Second, numerical simulations of the NINB equations, coupled with a k-epsilon turbulence model, are performed with the finite-volume method. Wind turbines are modeled with the actuator-line model using SOWFA (Software for Offshore/onshore Wind Farm Applications). Third, NINB results are compared with the traditional incompressible buoyant simulations performed by SOWFA with the same set up. The results show differences between NINB and traditional simulations in the neutral atmosphere with a wind turbine. The largest differences in wind speed (up to 1 m/s), turbulent kinetic energy (~10%), dissipation rate (~5%), and shear stress (~10%) occur near the turbine tip region. The power generation differences are 5-15% (depending on setup). These preliminary results suggest that compressibility effects are non-negligible around wind turbines and should be taken into account when forecasting wind power. Since only a few extra terms are introduced, the NINB framework may be an alternative to the traditional incompressible Boussinesq framework for studying the turbulent ABL in general (i.e., without turbines) in the absence of shock waves.
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.
2D Mixed Convection Thermal Incompressible Viscous Flows
NASA Astrophysics Data System (ADS)
Bermudez, Blanca; Nicolas, Alfredo
2005-11-01
Mixed convection thermal incomprressible viscous fluid flows in rectangular cavities are presented. These kind of flows may be governed by the time-dependent Boussinesq approximation in terms of the stream function-vorticity variables formulation. The results are obtained with a simple numerical scheme based mainly on a fixed point iterative process applied to the non-linear system of elliptic equations that is obtained after a second order time discretization. Numerical experiments are reported for the problem of a cavity with fluid boundary motion on the top. Some results correspond to validation examples and others, to the best of our knowledge, correspond to new results. To show that the new results are correct, a mesh size and time independence studies are carried out, and the acceptable errors are measured point-wise. For the optimal mesh size and time step the final times when the steady state is reached, as solution from the unsteady problem, are reported; it should be seen that they are larger than the ones for natural convection which, physically speaking, show the agreement that mixed convection flows are more active than those of natural convection due to the fluid boundary motion on the top of the cavity. The flow parameters are: the Reynolds number, the Grashof number and the aspect ratio.
Potts, J.M.
1984-09-01
The use of fertilizer in the United States has increased spectacularly in the past 20 years. In 1981 plant nutrient use (N + P/sub 2/O/sub 5/ + K/sub 2/O) totaled 23.5 million short tons - compared with only 7.5 million tons in 1960 (table 2). Nutrient use doubled from 1960 to 1970 and tripled from 1960 to 1981. In 1981 fluid nutrient use (mixtures plus nitrogen solutions) totaled 4.1 million tons, more than doubling since 1970 and increasing from 6.3% to 17.5% of the total nutrient use since 1960. Fluid mixtures (NPK) use in 1981 totaled 1.8 million tons of nutrients - about 17% of total mixed fertilizers or 7.5% of total nutrients used. The proportion of total fertilizer nutrients applied in fluid from increases greatly if anhydrous ammonia is included. The 4.6 million tons of nitrogen applied as anhydrous ammonia in 1981 increases total fluid nutrients to 8.1 million tons - 34.5% of the total nutrients applied in the United States. Fluid fertilizer use has grown nearly twice as fast as total fertilizer use, averaging more than 15% per year increase between 1960 and 1970, and an 11% increase between 1960 and 1980. A large part of this increase occurred during the introductory stages of the new product form and was aided by rapid advances in technology.
NASA Astrophysics Data System (ADS)
Sonntag, Simon J.; Kaufmann, Tim A. S.; Büsen, Martin R.; Laumen, Marco; Linde, Torsten; Schmitz-Rode, Thomas; Steinseifer, Ulrich
2013-04-01
Heart disease is one of the leading causes of death in the world. Due to a shortage in donor organs artificial hearts can be a bridge to transplantation or even serve as a destination therapy for patients with terminal heart insufficiency. A pusher plate driven pulsatile membrane pump, the Total Artificial Heart (TAH) ReinHeart, is currently under development at the Institute of Applied Medical Engineering of RWTH Aachen University.This paper presents the methodology of a fully coupled three-dimensional time-dependent Fluid Structure Interaction (FSI) simulation of the TAH using a commercial partitioned block-Gauss-Seidel coupling package. Partitioned coupling of the incompressible fluid with the slender flexible membrane as well as a high fluid/structure density ratio of about unity led inherently to a deterioration of the stability (‘artificial added mass instability’). The objective was to conduct a stable simulation with high accuracy of the pumping process. In order to achieve stability, a combined resistance and pressure outlet boundary condition as well as the interface artificial compressibility method was applied. An analysis of the contact algorithm and turbulence condition is presented. Independence tests are performed for the structural and the fluid mesh, the time step size and the number of pulse cycles. Because of the large deformation of the fluid domain, a variable mesh stiffness depending on certain mesh properties was specified for the fluid elements. Adaptive remeshing was avoided. Different approaches for the mesh stiffness function are compared with respect to convergence, preservation of mesh topology and mesh quality. The resulting mesh aspect ratios, mesh expansion factors and mesh orthogonalities are evaluated in detail. The membrane motion and flow distribution of the coupled simulations are compared with a top-view recording and stereo Particle Image Velocimetry (PIV) measurements, respectively, of the actual pump.
On the method of pseudo compressibility for numerically solving incompressible flows
NASA Technical Reports Server (NTRS)
Chang, J. L. C.; Kwak, D.
1984-01-01
Pseudo compressibility is used for numerically solving incompressible flows to achieve computational efficiency. The use of pseudo compressibility results in a system of hyperbolic-type equations of motion that introduce waves of finite speed. The interactions of the wave propagation and the vorticity spreading are analyzed. A criterion governing the dependence of the pseudo compressiblity on the Reynolds number and the characteristic length of the flow geometry is obtained that allows for a proper convergence. It is demonstrated that the solution does tend to the incompressible limit. External and internal viscous flow test problems are presented to verify the theory.
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.
NASA Astrophysics Data System (ADS)
Yan, Y. Y.; Zu, Y. Q.
2007-11-01
This paper reports a new numerical scheme of the lattice Boltzmann method for calculating liquid droplet behaviour on particle wetting surfaces typically for the system of liquid-gas of a large density ratio. The method combines the existing models of Inamuro et al. [T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628-644] and Briant et al. [A.J. Briant, P. Papatzacos, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid-gas system, Philos. Trans. Roy. Soc. London A 360 (2002) 485-495; A.J. Briant, A.J. Wagner, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid-gas systems. Phys. Rev. E 69 (2004) 031602; A.J. Briant, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: II. Binary fluids, Phys. Rev. E 69 (2004) 031603] and has developed novel treatment for partial wetting boundaries which involve droplets spreading on a hydrophobic surface combined with the surface of relative low contact angles and strips of relative high contact angles. The interaction between the fluid-fluid interface and the partial wetting wall has been typically considered. Applying the current method, the dynamics of liquid drops on uniform and heterogeneous wetting walls are simulated numerically. The results of the simulation agree well with those of theoretical prediction and show that the present LBM can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.
NASA Astrophysics Data System (ADS)
Kikuchi, T.; Hashimoto, K. K.; Tomizawa, I.; Ebihara, Y.; Nishimura, Y.; Araki, T.; Shinbori, A.; Veenadhari, B.; Tanaka, T.; Nagatsuma, T.
2016-02-01
The ionospheric plasma in midlatitude moves upward/downward during the geomagnetic sudden commencement causing the HF Doppler frequency changes; SCF (+ -) and (- +) on the dayside and nightside, respectively, except for the SCF (+ -) in the evening as found by Kikuchi et al. (1985). Although the preliminary and main frequency deviations (PFD, MFD) of the SCF have been attributed to the dusk-to-dawn and dawn-to-dusk potential electric fields, there still remain questions if the positive PFD can be caused by the compressional magnetohydrodynamic (MHD) wave and what causes the evening anomaly of the SCF. With the HF Doppler sounder, we show that the dayside ionosphere moves upward toward the Sun during the main impulse (MI) of the SC, when the compressional wave is supposed to push the ionosphere downward. The motion of the ionosphere is shown to be correlated with the equatorial electrojet, matching the potential electric field transmitted with the ionospheric currents from the polar ionosphere. We confirmed that the electric field of the compressional wave is severely suppressed by the conducting ionosphere and reproduced the SC electric fields using the global MHD simulation in which the potential solver is employed. The model calculations well reproduced the preliminary impulse and MI electric fields and their evening anomaly. It is suggested that the electric potential is transmitted from the polar ionosphere to the equator by the zeroth-order transverse magnetic (TM0) mode waves in the Earth-ionosphere waveguide. The near-instantaneous transmission of the electric potential leads to instantaneous global response of the incompressible ionosphere.
A two-dimensional adaptive spectral element method for the direct simulation of incompressible flow
NASA Astrophysics Data System (ADS)
Hsu, Li-Chieh
The spectral element method is a high order discretization scheme for the solution of nonlinear partial differential equations. The method draws its strengths from the finite element method for geometrical flexibility and spectral methods for high accuracy. Although the method is, in theory, very powerful for complex phenomena such as transitional flows, its practical implementation is limited by the arbitrary choice of domain discretization. For instance, it is hard to estimate the appropriate number of elements for a specific case. Selection of regions to be refined or coarsened is difficult especially as the flow becomes more complex and memory limits of the computer are stressed. We present an adaptive spectral element method in which the grid is automatically refined or coarsened in order to capture underresolved regions of the domain and to follow regions requiring high resolution as they develop in time. The objective is to provide the best and most efficient solution to a time-dependent nonlinear problem by continually optimizing resource allocation. The adaptivity is based on an error estimator which determines which regions need more resolution. The solution strategy is as follows: compute an initial solution with a suitable initial mesh, estimate errors in the solution locally in each element, modify the mesh according to the error estimators, interpolate old mesh solutions onto the new elements, and resume the numerical solution process. A two-dimensional adaptive spectral element method for the direct simulation of incompressible flows has been developed. The adaptive algorithm effectively diagnoses and refines regions of the flow where complexity of the solution requires increased resolution. The method has been demonstrated on two-dimensional examples in heat conduction, Stokes and Navier-Stokes flows.
NASA Astrophysics Data System (ADS)
Xie, Bin; , Satoshi, Ii; Ikebata, Akio; Xiao, Feng
2014-11-01
A robust and accurate finite volume method (FVM) is proposed for incompressible viscous fluid dynamics on triangular and tetrahedral unstructured grids. Differently from conventional FVM where the volume integrated average (VIA) value is the only computational variable, the present formulation treats both VIA and the point value (PV) as the computational variables which are updated separately at each time step. The VIA is computed from a finite volume scheme of flux form, and is thus numerically conservative. The PV is updated from the differential form of the governing equation that does not have to be conservative but can be solved in a very efficient way. Including PV as the additional variable enables us to make higher-order reconstructions over compact mesh stencil to improve the accuracy, and moreover, the resulting numerical model is more robust for unstructured grids. We present the numerical formulations in both two and three dimensions on triangular and tetrahedral mesh elements. Numerical results of several benchmark tests are also presented to verify the proposed numerical method as an accurate and robust solver for incompressible flows on unstructured grids.
Malinconico, M.L.; Sanford, W.E.; Wright, Horton W.J.J.
2009-01-01
Vitrinite reflectance data from the International Continental Scientific Drilling Program (ICDP)-U.S. Geological Survey (USGS) Eyreville deep cores in the centralcrater moat of the Chesapeake Bay impact structure and the Cape Charles test holes on the central uplift show patterns of postimpact maximum-temperature distribution that result from a combination of conductive and advective heat flow. Within the crater-fill sediment-clast breccia sequence at Eyreville, an isoreflectance (-0.44% Ro) section (525-1096 m depth) is higher than modeled background coastal-plain maturity and shows a pattern typical of advective fluid flow. Below an intervening granite slab, a short interval of sediment-clast breccia (1371-1397 m) shows a sharp increase in reflectance (0.47%-0.91% Ro) caused by conductive heat from the underlying suevite (1397-1474 m). Refl ectance data in the uppermost suevite range from 1.2% to 2.1% Ro. However, heat conduction alone is not sufficient to affect the temperature of sediments more than 100 m above the suevite. Thermal modeling of the Eyreville suevite as a 390 ??C cooling sill-like hot rock layer supplemented by compaction- driven vertical fluid flow (0.046 m/a) of cooling suevitic fluids and deeper basement brines (120 ??C) upward through the sediment breccias closely reproduces the measured reflectance data. This scenario would also replace any marine water trapped in the crater fill with more saline brine, similar to that currently in the crater, and it would produce temperatures sufficient to kill microbes in sediment breccias within 450 m above the synimsuevite. A similar downhole maturity pattern is present in the sediment-clast breccia over the central uplift. High-reflectance (5%-9%) black shale and siltstone clasts in the suevite and sediment-clast breccia record a pre-impact (Paleozoic?) metamorphic event. Previously published maturity data in the annular trough indicate no thermal effect there from impact-related processes. ?? 2009 The
SOLA-VOF: A solution algorithm for transient fluid flow with multiple free boundaries
NASA Astrophysics Data System (ADS)
Nichols, B. D.; Hirt, C. W.; Hotchkiss, R. S.
1980-08-01
A computer program is presented for the solution of two dimensional transient fluid flow with free boundaries. The SOLA-VOF program, which is based on the concept of a fractional volume of fluid is more flexible and efficient than other methods for treating arbitrary free boundaries. Its basic model of operation is for single fluid calculations having multiple free surfaces. However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface. In either case, the fluids may be treated as incompressible or as having limited compressibility. Surface tension forces with wall adhesion are permitted in both cases.
Unsteady three-dimensional incompressible flow interaction in multiple-blade-row turbomachinery
NASA Astrophysics Data System (ADS)
Busby, Judy Ann
Marine propulsors operate in an inherently unsteady flowfield. To design a propulsor that meets the conditions imposed by hydrodynamic and hydroacoustic requirements, knowledge of component interactions and unsteady flow patterns throughout the propulsor is essential. At the present time, the effect of the unsteady flow on the performance of the propulsor is not thoroughly understood. The goal of this work is to use computational fluid dynamics (CFD) coupled with measurements and analytic methods to provide some insight into the physics associated with unsteady propulsor flows. The unsteady, incompressible Reynolds-Averaged Navier Stokes (RANS) code developed at Mississippi State University has been extended for use in analyzing the unsteady flow interaction between blade rows in relative motion. The approach used to model the dynamic interface between the blade rows is the localized grid distortion technique of Janus. The spatial and temporal discretizations result in third order spatial accuracy and second order (implicit) temporal accuracy. To validate the dynamic grid capabilities, computed results for the unsteady flow around a two-dimensional hydrofoil undergoing a high, reduced-frequency gust loading are compared with measured data. The unsteady gusts are generated by a pair of oscillating foils (flappers) upstream of the hydrofoil. A dynamic grid is used around the oscillating foils. The results from a parametric study indicate that 500 time steps per flapper period with three subiterations at each time step are sufficient to capture the time-accurate behavior of both the inviscid and viscous flow fields. The algorithm is then used to compute the unsteady flow through a three-dimensional, high Reynolds number pump consisting of 13 stator blades and 7 rotor blades. A detailed analysis of the primary, secondary and unsteady flow effects is presented along with an investigation of the effects of sub-iterations on the time-accuracy on the solution. The unsteady
Cassandro, Ettore; Cassandro, Claudia; Sequino, Giuliano; Scarpa, Alfonso; Petrolo, Claudio; Chiarella, Giuseppe
2015-01-01
While pulsatile tinnitus (PT) and dural arteriovenous fistula (DAVF) are not rarely associated, the finding of a conductive hearing loss (CHL) in this clinical picture is unusual. Starting from a case of CHL and PT, diagnosed to be due to a DAVF, we analyzed relationship between intracranial vascular abnormalities and inner ear fluids. DAVF was treated with endovascular embolization. Following this, there was a dramatic recovery of PT and of CHL, confirming their cause-effect link with DAVF. We critically evaluated the papers reporting this association. This is the first case of CHL associated with PT and DAVF. We describe the most significant experiences and theories reported in literature, with a personal analysis about the possible relationship between vascular intracranial system and labyrinthine fluids. In conclusion, we believe that this association may be a challenge for otolaryngologists. So we suggest to consider the possibility of a DAVF or other AVMs when PT is associated with CHL, without alterations of tympanic membrane and middle ear tests. PMID:26693371
Least-squares finite element method for fluid dynamics
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
Irrotational, Two-Dimensional Surface Waves in Fluids
NASA Astrophysics Data System (ADS)
Unruh, William G.
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying bottom topography. Most importantly, the conserved norm for the surface waves is derived, important for quantisation of these waves and their use in analogue models for black holes.
An Exact Solution to the Draining Reservoir Problem of the Incompressible and Non-Viscous Liquid
ERIC Educational Resources Information Center
Hong, Seok-In
2009-01-01
The exact expressions for the drain time and the height, velocity and acceleration of the free surface are found for the draining reservoir problem of the incompressible and non-viscous liquid. Contrary to the conventional approximate results, they correctly describe the initial time dependence of the liquid velocity and acceleration. Torricelli's…
Incompressible states of a two-component Fermi gas in a double-well optical lattice
Crepin, Francois; Simon, Pascal; Citro, Roberta
2010-07-15
We propose a scheme to investigate the effect of frustration on the magnetic phase transitions of cold atoms confined in an optical lattice. We also demonstrate how to get two-leg spin ladders with frustrated spin-exchange coupling that display a phase transition from a spin liquid to a fully incompressible state. Further, various experimental quantities are analyzed for describing this phase.
NASA Technical Reports Server (NTRS)
Biringen, S.; Cook, C.
1988-01-01
Pressure boundary conditions satisfying the normal momentum equation at solid boundaries with second-order accuracy are developed. Implementation of these conditions in an explicit numerical procedure for the two-dimensional incompressible Navier-Stokes equations enables convergent and accurate solutions for the driven cavity problem provided that the integral constraint of the Neumann boundary condtions is satisfied.
NASA Astrophysics Data System (ADS)
Bose, Sayan; Banerjee, Moloy
2015-07-01
Magnetic nanoparticles drug carriers continue to attract considerable interest for drug targeting in the treatment of cancer and other pathological conditions. Guiding magnetic iron oxide nanoparticles with the help of an external magnetic field to its target is the basic principle behind the Magnetic Drug Targeting (MDT). It is essential to couple the ferrohydrodynamic (FHD) and magnetohydrodynamic (MHD) principles when magnetic fields are applied to blood as a biomagnetic fluid. The present study is devoted to study on MDT technique by particle tracking in the presence of a non uniform magnetic field in a stenosed aortic bifurcation. The present numerical model of biomagnetic fluid dynamics (BFD) takes into accounts both magnetization and electrical conductivity of blood. The blood flow in the bifurcation is considered to be incompressible and Newtonian. An Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of the magnetic particles in the flow using ANSYS FLUENT two way particle-fluid coupling. An implantable infinitely long cylindrical current carrying conductor is used to create the requisite magnetic field. Targeted transport of the magnetic particles in a partly occluded vessel differs distinctly from the same in a regular unblocked vessel. Results concerning the velocity and temperature field indicate that the presence of the magnetic field influences the flow field considerably and the disturbances increase as the magnetic field strength increases. The insert position is also varied to observe the variation in flow as well as temperature field. Parametric investigation is conducted and the influence of the particle size (dp), flow Reynolds number (Re) and external magnetic field strength (B0) on the "capture efficiency" (CE) is reported. The difference in CE is also studied for different particle loading condition. According to the results, the magnetic field increased the particle concentration in the target region
General Transient Fluid Flow Algorithm
1992-03-12
SALE2D calculates two-dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude resultsmore » from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a two-dimensional network of quadrilateral cells for either cylindrical or Cartesian coordinates, and a variety of user-selectable boundary conditions are provided in the program.« less
NASA Astrophysics Data System (ADS)
Le Chenadec, Vincent; Bay, Yong Yi
2015-11-01
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods also introduce new challenges, in that the formulation of accurate and well-posed discrete operators is not trivial. A cut-cell method for the solution of the incompressible Navier-Stokes equation is proposed for staggered Cartesian grids. In both scalar and vector cases, the emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, different forms are proposed (divergence, advective and skew-symmetric), and shown to be equivalent when the discrete continuity equation is satisfied. This ensures mass, momentum and kinetic energy conservation. For diffusive transport, conservative and symmetric operators are proposed for both Dirichlet and Neumann boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The accuracy of method is finally assessed in standard test cases.
NASA Astrophysics Data System (ADS)
Ren, Feng; Song, Baowei; Sukop, Michael C.
2016-11-01
This article describes the simulation of three-dimensional buoyancy-driven bubble rise using a phase-field-based incompressible Lattice Boltzmann model. The effect of the Cahn-Hilliard mobility parameter, which is the rate of diffusion relaxation from non-equilibrium toward equilibrium state of chemical potential, is evaluated in detail. In contrast with previous work that pursues a high density ratio of binary fluids in the hydrodynamic equation, we apply a large dynamic viscosity ratio, together with a matched density pair and a separate compensating gas phase buoyant force, and the numerical results fit previous experimental results well. Through analysis, it is noted that for cases with moderate Reynolds number, a large value of mobility keeps a relatively sharp interface, while smaller values of mobility would result in diffusive interfacial regions. Moreover, for cases with large Reynolds number, small bubbles at the tail tend to separate more easily when the value of mobility is larger. This article offers some potentially useful details for performing phase-field-based simulations.
Physical aspects of computing the flow of a viscous fluid
NASA Technical Reports Server (NTRS)
Mehta, U. B.
1984-01-01
One of the main themes in fluid dynamics at present and in the future is going to be computational fluid dynamics with the primary focus on the determination of drag, flow separation, vortex flows, and unsteady flows. A computation of the flow of a viscous fluid requires an understanding and consideration of the physical aspects of the flow. This is done by identifying the flow regimes and the scales of fluid motion, and the sources of vorticity. Discussions of flow regimes deal with conditions of incompressibility, transitional and turbulent flows, Navier-Stokes and non-Navier-Stokes regimes, shock waves, and strain fields. Discussions of the scales of fluid motion consider transitional and turbulent flows, thin- and slender-shear layers, triple- and four-deck regions, viscous-inviscid interactions, shock waves, strain rates, and temporal scales. In addition, the significance and generation of vorticity are discussed. These physical aspects mainly guide computations of the flow of a viscous fluid.
Field application of lightweight, hollow-glass-sphere drilling fluid
1997-11-01
A new class of underbalanced drilling fluids being developed under US Dept. of Energy (US DOE) sponsorship was recently successfully field tested. The fluid uses hollow glass spheres (HGS`s) to decrease the fluid density to less than that of the base mud while maintaining incompressibility. Concentrations of up to 20 vol% were used to decrease the fluid density to 0.8 lbm/gal less than normally used in the field. Potential benefits of using these fluids include higher penetration rates, decreased formation damage, and lost-circulation mitigation. When used in place of aerated fluid, they can eliminate compressor usage and allow the use of mud-pulse measurement-while-drilling tools. These and other recent advances in technology have spurred interest in underbalanced drilling to the highest level in 30 years. Industry-wide surveys indicate that more than 12% of wells drilled in the US in 1997 will intentionally use underbalanced techniques.
Domain decomposition algorithms and computational fluid dynamics
NASA Technical Reports Server (NTRS)
Chan, Tony F.
1988-01-01
Some of the new domain decomposition algorithms are applied to two model problems in computational fluid dynamics: the two-dimensional convection-diffusion problem and the incompressible driven cavity flow problem. First, a brief introduction to the various approaches of domain decomposition is given, and a survey of domain decomposition preconditioners for the operator on the interface separating the subdomains is then presented. For the convection-diffusion problem, the effect of the convection term and its discretization on the performance of some of the preconditioners is discussed. For the driven cavity problem, the effectiveness of a class of boundary probe preconditioners is examined.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
NASA Astrophysics Data System (ADS)
Wang, Y.; Shu, C.; Shao, J. Y.; Wu, J.; Niu, X. D.
2015-06-01
In this work a mass-conserved diffuse interface method is proposed for simulating incompressible flows of binary fluids with large density ratio. In the method, a mass correction term is introduced into the Cahn-Hilliard equation to compensate the mass losses or offset the mass increases caused by the numerical and modeling diffusion. Since the mass losses or increases are through the phase interfaces and at each time step, their values are very small, to keep mass conservation, mass sources or sinks are introduced and uniformly distributed in the volume of diffuse layer. With the uniform distribution, the mass correction term representing mass sources or sinks is derived analytically by applying mass conservation principle. By including the mass correction, the modified Cahn-Hilliard equation is solved by the fifth-order upwind scheme to capture the phase field of the bindery fluids. The flow field is simulated by the newly-developed multiphase lattice Boltzmann flux solver [20]. The proposed approach is validated by simulating the Laplace law, the merging of two bubbles, Rayleigh-Taylor instability and bubble rising under gravity with density ratio of 1000 and viscosity ratio of 100. Numerical results of interface shapes and flow properties agree well with both analytical solutions and benchmark data in the literature. Numerical results also show that the mass is well-conserved in all cases considered. In addition, it is demonstrated that the mass correction term at each time step is in the order of 10-4 ∼10-5, which is a small number compared with the magnitude of order parameter.
NASA Astrophysics Data System (ADS)
Karsyan, A. Zh.
2014-07-01
A steady problem of a slow axisymmetric flow of a viscous incompressible fluid around an oblate spheroid covered by a viscous film is solved analytically with the use of the Stokes approximation. Surface tension on the interface between the fluids is taken into account. Expressions for velocity components and stream functions are presented. A formula for determining the force action of the incoming flow onto the oblate spheroid is derived.
A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries
Trebotich, D; Miller, G H; Colella, P; Graves, D T; Martin, D F; Schwartz, P O
2004-11-18
We present a stable and convergent method for the computation of flows of DNA-laden fluids in microchannels with complex geometry. The numerical strategy combines a ball-rod model representation for polymers tightly coupled with a projection method for incompressible viscous flow. We use Cartesian grid embedded boundary methods to discretize the fluid equations in the presence of complex domain boundaries. A sample calculation is presented showing flow through a packed array microchannel in 2D.
Volume of fluid (VOF) method for the dynamics of free boundaries
Hirt, C.W.; Nichols, B.D.
1981-01-01
Several methods have been previously used to approximate free boundaries in finite-difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLA-VOF, that uses the VOF technique to track free fluid surfaces.
Computational Fluid Dynamics Library
2005-03-04
CFDLib05 is the Los Alamos Computational Fluid Dynamics LIBrary. This is a collection of hydrocodes using a common data structure and a common numerical method, for problems ranging from single-field, incompressible flow, to multi-species, multi-field, compressible flow. The data structure is multi-block, with a so-called structured grid in each block. The numerical method is a Finite-Volume scheme employing a state vector that is fully cell-centered. This means that the integral form of the conservation lawsmore » is solved on the physical domain that is represented by a mesh of control volumes. The typical control volume is an arbitrary quadrilateral in 2D and an arbitrary hexahedron in 3D. The Finite-Volume scheme is for time-unsteady flow and remains well coupled by means of time and space centered fluxes; if a steady state solution is required, the problem is integrated forward in time until the user is satisfied that the state is stationary.« less
High-order ALE schemes for incompressible capillary flows
NASA Astrophysics Data System (ADS)
Montefuscolo, Felipe; Sousa, Fabricio S.; Buscaglia, Gustavo C.
2014-12-01
The spatial discretization of problems with moving boundaries is considered, incorporating the temporal evolution of not just the mechanical variables, but also of the nodal positions of the moving mesh. The outcome is a system of Differential-Algebraic Equations (DAE) of index 2 or, in the case of inertialess flow, just 1. From the DAE formulation it its possible to define strategies to build schemes of arbitrary accuracy. We introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones. This class of schemes has been the one adopted by the majority of practitioners of Computational Fluid Dynamics up to now. The proposed schemes indeed achieve the design accuracy, and further show stability restrictions that are not significantly more severe than those of popular first order schemes. The numerical experimentation is performed on capillary problems, discretized by both div-stable (P2/P1, P1+/P1) and equal-order (P1/P1, stabilized) finite elements, and incorporating surface tension and triple (contact) line effects.
NASA Astrophysics Data System (ADS)
Prasannakumara, B. C.; Gireesha, B. J.; Manjunatha, P. T.
2015-09-01
A comprehensive numerical study is conducted to investigate the effect of melting on flow and heat transfer of incompressible viscous dusty fluid near two-dimensional stagnation-point flow over a stretching surface, in the presence of thermal radiation, non-uniform heat source/sink and applied magnetic field. Using suitable transformations, the governing nonlinear partial differential equations are transformed into a set of coupled nonlinear ordinary differential equations and then they are solved numerically. The influence of the various interesting parameters on the flow and heat transfer is analyzed and discussed in detail through plotted graphs. Comparison of the present results with existing results is shown and a good agreement is observed. We found that the velocity and temperature fields increase with an increase in the melting process of the stretching sheet.
NASA Astrophysics Data System (ADS)
Attia, H. A.; Abdeen, M. A. M.
2013-03-01
Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.
Variational principles for stochastic fluid dynamics
Holm, Darryl D.
2015-01-01
This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083
MHD stability of incompressible coronal loops with radiative energy loss
NASA Technical Reports Server (NTRS)
An, C.-H.
1983-01-01
Previous studies of the magnetohydrodynamic (MHD) stability of solar coronal loops have not taken into account the effects of radiative energy loss in the energy equation. However, since coronal loops continuously lose energy by radiation and heat conduction, it is important to understand how these energy loss mechanisms affect MHD stability. We investigate the problem assuming that a magnetic loop has cylindrical geometry. As a first step, stability is studied for a localized mode, and the result is applied to a specific equilibrium. We find that the radiative energy loss effect not only changes the growth rate of ideally unstable modes, but also alters the stability boundary predicted by ideal MHD theory.
Statistical properties of three-dimensional two-fluid plasma model
Qaisrani, M. Hasnain; Xia, ZhenWei; Zou, Dandan
2015-09-15
The nonlinear dynamics of incompressible non-dissipative two-fluid plasma model is investigated through classical Gibbs ensemble methods. Liouville's theorem of phase space for each wave number is proved, and the absolute equilibrium spectra for Galerkin truncated two-fluid model are calculated. In two-fluid theory, the equilibrium is built on the conservation of three quadratic invariants: the total energy and the self-helicities for ions and electrons fluid, respectively. The implications of statistic equilibrium spectra with arbitrary ratios of conserved invariants are discussed.
Falkner-Skan Boundary Layer Flow of a Sisko Fluid
NASA Astrophysics Data System (ADS)
Khan, Masood; Shahzad, Azeem
2012-09-01
In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.
Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media
NASA Astrophysics Data System (ADS)
Liu, Qing; He, Ya-Ling
2015-07-01
In this paper, a two-dimensional eight-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy model. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous matrix are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman-Enskog analysis, the incompressible generalized Navier-Stokes equations can be recovered. Numerical simulations of several typical porous flows are carried out to validate the present MRT-LB model. It is found that the present numerical results agree well with the analytical solutions and/or other numerical results reported in the literature.
Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity
Ortiz, A; Puso, M A; Sukumar, N
2009-09-04
Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation.
NASA Astrophysics Data System (ADS)
Serson, D.; Meneghini, J. R.; Sherwin, S. J.
2016-07-01
This paper presents methods of including coordinate transformations into the solution of the incompressible Navier-Stokes equations using the velocity-correction scheme, which is commonly used in the numerical solution of unsteady incompressible flows. This is important when the transformation leads to symmetries that allow the use of more efficient numerical techniques, like employing a Fourier expansion to discretize a homogeneous direction. Two different approaches are presented: in the first approach all the influence of the mapping is treated explicitly, while in the second the mapping terms related to convection are treated explicitly, with the pressure and viscous terms treated implicitly. Through numerical results, we demonstrate how these methods maintain the accuracy of the underlying high-order method, and further apply the discretisation strategy to problems where mixed Fourier-spectral/hp element discretisations can be applied, thereby extending the usefulness of this discretisation technique.
Study of spatial growth of disturbances in an Incompressible Double Shear Layer flow configuration
NASA Astrophysics Data System (ADS)
Natarajan, Hareshram; Jacobs, Gustaaf
2014-11-01
The spatial growth of disturbance within the linear instability regime in an incompressible 2D double shear layer flow configuration is studied by performing a Direct Numerical Simulation. The motivation of this study is to characterize the effect of the presence of an additional shear layer on the spatial growth of a shear layer instability. Initially, a DNS of an incompressible single shear layer is performed and the spatial growth rate of various disturbance frequency modes are validated with Linear Stability Analysis. The addtional shear layer is found to impact the spatial growth rates of the different disturbances and the frequency of the mode with the maximum growth rate is found to be shifted.
Incompressible viscous flow computations for the pump components and the artificial heart
NASA Technical Reports Server (NTRS)
Kiris, Cetin
1992-01-01
A finite-difference, three-dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. In this work, the equations are solved in steadily rotating reference frames by using the steady-state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two. Included in the appendix is a paper on incompressible viscous flow through artificial heart devices with moving boundaries. Time-accurate calculations, such as impeller and diffusor interaction, will be reported in future work.
Thermodynamic stability and unusual strength of ultra-incompressible rhenium nitrides
Zhang, R. F.; Lin, Zhijun; Mao, Ho-kwang; Zhao, Yusheng
2011-02-11
We report on a comprehensive study of thermodynamic and mechanical properties as well as a bond-deformation mechanism on ultra-incompressible Re{sub 2} N and Re{sub 3} N. The introduction of nitrogen into the rhenium lattice leads to thermodynamic instability in Re{sub 2} N at ambient conditions and enhanced incompressibility and strength for both rhenium nitrides. Rhenium nitrides, however, show substantially lower ideal shear strength than hard ReB{sub 2} and superhard c -BN, suggesting that they cannot be intrinsically superhard. An intriguing soft “ionic bond mediated plastic deformation” mechanism is revealed to underline the physical origin of their unusual mechanical strength. These results suggest a need to reformulate the design concept of intrinsically superhard transition-metal nitrides, borides, and carbides.
Velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows
Meir, A.J.
1994-12-31
In this work we discuss some aspects of the velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows. We describe reasonable boundary conditions that should be imposed on the vorticity and a compatibility condition that the vorticity must satisfy. This formulation may give rise to efficient numerical algorithms for approximating solutions of the Stokes problem, which in turn yields an iterative method for approximating solutions of the Navier-Stokes equations.
Convergence of Solutions to the Boltzmann Equation in the Incompressible Euler Limit
NASA Astrophysics Data System (ADS)
SAINT-RAYMOND, LAURE
We consider here the problem of deriving rigorously, for well-prepared initial data and without any additional assumption, dissipative or smooth solutions of the incompressible Euler equations from renormalized solutions of the Boltzmann equation. This completes the partial results obtained by Golse [B. Perthame and L. Desvillettes eds., Series in Applied Mathematics 4 (2000), Gauthier-Villars, Paris] and Lions & Masmoudi [Arch. Rational Mech. Anal. 158 (2001), 195-211].
Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations
Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun
2013-01-01
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888
Stability Analysis of Large-Scale Incompressible Flow Calculations on Massively Parallel Computers
LEHOUCQ,RICHARD B.; ROMERO,LOUIS; SALINGER,ANDREW G.
1999-10-25
A set of linear and nonlinear stability analysis tools have been developed to analyze steady state incompressible flows in 3D geometries. The algorithms have been implemented to be scalable to hundreds of parallel processors. The linear stability of steady state flows are determined by calculating the rightmost eigenvalues of the associated generalize eigenvalue problem. Nonlinear stability is studied by bifurcation analysis techniques. The boundaries between desirable and undesirable operating conditions are determined for buoyant flow in the rotating disk CVD reactor.
INS3D: An incompressible Navier-Stokes code in generalized three-dimensional coordinates
NASA Technical Reports Server (NTRS)
Rogers, S. E.; Kwak, D.; Chang, J. L. C.
1987-01-01
The operation of the INS3D code, which computes steady-state solutions to the incompressible Navier-Stokes equations, is described. The flow solver utilizes a pseudocompressibility approach combined with an approximate factorization scheme. This manual describes key operating features to orient new users. This includes the organization of the code, description of the input parameters, description of each subroutine, and sample problems. Details for more extended operations, including possible code modifications, are given in the appendix.
Least-squares finite element solution of 3D incompressible Navier-Stokes problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.
1992-01-01
Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.
NASA Astrophysics Data System (ADS)
Sun, Y.; Shu, C.; Teo, C. J.; Wang, Y.; Yang, L. M.
2015-11-01
In this paper, a gas-kinetic flux solver (GKFS) is presented for the simulation of incompressible and compressible viscous flows. In this solver, the finite volume method is applied to discretize the Navier-Stokes equations. The inviscid and viscous fluxes at the interface are obtained simultaneously via the gas-kinetic scheme, which locally reconstruct the solution for the continuous Boltzmann equation. Different from the conventional gas-kinetic BGK scheme [1], a simple way is presented in this work to evaluate the non-equilibrium distribution function, which is calculated by the difference of equilibrium distribution functions at the cell interface and its surrounding points. As a consequence, explicit formulations for computing the conservative flow variables and fluxes are simply derived. In particular, three specific schemes are proposed and validated via several incompressible and compressible test examples. Numerical results show that all three schemes can provide accurate numerical results for incompressible flows. On the other hand, Scheme III is much more stable and consistent in simulation of compressible flows.
A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains
NASA Astrophysics Data System (ADS)
Liska, Sebastian; Colonius, Tim
2016-07-01
A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered Cartesian grid. Operations are limited to a finite computational domain through a lattice Green's function technique. This technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators. The differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half-explicit Runge-Kutta scheme for the convective term. A projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme. Linear complexity, fast computation rates, and parallel scalability are achieved using recently developed fast multipole methods for difference equations. The accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings.
Nurijanyan, S.; Vegt, J.J.W. van der; Bokhove, O.
2013-05-15
A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for the linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions, which poses numerical challenges. These challenges concern: (i) discretisation of a divergence-free velocity field; (ii) discretisation of geostrophic boundary conditions combined with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved, for example: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible flows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal flow at solid walls in a weak form and geostrophic tangential flow along the wall; and, (iii) by applying a symplectic time discretisation. We compared our simulations with exact solutions of three-dimensional incompressible flows, in (non) rotating periodic and partly periodic cuboids (Poincaré waves). Additional verifications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls. Finally, a simulation in a tilted rotating tank, yielding more complicated wave dynamics, demonstrates the potential of our new method.
ERIC Educational Resources Information Center
Drazin, Philip
1987-01-01
Outlines the contents of Volume II of "Principia" by Sir Isaac Newton. Reviews the contributions of subsequent scientists to the physics of fluid dynamics. Discusses the treatment of fluid mechanics in physics curricula. Highlights a few of the problems of modern research in fluid dynamics. Shows that problems still remain. (CW)
NASA Technical Reports Server (NTRS)
Hendricks, R. C.; Baron, A. K.; Peller, I. C.
1975-01-01
A FORTRAN IV subprogram called GASP is discussed which calculates the thermodynamic and transport properties for 10 pure fluids: parahydrogen, helium, neon, methane, nitrogen, carbon monoxide, oxygen, fluorine, argon, and carbon dioxide. The pressure range is generally from 0.1 to 400 atmospheres (to 100 atm for helium and to 1000 atm for hydrogen). The temperature ranges are from the triple point to 300 K for neon; to 500 K for carbon monoxide, oxygen, and fluorine; to 600 K for methane and nitrogen; to 1000 K for argon and carbon dioxide; to 2000 K for hydrogen; and from 6 to 500 K for helium. GASP accepts any two of pressure, temperature and density as input conditions along with pressure, and either entropy or enthalpy. The properties available in any combination as output include temperature, density, pressure, entropy, enthalpy, specific heats, sonic velocity, viscosity, thermal conductivity, and surface tension. The subprogram design is modular so that the user can choose only those subroutines necessary to the calculations.
Fluid property measurements study
NASA Technical Reports Server (NTRS)
Devaney, W. E.
1976-01-01
Fluid properties of refrigerant-21 were investigated at temperatures from the freezing point to 423 Kelvin and at pressures to 1.38 x 10 to the 8th power N/sq m (20,000 psia). The fluid properties included were: density, vapor pressure, viscosity, specific heat, thermal conductivity, thermal expansion coefficient, freezing point and bulk modulus. Tables of smooth values are reported.
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Relativistic fluid dynamics. Proceedings.
NASA Astrophysics Data System (ADS)
Anile, A. M.; Choquet-Bruhat, Y.
Contents: 1. Covariant theory of conductivity in ideal fluid or solid media (B. Carter). 2. Hamiltonian techniques for relativistic fluid dynamics and stability theory (D. D. Holm). 3. Covariant fluid mechanics and thermodynamics: an introduction (W. Israel). 4. Relativistic plasmas (H. Weitzner). 5. An improved relativistic warm plasma model (A. M. Anile, S. Pennisi). 6. Relativistic extended thermodynamics II (I. Müller). 7. Relativistic extended thermodynamics: general assumptions and mathematical procedure (T. Ruggeri). 8. Relativistic hydrodynamics and heavy ion reactions (D. Strottman). 9. Some problems in relativistic hydrodynamics (C. G. van Weert).
Lekia, S.D.L. ); Evans, R.D. )
1995-02-01
Equations are derived from first principles for predicting the behavior of sucker-rod pumping systems including the effects of rod and fluid dynamics, and kinematics of the surface pumping unit. Equations are also developed for both incompressible and slightly compressible fluid flow scenarios. The resulting composite rod and fluid dynamic model is solved using the MacCormack Explicit Numerical Scheme. Example problems used to validate this model are presented in a companion paper.
Minimizing the Fluid Used to Induce Fracturing
NASA Astrophysics Data System (ADS)
Boyle, E. J.
2015-12-01
The less fluid injected to induce fracturing means less fluid needing to be produced before gas is produced. One method is to inject as fast as possible until the desired fracture length is obtained. Presented is an alternative injection strategy derived by applying optimal system control theory to the macroscopic mass balance. The picture is that the fracture is constant in aperture, fluid is injected at a controlled rate at the near end, and the fracture unzips at the far end until the desired length is obtained. The velocity of the fluid is governed by Darcy's law with larger permeability for flow along the fracture length. Fracture growth is monitored through micro-seismicity. Since the fluid is assumed to be incompressible, the rate at which fluid is injected is balanced by rate of fracture growth and rate of loss to bounding rock. Minimizing injected fluid loss to the bounding rock is the same as minimizing total injected fluid How to change the injection rate so as to minimize the total injected fluid is a problem in optimal control. For a given total length, the variation of the injected rate is determined by variations in overall time needed to obtain the desired fracture length, the length at any time, and the rate at which the fracture is growing at that time. Optimal control theory leads to a boundary condition and an ordinary differential equation in time whose solution is an injection protocol that minimizes the fluid used under the stated assumptions. That method is to monitor the rate at which the square of the fracture length is growing and adjust the injection rate proportionately.
NASA Astrophysics Data System (ADS)
Heard, Gary Wayne
A new approach to solution-adaptive grid refinement using the finite element method and Flowfield-Dependent Variation (FDV) theory applied to the Navier-Stokes system of equations is discussed. Flowfield-Dependent Variation (FDV) parameters are introduced into a modified Taylor series expansion of the conservation variables, with the Navier-Stokes system of equations substituted into the Taylor series. The FDV parameters are calculated from the current Fowfield conditions, and automatically adjust the resulting equations from elliptic to parabolic to hyperbolic in type to assure solution accuracy in evolving fluid flowfields that may consist of interactions between regions of compressible and incompressible flow, viscous and inviscid flow, and turbulent and laminar flow. The system of equations is solved using an element-by-element iterative GMRES solver with the elements grouped together to allow the element operations to be performed in parallel. The FDV parameters play many roles in the numerical scheme. One of these roles is to control formations of shock wave discontinuities in high speeds and pressure oscillations in low speeds. To demonstrate these abilities, various example problems are shown, including supersonic flows over a flat plate and a compression corner, and flows involving triple shock waves generated on fin geometries for high speed compressible flows. Furthermore, analysis of low speed incompressible flows is presented in the form of flow in a lid-driven cavity at various Reynolds numbers. Another role of the FDV parameters is their use as error indicators for a solution-adaptive mesh. The finite element grid is refined as dictated by the magnitude of the FDV parameters. Examples of adaptive grids generated using the FDV parameters as error indicators are presented for supersonic flow over flat plate/compression ramp combinations in both two and three dimensions. Grids refined using the FDV parameters as error indicators are comparable to ones
Barker, Andrew T. Cai Xiaochuan
2010-02-01
We introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries. The incompressible Navier-Stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls. Our method features an unstructured dynamic mesh capable of modeling complicated geometries, an arbitrary Lagrangian-Eulerian framework that allows for large displacements of the moving fluid domain, monolithic coupling between the fluid and structure equations, and fully implicit time discretization. Simulations based on blood vessel geometries derived from patient-specific clinical data are performed on large supercomputers using scalable Newton-Krylov algorithms preconditioned with an overlapping restricted additive Schwarz method that preconditions the entire fluid-structure system together. The algorithm is shown to be robust and scalable for a variety of physical parameters, scaling to hundreds of processors and millions of unknowns.
NASA Technical Reports Server (NTRS)
Lakshminarayana, B.
1991-01-01
Various computational fluid dynamic techniques are reviewed focusing on the Euler and Navier-Stokes solvers with a brief assessment of boundary layer solutions, and quasi-3D and quasi-viscous techniques. Particular attention is given to a pressure-based method, explicit and implicit time marching techniques, a pseudocompressibility technique for incompressible flow, and zonal techniques. Recommendations are presented with regard to the most appropriate technique for various flow regimes and types of turbomachinery, incompressible and compressible flows, cascades, rotors, stators, liquid-handling, and gas-handling turbomachinery.
Grey-body surface radiation coupled with conduction and convection for general geometries
NASA Astrophysics Data System (ADS)
Engelman, Michael; Jamnia, Mohammad-Ali
1991-11-01
This paper presents a numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level. The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.
Benedetti, G.A.
1990-11-01
When a fluid flows inside a tube, the deformations of the tube can interact with the fluid flowing within it and these dynamic interactions can result in significant lateral motions of the tube and the flowing fluid. The purpose of this report is to examine the dynamic stability of a spinning tube through which an incompressible frictionless fluid is flowing. The tube can be considered as either a hollow beam or a hollow cable. The analytical results can be applied to spinning or stationary tubes through which fluids are transferred; e.g., liquid coolants, fuels and lubricants, slurry solutions, and high explosives in paste form. The coupled partial differential equations are determined for the lateral motion of a spinning Bernoulli-Euler beam or a spinning cable carrying an incompressible flowing fluid. The beam, which spins about an axis parallel to its longitudinal axis and which can also be loaded by a constant axial force, is straight, uniform, simply supported, and rests on a massless, uniform elastic foundation that spins with the beam. Damping for the beam and foundation is considered by using a combined uniform viscous damping coefficient. The fluid, in addition to being incompressible, is frictionless, has a constant density, and flows at a constant speed relative to the longitudinal beam axis. The Galerkin method is used to reduce the coupled partial differential equations for the lateral motion of the spinning beam to a coupled set of 2N, second order, ordinary differential equations for the generalized beam coordinates. By simplifying these equations and examining the roots of the characteristic equation, an analytical solution is obtained for the lateral dynamic instability of the beam (or cable). The analytical solutions determined the minimum critical fluid speed and the critical spin speeds, for a specified fluid speed, in terms of the physical parameters of the system.
Dynamics of multicomponent vesicles in a viscous fluid
Sohn, Jin Sun Tseng, Y-H Li Shuwang Voigt, Axel Lowengrub, John S.
2010-01-01
We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibility of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.
Calculate pipeline flow of compressible fluids
Cochran, T.W.
1996-02-01
When designing plants, performing safety studies, and analyzing plant problems and opportunities, estimates of the flowrate of compressible fluids in pipelines are often required. In fact, the impact of piping systems on process plant economics is so great that the initial investment in piping systems for new installations has been estimated to range from 18 to 61% of the equipment costs and from 7 to 15% of the total cost of the installed plant. Likewise, operating (energy) and maintenance costs for piping systems are significant. Considering this, practical sizing and analysis methods for pipelines are essential. In sizing pipe for incompressible fluids (that is, liquids), the Darcy or Fanning equation is typically used with the appropriate friction-factor correlation. This analysis is greatly simplified by the constant fluid density. However, with compressible fluids (gases and vapors), density, and hence velocity, may change considerably from one end of the pipe to the other. This, along with the limitations imposed by choked flow, complicates the analysis. Here the authors analyze methods for determining compressible fluid flow that are rigorous enough to handle most industrial situations, yet simple enough to be easily programmed into a personal computer. The theory and derivation of the basic equations are described very well in texts by Levenspiel and Saad.
Uniform Bound of the Highest Energy for the Three Dimensional Incompressible Elastodynamics
NASA Astrophysics Data System (ADS)
Lei, Zhen; Wang, Fan
2015-05-01
This article concerns the time growth of Sobolev norms of classical solutions to the three dimensional incompressible isotropic elastodynamics with small initial displacements. Given initial data in for a fixed big integer k, the global well-posedness of this Cauchy problem has been established by Sideris and Thomases in (Commun Pure Appl Math 58(6):750-788, 2005) and (J Hyperbolic Differ Equ 3(4):673-690, 2006, Commun Pure Appl Math 60(12):1707-1730, 2007), where the highest-order generalized energy E k ( t) may have a certain growth in time. Alinhac conjectured that such a growth in time may be a true phenomenon, in (Geometric analysis of hyperbolic differential equations: an introduction, lecture note series: 374. Mathematical Society, London) he proved that E k ( t) is still uniformly bounded in time only for the three dimensional scalar quasilinear wave equation under a null condition. In this paper, we show that the highest-order generalized energy E k ( t) is still uniformly bounded for the three dimensional incompressible isotropic elastodynamics. The equations of incompressible elastodynamics can be viewed as nonlocal systems of wave type and are inherently linearly degenerate in the isotropic case. There are three ingredients in our proof: the first is that we still have a decay rate of when we do the highest energy estimate away from the light cone even though in this case the Lorentz invariance is not available. The second one is that the norm of the good unknowns, in particular , is shown to have a decay rate of near the light cone. The third one is that the pressure is estimated in a novel way as a nonlocal nonlinear term with null structure, as has been recently observed in [16]. The proof employs the generalized energy method of Klainerman, enhanced by weighted L 2 estimates and the ghost weight introduced by Alinhac.
Second-Law Analysis of the Peristaltic Flow of an Incompressible Viscous Fluid in a Curved Channel
NASA Astrophysics Data System (ADS)
Narla, V. K.; Prasad, K. M.; Ramana Murthy, J. V.
2016-03-01
The present investigation extends a consideration of peristaltic flow in curved channels through the second-law analysis. The lubrication approximation is employed to linearize the momentum, energy, and entropy generation rate equations. The stream function and temperature distribution are used to calculate the entropy generation number and the Bejan number. It is shown that the entropy generation rate in a peristaltic pump increases with the occlusion parameter. The entropy generation increases at the upper wall and decreases near the lower wall of the peristaltic channel as the curvature parameter increases. A curved surface acts as a strong source of entropy generation.