Exact Pressure Evolution Equation for Incompressible Fluids
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Aslan, N.; Mond, M.; Nicolini, P.
2008-12-01
An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure without solving the Poisson equation. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. This amounts to transform an elliptic type fluid equation into a suitable hyperbolic equation, a result which usually is reached only by means of an asymptotic formulation. Besides being a still unsolved mathematical problem, the issue is relevant for at least two reasons: a) the proliferation of numerical algorithms in computational fluid dynamics which reproduce the behavior of incompressible fluids only in an asymptotic sense (see below); b) the possible verification of conjectures involving the validity of appropriate equations of state for the fluid pressure. Another possible motivation is, of course, the ongoing quest for efficient numerical solution methods to be applied for the construction of the fluid fields {ρ,V,p}, solutions of the initial and boundary-value problem associated to the incompressible N-S equations (INSE). In this paper we intend to show that an exact solution to this problem can be achieved adopting the approach based on inverse kinetic theory (IKT) recently developed for incompressible fluids by Tessarotto et al. [7, 6, 7, 8, 9]. In particular we intend to prove that the evolution of the fluid fields can be achieved by means of a suitable dynamical system, to be identified with the so-called Navier-Stokes (N-S) dynamical system. As a consequence it is found that the fluid pressure obeys a well-defined evolution equation. The result appears
Approximate methods for equations of incompressible fluid
NASA Astrophysics Data System (ADS)
Galkin, V. A.; Dubovik, A. O.; Epifanov, A. A.
2017-02-01
Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out.
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
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.
NASA Astrophysics Data System (ADS)
Churkina, O. I.; Sheriazdanov, G. B.
1980-12-01
The paper examines a jet flow with variable conductivity in a layer of mixing proportional to the longitudinal velocity. Moreau's (1963) procedure is used to reduce the boundary layer equations to an ordinary differential equation. A first-approximation expression is obtained for the distribution of longitudinal velocity. It is shown that an increase of magnetic interaction leads to an increased deformation of the velocity profile and to a broadening of the mixing region.
NASA Astrophysics Data System (ADS)
Churkina, O. I.; Sheriazdanov, G. B.
1981-04-01
The paper examines a jet flow with variable conductivity in a layer of mixing proportional to the longitudinal velocity. Moreau's (1963) procedure is used to reduce the boundary layer equations to an ordinary differential equation. A first-approximation expression is obtained for the distribution of longitudinal velocity. It is shown that an increase of magnetic interaction leads to an increased deformation of the velocity profile and to a broadening of the mixing region.
Incompressible fluid flows in rapidly rotating cavities
NASA Astrophysics Data System (ADS)
Fournier, Alexandre
The subject of incompressible fluid flows in rapidly rotating cavities, relevant to the dynamics of the Earth's outer core, is addressed here by means of numerical modeling. We recall in the introduction what makes this topic fascinating and challenging, and emphasize the need for new, more flexible numerical approaches in line with the evolution of today's parallel computers. Relying upon recent advances in numerical analysis, we first introduce in chapter 2 a spectral element model of the axisymmetric Navier-Stokes equation, in a rotating reference frame. Comparisons with analytical or published numerical solutions are made for various test problems, which highlight the spectral convergence properties and adaptivity of the approach. In chapter 3, we couple this axisymmetric kernel with a Fourier expansion in longitude in order to describe the dynamics of three-dimensional convection flows. Again, several reference problems are studied. In the specific case of a rotating fluid undergoing thermal convection, this so-called Fourier-spectral element method (FSEM) proves to be as accurate as standard pseudo-spectral techniques. Having this numerical tool anchored on solid grounds, we study in chapter 4 fluid flows driven by thermal convection and precession at the same time. A new topic in the vast field of fluid mechanics, convecto-precessing flows are of particular importance for the Earth's core, and the equations governing their evolution are derived in detail. We solve these using the FSEM; results seem to indicate that to first order, thermal convection and precession ignore each other. We discuss the relevance of these calculations for the Earth's core and outline directions for future related research.
Bose Fluids Above Tc: Incompressible Vortex Fluids and ``Supersolidity''
NASA Astrophysics Data System (ADS)
Anderson, P. W.
2008-05-01
This Letter emphasizes that nonlinear rotational or diamagnetic susceptibility is characteristic of Bose fluids above their superfluid TC’s. For sufficiently slow rotation or, for superconductors, weak B fields, this amounts to an incompressible response to vorticity. The cause is that there are terms missing in the conventionally accepted model Hamiltonian for quantized vortices in the Bose fluid. The resulting susceptibility can account for recent observations of Chan et al. [Nature (London)NATUAS0028-0836 427, 225 (2004); 10.1038/nature02220ScienceSCIEAS0036-8075 305, 1941 (2004)10.1126/science.1101501] on solid He and Ong et al. [Europhys. Lett.EULEEJ0295-5075 72, 451 (2005)10.1209/epl/i2005-10254-4] on cuprate superconductors.
Reference Map Technique for Incompressible Fluid-Structure Interaction Problems
NASA Astrophysics Data System (ADS)
Rycroft, Chris; Wu, Chen-Hung; Yu, Yue; Kamrin, Ken
2016-11-01
We present a fully Eulerian approach to simulate soft structures immersed in an incompressible fluid. The flow is simulated on a fixed grid using a second order projection method to solve the incompressible Navier-Stokes equations, and the fluid-structure interfaces are modeled using the level set method. By introducing a reference map variable to model finite-deformation constitutive relations in the structure on the same grid as the fluid, the interfacial coupling is highly simplified. This fully Eulerian approach provides a computationally efficient alternative to moving mesh approaches. Example simulations featuring many-body contacts and flexible swimmers will be presented.
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.
Kinetic model of turbulence in an incompressible fluid
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1978-01-01
A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.
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.
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.
Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids
NASA Astrophysics Data System (ADS)
Marsden, Jerrold; Weinstein, Alan
1983-05-01
This paper is a study of incompressible fluids, especially their Clebsch variables and vortices, using symplectic geometry and the Lie-Poisson structure on the dual of a Lie algebra. Following ideas of Arnold and others it is shown that Euler's equations are Lie-Poisson equations associated to the group of volume-preserving diffeomorphisms. The dual of the Lie algebra is seen to be the space of vortices, and Kelvin's circulation theorem is interpreted as preservation of coadjoint orbits. In this context, Clebsch variables can be understood as momentum maps. The motion of N point vortices is shown to be identifiable with the dynamics on a special coadjoint orbit, and the standard canonical variables for them are a special kind of Clebsch variables. Point vortices with cores, vortex patches, and vortex filaments can be understood in a similar way. This leads to an explanation of the geometry behind the Hald-Beale-Majda convergence theorems for vorticity algorithms. Symplectic structures on the coadjoint orbits of a vortex patch and filament are computed and shown to be closely related to those commonly used for the KdV and the Schrödinger equations respectively.
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).
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
Young Measures Generated by Ideal Incompressible Fluid Flows
NASA Astrophysics Data System (ADS)
Székelyhidi, László; Wiedemann, Emil
2012-10-01
In their seminal paper, D iP erna and M ajda (Commun Math Phys 108(4):667-689, 1987) introduced the notion of a measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.
NASA Astrophysics Data System (ADS)
Baishemirov, Zharasbek; Tang, Jian-Gang; Imomnazarov, Kholmatzhon; Mamatqulov, Musajon
2016-12-01
The solution to equations of two viscous homogeneous incompressible fluid media with the pressure phase equilibrium in the case of a constant phase is obtained. The influence of the physical phase densities, saturation, volume and viscosity of substances constituting a two-phase continuum in the flow velocity and pressure is shown. Also, the solution admitting a limiting transition to the known solution of the problem of a flow of a viscous incompressible single-phase medium is constructed.
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.
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…
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.
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.
PDM performance Test Results and Preliminary Analysis: Incompressible and Compressible Fluids
Dreesen, D.S.; Gruenhagan, E.; Cohen, J.C.; Moran, D.W.
1999-02-01
Three, small diameter, Moineau, positive displacement (drilling) motors (PDMs) were dynamometer tested using water, air-water mist, air-water foam, and aerated water. The motors included (1) a 1.5-inch OD, single-lobe mud motor; (2) a 1.69-inch OD, 5:6 multi-lobe mud motor; and (3) a 1.75-inch OD, 5:6 multi-lobe air motor. This paper describes the test apparatus, procedures, data analysis, and results. Incompressible and compressible fluid performance are compared; linear performance, predicted by a positive displacement motor model, is identified where it occurs. Preliminary results and conclusions are (1) the performance of all three motors is accurately modeled using a two-variable, linear model for incompressible fluid and (2) the model was not successfully adapted to model compressible fluid performance.
Small Moving Rigid Body into a Viscous Incompressible Fluid
NASA Astrophysics Data System (ADS)
Lacave, Christophe; Takahashi, Takéo
2017-03-01
We consider a single disk moving under the influence of a two dimensional viscous fluid and we study the asymptotic as the size of the solid tends to zero. If the density of the solid is independent of ɛ, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal L p - L q decay estimates of the semigroup associated to the fluid-rigid body system and to a fixed point argument. Next, we will deduce the convergence to the solution of the Navier-Stokes equations in R2.
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.
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.
1977-01-01
Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Together with the hydrostatic effects that were analyzed in an earlier paper, 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.
NASA Astrophysics Data System (ADS)
Xu, Li; Zhang, Ping; Zhang, Zhifei
2013-06-01
Motivated by Beale (Commun Pure Appl Math 34:359-392, 1981; Arch Ration Mech Anal 84:307-352, 1983/1984), we investigate the global well-posedness of a free boundary problem of a three-dimensional incompressible viscoelastic fluid system in an infinite strip and with surface tension on the upper free boundary, provided that the initial data is sufficiently close to the equilibrium state.
Zu, Y Q; He, S
2013-04-01
A lattice Boltzmann model (LBM) is proposed based on the phase-field theory to simulate incompressible binary fluids with density and viscosity contrasts. Unlike many existing diffuse interface models which are limited to density matched binary fluids, the proposed model is capable of dealing with binary fluids with moderate density ratios. A new strategy for projecting the phase field to the viscosity field is proposed on the basis of the continuity of viscosity flux. The new LBM utilizes two lattice Boltzmann equations (LBEs): one for the interface tracking and the other for solving the hydrodynamic properties. The LBE for interface tracking can recover the Chan-Hilliard equation without any additional terms; while the LBE for hydrodynamic properties can recover the exact form of the divergence-free incompressible Navier-Stokes equations avoiding spurious interfacial forces. A series of 2D and 3D benchmark tests have been conducted for validation, which include a rigid-body rotation, stationary and moving droplets, a spinodal decomposition, a buoyancy-driven bubbly flow, a layered Poiseuille flow, and the Rayleigh-Taylor instability. It is shown that the proposed method can track the interface with high accuracy and stability and can significantly and systematically reduce the parasitic current across the interface. Comparisons with momentum-based models indicate that the newly proposed velocity-based model can better satisfy the incompressible condition in the flow fields, and eliminate or reduce the velocity fluctuations in the higher-pressure-gradient region and, therefore, achieve a better numerical stability. In addition, the test of a layered Poiseuille flow demonstrates that the proposed scheme for mixture viscosity performs significantly better than the traditional mixture viscosity methods.
NASA Technical Reports Server (NTRS)
Beatty, T. D.
1975-01-01
A theoretical method is presented for the computation of the flow field about an axisymmetric body operating in a viscous, incompressible fluid. A potential flow method was used to determine the inviscid flow field and to yield the boundary conditions for the boundary layer solutions. Boundary layer effects in the forces of displacement thickness and empirically modeled separation streamlines are accounted for in subsequent potential flow solutions. This procedure is repeated until the solutions converge. An empirical method was used to determine base drag allowing configuration drag to be computed.
Topological selection mechanism for conservation laws in incompressible stratified Euler fluids
NASA Astrophysics Data System (ADS)
Ortenzi, Giovanni; Chen, Shengqian; Camassa, Roberto; Falqui, Gregorio; Pedroni, Marco
2014-11-01
With his Kaffeeloeffel thought (``gedanken'') experiment, in 1910 Klein suggested that a topological change of an ideal fluid's domain can provide a mechanism for breaking the conservation of circulation enforced by Kelvin's Theorem. In our study, we extend this idea to more general conservation laws and explore the role of topological properties in the dynamics of an incompressible Euler fluid with stratification. In particular, we show that topologically non-trivial configurations of stratified fluid domains generate selection mechanisms for conserved quantities other than vorticity. In the talk we concentrate on the simple example of an air-water system in a channel, which encapsulates all the main points of these selection mechanisms. Among other examples, we show that the connection properties of the air domain affect total horizontal momentum conservation, despite the translational invariance of the system and its consequences by Noether's Theorem.
NASA Astrophysics Data System (ADS)
Mondal, Pranab Kumar; DasGupta, Debabrata; Bandopadhyay, Aditya; Ghosh, Uddipta; Chakraborty, Suman
2015-03-01
We consider electrically driven dynamics of an incompressible binary fluid, with contrasting densities and viscosities of the two phases, flowing through narrow fluidic channel with walls with predefined surface wettabilities. Through phase field formalism, we describe the interfacial kinetics in the presence of electro-hydrodynamic coupling and address the contact line dynamics of the two-fluid system. We unveil the interplay of the substrate wettability and the contrast in the fluid properties culminating in the forms of two distinct regimes—interface breakup regime and a stable interface regime. Through a parametric study, we demarcate the effect of the density and viscosity contrasts along with the electrokinetic parameters such as the surface charge and ionic concentration on the underlying contact-line-dynamics over interfacial scales.
A fast pressure-correction method for incompressible two-fluid flows
NASA Astrophysics Data System (ADS)
Dodd, Michael S.; Ferrante, Antonino
2014-09-01
We have developed a new pressure-correction method for simulating incompressible two-fluid flows with large density and viscosity ratios. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation, which can be solved with an FFT-based, fast Poisson solver. This reduction is achieved by splitting the variable density pressure gradient term in the governing equations. The validity of this splitting is demonstrated from our numerical tests, and it is explained from a physical viewpoint. In this paper, the new pressure-correction method is coupled with a mass-conserving volume-of-fluid method to capture the motion of the interface between the two fluids but, in general, it could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking. First, we verified the new pressure-correction method using the capillary wave test-case up to density and viscosity ratios of 10,000. Then, we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value. Next, the method is shown to be second-order accurate in space and time independent of the VoF method, and it conserves mass, momentum, and kinetic energy in the inviscid limit. Also, we show that for solving the two-fluid Navier-Stokes equations, the method is 10-40 times faster than the standard pressure-correction method, which uses multigrid to solve the variable coefficient Poisson equation. Finally, we show that the method is capable of performing fully-resolved direct numerical simulation (DNS) of droplet-laden isotropic turbulence with thousands of droplets using a computational mesh of 10243 points.
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.
Swimming of a deformable slab in a viscous incompressible fluid with inertia
NASA Astrophysics Data System (ADS)
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.
The capturing of free surfaces in incompressible multi-fluid flows
NASA Astrophysics Data System (ADS)
Pan, Dartzi; Chang, Chih-Hao
2000-05-01
By treating it as a contact discontinuity in the density field, a free surface between two immiscible fluids can be automatically captured by the enforcement of conservation laws. A surface-capturing method of this kind requires no special tracking or fitting treatment for the free surface, thereby offering the advantage of algorithm simplicity over the surface-tracking or the surface-fitting method. A surface-capturing method based on a new multi-fluid incompressible Navier-Stokes formulation is developed. It is applied to a variety of free-surface flows, including the Rayleigh-Taylor instability problem, the ship waves around a Wigley hull and a model bubble-rising problem to demonstrate the validity and versatility of the present method. Copyright
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.
2016-12-01
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.
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.
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.
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].
Atabek, H. B.; Lew, H. S.
1966-01-01
To have a better understanding of the flow of blood in arteries a theoretical analysis of the pressure wave propagation through a viscous incompressible fluid contained in an initially stressed tube is considered. The fluid is assumed to be Newtonian. The tube is taken to be elastic and isotropic. The analysis is restricted to tubes with thin walls and to waves whose wavelengths are very large compared with the radius of the tube. It is further assumed that the amplitude of the pressure disturbance is sufficiently small so that nonlinear terms of the inertia of the fluid are negligible compared with linear ones. Both circumferential and longitudinal initial stresses are considered; however, their origins are not specified. Initial stresses enter equations as independent parameters. A frequency equation, which is quadratic in the square of the propagation velocity is obtained. Two out of four roots of this equation give the velocity of propagation of two distinct outgoing waves. The remaining two roots represent incoming waves corresponding to the first two waves. One of the waves propagates more slowly than the other. As the circumferential and/or longitudinal stress of the wall increases, the velocity of propagation and transmission per wavelength of the slower wave decreases. The response of the fast wave to a change in the initial stress is on the opposite direction. PMID:19210972
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.
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)
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)
Tessarotto, M.; Ellero, M.; Sarmah, D.; Nicolini, P.
2008-12-01
Extending the statistical approach proposed in a parallel paper [1], purpose of this work is to propose a stochastic inverse kinetic theory for small-scale hydrodynamic turbulence based on the introduction of a suitable local phase-space probability density function (pdf). In particular, we pose the problem of the construction of Fokker-Planck kinetic models of hydrodynamic turbulence. The approach here adopted is based on the so-called IKT approach (inverse kinetic theory), developed by Tessarotto et al. (2004-2008) which permits an exact phase-space description of incompressible fluids based on the adoption of a local pdf. We intend to show that for prescribed models of stochasticity the present approach permits to determine uniquely the time evolution of the stochastic fluid fields. The stochastic-averaged local pdf is shown to obey a kinetic equation which, although generally non-Markovian, locally in velocity-space can be approximated by means of a suitable Fokker-planck kinetic equation. As a side result, the same pdf is proven to have generally a non-Gaussian behavior.
A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids
NASA Astrophysics Data System (ADS)
Krishna Kishor, D.; Gopalakrishnan, S.; Ganguli, Ranjan
2010-04-01
A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test on a standard rectangular rigid tank partially filled with liquid. The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence. The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements, and the obtained results are compared with available results in the published literature.
Hydrodynamical force on a solid sphere in an incompressible inviscid fluid
NASA Astrophysics Data System (ADS)
Alarki, Rabab; Palaniappan, D.
2016-11-01
Simple analytic results for the hydrodynamical force exerted on a rigid sphere of radius a placed in singularity driven potential flows are determined. The motion induced singularities considered are (i) a source; (ii) a dipole; and (iii) a vortex ring, located at (0 , 0 , c) , where c > a . The calculation is based on the exact solutions of the classical Neummann boundary value problem for a spherical boundary in inviscid hydrodynamics. The expressions for the force due to source and dipole are found to be algebraic in a/c, the radius-location ratio, while the result for a vortex ring is expressed in an integral form. Our analysis shows that the force due to a tangentially oriented initial dipole is less than that of a dipole in the radial direction. Graphical illustration are presented demonstrating the variation of the force with respect to a/c. The results may also be of intersect in the study of superfluids - treated as incompressible fluids - such as liquid helium or the interior of a neutron star. Supported by King Abdullah Foreign Scholarship Proram, Saudi Ministry of Education.
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.
NASA Astrophysics Data System (ADS)
Georgievskii, D. V.
2007-06-01
physical parameter α can be imposed. These variations imply perturbations of the tensor function itself. The components of such perturbations linear and quadratic in α are determined. In each of the approximations, we write out a closed system of equations consisting of the equations of motion (linear in the variables of the respective approximation) and the incompressibility condition. We analyze tensor-linear functions with arbitrary scalar rheology inmore detail. Materials with such constitutive relations include non-Newtonian viscous fluids and viscoplastic materials. Viscoplastic materials are characterized by the existence of rigidity zones, where the stress intensity is less than the yield strength. We derive equations for the boundaries of the rigidity zones in the perturbed motion, in particular, for the case in which the unperturbed medium is a viscous Newtonian fluid. Throughout the paper, index-free notation is used.
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 Technical Reports Server (NTRS)
Sohn, Jeong L.
1988-01-01
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.
Steady incompressible potential flow around lifting bodies immersed in a fluid. M.S. Thesis
NASA Technical Reports Server (NTRS)
Chiuchiolo, E. A.
1974-01-01
The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).
NASA Astrophysics Data System (ADS)
Cochran, Robert James
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 Q-2Q1 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 (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. Attempts to extend the formulation beyond the flat channel were not successful due to oscillatory
A Multiblock Approach for Calculating Incompressible Fluid Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Sheng, Chunhua; Whitfield, David L.; Anderson, W. Kyle
1997-01-01
A multiblock approach is presented for solving two-dimensional incompressible turbulent flows on unstructured grids. The artificial compressibility form of the governing equations is solved by a vertex-centered, finite-volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work introduces a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements while not increasing the CPU time. Results presented in this work shows that the current multiblock algorithm requires 70% less memory than the single block algorithm.
Uma, B; Radhakrishnan, R; Eckmann, D M; Ayyaswamy, P S
2013-01-01
A hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed in simulating the thermal motion of the particle suspended in the fluid contained in a cylindrical vessel. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obeys Stokes-Einstein and Stokes-Einstein-Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery.
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.
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.
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
NASA Astrophysics Data System (ADS)
Zhou, J. X.; Shen, X.; Yin, Y. J.; Guo, Z.; Wang, H.
2015-06-01
In this paper, Gas-liquid two phase flow mathematic models of incompressible fluid were proposed to explore the feature of fluid under certain centrifugal force in vertical centrifugal casting (VCC). Modified projection-level-set method was introduced to solve the mathematic models. To validate the simulation results, two methods were used in this study. In the first method, the simulation result of basic VCC flow process was compared with its analytic solution. The relationship between the numerical solution and deterministic analytic solution was presented to verify the correctness of numerical algorithms. In the second method, systematic water simulation experiments were developed. In this initial experiment, special experimental vertical centrifugal device and casting shapes were designed to describe typical mold-filling processes in VCC. High speed camera system and data collection devices were used to capture flow shape during the mold-filling process. Moreover, fluid characteristic at different rotation speed (from 40rpm, 60rpmand 80rpm) was discussed to provide comparative resource for simulation results. As compared with the simulation results, the proposed mathematical models could be proven and the experimental design could help us advance the accuracy of simulation and further studies for VCC.
LeČOns Sur Les Ondes De Gravité Des Fluides Incompressibles
NASA Astrophysics Data System (ADS)
van den Dungen, F. H.
Le 3 Janvier 1814 au moment où les Alliés franchissant le Rhin allaient entamer la campagne de France, la classe des Sciences de l'Institut de France proposait comme sujet du grand prix de mathématique à décerner en Janvier 1816 la question suivante: "La théorie de la propagation des ondes à la surface d'un fluide pesant d'une profondeur infinie".
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.
Incompressible fluid flow and heat transfer through a nonsaturated porous medium
NASA Astrophysics Data System (ADS)
Saldanha da Gama, R. M.; Martins-Costa, M. L.
This work studies a nonsaturated flow and the heat transfer associated phenomenon of a newtonian fluid through a rigid porous matrix, using a mixture theory approach in its modelling. The mixture consists of three overlapping continuous constituents: a solid (porous medium), a liquid and an inert gas, included to account for the compressibility of the system as a whole. A set of four nonlinear partial differential equations describe the problem whose hydrodynamical part is approximated by means of a Glimm's scheme combined with an operator splitting technique.
NASA Astrophysics Data System (ADS)
Begue, C.; Periaux, J.; Perrier, P.; Pouletty, C.
1985-11-01
A self-adaptive finite-element method, coupled to a homogenization model of turbulence, is presented for the numerical simulation of unsteady turbulent flow of viscous fluids in air intakes. The nonlinear subproblem due to the convection is solved by an iterative algorithm, and the linear Stokes subproblem due to the diffusion is solved by a Hood-Taylor type iterative algorithm. An efficient and precise minielement approximation is used, and the adaptive mesh procedure is automatic in the calculation, using the physical criteria of rotation and divergence to determine the submeshing zones. The numerical method is demonstrated for the example of three-dimensional laminar flow around and in air intake at a Reynolds number of 200.
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.
Fluid volume displacement at the oval and round windows with air and bone conduction stimulation
NASA Astrophysics Data System (ADS)
Stenfelt, Stefan; Hato, Naohito; Goode, Richard L.
2004-02-01
The fluids in the cochlea are normally considered incompressible, and the fluid volume displacement of the oval window (OW) and the round window (RW) should be equal and of opposite phase. However, other channels, such as the cochlear and vestibular aqueducts, may affect the fluid flow. To test if the OW and RW fluid flows are equal and of opposite phase, the volume displacement was assessed by multiple point measurement at the windows with a laser Doppler vibrometer. This was done during air conduction (AC) stimulation in seven fresh human temporal bones, and with bone conduction (BC) stimulation in eight temporal bones and one human cadaver head. With AC stimulation, the average volume displacement of the two windows is within 3 dB, and the phase difference is close to 180° for the frequency range 0.1 to 10 kHz. With BC stimulation, the average volume displacement difference between the two windows is greater: below 2 kHz, the volume displacement at the RW is 5 to 15 dB greater than at the OW and above 2 kHz more fluid is displaced at the OW. With BC stimulation, lesions at the OW caused only minor changes of the fluid flow at the RW.
NASA Astrophysics Data System (ADS)
Dolai, Bivash; Prajapati, R. P.; Chhajlani, R. K.
2016-11-01
We investigate the effect of different dust flow velocities and two dimensional magnetic fields on the combined Kelvin-Helmholtz instability (KHI) and Rayleigh-Taylor instability (RTI) of two superimposed incompressible dusty fluids. A single fluid reduced dusty magnetohydrodynamic model is obtained for the three component magnetized incompressible dusty plasma, and it is assumed that a plane interface of infinite boundaries separates heavy and light dusty fluids at z = 0. The general dispersion relations for RT and KH configurations are obtained using appropriate boundary conditions and discussed in the case of equal and different dust fluid flow velocities. In the case of the stable RT configuration, we find that the condition of RTI depends upon both longitudinal and transverse magnetic field components and relative dust flow velocity. In the case of the KH configuration, the effect of magnetic field and relative dust flow velocity is observed and it is shown that dust flow velocity must be larger than a particular value of Alfven speed in order to excite KHI. Numerical calculations have been performed to illustrate the linear growth rates of RTI and KHI in both magnetized and unmagnetized dusty plasmas. We observe that the magnetic field has stabilizing whereas the dust Atwood number has destabilizing influence on the growth rate of RTI. The different dust flow velocities have destabilizing whereas magnetic field has stabilizing influence on the growth rate of KHI in dusty plasmas. The dust Mach number yields a stabilizing influence on the linear growth rate of KHI.
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.
Dharodi, Vikram; Das, Amita Patel, Bhavesh; Kaw, Predhiman
2016-01-15
The strongly coupled dusty plasma has often been modelled by the Generalized Hydrodynamic (GHD) model used for representing visco-elastic fluid systems. The incompressible limit of the model which supports transverse shear wave mode is studied in detail. In particular, dipole structures are observed to emit transverse shear waves in both the limits of sub- and super-luminar propagation, where the structures move slower and faster than the phase velocity of the shear waves, respectively. In the sub-luminar limit the dipole gets engulfed within the shear waves emitted by itself, which then backreacts on it and ultimately the identity of the structure is lost. However, in the super-luminar limit the emission appears like a wake from the tail region of the dipole. The dipole, however, keeps propagating forward with little damping but minimal distortion in its form. A Poynting-like conservation law with radiative, convective, and dissipative terms being responsible for the evolution of W, which is similar to “enstrophy” like quantity in normal hydrodynamic fluid systems, has also been constructed for the incompressible GHD equations. The conservation law is shown to be satisfied in all the cases of evolution and collision amidst the nonlinear structures to a great accuracy. It is shown that monopole structures which do not move at all but merely radiate shear waves, the radiative term, and dissipative losses solely contribute to the evolution of W. The dipolar structures, on the other hand, propagate in the medium and hence convection also plays an important role in the evolution of W.
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.
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.
NASA Astrophysics Data System (ADS)
Huang, Jingchi; Paicu, Marius; Zhang, Ping
2013-08-01
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data {a_0 in L^infty ({R}^d), u_0 = (u_0^h, u_0^d) in dot{B}^{-1+d/p}_{p, r} ({R}^d)}, which satisfy {(μ \\| a_0 \\|_{L^infty} + \\|u_0^h\\|_{dot{B}^{-1+d/p}_{p, r}}) exp(C_r{μ^{-2r}}\\|u_0^d\\|_{dot{B}^{-1+d/p}_{p,r}}^{2r}) ≤q c_0μ} for some positive constants c 0, C r and 1 < p < d, 1 < r < ∞. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity fields. Furthermore, with additional regularity assumptions on the initial velocity or on the initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L p ( L q ) regularity theorem for the heat kernel plays an essential role in this context.
Thermal conductivity of the Lennard-Jones chain fluid model
NASA Astrophysics Data System (ADS)
Galliero, Guillaume; Boned, Christian
2009-12-01
Nonequilibrium molecular dynamics simulations have been performed to estimate, analyze, and correlate the thermal conductivity of a fluid composed of short Lennard-Jones chains (up to 16 segments) over a large range of thermodynamic conditions. It is shown that the dilute gas contribution to the thermal conductivity decreases when the chain length increases for a given temperature. In dense states, simulation results indicate that the residual thermal conductivity of the monomer increases strongly with density, but is weakly dependent on the temperature. Compared to the monomer value, it has been noted that the residual thermal conductivity of the chain was slightly decreasing with its length. Using these results, an empirical relation, including a contribution due to the critical enhancement, is proposed to provide an accurate estimation of the thermal conductivity of the Lennard-Jones chain fluid model (up to 16 segments) over the domain 0.8≤T∗≤6 and 0≤ρ∗≤1 . Additionally, it has been noted that all reduced thermal conductivity values of the Lennard-Jones chain fluid model merge on the same “universal” curve when plotted as a function of the excess entropy. Furthermore, it is shown that the reduced configurational thermal conductivity of the Lennard-Jones chain fluid model is approximately proportional to the reduced excess entropy for all fluid states and all chain lengths.
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.
An Investigation of Magneto-Acoustic Effects in Conductive Fluids.
1979-12-01
California AN INVE STIGATION OF #AGNETO-# COUSTIC EFFECTS IN CONDUCTIVE FLUIDS$ by /0Robert Franz/Klaus Thesis Advisor: P.H. Moose Approved for public...NUMIUEN OEM=. 112: L RECIPIENT’S CATALOG MUMER ,. TvITLI ad a ..mbo) L TtP oF REPORT6, P.moo CovEMo0 An Investigation of Magneto-Acoustic Master’s...Thesis; Effects in Conductive Fluids December 1979 6. PERPOUMmD ORe. REPORT NumaI 7. AUTNOR A ) A 0 ANNUM N Robert Franz Klaus 9. P019PPa"ING oNI N0ZATION
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.
NASA Astrophysics Data System (ADS)
Jia, Shu-Liang; Gao, Yi-Tian; Hu, Lei; Huang, Qian-Min; Hu, Wen-Qiang
2017-02-01
Under investigation in this paper is a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid. With the aid of the bilinear form, Nth-order soliton-like solutions are obtained via the Pffafian method, rational solutions are derived with the ansätz method and periodic wave solutions are constructed via the Riemann theta function. The analytic solutions obtained via the Pffafian method are similar to the kink solitons, while, the interaction regions with little peaks are different from those of the usual kink solitons. The rational solutions which have one upper lump and one down deep hole are the bright-dark solitary wave solutions. For the rational solutions which combine the kink solitary wave with breather-like wave, asymptotic behaviors show that the breather-like wave disappears with the evolution of t. Relations between the one-soliton solutions and one-periodic wave solutions are analysed, which exhibit the asymptotic behaviors of the periodic waves.
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.
Acoustic waves superimposed on incompressible flows
NASA Technical Reports Server (NTRS)
Hodge, Steve
1990-01-01
The use of incompressible approximations in deriving solutions to the Lighthill wave equation was investigated for problems where an analytical solution could be found. A particular model problem involves the determination of the sound field of a spherical oscillating bubble in an ideal fluid. It is found that use of incompressible boundary conditions leads to good approximations in the important region of high acoustic wave number.
Simultaneous Rheoelectric Measurements of Strongly Conductive Complex Fluids
NASA Astrophysics Data System (ADS)
Helal, Ahmed; Divoux, Thibaut; McKinley, Gareth H.
2016-12-01
We introduce an modular fixture designed for stress-controlled rheometers to perform simultaneous rheological and electrical measurements on strongly conductive complex fluids under shear. By means of a nontoxic liquid metal at room temperature, the electrical connection to the rotating shaft is completed with minimal additional mechanical friction, allowing for simultaneous stress measurements at values as low as 1 Pa. Motivated by applications such as flow batteries, we use the capabilities of this design to perform an extensive set of rheoelectric experiments on gels formulated from attractive carbon-black particles, at concentrations ranging from 4 to 15 wt %. First, experiments on gels at rest prepared with different shear histories show a robust power-law scaling between the elastic modulus G0' and the conductivity σ0 of the gels—i.e., G0'˜σ0α, with α =1.65 ±0.04 , regardless of the gel concentration. Second, we report conductivity measurements performed simultaneously with creep experiments. Changes in conductivity in the early stage of the experiments, also known as the Andrade-creep regime, reveal for the first time that plastic events take place in the bulk, while the shear rate γ ˙ decreases as a weak power law of time. The subsequent evolution of the conductivity and the shear rate allows us to propose a local yielding scenario that is in agreement with previous velocimetry measurements. Finally, to establish a set of benchmark data, we determine the constitutive rheological and electrical behavior of carbon-black gels. Corrections first introduced for mechanical measurements regarding shear inhomogeneity and wall slip are carefully extended to electrical measurements to accurately distinguish between bulk and surface contributions to the conductivity. As an illustrative example, we examine the constitutive rheoelectric properties of five different grades of carbon-black gels and we demonstrate the relevance of this rheoelectric apparatus as a
NASA Astrophysics Data System (ADS)
Zheng, L. C.; Zhang, X. X.; Boubaker, K.; Yücel, U.; Gargouri-Ellouze, E.; Yıldırım, A.
2011-08-01
In this paper, a new model is proposed for the heat transfer characteristics of power law non- Newtonian fluids. The effects of power law viscosity on temperature field were taken into account by assuming that the temperature field is similar to the velocity field with modified Fourier's law of heat conduction for power law fluid media. The solutions obtained by using Boubaker Polynomials Expansion Scheme (BPES) technique are compared with those of the recent related similarity method in the literature with good agreement to verify the protocol exactness.
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.
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 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.
Metastable Lennard-Jones fluids. II. Thermal conductivity.
Baidakov, Vladimir G; Protsenko, Sergey P
2014-06-07
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 → ∞.
Thermal conductivity measurement of fluids using the 3ω method
NASA Astrophysics Data System (ADS)
Lee, Seung-Min
2009-02-01
We have developed a procedure to measure the thermal conductivity of dielectric liquids and gases using a steady state ac hot wire method in which a thin metal wire is used as a heater and thermometer. The temperature response of the heater wire was measured in a four-probe geometry using an electronic circuit developed for the conventional 3ω method. The measurements have been performed in the frequency range from 1 mHz to 1 kHz. We devised a method to transform the raw data into well-known linear logarithmic frequency dependence plot. After the transformation, an optimal frequency region of the thermal conductivity data was clearly determined as has been done with the data from thin metal film heater. The method was tested with air, water, ethanol, mono-, and tetraethylene glycol. Volumetric heat capacity of the fluids was also calculated with uncertainty and the capability as a probe for metal-liquid thermal boundary conductance was discussed.
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.
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.
Intracranial pressure and cerebrospinal fluid outflow conductance in healthy subjects.
Albeck, M J; Børgesen, S E; Gjerris, F; Schmidt, J F; Sørensen, P S
1991-04-01
Conductance of cerebrospinal fluid (CSF) outflow (Cout) is an important parameter to be considered in patients with CSF circulation abnormalities. In patients with normal-pressure hydrocephalus it is the single most important parameter in determining if the patient needs CSF shunting. The lower normal limit for Cout has been estimated from the effect of shunting in patients with normal-pressure hydrocephalus, from patients retrospectively reevaluated after recovering from illness, and from patients with known abnormalities in the brain or the CSF system. The true value of Cout in normal individuals, however, has hitherto not been reported. In the present study, Cout has been measured by a lumbar infusion test in eight young volunteers with no suspicion of disease. The mean intracranial pressure (ICP) was 11 mm Hg and a linear relationship was found between CSF absorption and ICP. The mean Cout was 0.11 ml/min/mm Hg and the lower 95% confidence level was 0.10 ml/min/mm Hg. These values are in accordance with those obtained from previous studies.
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.
Inverse Kinetic Theory for Incompressible Thermofluids
NASA Astrophysics Data System (ADS)
Cremaschini, C.; Tessarotto, M.
2008-12-01
An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed fluid. From the mathematical viewpoint this involves the formal description of a fluid by means of a classical dynamical system which advances in time the relevant fluid fields. The possibility of defining an IKT for the 3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero et al., 2004-2007) raises the interesting question whether the theory can be applied also to thermofluids, in such a way to satisfy also the second principle of thermodynamics. The goal of this paper is to prove that such a generalization is actually possible, by means of a suitable extended phase-space formulation. We consider, as a reference test, the case of non-isentropic incompressible thermofluids, whose dynamics is described by the Fourier and the incompressible Navier-Stokes equations, the latter subject to the conditions of validity of the Boussinesq approximation.
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.
a Combustion Model for Incompressible Flows
NASA Astrophysics Data System (ADS)
Calzada, Maria Eugenia
We study the flow of a pre-mixed, reactive, incompressible, viscous fluid, using a combination of vortex methods and a flame propagation algorithm based on Huyghens' principle. The random vortex methods are lagrangian methods used to resolve the motion of incompressible fluids regulated by the Navier -Stokes equations. They are best suited for flows at high Reynolds numbers. Detailed description of the vortex blobs, and vortex sheets methods is given together with the presentation of a hybrid vortex method that relates the two. The combustion part of the problem is modeled by a variation of the SLIC (Simple Line Interface Calculation) algorithm, that involves the use of a flame dictionary which contains flame speeds and preheat thicknesses. The combined algorithms are tested on a cold flat late with different free stream velocities. The numerical results show the effects of cold boundaries, turbulence, and exothermicity on the burning process.
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.
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.
Analytical study on two-phase MHD flow of electrically conducting magnetic fluid
Okubo, Masaaki; Ishimoto, Jun; Nishiyama, Hideya; Kamiyama, Shinichi
1994-01-01
An energy conversion system using magnetic fluids proposed by Resler and Rosensweig was based on the principle that the magnetization of magnetic fluids changes with temperature. However, significant results have not been obtained up to the present. To overcome this limit and to increase the acceleration of fluid flow the authors have contributed a new energy conversion system using two-phase flow produced by heat addition. This idea came from the two-phase liquid-metal MHD power generation system proposed by Petrick and Branover. If temperature sensitive magnetic fluids are used, such a system can produce a larger force than conventional systems because the properties of apparent magnetization change not only by temperature rise but also by gas inclusion. In the present paper, an analytical study is extended to the case of electrically conducting magnetic fluid as a basic study for demonstrating the possibility of application of electrically conducting magnetic fluid to working fluid in a liquid-metal MHD power generation system. Electrically conducting magnetic fluid is usually prepared by dispersing fine iron particles into a liquid metal such as mercury. To prevent a solidification of particles and keep a homogeneous dispersion, a thin film of tin is attached to the particle`s surface. Thus the electrically conducting liquid behaves as fluid itself having magnetization. The equations governing a one-dimensional boiling two-phase duct flow of such an electrically conducting magnetic fluid in a traverse magnetic field are numerically solved. The analytical results of the two-phase flow characteristics of the magnetic fluid are compared with ones of an electrically conducting nonmagnetic fluid.
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.
Lee, Yung-Chun; Kuo, Shi Hoa
2006-09-01
This paper proposes a novel experimental method for measuring the propagating characteristics of leaky Lamb waves in a piezoelectric plate surrounded by a fluid. It is a differential type of measurement and is very sensitive to the velocity change and wave attenuation of leaky Lamb waves induced by fluid-loading effects. Experimental measurements on an X-cut LiNbO3 plate immersed in a dielectric and conductive fluid have been carried out. The velocity change and wave attenuation of the leaky Lamb waves caused by dielectric and conductive loadings of the fluid have been experimentally determined. The measured data have been compared with the theoretical ones that are calculated from a partial wave analysis. For the wave velocity, very good agreements between the experimental and theoretical results are observed. For the wave attenuation, there are some discrepancies, but an important characteristic in the relationship between wave attenuation and fluid conductivity as predicted by the theory have been verified experimentally.
Stochastic nonhomogeneous incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
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
Magnetoconvection in a rotating fluid between walls of very low thermal conductivity
NASA Astrophysics Data System (ADS)
Davalos, L. A. O.
1984-07-01
The linear steady convection of a fluid layer between rigid thermally and electrically non-conducting walls is investigated from three different stand-points: (1) convection of a rotating fluid, (2) magnetoconvection and (3) magnetoconvection in a rotating fluid. The new dependences of the critical Rayleigh and wavenumbers on the Taylor and Chandrasekhar numbers are discussed. It is shown that in contrast with fluids in the same conditions but with walls of different thermal conductivity, the fluid in the present case is always the most thermally unstable for every Taylor and Chandrasekhar numbers. Moreover, in the present case the horizontal scale of the cell pattern is always the largest. Also, when rotation and magnetic field act simultaneously, in the region of strong interaction the stability of the magnetofluid is highly decreased and the critical wavenumber is always zero.
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.
Thermal conductivity and viscosity of self-assembled alcohol/polyalphaolefin nanoemulsion fluids
2011-01-01
Very large thermal conductivity enhancement had been reported earlier in colloidal suspensions of solid nanoparticles (i.e., nanofluids) and more recently also in oil-in-water emulsions. In this study, nanoemulsions of alcohol and polyalphaolefin (PAO) are spontaneously generated by self-assembly, and their thermal conductivity and viscosity are investigated experimentally. Alcohol and PAO have similar thermal conductivity values, so that the abnormal effects, such as particle Brownian motion, on thermal transport could be deducted in these alcohol/PAO nanoemulsion fluids. Small angle neutron-scattering measurement shows that the alcohol droplets are spheres of 0.8-nm radius in these nanoemulsion fluids. Both thermal conductivity and dynamic viscosity of the fluids are found to increase with alcohol droplet loading, as expected from classical theories. However, the measured conductivity increase is very moderate, e.g., a 2.3% increase for 9 vol%, in these fluids. This suggests that no anomalous enhancement of thermal conductivity is observed in the alcohol/PAO nanoemulsion fluids tested in this study. PMID:21711807
Conductivity measurements on H2O-bearing CO2-rich fluids
Capobianco, Ryan M.; Miroslaw S. Gruszkiewicz; Bodnar, Robert J.; ...
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
4D ERT-based calibration and prediction of biostimulant induced changes in fluid conductivity
NASA Astrophysics Data System (ADS)
Johnson, T. C.; Versteeg, R. J.; Day-Lewis, F. D.; Major, W. R.; Wright, K. E.
2008-12-01
In-situ bioremediation is an emerging and cost-effective method of removing organic contaminants from groundwater. The performance of bioremedial systems depends on the adequate delivery and distribution of biostimulants to contaminated zones. Monitoring the distribution of biostimulants using monitoring wells is expensive, time consuming, and provides inadequate information between sampling wells. We discuss a Hydrogeophysical Performance Monitoring System (HPMS) deployed to monitor bioremediation efforts at a TCE-contaminated Superfund site in Brandywine MD. The HPMS enables autonomous electrical geophysical data acquisition, processing, quality-assurance/quality-control, and inversion. Our objective is to demonstrate the feasibility and cost effectiveness of the HPMS to provide near real-time information on the spatiotemporal behavior of injected biostimulants. As a first step, we use time-lapse electrical resistivity tomography (ERT) to estimate changes in bulk conductivity caused by the injectate. We demonstrate how ERT-based bulk conductivity estimates can be calibrated with a small number of fluid conductivity measurements to produce ERT-based estimates of fluid conductivity. The calibration procedure addresses the spatially variable resolution of the ERT tomograms. To test the validity of these estimates, we used the ERT results to predict the fluid conductivity at tens of points prior to field sampling of fluid conductivity at the same points. The comparison of ERT-predicted vs. observed fluid conductivity displays a high degree of correlation (correlation coefficient over 0.8), and demonstrates the ability of the HPMS to estimate the four-dimensional (4D) distribution of fluid conductivity caused by the biostimulant injection.
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.
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.
NASA Astrophysics Data System (ADS)
Yano, Ryosuke
2017-01-01
The thermal conduction and convection of thermally relativistic fluids between two parallel walls under the gravitational force are discussed both theoretically and numerically. In the theoretical discussion, the Lorentz contraction is assumed to be negligible and spacetime is assumed to be flat. For understanding of the thermal conduction and convection of thermally relativistic fluids between two parallel walls under the gravitational force, the relativistic Boltzmann equation is solved using the direct simulation Monte Carlo method, numerically. Numerical results indicate that strongly nonequilibrium states are formed in vicinities of two walls, which do not allow us to discuss the transition of the thermal conduction to the thermal convection of thermally relativistic fluids under the gravitational force in the framework of the relativistic Navier-Stokes-Fourier equation, when the flow-field is under the transition regime between the rarefied and continuum regimes, whereas such strongly nonequilibrium states are not formed in vicinities of two walls under the nonrelativistic limit.
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.
Liu, L J; Schlesinger, M
2015-09-07
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).
Lattice Boltzmann Method for Two-Dimensional Unsteady Incompressible Flow
NASA Astrophysics Data System (ADS)
Mužík, Juraj
2016-12-01
A Lattice Boltzmann method is used to analyse incompressible fluid flow in a two-dimensional cavity and flow in the channel past cylindrical obstacle. The method solves the Boltzmann's transport equation using simple computational grid - lattice. With the proper choice of the collision operator, the Boltzmann's equation can be converted into incompressible Navier-Stokes equation. Lid-driven cavity benchmark case for various Reynolds numbers and flow past cylinder is presented in the article. The method produces stable solutions with results comparable to those in literature and is very easy to implement.
NASA Astrophysics Data System (ADS)
Kenjeres, S.
2016-09-01
In the present paper we give a concise review of some recent highlights of our research dealing with electromagnetic control of flow, mixing and heat transfer of electrically conductive or magnetized fluids. We apply a combination of state-of-art numerical (DNS and LES) and experimental (PIV and LIF) techniques to provide fundamental insights into the complex phenomena of interactions between imposed (or induced) electromagnetic fields and underlying fluid flow. Our analysis covers an extensive range of working fluids, i.e. weakly- and highly-electrically-conductive, as well as magnetized fluids. These interactions are defined through the presence of different types of body forces acting per volume of fluid. A fully closed system of governing equations containing an extended set of the Navier-Stokes and a simplified set of the Maxwell equations is presented. The four characteristic examples are selected: the electromagnetic control of self-sustained jet oscillations, the electromagnetic enhancement of heat transfer in thermal convection, the wake interactions behind magnetic obstacles and finally, the thermo-magnetic convection in differentially heated cubical enclosure. The comparative assessment between experimental and numerical results is presented. It is concluded that generally good agreement between simulations and experiments is obtained for all cases considered, proving the concept of electromagnetic modulation, which can be used in numerous technological applications.
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.
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.
NASA Technical Reports Server (NTRS)
Voorhies, Goerte V.; Nishihama, Masahiro
1994-01-01
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.
NASA Technical Reports Server (NTRS)
Parker, E. N.
1982-01-01
The dynamical conditions that exist when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array are treated. It is shown that in general there is no hydrostatic equilibrium. In place of equilibrium, there is a dynamical nonequilibrium, which leads to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting); this in turn forms tubes of large diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, being dissipated into small-scale motions of the fluid and thence into heat. Referring to the sun, it is pointed out that the twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above.
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
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.
Obied Allah, M. H.
2013-04-15
In this work, a viscous potential flow analysis is used to investigate capillary surface waves between two horizontal finite fluid layers. The two layers have finite conductivities and admit mass and heat transfer. A general dispersion relation is derived. The presence of finite conductivities together with the dielectric permeabilities makes the horizontal electric field play a dual role in the stability criterion. The phenomenon of negative viscosity is observed. A new growth rate parameter, depending on the kinematical viscosity of the lower fluid layer, is found and has a stabilizing effect on the unstable modes. The growth rates and neutral stability curve are given and applied to air-water interface. The effects of various parameters are discussed for the Kelvin-Helmholtz and the Rayleigh-Taylor instabilities.
Richard C. Martineau; Ray A. Berry; Aur´elia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2010-06-01
This manuscript 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 specific force quantities and velocity and temperature 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.
A Riemann problem based method for solving compressible and incompressible flows
NASA Astrophysics Data System (ADS)
Lu, Haitian; Zhu, Jun; Wang, Chunwu; Wang, Donghong; Zhao, Ning
2017-02-01
A Riemann problem based method for solving two-medium flow including compressible and incompressible regions is presented. The material interface is advanced by front tracking method and the material interface boundary conditions are defined by modified ghost fluid method. A coupled compressible and incompressible Riemann problem constructed in the normal direction of the material interface is proposed to predict the interfacial states. With the ghost fluid states, the compressible and incompressible flows are solved by discontinuous Galerkin method. An incompressible discontinuous Galerkin method with nonuniform time step is also deduced. For shock wave formed in compressible flow, the numerical errors for the ghost fluid method in earlier works are analyzed and discussed in the numerical examples. It shows that the proposed method can provide reasonable results including shock wave location.
Frequency-dependent stability of parallel-plate electrostatic actuators in conductive fluids
NASA Astrophysics Data System (ADS)
Sounart, T. L.; Panchawagh, H. V.; Mahajan, R. L.
2010-05-01
We present an electromechanical stability analysis of passivated parallel-plate electrostatic actuators in conductive dielectric media and show that the pull-in instability can be eliminated by tuning the applied frequency below a design-dependent stability limit. A partial instability region is also obtained, where the actuator jumps from the pull-in displacement to another stable position within the gap. The results predict that the stability limit is always greater than the critical actuation frequency, and therefore any device that is feasible to actuate in a conductive fluid can be operated with stability over the full range of motion.
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.
A borehole fluid conductivity logging method for the determination of fracture inflow parameters
Tsang, Chin-Fu
1987-10-01
It is of much current interest to determine the flow characteristics of fractures intersecting a wellbore to provide data in the estimation of the hydrologic behavior of fractured rocks. The fluid inflow rates from the fractures into the wellbore are important quantities to measure. Often these inflows are at very low rates. One often finds that only a few percent of the fractures identified by core inspection and geophysical logging are water-conducting fractures, the rest being closed, clogged, or isolated from the water flow system. A new procedure is proposed and a corresponding method of analysis developed to locate water-conducting fractures and obtain fracture inflow parameters by means of a time sequence of electric conductivity logs of the borehole fluid. The physical basis of the analysis method is discussed. The procedure is applied to an existing set of data, which shows initiation and growth of nine conductivity peaks in a 900-m section of a 1690-m borehole, corresponding to nine water-conducting fractures intersecting the borehole. We are able to match all nine peaks and determine the flow rates from these fractures. 16 refs., 28 figs., 5 tabs.
A High-Temperature Transient Hot-Wire Thermal Conductivity Apparatus for Fluids.
Perkins, R A; Roder, H M; Nieto de Castro, C A
1991-01-01
A new apparatus for measuring both the thermal conductivity and thermal diffusivity of fluids at temperatures from 220 to 775 K at pressures to 70 MPa is described. The instrument is based on the step-power-forced transient hot-wire technique. Two hot wires are arranged in different arms of a Wheatstone bridge such that the response of the shorter compensating wire is subtracted from the response of the primary wire. Both hot wires are 12.7 µm diameter platinum wire and are simultaneously used as electrical heat sources and as resistance thermometers. A microcomputer controls bridge nulling, applies the power pulse, monitors the bridge response, and stores the results. Performance of the instrument was verified with measurements on liquid toluene as well as argon and nitrogen gas. In particular, new data for the thermal conductivity of liquid toluene near the saturation line, between 298 and 550 K, are presented. These new data can be used to illustrate the importance of radiative heat transfer in transient hot-wire measurements. Thermal conductivity data for liquid toluene, which are corrected for radiation, are reported. The precision of the thermal conductivity data is ± 0.3% and the accuracy is about ±1%. The accuracy of the thermal diffusivity data is about ± 5%. From the measured thermal conductivity and thermal diffusivity, we can calculate the specific heat, Cp , of the fluid, provided that the density is measured, or available through an equation of state.
NASA Astrophysics Data System (ADS)
Ruan, Xiaohui; Wang, Yu; Xuan, Shouhu; Gong, Xinglong
2017-03-01
In this work, the influence of oscillatory shear on the magnetic field dependent electric conductivity of the magnetorheological fluid (MRF) was reported. Upon applying a 0.96 T magnetic field, the electric conductivity could increase about 1500 times larger than the one without magnetic field. By increasing the volume fraction of carbonyl iron particles in the MRF from 5% to 30%, the electric conductivity increased about 565 times. Under applying an oscillatory shear, the resistance of the MRF decreased and it oscillated synchronously with the oscillatory shear. Interestingly, the larger shear strain led to larger oscillatory amplitude of the resistance. A particle–particle resistance model and a semi-empirical formula were proposed to investigate the influence of the oscillatory shear on the electric conductivity. The fitting results matched the experimental results very well. At last, a possible mechanism was proposed to explain the changes of resistance.
On the characteristics-based ACM for incompressible flows
NASA Astrophysics Data System (ADS)
Su, Xiaohui; Zhao, Yong; Huang, Xiaoyang
2007-11-01
In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475-484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667-685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466-1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309-325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657-663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584-607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5-7) (2000) 733-756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5
Børgesen, S E; Gjerris, F; Sørensen, S C
1979-04-01
Forty patients with clinical evidence of normal-pressure hydrocephalus were studied by monitoring intraventricular pressure during a 24-hour period, and by a lumboventricular perfusion test for measurement of the conductance to outflow of cerebrospinal fluid (CSF). The purpose of the study was to investigate whether there is a relationship between intraventricular pressure and conductance to outflow of CSF, and whether it is possible to use the results from pressure monitoring in the selection of patients who may be expected to benefit from shunting therapy. The conductance to outflow was used as an evaluation factor in the selection of patients to be treated by a shunt. The conductance to CSF outflow differed by twelvefold between the lowest and highest values. The level of resting intraventricular pressure was within normal limits in all patients. Accordingly, there was no evidence of a relationship between conductance to outflow and intraventricular pressure. So-called B-waves were seen more frequently in patients with decreased conductance to outflow, but were also present in patients with high conductance to outflow. Therefore, the presence of B-waves does not imply a low conductance to outflow of CSF.
Instabilities of conducting fluid flows in cylindrical shells under external forcing
NASA Astrophysics Data System (ADS)
Burguete, Javier; Miranda, Montserrat
2010-11-01
Flows created in neutral conducting flows remain one of the less studied topics of fluid dynamics, in spite of their relevance both in fundamental research (dynamo action, turbulence suppression) and applications (continuous casting, aluminium production, biophysics). Here we present the effect of a time-dependent magnetic field parallel to the axis of circular cavities. Due to the Lenz's law, the time-dependent magnetic field generates an azymuthal current, that produces a radial force. This force produces the destabilization of the static fluid layer, and a flow is created. The geommetry of the experimental cell is a disc layer with external diameter smaller than 94 mm, with or without internal hole. The layer is up to 20mm depth, and we use as conducting fluid an In-Ga-Sn alloy. There is no external current applied on the problem, only an external magnetic field. This field evolves harmonically with a frequency up to 10Hz, small enough to not to observe skin depth effects. The magnitude ranges from 0 to 0.1 T. With a threshold of 0.01T a dynamical behaviour is observed, and the main characteristics of this flow have been determined: different temporal resonances and spatial patterns with differents symmetries (squares, hexagonal, triangles,...).
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.
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.
Spatial variation of the magnetic field inside laminar flows of a perfect conductive fluid
NASA Astrophysics Data System (ADS)
Duka, Bejo; Boçi, Sonila
2017-01-01
The steady state of a perfect conductive fluid in laminar flow resulting from the ‘Hall effect’ is studied. Using the Maxwell equations, the spatial variation of the magnetic field in the steady state is calculated for three cases of different fluid flow geometries: flow between two infinite parallel planes, flow between two coaxial infinite-long cylinders and flow between two concentric spheres. According to our calculation of the three cases, the spatial variation of the magnetic field depends on the flow velocity. The magnetic field is strengthened in layers where the velocity is greater, but this dependency is negligible for non relativistic flows. Our approach in this study provides an example of how to receive interesting results using only basic knowledge of physics and mathematics.
NASA Astrophysics Data System (ADS)
Parlak, Z.; Biet, C.; Zauscher, S.
2013-08-01
We describe the physical understanding of a method which differentiates between the frequency shift caused by fluid viscosity and density from that caused by mass adsorption in the resonance of a quartz crystal resonator. This method uses the normalized conductance of the crystal to determine a critical frequency at which the fluid mass and fluid loss compensate each other. Tracking the shift in this critical frequency allows us to determine purely mass adsorption on the crystal. We extended this method to Maxwellian fluids for understanding the mass adsorption in non-Newtonian fluids. We validate our approach by real-time mass adsorption measurements using glycerol and albumin solutions.
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.
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.
NASA Astrophysics Data System (ADS)
Brenner, Howard
2011-10-01
Linear irreversible thermodynamic principles are used to demonstrate, by counterexample, the existence of a fundamental incompleteness in the basic pre-constitutive mass, momentum, and energy equations governing fluid mechanics and transport phenomena in continua. The demonstration is effected by addressing the elementary case of steady-state heat conduction (and transport processes in general) occurring in quiescent fluids. The counterexample questions the universal assumption of equality of the four physically different velocities entering into the basic pre-constitutive mass, momentum, and energy conservation equations. Explicitly, it is argued that such equality is an implicit constitutive assumption rather than an established empirical fact of unquestioned authority. Such equality, if indeed true, would require formal proof of its validity, currently absent from the literature. In fact, our counterexample shows the assumption of equality to be false. As the current set of pre-constitutive conservation equations appearing in textbooks are regarded as applicable both to continua and noncontinua (e.g., rarefied gases), our elementary counterexample negating belief in the equality of all four velocities impacts on all aspects of fluid mechanics and transport processes, continua and noncontinua alike.
Numerical analysis of incompressible viscous flow around a bubble
NASA Astrophysics Data System (ADS)
Sugano, Minoru; Ishii, Ryuji; Morioka, Shigeki
1992-12-01
A numerical simulation of flows around a deformable gas bubble rising through an incompressible viscous fluid is carried out on a supercomputer Fujitsu VP-2600 at the Data Processing Center of Kyoto University. The solution algorithm is a modified MAC (Marker And Cell) method. For the grid generation, an orthogonal mapping proposed by Ryskin and Leal is applied. The numerical results are compared with Ryskin and Leal's results and previous experiments. It will be shown that a good agreement is obtained between them.
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).
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.
The incompressibility assumption in computational simulations of nasal airflow.
Cal, Ismael R; Cercos-Pita, Jose Luis; Duque, Daniel
2017-04-03
Most of the computational works on nasal airflow up to date have assumed incompressibility, given the low Mach number of these flows. However, for high temperature gradients, the incompressibility assumption could lead to a loss of accuracy, due to the temperature dependence of air density and viscosity. In this article we aim to shed some light on the influence of this assumption in a model of calm breathing in an Asian nasal cavity, by solving the fluid flow equations in compressible and incompressible formulation for different ambient air temperatures using the OpenFOAM package. At low flow rates and warm climatological conditions, similar results were obtained from both approaches, showing that density variations need not be taken into account to obtain a good prediction of all flow features, at least for usual breathing conditions. This agrees with most of the simulations previously reported, at least as far as the incompressibility assumption is concerned. However, parameters like nasal resistance and wall shear stress distribution differ for air temperatures below [Formula: see text]C approximately. Therefore, density variations should be considered for simulations at such low temperatures.
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.
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
Electrical conductivity of NaCl-bearing aqueous fluids to 600 °C and 1 GPa
NASA Astrophysics Data System (ADS)
Sinmyo, Ryosuke; Keppler, Hans
2017-01-01
The electrical conductivity of aqueous fluids containing 0.01, 0.1, and 1 M NaCl was measured in an externally heated diamond cell to 600 °C and 1 GPa. These measurements therefore more than double the pressure range of previous data and extend it to higher NaCl concentrations relevant for crustal and mantle fluids. Electrical conductivity was generally found to increase with pressure and fluid salinity. The conductivity increase observed upon variation of NaCl concentration from 0.1 to 1 M was smaller than from 0.01 to 0.1 M, which reflects the reduced degree of dissociation at high NaCl concentration. Measured conductivities can be reproduced ( R 2 = 0.96) by a numerical model with log σ = -1.7060- 93.78/ T + 0.8075 log c + 3.0781 log ρ + log Λ 0( T, ρ), where σ is the conductivity in S m-1, T is temperature in K, c is NaCl concentration in wt%, ρ is the density of pure water (in g/cm3) at given pressure and temperature, and Λ 0 ( T, ρ) is the molar conductivity of NaCl in water at infinite dilution (in S cm2 mol-1), Λ 0 = 1573-1212 ρ + 537 062/ T-208 122 721/ T 2. This model allows accurate predictions of the conductivity of saline fluids throughout most of the crust and upper mantle; it should not be used at temperatures below 100 °C. In general, the data show that already a very small fraction of NaCl-bearing aqueous fluid in the deep crust is sufficient to enhance bulk conductivities to values that would be expected for a high degree of partial melting. Accordingly, aqueous fluids may be distinguished from hydrous melts by comparing magnetotelluric and seismic data. H2O-NaCl fluids may enhance electrical conductivities in the deep crust with little disturbance of v p or v p/ v s ratios. However, at the high temperatures in the mantle wedge above subduction zones, the conductivity of hydrous basaltic melts and saline aqueous fluids is rather similar, so that distinguishing these two phases from conductivity data alone is difficult. Observed
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
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.
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.
Impulsively started incompressible turbulent jet
Witze, P O
1980-10-01
Hot-film anemometer measurements are presented for the centerline velocity of a suddenly started jet of air. The tip penetration of the jet is shown to be proportional to the square-root of time. A theoretical model is developed that assumes the transient jet can be characterized as a spherical vortex interacting with a steady-state jet. The model demonstrates that the ratio of nozzle radius to jet velocity defines a time constant that uniquely characterizes the behavior and similarity of impulsively started incompressible turbulent jets.
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
... 10 Energy 1 2014-01-01 2014-01-01 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...
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...
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
... 10 Energy 1 2012-01-01 2012-01-01 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...
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
... 10 Energy 1 2011-01-01 2011-01-01 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...
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
... 10 Energy 1 2013-01-01 2013-01-01 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...
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.
Andersson, K; Manchester, I R; Andersson, N; Shiriaev, A; Malm, J; Eklund, A
2007-11-01
Idiopathic normal pressure hydrocephalus (INPH) patients have a disturbance in the dynamics of the cerebrospinal fluid (CSF) system. The outflow conductance, C, of the CSF system has been suggested to be prognostic for positive outcome after treatment with a CSF shunt. All current methods for estimation of C have drawbacks; these include lack of information on the accuracy and relatively long investigation times. Thus, there is a need for improved methods. To accomplish this, the theoretical framework for a new adaptive observer (OBS) was developed which provides real-time estimation of C. The aim of this study was to evaluate the OBS method and to compare it with the constant pressure infusion (CPI) method. The OBS method was applied to data from infusion investigations performed with the CPI method. These consisted of repeated measurements on an experimental set-up and 30 patients with suspected INPH. There was no significant difference in C between the CPI and the OBS method for the experimental set-up. For the patients there was a significant difference, -0.84+/-1.25 microl (s kPa)(-1), mean +/- SD (paired sample t-test, p<0.05). However, such a difference is within clinically acceptable limits. This encourages further development of this new real-time approach for estimation of the outflow conductance.
NASA Technical Reports Server (NTRS)
Kyrlidis, A.; Brown, R. A.; Walker, J. S.
1990-01-01
The use of strong magnetic fields for the control of particle settling in metallic systems is investigated by altering the fluid mechanics in the melt. The fluid mechanism of particle settling is analyzed for the motion around single, axisymmetric particles in the limit of creeping flow for a fluid with a large electrical conductivity. The drag is found to increase proportionately to the intensity of the magnetic field or the Hartmann number Ha. The flowfield forms boundary layers, which thin out with increasing Ha, along the surfaces parallel to the flow. For axisymmetric bodies, the boundary layer separates as the poles of the surface are approached and encloses regions of almost stagnant fluid. These regions spread upstream and downstream along the body with increasing Ha, thereby trapping the particle in a column of stagnant fluid.
NASA Astrophysics Data System (ADS)
Schepers, A.; Milsch, H.
2009-04-01
In the context of low enthalpy geothermal energy production from deep sedimentary reservoirs laboratory experiments and simulations in the system quartz-feldspar-water were conducted. To constrain the effect of fluid-rock interactions on permeability under hydrothermal in situ conditions an interdisciplinary approach covering petrophysical, petrological and hydrogeochemical methods was applied. Long-term flow-through experiments were conducted under hydrostatic pressure conditions in a HPT-permeameter. Two arkosic sandstones, one pure quartz arenite (Fontainebleau) as well as one sandwich sample containing a quartz-feldspar powder of defined grain size and composition were investigated. The pore fluid was distilled water. At a maximum temperature of 160°C both permeability and electrical rock conductivity were simultaneously monitored. The maximum run duration was three months. Complementary batch experiments were performed with quartz-feldspar powders to constrain the mechanisms and kinetics of potentially occurring hydrothermal reactions. The resulting fluids were analysed with ICP-OES and the reacted powders were characterised with XRD and SEM. Additionally, the hydrothermal reactions were modelled with PHREEQC. It will be demonstrated that permeability decreases in the course of the experiments. However, compared to similar experiments conducted under deviatoric stress conditions (Tenthorey et al., 1998) the decrease in permeability is low. For both arkosic sandstones and at stagnant flow conditions the electrical rock conductivity showed an asymptotical increase indicating that the respective pore fluid approaches a saturation state. Furthermore, fluid samples taken at the end of the Fontainebleau experiment exhibit supersaturation with respect to quartz. In addition, PHREEQC simulations of the feldspar-quartz-water equilibrium indicate that different clay minerals and gibbsite are supersaturated in the resulting fluid. Consequently and despite the sluggish
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.
Preconditioning and the limit to the incompressible flow equations
NASA Technical Reports Server (NTRS)
Turkel, E.; Fiterman, A.; Vanleer, B.
1993-01-01
The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.
On incompressibility of a matrix in naturally occurring composites
NASA Astrophysics Data System (ADS)
Gorbatikh, Larissa; Pingle, Pawan
2007-12-01
The work illustrates that a soft matrix, which has the Poisson ratio close to 0.5 and is reinforced with a rigid-line inclusion, possesses an interesting behavior at the inclusion/matrix interface. It experiences a hydrostatic stress state and behaves as an incompressible fluid under longitudinal and transverse loads. The stress singularities are eliminated ahead of the inclusion tips, and when interface defects are formed, their effect on the composite compliance is minimal. These observations have far reaching applications when one is interested in mechanisms of multifunctional property improvement of composites (such as toughness and stiffness) learned from naturally occurring composites.
Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics
NASA Astrophysics Data System (ADS)
Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; Tartakovsky, Alexandre M.; Parks, Michael L.
2017-04-01
We present a consistent implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.
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.
Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics
Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; ...
2017-01-03
In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.
Thermal convection in a magnetized conducting fluid with the Cattaneo-Christov heat-flow model
NASA Astrophysics Data System (ADS)
Bissell, J. J.
2016-11-01
By substituting the Cattaneo-Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number Rc(c )(Q ) which exhibits inhibition of convection by the field according to Rc(c )→π2Q as Q →∞ , where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number Rc(o )(Q ,P1,P2,C ) is given by a more complicated function of the thermal Prandtl number P1, magnetic Prandtl number P2 and Cattaneo number C. To elucidate features of this dependence, we neglect P2 (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour Rc(o )→π √{Q }/ C , as Q →∞ . One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value CT(Q); indeed, crucially we show that when Q is large, CT∝1 / √{Q }, meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.
Turbulent Dynamo in a Conducting Fluid and a Partially Ionized Gas
NASA Astrophysics Data System (ADS)
Xu, Siyao; Lazarian, A.
2016-12-01
By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P m and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P m in a conducting fluid and { R } (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1991-01-01
An algorithm is presented for unsteady two-dimensional incompressible Navier-Stokes calculations. This algorithm is based on the fourth order partial differential equation for incompressible fluid flow which uses the streamfunction as the only dependent variable. The algorithm is second order accurate in both time and space. It uses a multigrid solver at each time step. It is extremely efficient with respect to the use of both CPU time and physical memory. It is extremely robust with respect to Reynolds number.
Turbulent crossed fluxes in incompressible flows
Sancho
2000-02-01
We show in the framework of the stochastic calculus the existence of turbulent crossed fluxes in incompressible flows. Physically, these fluxes are related to the dependence of the phenomenological coefficients on the temperature and concentration variables.
Gaballa, M A; Raya, T E; Simon, B R; Goldman, S
1992-07-01
To characterize the interaction between mechanical and fluid transport properties in hypertension, we measured in vivo elastic material constants and hydraulic conductivity in intact segments of carotid arteries in normal and spontaneously hypertensive rats (SHR). With the use of a finite element model, the arterial wall was modeled as a large-deformation, two-phase (solid/fluid) medium, which accounts for the existence and motion of the tissue fluid. Measurements of internal diameter and transmural pressures were obtained during continuous increases in pressure from 0 to 200 mm Hg. Strain and stress components were calculated based on a pseudostrain exponential energy density function. To measure the hydraulic conductivity, segments of the carotid artery were isolated, filled with a 4% oxygenated albumin-Tyrode's solution, and connected to a capillary tube. The movement of the meniscus of the capillary tube represented the fluid filtration across the artery. To study the influence of transmural pressure on hydraulic conductivity, measurement of fluid filtration across the arterial wall was obtained at transmural pressures of 50 and 100 mm Hg. The material constants in the SHR (n = 9) were higher (p less than 0.05 for all variables) than in normal rats (n = 10): c = 1,343 +/- 96 versus 1,158 +/- 65 mm Hg, b1 = 1.84 +/- 0.24 versus 1.22 +/- 0.22, b2 = 0.769 +/- 0.114 versus 0.616 +/- 0.11, b3 = 0.017 +/- 0.005 versus 0.0065 +/- 0.002, b4 = 0.206 +/- 0.04 versus 0.083 +/- 0.03, b5 = 0.0594 +/- 0.007 versus 0.0217 +/- 0.006, and b6 = 0.22 +/- 0.09 versus 0.123 +/- 0.02, respectively. The hydraulic conductivity of the total wall, calculated from the filtration data, was lower (p less than 0.05) at both 50 and 100 mm Hg in the SHR (n = 6) compared with normal rats (n = 7): 1.12 +/- 0.31 x 10(-8) and 0.72 +/- 0.23 x 10(-8) versus 1.95 +/- 0.53 x 10(-8) and 1.35 +/- 0.47 x 10(-8) cm/(sec.mm Hg), respectively. The intergroup comparisons between 50 and 100 mm Hg in both SHR
Effect of resting pressure on the estimate of cerebrospinal fluid outflow conductance
2011-01-01
Background A lumbar infusion test is commonly used as a predictive test for patients with normal pressure hydrocephalus and for evaluation of cerebrospinal fluid (CSF) shunt function. Different infusion protocols can be used to estimate the outflow conductance (Cout) or its reciprocal the outflow resistance (Rout), with or without using the baseline resting pressure, Pr. Both from a basic physiological research and a clinical perspective, it is important to understand the limitations of the model on which infusion tests are based. By estimating Cout using two different analyses, with or without Pr, the limitations could be explored. The aim of this study was to compare the Cout estimates, and investigate what effect Prhad on the results. Methods Sixty-three patients that underwent a constant pressure infusion protocol as part of their preoperative evaluation for normal pressure hydrocephalus, were included (age 70.3 ± 10.8 years (mean ± SD)). The analysis was performed without (Cexcl Pr) and with (Cincl Pr) Pr. The estimates were compared using Bland-Altman plots and paired sample t-tests (p < 0.05 considered significant). Results Mean Cout for the 63 patients was: Cexcl Pr = 7.0 ± 4.0 (mean ± SD) μl/(s kPa) and Cincl Pr = 9.1 ± 4.3 μl/(s kPa) and Rout was 19.0 ± 9.2 and 17.7 ± 11.3 mmHg/ml/min, respectively. There was a positive correlation between methods (r = 0.79, n = 63, p < 0.01). The difference, ΔCout= -2.1 ± 2.7 μl/(s kPa) between methods was significant (p < 0.01) and ΔRout was 1.2 ± 8.8 mmHg/ml/min). The Bland-Altman plot visualized that the variation around the mean difference was similar all through the range of measured values and there was no correlation between ΔCout and Cout. Conclusions The difference between Cout estimates, obtained from analyses with or without Pr, needs to be taken into consideration when comparing results from studies using different infusion test protocols. The study suggests variation in CSF formation rate
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.
Børgesen, S E; Gjerris, F; Sørensen, S C
1979-10-01
Conductance to outflow of cerebrospinal fluid (CSF) has been measured by both a lumboventricular perfusion and a bolus injection method in 24 patients with normal-pressure hydrocephalus. One purpose was to investigate whether the less time-consuming technique of bolus, injection gave results comparable to the results obtained by the lumboventricular perfusion technique. There was a poor correlation between the results obtained by the two measurements of conductance to outflow of CSF. It is concluded that the bolus-injection technique cannot substitute for the lumboventricular perfusion test. Compliance of the CSF space was measured by the bolus injection. The presence of B-waves, recorded from long-term intraventricular pressure monitoring, could be correlated to the sum of conductance to outflow and compliance. The correlation offers a possible explanation of the nature of B-waves.
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.
Fluid mechanics in fluids at rest
NASA Astrophysics Data System (ADS)
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 vv. 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.10.1016/j.ijengsci.2012.01.006 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
Direct numerical simulation of incompressible axisymmetric flows
NASA Technical Reports Server (NTRS)
Loulou, Patrick
1994-01-01
In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.
NASA Astrophysics Data System (ADS)
Pahar, Gourabananda; Dhar, Anirban
2017-04-01
A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.
NASA Astrophysics Data System (ADS)
Schepers, Ansgar; Milsch, Harald
2010-05-01
Geothermal energy production from deep sedimentary reservoirs interferes with thermodynamic fluid-mineral equilibria. Different dissolution and/or precipitation reactions might thus be induced, which affect the rock physical transport properties electrical rock conductivity σrock and permeability k. In general, this work addresses the risk assessment for geothermal energy production from deep sedimentary reservoirs in terms of formation damage. In this context it is important to constrain the processes leading to potential changes in k, evaluate whether they occur under in-situ T - p - X conditions, and - if yes - provide tools to monitor changes in the physico-chemical properties of the fluid-rock system. In the model system quartz-feldspar-water we conducted long-term hydrothermal flow-through and batch experiments under hydrostatic pressure conditions. The temperature range applied in the experiments covered 70 to 160° C to simulate conditions pertaining to a low enthalpy geothermal energy production scenario. The evolutions of σrock and k of feldspar-rich Rotliegend sandstone samples and analogue materials were monitored by means of a HPT-permeameter. Concentrations of the system's major cations ci (i = Na+, Al3+, Si4+, K+, Ca2+) in the (pore)fluids were measured using ICP-OES and were correlated to the electrical fluid conductivity σfluid. Microstructural and mineralogical investigations on the solid phases were performed by SEM and XRD, respectively. In the first part of this study we investigated the relationship between σrock and the chemical saturation state of this specific fluid-rock system. It can be demonstrated that σrock is qualitatively dependent on changes in σfluid. Thus, monitoring of easily accessible σrock can be used to get insights into the chemical evolution of the present fluid-rock system. Hydrogeochemical modeling of the resulting porefluids showed that the system is supersaturated with respect to clay minerals and gibbsite
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.
NASA Astrophysics Data System (ADS)
Forero-Sandoval, I. Y.; Vega-Flick, A.; Alvarado-Gil, J. J.; Medina-Esquivel, R. A.
2017-02-01
The thermal conductivity and viscosity of a magnetorheological suspension composed of carbonyl iron particles immerse in silicone oil were studied. Thermal wave resonant cavity was employed to measure the thermal diffusivity of the magnetorheological fluid as a function of an externally applied magnetic field. The dynamic viscosity was also measured and its relationship with the concentration of the particles and the magnetic field strength was investigated. The results show that higher concentrations of carbonyl iron particles as well as higher magnetic field intensities lead to a significant increase in thermal conductivity. The relationship between the thermal conductivity and the dynamic viscosity was explored. Our measurements were examined using an analytical relation between the thermal conductivity and the dynamic viscosity. The results show that by using highly viscous materials, the order induced in the micro particles can be kept for a relatively long time and therefore the increase in thermal conductivity can also be maintained.
NASA Astrophysics Data System (ADS)
Gartling, D. K.; Hickox, C. E.
1982-10-01
The theoretical background for the finite element computer program MARIAH is presented. The MARIAH code is designed for the analysis of incompressible fluid flow and heat transfer in saturated porous media. A description of the fluid/thermal boundary value problem treated by the program is presented and the finite element method and associated numerical methods used in MARIAH are discussed. Instructions for use of the program are documented in the Sandia National Laboratories report, SAND79-1623.
Analysis of an Incompressible Navier-Stokes-Maxwell-Stefan System
NASA Astrophysics Data System (ADS)
Chen, Xiuqing; Jüngel, Ansgar
2015-12-01
The Maxwell-Stefan equations for the molar fluxes, supplemented by the incompressible Navier-Stokes equations governing the fluid velocity dynamics, are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture under isothermal conditions. The global-in-time existence of bounded weak solutions to the strongly coupled model and their exponential decay to the homogeneous steady state are proved. The mathematical difficulties are due to the singular Maxwell-Stefan diffusion matrix, the cross-diffusion terms, and the different molar masses of the fluid components. The key idea of the proof is the use of a new entropy functional and entropy variables, which allows for a proof of positive lower and upper bounds of the mass densities without the use of a maximum principle.
Electrical and Hydraulic Properties of Humified Bog Peat as a Function of Pore-fluid Conductivity
NASA Astrophysics Data System (ADS)
Comas, X.; Slater, L.
2003-12-01
The electrical properties of organic sediments and their relationship to physical properties are poorly understood. A simple approach to relate electrical properties to physical properties commonly applied to inorganic sediments is to model the electrolytic conductivity and the surface conductivity as parallel conduction paths. Low-frequency electrical measurements were made in conjunction with hydraulic conductivity measurements on peat samples from an 11 m section collected in a large freshwater peatland. The electrical and hydraulic measurements were made as a function of NaCl concentration and depth of burial. In all cases, the electrical conductivity of the peat was not well modeled by the parallel conduction path model, with the model yielding formation factor values close to one. Sample measurements along the section suggest a slight increase in the formation factor and surface conductivity values with depth. Hydraulic conductivity measured by constant head method shows a marked increase with increasing NaCl concentration, which we believe results from expansion of macropore porosity by chemical dilation as proposed by others. Attempts to return the samples to their original conditions by decreasing the salinity only partially restored the hydraulic conductivity values, indicating a permanent disruption of the hydraulic properties of the peat. The increase of surface electrical conductivity and hydraulic conductivity with depth may indicate a close correlation with the high cation exchange capacity of organic matter and its tendency for chemical dilation as decomposition of organic matter increases with depth. We propose that the electrical conductivity of peat cannot be modeled by an electrolytic and a surface conduction path in parallel. The increase in the electrolytic conduction causes ionic accumulation and dispersion processes, expanding the macropore porosity and hence inducing a decrease in the formation factor values. A proper electrical model for
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.
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
Incompressible Rayleigh–Taylor Turbulence
NASA Astrophysics Data System (ADS)
Boffetta, Guido; Mazzino, Andrea
2017-01-01
Basic fluid equations are the main ingredient in the development of theories of Rayleigh–Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh–Taylor instability, here only phenomenological theories are currently available. The present review provides an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh–Taylor turbulence together with numerical and experimental evidence for their support. Although the focus is mainly on the classical Boussinesq Rayleigh–Taylor turbulence of miscible fluids, the review extends to other fluid systems with viscoelastic behavior, affected by rotation of the reference frame, and, finally, in the presence of reactions.
NASA Astrophysics Data System (ADS)
Doughty, Christine; Tsang, Chin-Fu; Rosberg, Jan-Erik; Juhlin, Christopher; Dobson, Patrick F.; Birkholzer, Jens T.
2016-11-01
Flowing fluid electrical conductivity (FFEC) logging is a hydrogeologic testing method that is usually conducted in an existing borehole. However, for the 2,500-m deep COSC-1 borehole, drilled at Åre, central Sweden, it was done within the drilling period during a scheduled 1-day break, thus having a negligible impact on the drilling schedule, yet providing important information on depths of hydraulically conductive zones and their transmissivities and salinities. This paper presents a reanalysis of this set of data together with a new FFEC logging data set obtained soon after drilling was completed, also over a period of 1 day, but with a different pumping rate and water-level drawdown. Their joint analysis not only results in better estimates of transmissivity and salinity in the conducting fractures intercepted by the borehole, but also yields the hydraulic head values of these fractures, an important piece of information for the understanding of hydraulic structure of the subsurface. Two additional FFEC logging tests were done about 1 year later, and are used to confirm and refine this analysis. Results show that from 250 to 2,000 m depths, there are seven distinct hydraulically conductive zones with different hydraulic heads and low transmissivity values. For the final test, conducted with a much smaller water-level drawdown, inflow ceased from some of the conductive zones, confirming that their hydraulic heads are below the hydraulic head measured in the wellbore under non-pumped conditions. The challenges accompanying 1-day FFEC logging are summarized, along with lessons learned in addressing them.
NASA Astrophysics Data System (ADS)
Doughty, Christine; Tsang, Chin-Fu; Rosberg, Jan-Erik; Juhlin, Christopher; Dobson, Patrick F.; Birkholzer, Jens T.
2017-03-01
Flowing fluid electrical conductivity (FFEC) logging is a hydrogeologic testing method that is usually conducted in an existing borehole. However, for the 2,500-m deep COSC-1 borehole, drilled at Åre, central Sweden, it was done within the drilling period during a scheduled 1-day break, thus having a negligible impact on the drilling schedule, yet providing important information on depths of hydraulically conductive zones and their transmissivities and salinities. This paper presents a reanalysis of this set of data together with a new FFEC logging data set obtained soon after drilling was completed, also over a period of 1 day, but with a different pumping rate and water-level drawdown. Their joint analysis not only results in better estimates of transmissivity and salinity in the conducting fractures intercepted by the borehole, but also yields the hydraulic head values of these fractures, an important piece of information for the understanding of hydraulic structure of the subsurface. Two additional FFEC logging tests were done about 1 year later, and are used to confirm and refine this analysis. Results show that from 250 to 2,000 m depths, there are seven distinct hydraulically conductive zones with different hydraulic heads and low transmissivity values. For the final test, conducted with a much smaller water-level drawdown, inflow ceased from some of the conductive zones, confirming that their hydraulic heads are below the hydraulic head measured in the wellbore under non-pumped conditions. The challenges accompanying 1-day FFEC logging are summarized, along with lessons learned in addressing them.
NASA Astrophysics Data System (ADS)
Kandasamy, R.; Muhaimin, I.; Amin, Norsarahaida S.
2010-01-01
This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.
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.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
Diffusion on Viscous Fluids, Existence and Asymptotic Properties of Solutions,
1983-09-01
Matematica - Politecuico di Milano (1982). 11.* P. Secchi "On the Initial Value ProbleM for the Nquations of Notion of Viscous Incompressible Fluids In...of two viscous Incompressible Fluids’, preprint DepartLmento dl matematica - Politecuico di Milano (1982). -15- 11. P. Secchi 00n the XnitiaI Value
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
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.
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.
Structure and computation of two-dimensional incompressible extended MHD
NASA Astrophysics Data System (ADS)
Grasso, D.; Tassi, E.; Abdelhamid, H. M.; Morrison, P. J.
2017-01-01
A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular, normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
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.
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.
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.
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.
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.
Development of an Efficient Solution Scheme for Incompressible Steady- State Flow
1989-04-01
Investigation," Technical Report REMR-HY-4, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Bernard, R. S., and Thompson , J . F . 1984. "Mass...0208, AIAA 24th Aerospace Sciences Meeting, Reno, NV. Mastin, C. W., and Thompson , J . F . 1978. "Three-Dimensional Body-Fitted Coordinate Systems for... Thompson , J . F . 1984. "A Vectorized Solution for Incompressible Flow," AIAA Paper 84-1534, AIAA 17th Fluid Dynamics, Plasma Dynamics, and Lasers Conference
NASA Astrophysics Data System (ADS)
Deuring, Paul; Kračmar, Stanislav; Nečasová, Šárka
We consider a stationary viscous incompressible flow around a translating and rotating body. Optimal rates of decay are derived for the velocity and its gradient, on the basis of a representation formula involving a fundamental solution constructed by R.B. Guenther and E.A. Thomann [The fundamental solution of the linearized Navier-Stokes equations for spinning bodies in three spatial dimensions - time dependent case, J. Math. Fluid Mech. 8 (2006) 77-98], for a linearized system.
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.
NASA Astrophysics Data System (ADS)
Umavathi, Jawali C.; Kumar, J. Prathap; Sheremet, Mikhail A.
2017-01-01
This paper investigates the influence of first order chemical reaction in a vertical double passage channel in the presence of applied electric field. The wall and ambient medium are maintained at constant but different temperatures and concentrations and the heat and mass transfer occur from the wall to the medium. The channel is divided into two passages by means of a thin perfectly conducting baffle. The coupled non-linear ordinary differential equations are solved analytically by using regular perturbation method (PM) valid for small values of Brinkman number. To understand the flow structure for large values of Brinkman number the governing equations are also solved by differential transform method (DTM) which is a semi-analytical method. The effects of thermal Grashof number (GrT = 1 , 5 , 10 , 15), mass Grashof number (GrC = 1 , 5 , 10 , 15), Brinkman number (Br = 0 , 0.1 , 0.5 , 1), first order chemical reaction parameter (α = 0.1 , 0.5 , 1 , 1.5), Hartmann number (M = 4 , 6 , 8 , 10) and electrical field load parameter (E = - 2 , - 1 , 0 , 1 , 2) on the velocity, temperature and concentration profiles, volumetric flow rate, total heat rate, skin friction and Nusselt number are analyzed. It was found that the thermal Grashof number, mass Grashof number and Brinkman number enhances the flow whereas the Hartmann number and chemical reaction parameter suppresses the flow field. Also the obtained results have revealed that the heat transfer enhancement depends on the baffle position.
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.
NASA Astrophysics Data System (ADS)
Yin, W.-L.
1984-04-01
It is shown that, in the case of non-zero charge density, the class of steady, plane, incompressible, aligned-fluid magnetofluiddynamic flows contains no rotational motions. Therefore, this class of flows is exhausted by the irrotational solutions of Kingston and Power.
Circulation-preserving plane flows of incompressible viscous fluids
NASA Astrophysics Data System (ADS)
Yin, W.-L.
1983-06-01
The present investigation is concerned with a systematic use of the method of complex variables in a study of (generally unsteady) plane solutions of the Navier-Stokes equation. Circulation-preserving flows are considered in the investigation. However, the employed method can also be applied to more general cases. A circulation-preserving plane solution of the Navier-Stokes equation possesses a biharmonic stream function. The stream function may, therefore, be expressed in terms of two complex analytic functions, taking into account Goursat's representation. Attention is given to differential equations in the complex form, the case of steady vorticity, the case of unsteady vorticity with a spatially constant vorticity gradient, solutions with logarithmic vorticity fields, and a proof of completeness.
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.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
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)].
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
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.
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
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
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.
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.
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.
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
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.
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...
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.
Hiemenz flow and heat transfer of a third grade fluid
NASA Astrophysics Data System (ADS)
Sahoo, Bikash
2009-03-01
The laminar flow and heat transfer of an incompressible, third grade, electrically conducting fluid impinging normal to a plane in the presence of a uniform magnetic field is investigated. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). By means of the similarity transformation, the governing non-linear partial differential equations are reduced to a system of non-linear ordinary differential equations and are solved by a second-order numerical technique. Effects of various non-Newtonian fluid parameters, magnetic parameter, Prandtl number on the velocity and temperature fields have been investigated in detail and shown graphically. It is found that the velocity gradient at the wall decreases as the third grade fluid parameter increases.
The Vibration of an Inviscid Incompressible Sessile Drop
NASA Astrophysics Data System (ADS)
Smith, Marc K.
2008-11-01
The fundamental frequencies and modes of vibration of a free spherical drop of inviscid incompressible fluid were computed 129 years ago by Lord Rayleigh. The analysis was possible because of simplifications resulting from the use of spherical coordinates. These same simplifications don't occur for a sessile drop, i.e., when the drop is supported on a horizontal planar surface, except for the case of a hemispherical drop. The present work describes an integrated analytical and numerical technique for the computation of the fundamental frequencies and modes of vibration of a supported sessile drop. Spherical coordinates are used to describe the interface shape, but the flow field inside the drop is computed numerically using the finite element method. Combining these techniques produces a linear eigenvalue problem that is solved numerically. Results will be presented for sessile drops with different contact angles without gravity and compared to experimental data. This technique can also be extended to sessile drops with gravity, in which the drop shape is flattened, and to substrate geometries that are not planar, such as a drop in a shallow cavity or hole.
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.
Steady incompressible variable thickness shear layer aerodynamics
NASA Technical Reports Server (NTRS)
Chi, M. R.
1976-01-01
A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non lifting problems. The slow variation of the boundary layer thickness is considered. The slowly varying behavior is treated by using multitime scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aerodynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow. The aerodynamic load is decreased by the shear layer, compared to the potential flow. The variable thickness shear layer decreases it less than the uniform thickness shear layer based upon equal maximum shear layer thicknesses.
The local nature of incompressibility of quantum Hall effect.
Kendirlik, E M; Sirt, S; Kalkan, S B; Ofek, N; Umansky, V; Siddiki, A
2017-01-10
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories.
The local nature of incompressibility of quantum Hall effect
NASA Astrophysics Data System (ADS)
Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Ofek, N.; Umansky, V.; Siddiki, A.
2017-01-01
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories.
The local nature of incompressibility of quantum Hall effect
Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Ofek, N.; Umansky, V.; Siddiki, A.
2017-01-01
Since the experimental realization of the integer quantum Hall effect in a two-dimensional electron system, the interrelation between the conductance quantization and the topological properties of the system has been investigated. Assuming that the two-dimensional electron system is described by a Bloch Hamiltonian, system is insulating in the bulk of sample throughout the quantum Hall plateau due to a magnetic field induced energy gap. Meanwhile, the system is conducting at the edges resembling a 2+1 dimensional topological insulator without time-reversal symmetry. Here, by our magneto-transport measurements performed on GaAs/AlGaAs high purity Hall bars with two inner contacts we show that incompressible strips formed at the edges result in Hall quantization, even if the bulk is compressible. Consequently, the relationship between the quantum Hall effect and topological bulk insulator breaks for specific field intervals within the plateaus. The measurement of conducting bulk, strongly challenges all existing single-particle theories. PMID:28071652
Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Hafez, Mohammed; Dacles, Jennifer
1989-01-01
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.
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.
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.
NASA Technical Reports Server (NTRS)
Chang, J. L. C.; Kwak, D.; Rogers, S. E.; Yang, R.-J.
1988-01-01
This paper discusses incompressible Navier-Stokes solution methods with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow solver code has been used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.
NASA Technical Reports Server (NTRS)
Chang, J. L. C.; Kwak, D.; Rogers, S. E.; Yang, R.-J.
1988-01-01
Incompressible Navier-Stokes solution methods are discussed with an emphasis on the pseudocompressibility method. A steady-state flow solver based on the pseudocompressibility approach is then described. This flow-solver code was used to analyze the internal flow in the Space Shuttle main engine hot-gas manifold. Salient features associated with this three-dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.
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.
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.
Small data global existence for a fluid-structure model
NASA Astrophysics Data System (ADS)
Ignatova, Mihaela; Kukavica, Igor; Lasiecka, Irena; Tuffaha, Amjad
2017-02-01
We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global existence and exponential decay of solutions for small initial data in a suitable Sobolev space.
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.
Incompressible flow in stepped labyrinth seals
NASA Technical Reports Server (NTRS)
Morrison, G. L.; Chi, D.
1985-01-01
A steped labyrinth seal was experimentally investigated to determine the effects of pressure ratio, shaft speed, number of teeth, and tooth/step location upon the leakage through the seal for incompressible flow. The dependence of the flow coefficient upon the number of throttles and pressure ratio are similar to those for straight-through labyrinth seals. It can be noted that the axial location of the throttle with respect to the step had a special effect upon the flow coefficient. That is, the dependency of the flow coefficient upon rotation rate and the number of throttles changes with axial location. It was found that the minimum flow coefficient was obtained when the seal teeth were centered on the step surface. Axial pressure distribution measurements show that when the teeth are centered on the step, the pressure drop from cavity to cavity is almost uniform. It is speculated that the obtaining of this uniform pressure gradient is the cause for the enhanced performance of the stepped labyrinth seal when operated in that configuration.
Exact solutions of the incompressible dissipative Hall magnetohydrodynamics
Xia, Zhenwei; Yang, Weihong
2015-03-15
By using analytical method, the exact solutions of the incompressible dissipative Hall magnetohydrodynamics (MHD) equations are derived. It is found that a phase difference may occur between the velocity and magnetic field fluctuations when the kinetic and magnetic Reynolds numbers are both very large. Since velocity and magnetic field fluctuations are both circular polarized, the phase difference makes them no longer parallel or anti-parallel like that in the incompressible ideal Hall MHD.
Large deformations of a new class of incompressible elastic bodies
NASA Astrophysics Data System (ADS)
Bustamante, R.; Orellana, O.; Meneses, R.; Rajagopal, K. R.
2016-06-01
The consequences of the constraint of incompressibility is studied for a new class of constitutive relation for elastic bodies, for which the left Cauchy-Green tensor is a function of the Cauchy stress tensor. The requirement of incompressibility is imposed directly in the constitutive relation, and it is not necessary to assume a priori that the stress tensor should be divided into two parts, a constraint stress and a constitutively specified part, as in the classical theory of nonlinear elasticity.
Method of investigation of deformations of solids of incompressible materials
NASA Astrophysics Data System (ADS)
Abdrakhmanova, A. I.; Garifullin, I. R.; Sultanov, L. U.
2016-11-01
The aim of this work is development mathematical models, algorithm for the investigation stress-strain state of elastic solids, taking into account the incompressibility materials. The constitutive equations are received using a potential energy of deformations. The system of the linear algebraic equations is received by linearization of a resolving equation. The penalty method is applied for a modelling of the incompressibility of the material. The finite element method is used for numerical solution of the problems.
General exact solution of incompressible potential flows around two circles
NASA Astrophysics Data System (ADS)
Qianxi, Wang; Lixian, Zhuang; Binggang, Tong
1993-02-01
Three exact solutions are obtained for 2-D incompressible potential flows around two moving circles in three cases: (i) expansion (or contraction) of themselves, (ii) approaching (or departing from) each other, (iii) moving perpendicularly to the line connecting the centres in opposite directions. Meanwhile, another set of two exact solutions is obtained for 2-D incompressible potential flows between two moving eccentric circles in two cases: moving parallely or perpendicularly to the line connecting the centres.
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
NASA Astrophysics Data System (ADS)
Pérez-Reyes, Ildebrando; Vargas-Aguilar, René O.
2016-11-01
The thickness and thermal conductivity of the bounding walls are of interest in the hydrodynamic stability of a viscoelastic fluid layer. In this work the linear hydrodynamic stability is studied by means of the Galerkin method. The two ideal cases of thermal insulating and perfect thermal conducting walls are bridged by taking into account these two properties. Curves of criticality for the Rayleigh number, the wavenumber and the frequency of oscillation against the thermal conductivity for fixed wall thickness, Prandtl number and relaxation and retardation times are presented. Here, the dimensionless retardation time E was set to 0.05 and 0.1 while the dimensionless relaxation time F was set to 0.1 and 100. The role of the thermal conductivity and of the thickness of the walls are discussed. One important result of this investigation is that for non ideal thermal conducting conditions the system is more stable when the thickness of the fluid layer is larger in comparison to that of the boundaries. A discussion on the effect of E and F on the stability is given as well. Ciencia Básica - Conacyt through Project No. 255839.
NASA Astrophysics Data System (ADS)
Lafarge, Denis
1993-02-01
Recently, Avellaneda and Torquato [Phys. Fluids A 3, 2529 (1991)] derived several expressions for both the static and dynamic permeability for flow through porous media, in terms of the characteristic viscous relaxation times. In this Brief Communication the focus is on the physical interpretation, Darcy's law is explicitly obtained, and a slightly misleading statement (which has no effect on the mathematics but may induce erroneous interpretations) is corrected.
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)
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
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.
An approximate projection method for incompressible flow
NASA Astrophysics Data System (ADS)
Stevens, David E.; Chan, Stevens T.; Gresho, Phil
2002-12-01
This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139-1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40-65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency.A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake.
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.
Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves
NASA Astrophysics Data System (ADS)
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), 10.1016/0021-8928(66)90066-9] 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), 10.1063/1.3005435; Exp. Fluids 50, 905 (2010), 10.1007/s00348-010-0942-9].
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.
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.
On Cattaneo-Christov heat flux in the flow of variable thermal conductivity Eyring-Powell fluid
NASA Astrophysics Data System (ADS)
Hayat, Tasawar; Khan, Muhammad Ijaz; Waqas, Muhammad; Alsaedi, Ahmed
Here Cattaneo-Christov heat flux model is employed for heat transfer in the stagnation point flow due to stretching cylinder. This consideration modifies the Fourier's law of heat conduction through thermal relaxation time. Temperature-dependent thermal conductivity is adopted. Constitutive equations for Eyring-Powell liquid are considered in the boundary layer flow analysis. Convergent solutions to the nonlinear formulation are derived and analyzed using homotopic procedure. Skin friction coefficient is tabulated and examined for various embedded parameters.
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
NASA Astrophysics Data System (ADS)
Alahyane, M.; Hakim, A.; Raghay, S.
2017-01-01
In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large category of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter and to find a sufficient condition for the convergence of the algorithm in general cases. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Doughty, Christine; Tsang, Chin-Fu; Hatanaka, Koichiro; Yabuuchi, Satoshi; Kurikami, Hiroshi
2008-08-01
The flowing fluid electric conductivity (FFEC) logging method is an efficient way to provide information on the depths, salinities, and inflow strengths of individual conductive features intercepted by a borehole, without the use of specialized probes. Using it in a multiple-flow rate mode allows, in addition, an estimate of the transmissivities and inherent (far-field) hydraulic heads in each of the conductive features. The multirate method was successfully applied to a 500-m borehole in a granitic formation and reported recently. The present paper describes the application of the method to two zones within a 1000-m borehole in sedimentary rock, which produced, for each zone, three sets of logs at different pumping rates, each set measured over a period of about 1 day. The data sets involve several complications, such as variable well diameter, gradual water level decline in the well during logging, possible fluid flow through the unfractured rock matrix, and effects of drilling mud. Various techniques were applied to analyze the FFEC logs: direct-fitting, mass integral, and the multirate method mentioned above. In spite of complications associated with the tests, analysis was able to identify 44 hydraulically conducting fractures distributed over the depth interval 150-775 m below ground surface. The salinities (in FEC), and transmissivities and hydraulic heads (in dimensionless form) of these 44 features were obtained and found to vary significantly among one another. These results were compared with transmissivity and head values inferred from eight packer tests that were conducted in this borehole over the same depth interval. FFEC results were found to be consistent with packer test results, thus demonstrating the robustness of the FFEC logging method under nonideal conditions.
Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows
NASA Astrophysics Data System (ADS)
Fu, S. C.; So, R. M. C.; Leung, W. W. F.
2010-08-01
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.
NASA Astrophysics Data System (ADS)
Bilal, S.; Khalil-ur-Rehman; Malik, M. Y.; Hussain, Arif; Khan, Mair
Present work is communicated to identify characteristics of magnetohydrodynamic (MHD) three dimensional boundary layer flow of Williamson fluid confined by a bidirectional stretched surface. Conductivity of working fluid is assumed to be temperature dependent. Generative/absorptive heat transfer is also taken into account. Mathematical model is formulated in the form of partial expressions and then transmuted into ordinary differential equations with the help of newfangled set of similarity transformations. The resulting non-linear differential system of equations is solved numerically with the aid of Runge-Kutta algorithm supported by shooting method. Flow features are exemplified quantitatively through graphs. Scintillating results for friction factor and convective heat transfer are computed and scrutinized tabularly. Furthermore, the accuracy of present results is tested with existing literature and we found an excellent agreement. It is inferred that velocity along x-direction mounts whereas along y-direction depreciates for incrementing values of stretching ratio parameter. Moreover, it is also elucidated that non-linearity index tends to decrement the velocity and thermal distributions of fluid flow.
NASA Astrophysics Data System (ADS)
Carrim, A. H.; Aziz, Taha; Mahomed, F. M.; Khalique, Chaudry Masood
2016-06-01
The effects of non-Newtonian fluids are investigated by means of an appropriate model studying the flow of a fourth grade fluid. The geometry of this model is described by the unsteady unidirectional flow of an incompressible fluid over an infinite flat plate within a porous medium. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The classical Lie symmetry approach is utilized in order to construct group invariant solutions to the governing higher-order nonlinear partial differential equation (PDE). The conditional symmetry approach has also been utilized to solve the governing model. Some new classes of conditional symmetry solutions have been obtained for the model equation in the form of closed-form exponential functions. The invariant solution corresponding to the nontraveling wave type is considered to be the most significant solution for the fluid flow model under investigation since it directly incorporates the physical behavior of the flow model.
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.
NASA Astrophysics Data System (ADS)
van Loef, J. J.
1984-06-01
A corresponding states analysis of the shear viscosity and the thermal conductivity of dense monatomic and molecular fluids composed of either diatomic molecules and CO 2 or light hydrocarbons is presented. The transport coefficients are reduced using Lennard-Jones parameters σ and ε/ kB, the values of which are chosen such that the reduced critical density and the reduced critical temperature have the same values for each of the fluids considered. Using evaluated transport coefficients along isotherms and isobars ( P ⩽ 100 MPa), it appears that the reduced fluidity and reduced thermal resistivity increase closely linearly with the reduced molar volume in a large fraction of the liquid range. Presenting a comprehensive set of data this way it is easy, a) to verify that the transport coefficients of monatomic fluids (except 4He) obey corresponding states principle, b) to compare the experimental data with molecular dynamical calculations, c) to estimate transport coefficients of the superheated monatomic liquid of known density, d) to investigate to which extent transport coefficients of molecular fluids correspond with those of the monatomic ones, e) to predict transport coefficients of a molecular liquid of a type similar to those for which η s and λ are available, provided the equation of state is known (e.g. CO, NO, C 2H 2), f) to discriminate data sources using a consistency test (e.g. η s of liquid CO and Cl 2), g) to predict transport coefficients of binary monatomic and molecular liquid mixtures provided their molar volume is known, using the Lorentz-Berthelot mixing rules to determine η and ε/ kB (e.g. (Ar + Kr), (Ar + CH 4), (Kr + CH 4) , (N 2 + CH 4)).
A Numerical Method for Incompressible Flow with Heat Transfer
NASA Technical Reports Server (NTRS)
Sa, Jong-Youb; Kwak, Dochan
1997-01-01
A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.
Combined AIE/EBE/GMRES approach to incompressible flows
NASA Astrophysics Data System (ADS)
Liou, J.; Tezduyar, T. E.
Adaptive implicit-explicit (AIE), grouped element-by-element (GEBE), and generalized minimum residuals (GMRES) solution techniques for incompressible flows are combined. In this approach, the GEBE and GMRES iteration methods are employed to solve the equation systems resulting from the implicitly treated elements, and therefore no direct solution effort is involved. The benchmarking results demonstrate that this approach can substantially reduce the CPU time and memory requirements in large-scale flow problems. Although the description of the concepts and the numerical demonstration are based on the incompressible flows, the approach presented here is applicable to larger class of problems in computational mechanics.
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)
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
Numerical simulation for peristaltic activity of Sutterby fluid with modified Darcy's law
NASA Astrophysics Data System (ADS)
Hayat, T.; Ayub, S.; Alsaedi, A.; Tanveer, A.; Ahmad, B.
The current work examines the peristaltic flow of Sutterby fluid in a planar symmetric channel. Electrically conducting fluid is considered via imposed magnetic field. An incompressible Sutterby fluid saturates the porous medium. Modified Darcy's law has been employed for the porous medium effect. The channel walls are compliant. Convective conditions of heat and mass transfer are imposed. Viscous dissipation and Joule heating are retained. Problem for large wavelength are numerically solved. The graphs are obtained for the velocity, temperature, concentration and heat transfer rate. Velocity and concentration profiles are observed to have opposite behavior for increasing Darcy number. It is found that the effect of Hartman number on the velocity and temperature profiles is similar. Further heat transfer coefficient strengthened when heat transfer Biot number is increased.
NASA Astrophysics Data System (ADS)
Naseri, A.; Lehmkuhl, O.; Gonzalez, I.; Oliva, A.
2016-09-01
This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability. Several coupling schemes are tested including fixed-point method with different static and dynamic relaxation, as well as Newton-Krylov method with approximated Jacobian. Numerical tests are conducted in the context of a biomechanical problem. Results indicate that the Newton-Krylov solver outperforms fixed point ones while introducing more complexity to the problem due to the evaluation of the Jacobian. Fixed-point solver with Aitken's relaxation method also proved to be a simple, yet efficient method for FSI simulations.
A comparison of numerical methods for non-Newtonian fluid flows in a sudden expansion
NASA Astrophysics Data System (ADS)
Ilio, G. Di; Chiappini, D.; Bella, G.
2016-06-01
A numerical study on incompressible laminar flow in symmetric channel with sudden expansion is conducted. In this work, Newtonian and non-Newtonian fluids are considered, where non-Newtonian fluids are described by the power-law model. Three different computational methods are employed, namely a semi-implicit Chorin projection method (SICPM), an explicit algorithm based on fourth-order Runge-Kutta method (ERKM) and a Lattice Boltzmann method (LBM). The aim of the work is to investigate on the capabilities of the LBM for the solution of complex flows through the comparison with traditional computational methods. In the range of Reynolds number investigated, excellent agreement with the literature results is found. In particular, the LBM is found to be accurate in the prediction of the fluid flow behavior for the problem under consideration.
NASA Astrophysics Data System (ADS)
Hussain, Arif; Malik, M. Y.; Bilal, S.; Awais, M.; Salahuddin, T.
Present communication presents numerical investigation of magnetohydrodynamic Sisko fluid flow over linearly stretching cylinder along with combined effects of temperature depending thermal conductivity and viscous dissipation. The arising set of flow govern equations are simplified under usual boundary layer assumptions. A set of variable similarity transforms are employed to shift the governing partial differential equations into ordinary differential equations. The solution of attained highly nonlinear simultaneous equations is computed by an efficient technique (shooting method). Numerical computations are accomplished and interesting aspects of flow velocity and temperature are visualized via graphs for different parametric conditions. A comprehensive discussion is presented to reveal the influence of flow parameters on wall shear stress and local Nusselt number via figures and tables.Furthermore, it is observed that magnetic field provides noticeable resistance to the fluid motion while both material parameter and curvature accelerates it. The progressing values of both Eckert number and thermal conductivity parameter have qualitively same effects i.e. they rise the temperature. Additionally, material parameter and curvature parameter increase the coefficient of skin friction absolutely and qualitively similar effects are noticed for Nusselt number against variations in Prandtl number and curvature parameter. On the other hand local Nusselt diminishes for larger values of Eckert number and power law index. The present results are compared with existing literature via tables, they have good covenant with previous results.
NASA Astrophysics Data System (ADS)
Kolesnichenko, A. V.
2010-08-01
This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism, this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects. Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002-2004; Kolesnichenko and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative
Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability
NASA Astrophysics Data System (ADS)
Belyaev, Mikhail A.
2017-02-01
We present an instability for exciting incompressible modes (e.g., gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, which carries a flux of energy and angular momentum with the opposite sign as the energy and angular momentum density of the stellar mode. We call this instability the acoustic Chandrasekhar–Friedman–Schutz (CFS) instability, because of the direct analogy to the CFS instability for exciting modes on a rotating star by emission of energy in the form of gravitational waves. However, the acoustic CFS instability differs from its gravitational wave counterpart in that the fluid medium in which the acoustic wave propagates (i.e., the accretion disk) typically rotates faster than the star in which the incompressible mode is sourced. For this reason, the instability can operate even for a non-rotating star in the presence of an accretion disk. We discuss applications of our results to high-frequency quasi-periodic oscillations in accreting black hole and neutron star systems and dwarf nova oscillations in cataclysmic variables.
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.
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
2012-01-03
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.
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
Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
NASA Astrophysics Data System (ADS)
Aluie, Hussein
2017-02-01
We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales ℓ. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the ‘bare’ velocity and magnetic fields are ‘renormalized’ by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. Particular attention is given to the effects of these subscale terms on the balances of the quadratic invariants of ideal incompressible MHD—energy, cross-helicity and magnetic helicity. At large coarse-graining length-scales, the direct dissipation of the invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we prove a very strong version of the Woltjer-Taylor conjecture
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.
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.
Numerical methods for incompressible viscous flows with engineering applications
NASA Technical Reports Server (NTRS)
Rose, M. E.; Ash, R. L.
1988-01-01
A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.
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.
An update on projection methods for transient incompressible viscous flow
Gresho, P.M.; Chan, S.T.
1995-07-01
Introduced in 1990 was the biharmonic equation (for the pressure) and the concomitant biharmonic miracle when transient incompressible viscous flow is solved approximately by a projection method. Herein is introduced the biharmonic catastrophe that sometimes occurs with these same projection methods.
A stable partitioned FSI algorithm for incompressible flow and deforming beams
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
A GPU-based incompressible Navier-Stokes solver on moving overset grids
NASA Astrophysics Data System (ADS)
Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2013-07-01
In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.
A hydrodynamic analysis of fluid flow between meshing spur gear teeth
NASA Astrophysics Data System (ADS)
Wittbrodt, M. J.; Pechersky, M. J.
1987-10-01
A one dimensional analysis of the fluid pumping action resulting from the meshing of spur gears was performed by writing a computer algorithm. Two separate analyses were conducted; one using incompressible and the other using compressible flow theory. The incompressible flow calculations correspond to heavily lubricated gears whereas the compressible flow calculations are representative of lightly lubricated gears. The analysis demonstrated that the velocity of the discharged fluid reached high velocities for both cases. The high meshing rate of the teeth along with the small discharge area is the cause for the high fluid velocities. Certain geometric design variables of the gears were seen to affect the peak velocities for each case. The variables most significantly affecting the peak velocity appear to be the drive ratio and the face width. The high velocities may contribute to the noise generated during meshing of gear teeth due to the jet noise as a result of the high velocity jets impinging on the enclosures surrounding the gears and the formation of shock waves at the exit plane of the teeth.
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.
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 Astrophysics Data System (ADS)
Vafai, Kambiz; Khan, Ambreen Afsar; Sajjad, Saba; Ellahi, Rahmat
2015-04-01
This article is concerned with the peristaltic pumping of an incompressible, electrically conducting third grade fluid in a uniform channel. The Hall effect under the influence of wall properties and heat transfer is taken into account. Mathematical modelling is based upon continuity, momentum, and energy equations. Closed form solutions for velocity, temperature, concentration, and heat transfer coefficient are obtained. Effects of pertinent parameters, such as third grade parameter Γ, Hall parameter M, amplitude ratio ɛ, Brickman number Br, Soret number Sc, wall tension E1 and elasticity parameters E2 and E3 on the velocity u, temperature θ, concentration φ, and heat transfer coefficient Z, are discussed through graphs.
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
Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
NASA Astrophysics Data System (ADS)
Cameron, Alexandre; Raynaud, Raphaël; Dormy, Emmanuel
2016-12-01
Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \\& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.
Robust boundary treatment for open-channel flows in divergence-free incompressible SPH
NASA Astrophysics Data System (ADS)
Pahar, Gourabananda; Dhar, Anirban
2017-03-01
A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.
Electron inertia effect on incompressible plasma flow in a planar channel
NASA Astrophysics Data System (ADS)
Gavrikov, M. B.; Taiurskii, A. A.
2015-10-01
> In this paper, we consider a one-fluid model of electromagnetic hydrodynamics (EMHD) of quasi-neutral plasma, with ion and electron inertia fully taken into account. The EMHD and the MHD models are compared with regard to solving the classical problem of steady flow of incompressible plasma in a planar channel. In the MHD theory, the solution is given by the Hartmann flow, whereas in the EMHD model, the diagram of the longitudinal velocity is shown to be significantly different from the Hartmann profile: in particular, near-wall flows and a counterflow appear, while the flow velocity may significantly deviate from the direction of the antigradient pressure causing plasma to flow (the so-called hydrodynamic `Hall effect'). This study shows that the EMHD and the MHD planar channel theories are practically the same for liquid metal plasma and are very different for gas plasma.
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.
NASA Astrophysics Data System (ADS)
Megahed, Ahmed M.
2015-03-01
An analysis was carried out to describe the problem of flow and heat transfer of Powell-Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell-Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.
NASA Astrophysics Data System (ADS)
Wiederhold, Andreas; Ebert, Reschad; Resagk, Christian; Research Training Group: "Lorentz Force Velocimetry; Lorentz Force Eddy Current Testing" Team
2016-11-01
We report about the feasibility of Lorentz force velocimetry (LFV) for various flow profiles. LFV is a contactless non-invasive technique to measure flow velocity and has been developed in the last years in our institute. This method is advantageous if the fluid is hot, aggressive or opaque like glass melts or liquid metal flows. The conducted experiments shall prove an increased versatility for industrial applications of this method. For the force measurement we use an electromagnetic force compensation balance. As electrolyte salty water is used with an electrical conductivity in the range of 0.035 which corresponds to tap water up to 20 Sm-1. Because the conductivity is six orders less than that of liquid metals, here the challenging bottleneck is the resolution of the measurement system. The results show only a slight influence in the force signal at symmetric and strongly asymmetric flow profiles. Furthermore we report about the application of LFV to stratified two-phase flows. We show that it is possible to detect interface instabilities, which is important for the dimensioning of liquid metal batteries. Deutsche Forschungsgemeinschaft DFG.
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)
Pedro, J. B.; Báez Vidal, A.; Lehmkuhl, O.; Pérez Segarra, C. D.; Oliva, A.
2016-09-01
The objective of the present work is to validate the compressible Large-Eddy Simulation (LES) models implemented in the in house parallel unstructured CFD code TermoFluids. Our research team has implemented and tested several LES models over the past years for the incompressible regimen. In order to be able to solve complex turbulent compressible flows, the models are revisited and modified if necessary. In addition, the performance of the implemented hybrid advection scheme is an issue of interest for the numerical simulation of turbulent compressible flows. The models are tested in the well known turbulent channel flow problem at different compressible regimens.
Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo
2016-06-01
Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: 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
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.
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.
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
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
A linearized and incompressible constitutive model for arteries.
Liu, Y; Zhang, W; Wang, C; Kassab, G S
2011-10-07
In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E₁ (circumferential), E₂ (axial), and E₃ (radial) are necessary to fit the data. The advantages and limitations of this model are discussed.
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.
Performance of Lagrangian descriptors and their variants in incompressible flows.
Ruiz-Herrera, Alfonso
2016-10-01
The method of Lagrangian Descriptors has been applied in many different contexts, specially in geophysical flows. In this paper, we analyze their performance in incompressible flows. We construct broad families of systems where this diagnostic fails in the detection of barriers to transport. Another aim of this manuscript is to illustrate the same deficiencies in the recent diagnostic proposed by Craven and Hernández.
NASA Astrophysics Data System (ADS)
Coppa, P.; Bovesecchi, G.; Fabrizi, F.
2010-08-01
Molten salts (sodium and potassium nitrides) are going to be used in many different plants as heat transferring fluids, e.g. concentration solar plants, nuclear power plants, etc. In fact they present may important advantages: their absolute safety and non toxicity, availability and low cost. But their use, e.g. in the energy receiving pipe in the focus of the parabolic mirror concentrator of the solar thermodynamic plant, requires the accurate knowledge of the thermophysical properties, above all thermal conductivity, viscosity, specific heat and thermal linear expansion, in the temperature range 200°C÷600°C. In the new laboratory by ENEA Casaccia, SolTerm Department all these properties are going to be measured. Thermal conductivity is measured with the standard probe method (linear heat source inserted into the material) manufacturing a special probe suited to the foreseen temperature range (190-550°C). The probe is made of a ceramic quadrifilar pipe containing in different holes the heater (Ni wire) and the thermometer (type J thermocouple). The thermal linear expansion will be measured by a special system designed and built to this end, measuring the sample dilatation by the reflection of a laser beam by the bottom of the meniscus in the liquid solid interface. The viscosity will be evaluated detecting the start of the natural convection in the same experiment as to measure thermal conductivity. In the paper the construction of the devices, the results of preliminary tests and an evaluation of the obtainable accuracy are reported.
Numerical Modeling of Conjugate Heat Transfer in Fluid Network
NASA Technical Reports Server (NTRS)
Majumdar, Alok
2004-01-01
Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.
Hiemenz flow of a micropolar viscoelastic fluid in hydromagnetics
NASA Astrophysics Data System (ADS)
El-Kabeir, S. M. M.
2005-10-01
Boundary-layer equations are solved for the hydromagnetic problem of two-dimensional Hiemenz flow, for a micropolar, viscoelastic, incompressible, viscous, electrically conducting fluid, impinging perpendicularly onto a plane in the presence of a transverse magnetic field. The governing system of equations is first transformed into a dimensionless form. The resulting equations then are solved by using the Runge-Kutta numerical integration procedure in conjunction with shooting technique. Numerical solutions are presented for the governing momentum and angular-momentum equations. The proposed approximate solution, although simple, is nevertheless sufficiently accurate for the entire investigated range of values of the Hartman number. The effect of micropolar and viscoelastic parameters on Hiemenz flow in hydromagnetics is discussed.
Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.
2017-02-01
The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.
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)
Besse, Nicolas; Frisch, Uriel
2017-01-01
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Frisch, Uriel
2017-04-01
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.
Mathematical Models in Dynamics of Incompressible Viscoelastic Media
NASA Astrophysics Data System (ADS)
Osipov, S. V.; Pukhnachev, V. V.; Pukhnacheva, T. P.
2010-11-01
A consistent model of incompressible viscoelastic Maxwell media is formulated. It corresponds to the choice of Jaumann rotational derivative in the constitutive relation. The governing system of equations has both real and complex characteristics. For this system, the solvability of initial-boundary value problem in the class of analytic functions is established, and for its linearized variant the solvability is shown in the class of functions of finite smoothness. It is shown that the smallness of non-diagonal terms of stress tensor entails absence of short-wave instability. A wide class of exact solutions to the motion of incompressible viscoelastic Maxwell medium is found. These solutions are partially invariant with respect to some sub-group of extended Galilei group which is admitted by equations of motion and their generalizations. The deformation of an viscoelastic strip with free boundaries is described, which moves either inertially or under the action of stretching or compressing longitudinal stresses, as well as shear stresses, applied to the free surface. The problem of filling of a spherical cavity by incompressible Maxwell medium under the action of constant pressure at infinity is considered. This is the generalization of the classic problem for viscous incompressible liquid. In both cases the cavity always shrinks to a point in a finite or infinite time. If the surface tension differs from zero, the collapse takes place in a finite time. Depending on the three dimensionless parameters (Reynolds number, capillary number and dimensionless relaxation time) both oscillatory and monotonic regimes of motion are possible. When the cavity radius is small, no oscillations can exist. A problem of filling of an spherical cavity with incompressible viscoelastic Kelvin-Voigt medium under the action of constant pressure at infinity is also considered. Unlike the case of Maxwell medium, here both the cavity collapse and stabilization of its radius to a positive
... up in the body. This is called fluid overload (volume overload). This can lead to edema (excess fluid in ... Water imbalance; Fluid imbalance - dehydration; Fluid buildup; Fluid overload; Volume overload; Loss of fluids; Edema - fluid imbalance; ...
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.
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.
A boundary element method for steady incompressible thermoviscous flow
NASA Technical Reports Server (NTRS)
Dargush, G. F.; Banerjee, P. K.
1991-01-01
A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modeling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.
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.
Computation of turbulent incompressible wing-body junction flow
NASA Technical Reports Server (NTRS)
Burke, R. W.
1989-01-01
A three-dimensional incompressible Reynolds-averaged Navier-Stokes solver is presently used in conjunction with a mixing-length turbulence model to characterize the flow around a wing that is mounted on a flat plate, in a wind tunnel, as well as the flow around a support strut within a turnaround duct. Good agreement is found between predicted and observed values of flat-plate static pressure, horseshoe vortex system size, and mean flow velocities in the case of the wing; the case of the strut in a duct is noted to exhibit many of the same overall flow features as the wing/plate.
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.
Visualization tools for vorticity transport analysis in incompressible flow.
Sadlo, Filip; Peikert, Ronald; Sick, Mirjam
2006-01-01
Vortices are undesirable in many applications while indispensable in others. It is therefore of common interest to understand their mechanisms of creation. This paper aims at analyzing the transport of vorticity inside incompressible flow. The analysis is based on the vorticity equation and is performed along pathlines which are typically started in upstream direction from vortex regions. Different methods for the quantitative and explorative analysis of vorticity transport are presented and applied to CFD simulations of water turbines. Simulation quality is accounted for by including the errors of meshing and convergence into analysis and visualization. The obtained results are discussed and interpretations with respect to engineering questions are given.
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.
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.
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.
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.
Effect of fluid compressibility on journal bearing performance
NASA Technical Reports Server (NTRS)
Dimofte, Florin
1993-01-01
An analysis was undertaken to determine the effect of fluid film compressibility on the performance of fluid film bearings. A new version of the Reynolds equation was developed, using a polytropic expansion, for both steady-state and dynamic conditions. Polytropic exponents from 1 (isothermal) to 1000 (approaching an incompressible liquid) were evaluated for two bearing numbers, selected from a range of practical interest for cryogenic application, and without cavitation. Bearing loads were insensitive to fluid compressibility for low bearing numbers, as was expected. The effect of compressibility on attitude angle was significant, even when the bearing number was low. A small amount of fluid compressibility was enough to obtain stable running conditions. Incompressible liquid lacked stability at all conditions. Fluid compressibility can be used to control the bearing dynamic coefficients, thereby influencing the dynamic behavior of the rotor-bearing system.
Incompressible material point method for free surface flow
NASA Astrophysics Data System (ADS)
Zhang, Fan; Zhang, Xiong; Sze, Kam Yim; Lian, Yanping; Liu, Yan
2017-02-01
To overcome the shortcomings of the weakly compressible material point method (WCMPM) for modeling the free surface flow problems, an incompressible material point method (iMPM) is proposed based on operator splitting technique which splits the solution of momentum equation into two steps. An intermediate velocity field is first obtained by solving the momentum equations ignoring the pressure gradient term, and then the intermediate velocity field is corrected by the pressure term to obtain a divergence-free velocity field. A level set function which represents the signed distance to free surface is used to track the free surface and apply the pressure boundary conditions. Moreover, an hourglass damping is introduced to suppress the spurious velocity modes which are caused by the discretization of the cell center velocity divergence from the grid vertexes velocities when solving pressure Poisson equations. Numerical examples including dam break, oscillation of a cubic liquid drop and a droplet impact into deep pool show that the proposed incompressible material point method is much more accurate and efficient than the weakly compressible material point method in solving free surface flow problems.
A Linearized and Incompressible Constitutive Model for Arteries
Liu, Y.; Zhang, W.; Wang, C.; Kassab, G. S.
2011-01-01
In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke’s law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young’s moduli E1 (circumferential), E2 (axial), and E3 (radial) are necessary to fit the data. The advantages and limitations of this model are discussed. PMID:21605567
Group invariant solution for a pre-existing fracture driven by a power-law fluid in permeable rock
NASA Astrophysics Data System (ADS)
Fareo, A. G.; Mason, D. P.
2016-06-01
Group invariant analytical and numerical solutions for the evolution of a two-dimensional fracture with nonzero initial length in permeable rock and driven by an incompressible non-Newtonian fluid of power-law rheology are obtained. The effect of fluid leak-off on the evolution of the power-law fluid fracture is investigated.
NASA Astrophysics Data System (ADS)
Tallet, A.; Allery, C.; Leblond, C.; Liberge, E.
2015-05-01
The pressure term which appears in the ROM (reduced order model) associated to the incompressible Navier-Stokes equations, in particular for the shear flows, plays an important role on the velocity. The aim of this paper is to propose a Proper Orthogonal Decomposition based reduced order model (POD-ROM) to obtain both the velocity and pressure fields for incompressible flows. Two PODs are performed, one for the velocity and the other for the pressure. Contrary to existing projection methods available in the literature, the temporal velocity and pressure coefficients are sought by minimizing the residual of the momentum equation only, without the need of a Poisson equation. For the numerical test cases considered in this paper, the proposed minimum residual projection enables to obtain accurately the pressure field, and in turn to slightly improve the velocity one. The method is tested on two fluid flows: a transient mixed-convection flow and a periodic flow around a circular cylinder. In this last case, the drag, lift and pressure coefficients, as well as the Strouhal number are properly recovered compared to those of the full model.
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
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
New developments in adaptive methods for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Oden, J. T.; Bass, Jon M.
1990-01-01
New developments in a posteriori error estimates, smart algorithms, and h- and h-p adaptive finite element methods are discussed in the context of two- and three-dimensional compressible and incompressible flow simulations. Applications to rotor-stator interaction, rotorcraft aerodynamics, shock and viscous boundary layer interaction and fluid-structure interaction problems are discussed.
Ness, L.A.
1989-11-07
This patent describes a surge bottle or pressure pulsation dampening device for cryogenic services. It comprises: a liquid sump section, wherein the liquid sump section is comprised of an enclosed area containing a volume of an incompressible fluid; a warm gas volume section, wherein the warm gas volume section is comprised of an enclosed area containing a volume of a compressible warm gas; and a laminar flow section which connects and allows for communication between the liquid sump section and the warm gas volume section. The laminar flow section is comprised of a number of small bore, thin walled tubes which contain the incompressible fluid in the end connected to the liquid sump section and the compressible warm gas in the end connected to the warm gas volume section wherein the bore of the tubes are such that any movement of the either the compressible warm gas or the incompressible fluid would be laminar flow. During operation, the incompressible fluid and the warm compressible gas within the small bore, thin walled tubes move or oscillate a short distance in each of the tubes with minimal intermixing of the incompressible fluid and the warm compressible gas thereby minimizing heat leak from the warm gas volume section to the liquid sump section into the liquid in the sump.
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
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.
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.
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, 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.
A consistent projection-based SUPG/PSPG XFEM for incompressible two-phase flows
NASA Astrophysics Data System (ADS)
Liao, Jian-Hui; Zhuang, Zhuo
2012-10-01
In this paper, a consistent projection-based streamline upwind/pressure stabilizing Petrov-Galerkin (SUPG/PSPG) extended finite element method (XFEM) is presented to model incompressible immiscible two-phase flows. As the application of linear elements in SUPG/PSPG schemes gives rise to inconsistency in stabilization terms due to the inability to regenerate the diffusive term from viscous stresses, the numerical accuracy would deteriorate dramatically. To address this issue, projections of convection and pressure gradient terms are constructed and incorporated into the stabilization formulation in our method. This would substantially recover the consistency and free the practitioner from burdensome computations of most items in the residual. Moreover, the XFEM is employed to consider in a convenient way the fluid properties that have interfacial jumps leading to discontinuities in the velocity and pressure fields as well as the projections. A number of numerical examples are analyzed to demonstrate the complete recovery of consistency, the reproduction of interfacial discontinuities and the ability of the proposed projection-based SUPG/PSPG XFEM to model two-phase flows with open and closed interfaces.
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.
Simulation of incompressible two-phase flow in porous media with large timesteps
NASA Astrophysics Data System (ADS)
Cogswell, Daniel; Szulczewski, Michael
2016-11-01
Simulations of flow in porous media suffer from severe timestep restrictions as the permeability and viscosity contrast become increasingly heterogeneous, even when solved with a fully implicit discretization. Previous efforts to alleviate these restrictions have focused on numerical methods, but the problem persists because it originates from the shape of the fractional flow function. Here we focus on regularizing the equations themselves with the addition of an energy constraint. The equations for the flow of two immiscible, incompressible fluid phases in porous media are recast as a gradient flow using the phase-field method, a macroscopic surface tension is introduced, and a convex energy splitting scheme is applied to enable unconditionally large timesteps. Using the phase-field formulation as a homotopy map, the unmodified flow equations can be solved with large timesteps, even with high degrees of heterogeneity in permeability and viscosity. For a 2D test problem, the homotopy method allows the timestep to be increased by more than four orders of magnitude relative to the unmodified equations.
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.
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.
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.
Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas
NASA Astrophysics Data System (ADS)
Caboussat, A.; Picasso, M.; Rappaz, J.
2005-03-01
A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the gas domain, the velocity is disregarded, the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law. The gas pressure is imposed as a normal force on the liquid-gas interface. An implicit splitting scheme is used to decouple the physical phenomena. Given the gas pressure on the interface, the method described in [J. Comput Phys. 155 (1999) 439; Int. J. Numer. Meth. Fluids 42(7) (2003) 697] is used to track the liquid domain and to compute the velocity and pressure fields in the liquid. Then the connected components of the gas domain are found using an original numbering algorithm. Finally, the gas pressure is updated from the ideal gas law in each connected component of gas. The implementation is validated in the frame of mould filling. Numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected.
Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow
NASA Astrophysics Data System (ADS)
Benhamou, B.; Galanis, N.; Laneville, A.
2000-12-01
This paper presents a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through-flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross-section, this flow consists of a pair of symmetrical counter-rotating vortices, which are alternatively clockwise and anti-clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance. Eventually, the flow field reaches a periodic regime that depends only on the axial position. The results show that the transient flow field depends on the pipe oscillation pattern (initial position and/or direction of initial movement). Copyright
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.
Wake effects on drift in two-dimensional inviscid incompressible flows
Melkoumian, Sergei; Protas, Bartosz
2014-12-15
This investigation analyzes the effect of vortex wakes on the Lagrangian displacement of particles induced by the passage of an obstacle in a two-dimensional incompressible and inviscid fluid. In addition to the trajectories of individual particles, we also study their drift and the corresponding total drift areas in the Föppl and Kirchhoff potential flow models. Our findings, which are obtained numerically and in some regimes are also supported by asymptotic analysis, are compared to the wakeless potential flow which serves as a reference. We show that in the presence of the Föppl vortex wake, some of the particles follow more complicated trajectories featuring a second loop. The appearance of an additional stagnation point in the Föppl flow is identified as a source of this effect. It is also demonstrated that, while the total drift area increases with the size of the wake for large vortex strengths, it is actually decreased for small circulation values. On the other hand, the Kirchhoff flow model is shown to have an unbounded total drift area. By providing a systematic account of the wake effects on the drift, the results of this study will allow for more accurate modeling of hydrodynamic stirring.
Conservative discontinuous Galerkin discretizations of the 2D incompressible Euler equation
NASA Astrophysics Data System (ADS)
Waelbroeck, Francois; Michoski, Craig; Bernard, Tess
2016-10-01
Discontinuous Galerkin (DG) methods provide local high-order adaptive numerical schemes for the solution of convection-diffusion problems. They combine the advantages of finite element and finite volume methods. In particular, DG methods automatically ensure the conservation of all first-order invariants provided that single-valued fluxes are prescribed at inter-element boundaries. For the 2D incompressible Euler equation, this implies that the discretized fluxes globally obey Gauss' and Stokes' laws exactly, and that they conserve total vorticity. Liu and Shu have shown that combining a continuous Galerkin (CG) solution of Poisson's equation with a central DG flux for the convection term leads to an algorithm that conserves the principal two quadratic invariants, namely the energy and enstrophy. Here, we present a discretization that applies the DG method to Poisson's equation as well as to the vorticity equation while maintaining conservation of the quadratic invariants. Using a DG algorithm for Poisson's equation can be advantageous when solving problems with mixed Dirichlet-Neuman boundary conditions such as for the injection of fluid through a slit (Bickley jet) or during compact toroid injection for tokamak startup.
A Coupled Finite Volume Solver for Incompressible Flows
NASA Astrophysics Data System (ADS)
Moukalled, F.; Darwish, M.
2008-09-01
This paper reports on a pressure-based coupled algorithm for the solution of laminar incompressible flow problems. The implicit pressure-velocity coupling is accomplished by deriving a pressure equation in a way similar to a segregated SIMPLE algorithm with the extended set of equations solved simultaneously and having diagonally dominant coefficients. The superiority of the coupled approach over the segregated approach is demonstrated by solving the lid-driven flow in a square cavity problem using both methodologies and comparing their computational costs. Results indicate that the number of iterations needed by the coupled solver is grid independent. Moreover, recorded CPU time values reveal that the coupled approach substantially reduces the computational cost with the reduction rate for the problem solved increasing as the grid size increases and reaching a value as high as 115.
Investigation of subgrid models in homogeneous incompressible turbulence
NASA Astrophysics Data System (ADS)
Teissedre, C.
1987-08-01
A data base of simulated homogeneous, incompressible turbulence in an anisotropic regime was derived using a direct simulation code on a parallel processing computer. The simulated distributions were used to validate subgrid models of the turbulent viscosity and similitude type (analogy between the near field of the cut-off and the subgrid field). The first type of model accounts for the evolution of turbulent kinetic energy well, while the second type, although it better represents the exact value of stress in the subgrid, seems to present a defect of nondissipation. Tests of a model of perturbation of nonlinear terms were performed in an isotropic situation with large structures. The results show the same kind of nondissipative behavior as for the similitude model.
Linear analysis of incompressible Rayleigh-Taylor instability in solids
NASA Astrophysics Data System (ADS)
Piriz, A. R.; López Cela, J. J.; 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.
Effect of crossflow on Goertler instability in incompressible boundary layers
NASA Technical Reports Server (NTRS)
Zurigat, Y. H.; Malik, M. R.
1994-01-01
Linear stability theory is used to study the effect of crossflow on Goertler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the crossflow stabilizes Goertler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on crossflow instability is destabilizing. Calculations show that the changeover from Goertler to crossflow instabilities is a function of Goertler number, pressure gradient, and sweep angle. The results demonstrate that Goertler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a crossflow Reynolds number. Thus, the changeover from Goertler to crossflow instability takes place at some critical crossflow Reynolds number whose value increases with Goertler number.
Ecke, R.; Li, Ning; Chen, Shiyi; Liu, Yuanming
1996-11-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project was a study of turbulence in fluids that are subject to different body forces and to external temperature gradients. Our focus was on the recent theoretical prediction that the Kolomogorov picture of turbulence may need to be modified for turbulent flows driven by buoyancy and subject to body forces such as rotational accelerations. Models arising from this research are important in global climate modeling, in turbulent transport problems, and in the fundamental understanding of fluid turbulence. Experimentally, we use (1) precision measurements of heat transport and local temperature; (2) flow visualization using digitally- enhanced optical shadowgraphs, particle-image velocimetry, thermochromic liquid-crystal imaging, laser-doppler velocimetry, and photochromic dye imaging; and (3) advanced image- processing techniques. Our numerical simulations employ standard spectral and novel lattice Boltzmann algorithms implemented on parallel Connection Machine computers to simulate turbulent fluid flow. In laboratory experiments on incompressible fluids, we measure probability distribution functions and two-point spatial correlations of temperature T and velocity V (both T-T and V-T correlations) and determine scaling relations for global heat transport with Rayleigh number. We also explore the mechanism for turbulence in thermal convection and the stability of the thermal boundary layer.
Fluid dynamics of bacterial turbulence.
Dunkel, Jörn; Heidenreich, Sebastian; Drescher, Knut; Wensink, Henricus H; Bär, Markus; Goldstein, Raymond E
2013-05-31
Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data.
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).
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.
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.
Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2017-01-01
An approximation to the added mass matrix of an assembly of spheres is constructed on the basis of potential flow theory for situations where one sphere is much larger than the others. In the approximation, the flow potential near a small sphere is assumed to be dipolar, but near the large sphere it involves all higher order multipoles. The analysis is based on an exact result for the potential of a magnetic dipole in the presence of a superconducting sphere. Subsequently, the approximate added mass hydrodynamic interactions are used in a calculation of the swimming velocity and rate of dissipation of linear chain structures consisting of a number of small spheres and a single large one, with account also of frictional hydrodynamic interactions. The results derived for periodic swimming on the basis of a kinematic approach are compared with the bilinear theory, valid for small amplitude of stroke, and with the numerical solution of the approximate equations of motion. The calculations interpolate over the whole range of scale number between the friction-dominated Stokes limit and the inertia-dominated regime.
Magnetohydrodynamic stagnation point flow towards a stretching vertical sheet in a micropolar fluid
NASA Astrophysics Data System (ADS)
Ishak, A.; Nazar, R.; Pop, I.
2007-03-01
The analysis of steady two-dimensional stagnation point flow of an incompressible micropolar and electrically conducting fluid subject to a transverse uniform magnetic field towards a stretching vertical sheet is investigated when the sheet is stretched in its own plane with a velocity and a temperature proportional to the distance from the stagnation point. The governing system of partial differential equations is transformed to ordinary differential equations, which then are solved numerically using a finite difference scheme known as the Keller-box method. The velocity, microrotation and temperature distributions as well as the skin friction coefficient and the local Nusselt number are obtained for various parameters. Both the assisting and the opposing buoyant flows are considered. It is found that dual solutions exist for the opposing flow, for some regions of the buoyancy parameter, while for the assisting flow the solution is unique. Tables 3, Figs 14, Refs 26.
NASA Astrophysics Data System (ADS)
Si, Dongqing; Jian, Yongjun
2015-03-01
By employing the perturbation method, the approximate analytical solutions of velocity and volume flow rate are presented for electromagnetohydrodynamic (EMHD) flow of an electrically conducting, incompressible and viscous Jeffrey fluid between two slit microparallel plates with corrugated walls. The corrugations of the two walls are described as periodic sinusoidal waves with small amplitude either in phase or half-period out of phase. The effects of the corrugations on the EMHD flow velocity are analyzed by using numerical computation. The variations of velocity profiles and mean velocity parameter and their dependences on the Reynolds number Re, Hartmann number Ha, dimensionless wave number λ of the wall perturbation, the dimensionless relaxation time λ1ω and retardation time λ2ω are explained graphically.
Influence of Young's moduli in 3D fluid-structure coupled models of the human cochlea
NASA Astrophysics Data System (ADS)
Böhnke, Frank; Semmelbauer, Sebastian; Marquardt, Torsten
2015-12-01
The acoustic wave propagation in the human cochlea was studied using a tapered box-model with linear assumptions respective to all mechanical parameters. The discretisation and evaluation is conducted by a commercial finite element package (ANSYS). The main difference to former models of the cochlea was the representation of the basilar membrane by a 3D elastic solid. The Young's moduli of this solid were modified to study their influence on the travelling wave. The lymph in the scala vestibuli and scala tympani was represented by a viscous and nearly incompressible fluid finite element approach. Our results show the maximum displacement for f = 2kHz at half of the length of the cochlea in accordance with former experiments. For low frequencies f <200 Hz nearly zero phase shifts were found, whereas for f =1 kHz it reaches values up to -12 cycles depending on the degree of orthotropy.
Transient, radial temperature distribution in a porous medium during fluid injection
Dunn, J.C.; Nilson, R.H.
1982-01-01
Analytical and numerical solutions are presented for the transient, radial temperature distribution in a porous medium which is subjected to a constant-rate injection of an incompressible fluid from a wellbore. The formulation includes energy transfer by conduction and convection, and the Danckwerts boundary condition is applied at the finite-radius wellbore. At late times, the numerical solutions approach a self-similar form which can be described in terms of the incomplete Gamma function. In typical petroleum and geothermal applications, convergence to the asymptotic similarity solutions occurs on a time scale of roughly one hour. The results are generally applicable to a broad range of convection-diffusion phenomena which are best described in radial coordinates.
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.
Steady laminar flow of fractal fluids
NASA Astrophysics Data System (ADS)
Balankin, Alexander S.; Mena, Baltasar; Susarrey, Orlando; Samayoa, Didier
2017-02-01
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived.
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.
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.
The exact calculation of quadrupole sources for some incompressible flows
NASA Technical Reports Server (NTRS)
Brentner, Kenneth S.
1988-01-01
This paper is concerned with the application of the acoustic analogy of Lighthill to the acoustic and aerodynamic problems associated with moving bodies. The Ffowcs Williams-Hawkings equation, which is an interpretation of the acoustic analogy for sound generation by moving bodies, manipulates the source terms into surface and volume sources. Quite often in practice the volume sources, or quadrupoles, are neglected for various reasons. Recently, Farassat, Long and others have attempted to use the FW-H equation with the quadrupole source and neglected to solve for the surface pressure on the body. The purpose of this paper is to examine the contribution of the quadrupole source to the acoustic pressure and body surface pressure for some problems for which the exact solution is known. The inviscid, incompressible, 2-D flow, calculated using the velocity potential, is used to calculate the individual contributions of the various surface and volume source terms in the FW-H equation. The relative importance of each of the sources is then assessed.
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.
Global small solutions of 2-D incompressible MHD system
NASA Astrophysics Data System (ADS)
Lin, Fanghua; Xu, Li; Zhang, Ping
2015-11-01
In this paper, we consider the global wellposedness of 2-D incompressible magneto-hydrodynamical system with smooth initial data which is close to some non-trivial steady state. It is a coupled system between the Navier-Stokes equations and a free transport equation with a universal nonlinear coupling structure. The main difficulty of the proof lies in exploring the dissipative mechanism of the system. To achieve this and to avoid the difficulty of propagating anisotropic regularity for the free transport equation, we first reformulate our system (1.1) in the Lagrangian coordinates (2.19). Then we employ anisotropic Littlewood-Paley analysis to establish the key a prioriL1 (R+ ; Lip (R2)) estimate for the Lagrangian velocity field Yt. With this estimate, we can prove the global wellposedness of (2.19) with smooth and small initial data by using the energy method. We emphasize that the algebraic structure of (2.19) is crucial for the proofs to work. The global wellposedness of the original system (1.1) then follows by a suitable change of variables.
Navier-Stokes computations of laminar compressible and incompressible vortex flows in a channel
NASA Astrophysics Data System (ADS)
Brockmeier, U.; Mitra, N. K.; Fiebig, M.
To investigate the structure of compressible and incompressible vortices behind a small delta wing in a channel at low Reynolds and Mach numbers, computer programs have been developed to solve complete three-dimensional Navier-Stokes and energy equations. Results show qualitatively similar vortex formation, flattening of the vortex core, and movement of the core away from the channel center and towards the bottom wall for both incompressible and compressible flows.
Accurate and robust methods for variable density incompressible flows with discontinuities
Rider, W.J.; Kothe, D.B.; Puckett, E.G.
1996-09-01
We are interested in the solution of incompressible flows which are characterized by large density variations, interfacial physics, arbitrary material topologies and strong vortical content. The issues present in constant density incompressible flow are exacerbated by the presence of density discontinuities. A much greater premium requirement is placed the positivity of computed quantities The mechanism of baroclinc vorticity generation exists ({gradient}p x {gradient}p) to further complicate the physics.
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.
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.
NASA Technical Reports Server (NTRS)
Rogers, S. E.; Kwak, D.; Chang, J. L. C.
1986-01-01
Numerically solving the incompressible Navier-Stokes equations is known to be time consuming and expensive. Testing of the INS3D computers code, which solves these equations with the use of the pseudocompressibility method, shows this method to be an efficient way to obtain the steady state solution. The effects of the waves introduced by the pseudocompressibility method are analyzed and criteria are set and tested for the choice of the pseudocompressibility parameter which governs the artificial sound speed. The code is tested using laminar flow over a two dimensional backward-facing step, and laminar flow over a two dimensional circular cylinder. The results of the computations over the backward-facing step are in excellent agreement with experimental results. The transient solution of the flow over the cylinder impulsively started from rest is in good agreement with experimental results. However, the computed frequency of periodic shedding of vortices behind the cylinder is not in agreement with the experimental value. For a three dimensional test case, computations were conducted for a cylinder end wall junction. The saddle point separation and horseshoe vortex system appear in the computed field. The solution also shows secondary vortex filaments which wrap around the cylinder and spiral up in the wake.
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
Evaluation of rotating, incompressibly lubricated, pressurized thrust bearings
NASA Technical Reports Server (NTRS)
Fleming, D. P.
1971-01-01
Program evaluates a series hybrid, fluid film ball bearing consisting of an orifice compensated pressurized thrust bearing in conjunction with a self-acting journal bearing. Oil viscosities corresponding to experimentally measured ball bearing outer-race temperatures were used.
Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; ...
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)
Dong, S.
2014-06-01
We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase-field framework for dealing with two-phase outflows or open boundaries. The set of two-phase outflow boundary conditions for the phase-field and flow variables are designed to prevent the un-controlled growth in the total energy of the two-phase system, even in situations where strong backflows or vortices may be present at the outflow boundaries. We also present an additional boundary condition for the phase field function, which together with the usual Dirichlet condition can work effectively as the phase-field inflow conditions. The numerical algorithm for dealing with these boundary conditions is developed on top of a strategy for de-coupling the computations of all flow variables and for overcoming the performance bottleneck caused by variable coefficient matrices associated with variable density/viscosity. The algorithm contains special constructions, for treating the variable dynamic viscosity in the outflow boundary condition, and for preventing a numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests with incompressible two-phase flows involving inflow and outflow boundaries demonstrate that, the two-phase outflow boundary conditions and the numerical algorithm developed herein allow for the fluid interface and the two-phase flow to pass through the outflow or open boundaries in a smooth and seamless fashion, and that our method produces stable simulations when large density ratios and large viscosity ratios are involved and when strong backflows are present at the outflow boundaries.
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.
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.
NASA Astrophysics Data System (ADS)
Hirsch, Charles; Periaux, J.; Kordulla, W.
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. For individual titles, see A95-95358 through A95-95507.
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).
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.
Rouze, Ned C; Wang, Michael H; Palmeri, Mark L; Nightingale, Kathy R
2013-11-15
Elastic properties of materials can be measured by observing shear wave propagation following localized, impulsive excitations and relating the propagation velocity to a model of the material. However, characterization of anisotropic materials is difficult because of the number of elasticity constants in the material model and the complex dependence of propagation velocity relative to the excitation axis, material symmetries, and propagation directions. In this study, we develop a model of wave propagation following impulsive excitation in an incompressible, transversely isotropic (TI) material such as muscle. Wave motion is described in terms of three propagation modes identified by their polarization relative to the material symmetry axis and propagation direction. Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material. Group propagation velocities are derived from the phase velocities to describe the propagation of wave packets away from the excitation region following localized excitation. The theoretical model is compared to the results of finite element (FE) simulations performed using a nearly incompressible material model with the five elasticity constants chosen to preserve the essential properties of the material in the incompressible limit. Propagation velocities calculated from the FE displacement data show complex structure that agrees quantitatively with the theoretical model and demonstrates the possibility of measuring all three elasticity constants needed to characterize an incompressible, TI material.
MHD Flow of the Micropolar Fluid between Eccentrically Rotating Disks
Srivastava, Neetu
2014-01-01
This analytical investigation examines the magnetohydrodynamic flow problem of an incompressible micropolar fluid between the two eccentrically placed disks. Employing suitable transformations, the flow governing partial differential equations is reduced to ordinary differential equations. An exact solution representing the different flow characteristic of micropolar fluid has been derived by solving the ordinary differential equations. Analysis of the flow characteristics of the micropolar fluid has been done graphically by varying the Reynolds number and the Hartmann number. This analysis has been carried out for the weak and strong interactions. PMID:27355040
A Lower Hybrid Fluid Model and Asymptotic Solutions
NASA Astrophysics Data System (ADS)
Wang, Xiaogang
2016-10-01
Hall MHD is for ion dynamics with a zero mass electron fluid. EMHD is for electron dynamics with fixed (infinity mass) ions. Also, other approximations such as electron incompressibility and low frequency appraisal (by ignoring the displacement current) have limited the application of EMHD. We then introduce a ``Lower Hybrid Fluid'' model by keeping the higher order mass ratio terms in the two-fluid model to investigate the problems in a hybrid scale range between the electron skin depth and the ion inertial length.
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.
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.
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.
Simulating incompressible flow on moving meshfree grids using General Finite Differences (GFD)
NASA Astrophysics Data System (ADS)
Vasyliv, Yaroslav; Alexeev, Alexander
2016-11-01
We simulate incompressible flow around an oscillating cylinder at different Reynolds numbers using General Finite Differences (GFD) on a meshfree grid. We evolve the meshfree grid by treating each grid node as a particle. To compute velocities and accelerations, we consider the particles at a particular instance as Eulerian observation points. The incompressible Navier-Stokes equations are directly discretized using GFD with boundary conditions enforced using a sharp interface treatment. Cloud sizes are set such that the local approximations use only 16 neighbors. To enforce incompressibility, we apply a semi-implicit approximate projection method. To prevent overlapping particles and formation of voids in the grid, we propose a particle regularization scheme based on a local minimization principle. We validate the GFD results for an oscillating cylinder against the lattice Boltzmann method and find good agreement. Financial support provided by National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.
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.
Phase-field modeling of isothermal quasi-incompressible multicomponent liquids.
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 space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Rhebergen, Sander; Cockburn, Bernardo; van der Vegt, Jaap J. W.
2013-01-01
We introduce a space-time discontinuous Galerkin (DG) finite element method for the incompressible Navier-Stokes equations. Our formulation can be made arbitrarily high-order accurate in both space and time and can be directly applied to deforming domains. Different stabilizing approaches are discussed which ensure stability of the method. A numerical study is performed to compare the effect of the stabilizing approaches, to show the method's robustness on deforming domains and to investigate the behavior of the convergence rates of the solution. Recently we introduced a space-time hybridizable DG (HDG) method for incompressible flows [S. Rhebergen, B. Cockburn, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, J. Comput. Phys. 231 (2012) 4185-4204]. We will compare numerical results of the space-time DG and space-time HDG methods. This constitutes the first comparison between DG and HDG methods.
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.
... carefully. Removing a sample of the fluid through amniocentesis can provide information about the sex, health, and development of the fetus. Images Amniocentesis Amniotic fluid Polyhydramnios Amniotic fluid References Cunningham FG, ...
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
Reproduction of solutions in the plane problem on motion of a free-boundary fluid
NASA Astrophysics Data System (ADS)
Karabut, E. A.; Zhuravleva, E. N.
2016-07-01
This study is devoted to finding exact solutions of the plane unsteady problem on the motion of an ideal incompressible free-boundary fluid. A certain procedure of reproduction making it possible to obtain a two-parametrical family of new exact solutions from one known solution is proposed.
Application of a Real-Fluid Turbomachinery Analysis to Rocket Turbopump Geometries
NASA Technical Reports Server (NTRS)
Dorney, Daniel J.; Sondak, Douglas L.; Marcu, Bogdan
2005-01-01
A three-dimensional flow solver has been developed for turbomachinery components utilizing real fluid properties. The code is applicable to both incompressible and compressible flow fields. In this study, the code has been applied to the analysis of inducer and impeller geometries representative of those used in rocket engine applications. The predicted results show good agreement with the available experimental data.
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.
Preconditioned methods for solving the incompressible and low speed compressible equations
NASA Technical Reports Server (NTRS)
Turkel, E.
1986-01-01
Acceleration methods are presented for solving the steady state incompressible equations. These systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state. The compressible equations in conservation form with slow flow are also considered. Two arbitrary functions, alpha and beta, are introduced in the general preconditioning. An analysis of this system is presented and an optimal value for beta is determined given a constant, alpha. It is further shown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed. Several generalizations to the compressible equations are presented which generalize previous results.
Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties
NASA Astrophysics Data System (ADS)
Capuano, F.; Coppola, G.; Rández, L.; de Luca, L.
2017-01-01
The application of pseudo-symplectic Runge-Kutta methods to the incompressible Navier-Stokes equations is discussed in this work. In contrast to fully energy-conserving, implicit methods, these are explicit schemes of order p that preserve kinetic energy to order q, with q > p. Use of explicit methods with improved energy-conservation properties is appealing for convection-dominated problems, especially in case of direct and large-eddy simulation of turbulent flows. A number of pseudo-symplectic methods are constructed for application to the incompressible Navier-Stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations.
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.
NASA Astrophysics Data System (ADS)
Schroeder, Philipp W.; Lube, Gert
2017-04-01
This paper presents heavily grad-div and pressure jump stabilised, equal- and mixed-order discontinuous Galerkin finite element methods for non-isothermal incompressible flows based on the Oberbeck-Boussinesq approximation. In this framework, the enthalpy-porosity model for multiphase flow in melting and solidification problems can be employed. By considering the differentially heated cavity and the melting of pure gallium in a rectangular enclosure, it is shown that both boundary layers and sharp moving interior layers can be handled naturally by the proposed class of non-conforming methods. Due to the stabilising effect of the grad-div term and the robustness of discontinuous Galerkin methods, it is possible to solve the underlying problems accurately on coarse, non-adapted meshes. The interaction of heavy grad-div stabilisation and discontinuous Galerkin methods significantly improves the mass conservation properties and the overall accuracy of the numerical scheme which is observed for the first time. Hence, it is inferred that stabilised discontinuous Galerkin methods are highly robust as well as computationally efficient numerical methods to deal with natural convection problems arising in incompressible computational thermo-fluid dynamics.
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.
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
Amsden, A. A.; Ruppel, H. M.; Hirt, C. W.
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 results 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.
Gupta, M. R.; Roy, Sourav; Khan, Manoranjan; Pant, H. C.; Sarkar, Susmita; Srivastava, M. K.
2009-03-15
The effect of compressibility and of density variation on Rayleigh-Taylor and Richtmyer-Meshkov instability of the temporal development of two fluid interfacial structures such as bubbles and spikes have been investigated. It is seen that the velocity of the tip of the bubble or spike increases (destabilization) if the local Atwood number increases due to density variation of either of the fluids. The opposite is the result, i.e., the bubble or spike tip velocity decreases (stabilization) if the density variation leads to lowering of the value of the local Atwood number. The magnitude of stabilization or destabilization is an increasing function of the product of the wave number k and interfacial pressure p{sub 0}. The effect of compressibility is quite varied. If the heavier (upper) fluid alone is incompressible ({gamma}{sub h}{yields}{infinity}), but the lighter fluid is compressible the growth rate is higher (destabilization) than when both the fluids are incompressible. Moreover the heavier fluid remaining incompressible the growth rate decreases (stabilization) as {gamma}{sub l} (finite) increases and ultimately tends to the incompressible limit value as {gamma}{sub l}{yields}{infinity}. With {gamma}{sub l}{yields}{infinity} but {gamma}{sub h} finite the growth increases (destabilization) as {gamma}{sub h} increases. When both {gamma}{sub h} and {gamma}{sub l} are finite (density {rho}{sub h}>density {rho}{sub l}) the growth is reduced when {gamma}{sub h}<{gamma}{sub l} compared to that when both fluids are incompressible and enhanced when {gamma}{sub h}>{gamma}{sub l}. The set of nonlinear equations describing the dynamics of bubbles and spikes in the presence of fluid density variations are not analytically integrable in closed form. The results derived by numerical solution methods are represented and interpreted in corresponding figures.
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.
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.
Fluid/gravity correspondence for massive gravity
NASA Astrophysics Data System (ADS)
Pan, Wen-Jian; Huang, Yong-Chang
2016-11-01
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a timelike hypersurface, we find that the perturbation effects of massive gravity in bulk can be completely governed by the incompressible Navier-Stokes equation living on the cutoff surface under the near horizon and nonrelativistic limits. Furthermore, we have concisely computed the ratio of dynamical viscosity to entropy density for two massive Einstein gravity theories, and found that they still saturate the Kovtun-Son-Starinets (KSS) bound.
NASA Astrophysics Data System (ADS)
Rypina, Irina I.
The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust three-gyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the
The Geometry of Non-Ideal Fluids
NASA Astrophysics Data System (ADS)
Rajeev, S. G.
2013-12-01
Arnold showed that the Euler equations of an ideal fluid describe geodesies on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the structure constants of a Lie algebra, along with inner products defining kinetic energy, Ohmic dissipation and the covariance of the forces. This allows us to construct tractable toy models for fluid mechanics with a finite number of degrees of freedom. We solve one of them to show how symmetries can be broken spontaneously.In another direction, we derive a deterministic equation that describes the most likely path connecting two points in the phase space of a randomly forced system: this is a WKB approximation to the Fokker-Plank-Kramer equation, analogous to the instantons of quantum theory. Applied to hydrodynamics, we derive a PDE system for Navier-Stokes instantons.
Actuator disk theory for incompressible highly rotating flows.
NASA Technical Reports Server (NTRS)
Oates, G. C.
1971-01-01
A solution has been obtained for a stator-rotor pair operating in an annulus with constant hub and tip radii. The stator and rotor are represented as actuator discs, and perfect fluid flow is assumed. The solutions are exact within these limitations, no linearization being required. The forms of blade loadings considered allow the introduction of large vorticity by either the rotor or stator. As a result, the rotor may be a ?nonconstant-work' row. The solutions obtained are of summational form, but many of the summations are obtained in closed form, the resultant formulas allowing rapid calculation of desired examples. An example numerical result is included.
Interpretations of Incompressible Continuous Spectrum Receptivity Curves for Transient Growth
NASA Astrophysics Data System (ADS)
Monschke, Jason; White, Edward
2013-11-01
Receptivity of transient disturbances to distributed surface roughness is not representable as a single value but is instead a complex-valued function with a different value for each continuous spectrum mode of the Orr-Sommerfeld/Squire equations. Specific characteristics of the curves give rise to streamwise vorticity of varying strength and at different locations within the boundary layer. The various combinations of streamwise vorticity and the initial streamwise velocity disturbance result in the many types of energy evolution seen in experiments and DNS. Following the work of Tumin [Phys. Fluids 15, 2525 (2003)], Denissen & White [Phys. Fluids 21, 114105 (2009)] developed a technique to decompose experimental measurements made downstream of a roughness array into the constituent continuous spectrum modes. These techniques provide for significant data reduction because receptivity curves encode the complete downstream evolution of the laminar boundary layer. Even though the decomposition uniquely characterizes receptivity to roughness, the small set of measured curves has hindered a systematic understanding of the physical meaning of roughness receptivity curves. Our findings help to associate specific receptivity-curve shapes with physically observable behavior. Supported by AFOSR under grant FA9550-11-1-0203.
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…
Investigation of an incompressible flow along a corner by an alternating direction implicit method
NASA Technical Reports Server (NTRS)
Goglia, G. L.; Patel, D. K.
1977-01-01
The axial corner flow is analyzed for the incompressible laminar boundary layer flow. The governing equations are derived from the Navier-Stokes equations by neglecting second derivative terms of the axial direction. An alternating direction implicit method is used to solve the equations in primitive variables.
Approximate analysis for resonance of an incompressible shear layer plus edges
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1984-01-01
A method for approximately analyzing the feedback between downstream and upstream edges in incompressible shear flow is described. The shear flow is modeled by a vortex sheet. Equations for resonance eigenvalues are derived. After the reduction of growth rate by finite shear layer thickness is allowed for, agreement is found between calculated resonances and those that have been observed experimentally.
NASA Astrophysics Data System (ADS)
Stein, David B.; Guy, Robert D.; Thomases, Becca
2017-04-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier-Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization.
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)
Brenner, Howard
2012-02-01
This paper illustrates, by example, the incompleteness of the Navier-Stokes-Fourier (NSF) equations for the case of thermally compressible fluids, namely fluids possessing a nonzero coefficient of thermal expansion. The work is a follow-up to a recent publication that offered elementary arguments quantifying that incompleteness but did not provide an explicit physical example thereof. The present example was chosen strictly for the simplicity of the calculations required to bring it to fruition, rather than for its importance in applications. The example analyzes steady-state, one-dimensional (albeit nonunidirectional) heat conduction through a quiescent fluid bounded by concentric spheres maintained at different temperatures. This example is counterpart to the classic NSF case of steady-state, one-dimensional (but now unidirectional) heat conduction through a quiescent fluid bounded by flat plates maintained at different temperatures. The contrasting results obtained for the two cases illustrates effects arising from the proposed amendments to the traditional NSF equations. For the case of gases the amended results indicate the possibility of their differing significantly from classical results based on the NSF equations when the gas is rarefied. For liquids, however, physically realizable values of the relevant parameters governing the amended equations are such that no sensible deviations from classical NSF behavior are observed. The difference owes to the relative incompressibility of liquids compared with gases. The smallness of the effect for liquids is, however, noted to be atypical of the amended consequences arising in circumstances where the temperature varies along, rather than purely normal to solid surfaces, as in the present concentric-sphere example. In that case Maxwell thermal creep effects would create more profound effects than in the present example, whether for liquids or gases.
Numerical solution of fluid-structure interaction represented by human vocal folds in airflow
NASA Astrophysics Data System (ADS)
Valášek, J.; Sváček, P.; Horáček, J.
2016-03-01
The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.
Shock compressing diamond to a conducting fluid.
Bradley, D K; Eggert, J H; Hicks, D G; Celliers, P M; Moon, S J; Cauble, R C; Collins, G W
2004-11-05
Laser generated shock reflectance data show that diamond undergoes a continuous transition from optically absorbing to reflecting between Hugoniot pressures 600
Shock Compressing Diamond to a Conducting Fluid
Bradley, D K; Eggert, J H; Hicks, D G; Celliers, P M; Moon, S J; Cauble, R C; Collins, G W
2004-07-29
Laser generated shock reflectance data show that diamond undergoes a continuous transition from optically absorbing to reflecting between Hugoniot pressures 600
The Vibration of an Inviscid Incompressible Sessile Drop
NASA Astrophysics Data System (ADS)
Smith, Marc
2009-11-01
The fundamental frequencies and normal modes of vibration of a sessile drop supported on a horizontal planar surface are found using an integrated analytical and numerical technique. Spherical coordinates are used to describe the interface shape, but the potential flow field inside the drop is computed numerically using the finite element method. The numerical velocity potentials at the interface for both the fluid inside the drop and outside are fitted using a Legendre series. When these series are combined in the interfacial normal-stress balance the result is a linear eigenvalue problem that is solved numerically. Results will be presented for sessile drops with different contact angles without gravity and compared to experimental data. This technique can also be extended to sessile drops with gravity, in which the drop shape is flattened, and to substrate geometries that are not planar, such as a drop in a shallow cavity or hole.
High accuracy solutions of incompressible Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Gupta, Murli M.
1990-01-01
In recent years, high accuracy finite difference approximations were developed for partial differential equations of elliptic type, with particular emphasis on the convection-diffusion equation. These approximations are of compact type, have a local truncation error of fourth order, and allow the use of standard iterative schemes to solve the resulting systems of algebraic equations. These high accuracy approximations are extended to the solution of Navier-Stokes equations. Solutions are obtained for the model problem of driven cavity and are compared with solutions obtained using other approximations and those obtained by other authors. It is discovered that the high order approximations do indeed produce high accuracy solutions and have a potential for use in solving important problems of viscous fluid flows.
NASA Astrophysics Data System (ADS)
Aziz, Taha; Magan, A. B.; Mahomed, F. M.
2015-02-01
An analysis is carried out to study the time-dependent flow of an incompressible electrically conducting fourth-grade fluid over an infinite porous plate. The flow is caused by the motion of the porous plate in its own plane with an impulsive velocity V( t). The governing nonlinear problem is solved by invoking the Lie group theoretic approach and a numerical technique. Travelling wave solutions of the forward and backward type, together with a steady state solution, form the basis of our analytical analysis. Further, the closed-form solutions are also compared against numerical results. The essential features of the embedded parameters are described. In particular, the physical significance of the plate suction/injection and magnetic field is studied.
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.
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
Variational principles for stochastic fluid dynamics.
Holm, Darryl D
2015-04-08
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.
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.
Load-estimation techniques for unsteady incompressible flows
NASA Astrophysics Data System (ADS)
Rival, David E.; Oudheusden, Bas van
2017-03-01
In a large variety of fluid-dynamic problems, it is often impossible to directly measure the instantaneous aerodynamic or hydrodynamic forces on a moving body. Examples include studies of propulsion in nature, either with mechanical models or living animals, wings, and blades subjected to significant surface contamination, such as icing, sting blockage effects, etc. In these circumstances, load estimation from flow-field data provides an attractive alternative method, while at the same time providing insight into the relationship between unsteady loadings and their associated vortex-wake dynamics. Historically, classical control-volume techniques based on time-averaged measurements have been used to extract the mean forces. With the advent of high-speed imaging, and the rapid progress in time-resolved volumetric measurements, such as Tomo-PIV and 4D-PTV, it is becoming feasible to estimate the instantaneous forces on bodies of complex geometry and/or motion. For effective application under these conditions, a number of challenges still exist, including the near-body treatment of the acceleration field as well as the estimation of pressure on the outer surfaces of the control volume. Additional limitations in temporal and spatial resolutions, and their associated impact on the feasibility of the various approaches, are also discussed. Finally, as an outlook towards the development of future methodologies, the potential application of Lagrangian techniques is explored.
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.
NASA Astrophysics Data System (ADS)
Kandasamy, Ramasamy; Muhaimin, Ismoen; Saim, Hashim Bin
2010-08-01
This paper concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equation corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. It is found that with the increase of magnetic field intensity the fluid velocity decreases but the temperature increases at a particular point of the heated stretching surface. Impact of thermophoresis particle deposition with chemical reaction in the presence of heat source/sink plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.
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.
Analytical modeling of magnetic Rayleigh-Taylor instabilities in compressible fluids
NASA Astrophysics Data System (ADS)
Liberatore, Stéphane; Bouquet, Serge
2008-11-01
The magnetic Rayleigh-Taylor instability (MRTI) is investigated in the case of compressible plasmas. The goal of this work is highlighting the influence of both the magnetic field and the compressibility of the material on the growth rate of the Rayleigh-Taylor instability, compared to the classical growth rate derived for incompressible fluids. Our analytical linear models are derived in the framework of the ideal magnetohydrodynamics theory. Three general dispersion relations are obtained: (1) Two for stratified fluids, including compressible (denoted CS∥ when the wave vector k is parallel to the equilibrium magnetic field B0 and CS⊥ when k ⊥B0) and incompressible (denoted IS∥ and IS⊥) and (2) one for incompressible uniform density fluids, including finite mass (denoted Ifm) and infinite (denoted IU). For k ⊥B0, Ifm, IU, and IS⊥ are unmagnetized cases. Comparisons of those various configurations are performed and several differences are pointed out. The main results are as follows: Stratification weakens the MRTI while compressibility has a destabilizing effect. The magnetic field enhances these phenomena. The CS∥ and IU configurations have an identical cutoff wave number. The upper fluid (also called heavy fluid) is more sensitive to compressibility than the light one when k ∥B0. Finally, the CS∥ case is more sensitive than the CS⊥ one to physical variations.
NASA Technical Reports Server (NTRS)
Kiris, Cetin; Kwak, Dochan
2001-01-01
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-Stokes equations. The performance of the two method are compared by obtaining unsteady solutions for the evolution of twin vortices behind a at plate. Calculated results are compared with experimental and other numerical results. For an un- steady ow which requires small physical time step, pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.
Nuclear matter incompressibility from a semi-empirical analysis of breathing-mode energies
NASA Astrophysics Data System (ADS)
Sharma, M. M.; Stocker, W.; Gleissl, P.; Brack, M.
1989-11-01
We check the validity and applicability of a liquid-drop model type expansion for the incompressibility KA of finite nuclei: K A = K V + K SA {-1}/{3} + (higher-order terms). Our theoretical considerations are based upon calculations of breathing-mode energies following from a density variational framework taking into account various Skyrme interactions. Using a semi-empirical procedure based upon this expansion of KA, we corroborate that new precision data for the monopole energies favour a volume coefficient KV (300±25) MeV and an appreciable surface coefficient KS (-750±80) MeV. We discuss the implication of this result for the incompressibility K∞ of infinite nuclear matter.
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.
Numerical simulation of the incompressible internal flow through a tilting disk valve
NASA Technical Reports Server (NTRS)
Chang, I-Dee; Rogers, Stuart E.; Kwak, Dochan; Kiris, Cetin
1990-01-01
A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady and unsteady flow calculations are performed by solving the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.
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.
Lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media
NASA Astrophysics Data System (ADS)
Grissa, Kods; Chaabane, Raoudha; Lataoui, Zied; Benselama, Adel; Bertin, Yves; Jemni, Abdelmajid
2016-10-01
The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.
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.
On the origins of vortex shedding in two-dimensional incompressible flows
NASA Astrophysics Data System (ADS)
Boghosian, M. E.; Cassel, K. W.
2016-12-01
An exegesis of a novel mechanism leading to vortex splitting and subsequent shedding that is valid for two-dimensional incompressible, inviscid or viscous, and external or internal or wall-bounded flows, is detailed in this research. The mechanism, termed the vortex shedding mechanism (VSM) is simple and intuitive, requiring only two coincident conditions in the flow: (1) the existence of a location with zero momentum and (2) the presence of a net force having a positive divergence. Numerical solutions of several model problems illustrate causality of the VSM. Moreover, the VSM criteria is proved to be a necessary and sufficient condition for a vortex splitting event in any two-dimensional, incompressible flow. The VSM is shown to exist in several canonical problems including the external flow past a circular cylinder. Suppression of the von Kármán vortex street is demonstrated for Reynolds numbers of 100 and 400 by mitigating the VSM.
NASA Astrophysics Data System (ADS)
Thompson, D. S.
1980-05-01
The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.
Adolf, D.; Anderson, R.; Garino, T.; Halsey, T.C.; Hance, B.; Martin, J.E.; Odinek, J.
1996-10-01
An Electrorheological fluid is normally a low-viscosity colloidal suspension, but when an electric field is applied, the fluid undergoes a reversible transition to a solid, being able to support considerable stress without yield. Commercial possibilities for such fluids are enormous, including clutches, brakes, valves,shock absorbers, and stepper motors. However, performance of current fluids is inadequate for many proposed applications. Our goal was to engineer improved fluids by investigating the key technical issues underlying the solid-phase yield stress and the liquid to solid switching time. Our studies focused on field-induced interactions between colloidal particles that lead to solidification, the relation between fluid structure and performance (viscosity, yield stress), and the time evolution of structure in the fluid as the field is switched on or off.
Computational Investigation of Incompressible Airfoil Flows at High Angles of Attack
1988-12-01
Incompressible Airfoil Flows at High Angles of Attack by John Mark Mathre Lieutenant, United States Navy B.S., United States Naval Academy, 1978 Submitted...Similarly, in the y-direction the Navier-Stokes equation is ODv v 3v I P Z) v 32v - + U- + v- =- - + V(- + -). (2.24) Zt Zx zy p Dy x 2 Y2 11 III. STEADY
Reattachment of a Three-Dimensional, Incompressible Jet to an Adjacent Axisymmetric Inclined Surface
1983-03-31
on, Repeft) IS. SUPPLEMENTARY NOTES I9. KEY WORDS (Continue on tavateo aide If necessary and identity by block number)THRUST EVERSER COANDA EFFECT ...mechanics of a thrust reverser jet reattaohing to an aircraft nozzle afterbody. The problem basically involves the Coanda effect flow of a three... Coanda effect flow of a three-dimensional, incompressible jet to an adjacent axisymmetric, inclined surface. The equationsO -en derived in integral
Grouped element-by-element iteration schemes for incompressible flow computations
NASA Astrophysics Data System (ADS)
Tezduyar, T. E.; Liou, J.
1989-05-01
Grouped element-by-element (GEBE) iteration schemes for incompressible flows are presented in the context of vorticity- stream function formulation. The GEBE procedure is a variation of the EBE procedure and is based on arrangement of the elements into groups with no inter-element coupling within each group. With the GEBE approach, vectorization and parallel implementation of the EBE method becomes more clear. The savings in storage and CPU time are demonstrated with two unsteady flow problems.
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.
An Incompressible Navier-Stokes with Particles Algorithm andParallel Implementation
Martin, Daniel F.; Colella, Phillip; Keen, Noel D.
2006-11-28
We present a variation of an adaptive projection method forcomputing solutions to the incompressible Navier-Stokes equations withsuspended particles. To compute the divergence-free component of themomentum forcing due to the particle drag, we employ an approach whichexploits the locality and smoothness of the Laplacian of the projectionoperator applied to the discretized particle drag force. We presentconvergence and performance results to demonstrate the effectiveness ofthis approach.
On the critical one-component velocity regularity criteria to 3-D incompressible MHD system
NASA Astrophysics Data System (ADS)
Liu, Yanlin
2016-05-01
Let (u , b) be a smooth enough solution of 3-D incompressible MHD system. We prove that if (u , b) blows up at a finite time T*, then for any p ∈ ] 4 , ∞ [, there holds ∫0T* (‖u3(t‧) ‖ H ˙ 1/2 +2/p p + ‖b(t‧) ‖ H ˙ 1/2 +2/p p) dt‧ = ∞. We remark that all these quantities are in the critical regularity of the MHD system.
A solution procedure for three-dimensional incompressible Navier-Stokes equation and its application
NASA Technical Reports Server (NTRS)
Kwak, D.; Chang, J. L. C.; Shanks, S. P.
1984-01-01
An implicit, finite-difference procedure is presented for numerically solving viscous incompressible flows. For convenience of applying the present method to three-dimensional problems, primitive variables, namely the pressure and velocities, are used. One of the major difficulties in solving incompressible flows that use primitive variables is caused by the pressure field solution method which is used as a mapping procedure to obtain a divergence-free velocity field. The present method is designed to accelerate the pressure-field solution procedure. This is achieved by the method of pseudocompressibility in which the time derivative pressure term is introduced into the mass conservation equation. The pressure wave propagation and the spreading of the viscous effect is investigated using simple test problems. The present study clarifies physical and numerical characteristics of the pseudo-compressible approach in simulating incompressible flows. Computed results for external and internal flows are presented to verify the present procedure. The present algorithm has been shown to be very robust and accurate if the selection of the pseudo-compressibility parameter has been made according to the guidelines given.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lakshminarayana, B.
1991-09-01
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.
NASA Astrophysics Data System (ADS)
Li, Cheng Gong; P-Y Maa, Jerome
2017-04-01
Numerical study on three-dimensional (3D), incompressible, four-sided lid (FSL) driven cavity flows has been conducted to show the effects of the transverse aspect ratio, K, on the flow field by using a multiple relaxation time lattice Boltzmann equation. The top wall is driven from left to right, the left wall is moved downward, whereas the right wall is driven upward, and the bottom wall is moved from right to left, all the four moving walls have the same speed and the others boundaries are fixed. Numerical computations are performed for several Reynolds numbers for laminar flows, up to 1000, with various transverse aspect ratios. The flow can reach a steady state and the flow pattern is symmetric with respect to the two cavity diagonals (i.e., the center of the cavity). At Reynolds number = 300, the flow structures of the 3D FSL cavity flow at steady state with various transverse aspect ratio, i.e., 3, 2, 1, 0.75, 0.5 and 0.25 only show the unstable symmetrical flow pattern. The stable asymmetrical flow pattern could be reproduced only by increasing the Reynolds number that is above a critical value which is dependent on the aspect ratio. It is found that an aspect ratio of more than 5 is needed to reproduce flow patterns, both symmetric and asymmetric flows, simulated by using 2D numerical models.
Bray, C.J.; Spooner, E.T.C. )
1992-01-01
Eighteen fluid inclusion volatile peaks have been detected and identified from 1-2 g samples (quartz) by gas chromatography using heated on-line crushing, helium carrier gas, a single porous polymer column, two temperature programmed conditions for separate sample aliquots, micro-thermal conductivity (TCD) and photoionization detectors (PID), and off-line digital peak processing. In order of retention time these volatile peaks are: N{sub 2}, Ar, CO, CH{sub 4}, CO{sub 2}, C{sub 2}H{sub 4}, C{sub 2}H{sub 6}, C{sub 2}H{sub 2}, COS, C{sub 3}H{sub 6}, C{sub 3}H{sub 8}, C{sub 3}H{sub 4} (propyne), H{sub 2}O, SO{sub 2} {plus minus} iso-C{sub 4}H{sub 10} {plus minus} C{sub 4}H{sub 8} (1-butene) {plus minus} CH{sub 3}SH, C{sub 4}H{sub 8} (iso-butylene), ( ) C{sub 4}H{sub 6} (1,3 butadiene), and {plus minus} n-C{sub 4}H{sub 10} {plus minus}C{sub 4}H{sub 8} (trans-2-butene). H{sub 2}O is analyzed directly. O{sub 2} can be analyzed cryogenically between N{sub 2} and Ar, but has not been detected in natural samples to date in this study. Initial inclusion volatile analyses of fluids of interpreted magmatic origin from the Cretaceous Boss Mtn. monzogranite stock-related MoS{sub 2} deposit, central British Columbia of 97 mol% H{sub 2}O, 3% CO{sub 2}, 140-150 ppm N{sub 2}, and 16-39 ppm CH{sub 4} are reasonable in comparison with high temperature volcanic gas analyses from four, active calc-alkaline volcanoes, e.g., the H{sub 2}O contents of volcanic gases from the White Island (New Zealand), Mount St. Helens (Washington, USA), Merapi (Bali, Indonesia), and Momotombo (Nicaragua) volcanoes are 88-95%, > 90%, 88-95% and 93%, respectively; CO{sub 2} contents are 3-10%, 1-10%, 3-8%, and 3.5%. It appears that low, but significant concentrations of alkanes, alkenes, and alkynes have been detected in magmatically derived fluids.
MHD micropumping of power-law fluids: A numerical solution
NASA Astrophysics Data System (ADS)
Moghaddam, Saied
2013-02-01
The performance of MHD micropumps is studied numerically assuming that the viscosity of the fluid is shear-dependent. Using power-law model to represent the fluid of interest, the effect of power-law exponent, N, is investigated on the volumetric flow rate in a rectangular channel. Assuming that the flow is laminar, incompressible, two-dimensional, but (approximately) unidirectional, finite difference method (FDM) is used to solve the governing equations. It is found that shear-thinning fluids provide a larger flow rate as compared to Newtonian fluids provided that the Hartmann number is above a critical value. There exists also an optimum Hartmann number (which is larger than the critical Hartmann number) at which the flow rate is maximum. The power-law exponent, N, strongly affects the optimum geometry depending on the Hartmann number being smaller or larger than the critical Hartmann number.
Optimal probes for withdrawal of uncontaminated fluid samples
NASA Astrophysics Data System (ADS)
Sherwood, J. D.
2005-08-01
Withdrawal of fluid by a composite probe pushed against the face z =0 of a porous half-space z >0 is modeled assuming incompressible Darcy flow. The probe is circular, of radius a, with an inner sampling section of radius αa and a concentric outer guard probe αa
Conductivity is a measure of the ability of water to pass an electrical current. Because dissolved salts and other inorganic chemicals conduct electrical current, conductivity increases as salinity increases.
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.
Steady flow for shear thickening fluids in domains with unbounded sections
NASA Astrophysics Data System (ADS)
Dias, Gilberlandio J.
2017-02-01
We solve the stationary Stokes and Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosity in domains with outlets containing unbounded cross sections, in the case of shear thickening viscosity. The flux assumes arbitrary given values and the growth of the cross sections are analyzed under different convergence hypotheses, inclusive the growth of Dirichlet's integral of the velocity field is deeply related the convergence hypotheses of such sections. We extend the results of the section 4 of [12, Ladyzhenskaya and Solonnikov] (for Newtonian fluids) to non-Newtonian fluids using the techniques found in [3, Dias and Santos].
Fluid flow structure around the mixer in a reactor with mechanical mixing
Lecheva, A.; Zheleva, I.
2015-10-28
Fluid flow structure around the mixer in a cylindrical reactor with mechanical mixing is studied and numerical results are presented in this article. The model area is complex because of the presence of convex corners of the mixer in the fluid flow. Proper boundary conditions for the vorticity calculated on the base of the stream function values near solid boundaries of the examined area are presented. The boundary value problem of motion of swirling incompressible viscous fluid in a vertical tank reactor with a mixer is solved numerically. The calculations are made by a computer code, written in MATLAB. The complex structure of the flow around the mixing disk is described and commented.
NASA Astrophysics Data System (ADS)
Kim, Woojin; Lee, Injae; Choi, Haecheon
2015-11-01
We present a weak coupling approach for the fluid-structure interaction using a discrete-forcing immersed boundary method. The incompressible Navier-Stokes equations and the motion of a solid body are based on the Eulerian and Lagrangian coordinates, respectively. A semi-implicit Euler method is applied to the governing equation of a solid body for obtaining provisional position and velocity of a solid body prior to implicitly solving each governing equation. Then, both equations are implicitly solved to obtain a sufficiently large computational time step size. The present weak-coupling approach shows a second-order temporal accuracy and stable solutions for the problems with a low density ratio (fluid to solid) without requiring an iterative method. With the present method, we simulate several fluid-structure interaction problems including the flows around a freely vibrating circular cylinder, a flexible beam attached to a circular cylinder, a flapping flag, a flexible plate, and an elastic vocal fold. The results obtained agree well with those from previous studies. All the simulations are conducted at maximum CFL numbers of 1.0-1.5. Supported by NRF-2012M2A8A4055647 and NRF-2014M3C1B1033848.
NASA Technical Reports Server (NTRS)
Krzywoblocki, M. Z. V.
1974-01-01
The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.
Density Stratification in Rotating Spherical Fluid Shells: Application to the Earth's Fluid Core
NASA Astrophysics Data System (ADS)
Kamruzzaman, M.
2015-12-01
The Earth's outer core is a rotating ellipsoidal shell of compressible, stratified and self-gravitating fluid. The Galerkin method is applied to study the effects of density stratification on the frequencies of the inertial modes for a compressible shell proportional to the realistic Earth's fluid core. The inertial modes of the core are the free oscillations with periods longer than half of a day and have the Coriolis force as their restoring force. Historically an incompressible and homogeneous fluid sphere is considered to study these modes and analytical solutions are known for the frequencies and the displacement eigenfunctions of this model. The three potential description (3PD) is used to a compressible and stratified fluid core model with different stratification parameters β, related to the local Brunt-Väisälä frequency. As a first approximation, however, we ignore the ellipticity of the core's figure. The 3PD scheme describes the exact linearized dynamics of rotating, self-gravitating, stratified, compressible and inviscid fluids. We show that, depending on the size of β, some modal frequencies and eigenfunctions are practically unaffected by stratification, some are changed and some modes may disappear. We also first derive the web of characteristics, which gives more information about the eigenfunctions of these modes, as functions of frequency and stratification for compressible and inviscid fluids.
NASA Astrophysics Data System (ADS)
German, Brian Joseph
This research develops a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map the given subsonic flow into a canonical Laplacian flow with the same boundary conditions. The effect of the transformation is to distort both the immersed profile shape and the domain interior nonuniformly as a function of local flow properties. The method represents the full nonlinear generalization of the classical methods of Prandtl-Glauert and Karman-Tsien. Unlike the classical methods which are "corrections," this method gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by an observed analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the d'Alembert wave equation under Lorentz transformations. This analogy is well known in an operational sense, being leveraged widely in linear unsteady aerodynamics and acoustics, stemming largely from the work of Kussner. Whereas elements of the special theory can be invoked for compressibility effects that are linear and global in nature, the question posed in this work was whether other mathematical techniques from the realm of relativity theory could be used to similar advantage for effects that are nonlinear and local. This line of thought led to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. A gauge transformation is used to geometrize compressibility through the metric tensor of the underlying space to produce an equivalent incompressible flow that lives not on a plane but on a curved surface. In this sense, forces owing to compressibility can be ascribed to the geometry of space in
ERIC Educational Resources Information Center
Hoon, S. B.; Tanner, B. K.
1985-01-01
Continues a discussion of magnetic fluids by providing background information on and procedures for conducting several demonstrations. Indicates that, with a little patience and ingenuity, only modest magnetic fields and about 20 ml of low-viscosity, commercial magnetite-water-based magnetic fluid are required. (JN)