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Showing papers on "Fluid dynamics published in 1991"


Journal ArticleDOI
TL;DR: In this article, the authors present a set of methods for the estimation of two-dimensional fluid flow, including a Fourier Galerkin method and a Chebyshev Collocation method.
Abstract: 1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.2.1. A Fourier Galerkin Method for the Wave Equation.- 1.2.2. A Chebyshev Collocation Method for the Heat Equation.- 1.2.3. A Legendre Tau Method for the Poisson Equation.- 1.2.4. Basic Aspects of Galerkin, Tau and Collocation Methods.- 1.3. The Equations of Fluid Dynamics.- 1.3.1. Compressible Navier-Stokes.- 1.3.2. Compressible Euler.- 1.3.3. Compressible Potential.- 1.3.4. Incompressible Flow.- 1.3.5. Boundary Layer.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.1.1. The Continuous Fourier Expansion.- 2.1.2. The Discrete Fourier Expansion.- 2.1.3. Differentiation.- 2.1.4. The Gibbs Phenomenon.- 2.2. Orthogonal Polynomials in ( - 1, 1).- 2.2.1. Sturm-Liouville Problems.- 2.2.2. Orthogonal Systems of Polynomials.- 2.2.3. Gauss-Type Quadratures and Discrete Polynomial Transforms.- 2.3. Legendre Polynomials.- 2.3.1. Basic Formulas.- 2.3.2. Differentiation.- 2.4. Chebyshev Polynomials.- 2.4.1. Basic Formulas.- 2.4.2. Differentiation.- 2.5. Generalizations.- 2.5.1. Jacobi Polynomials.- 2.5.2. Mapping.- 2.5.3. Semi-Infinite Intervals.- 2.5.4. Infinite Intervals.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.1.1. Fourier Galerkin.- 3.1.2. Fourier Collocation.- 3.1.3. Chebyshev Tau.- 3.1.4. Chebyshev Collocation.- 3.2. Convolution Sums.- 3.2.1. Pseudospectral Transform Methods.- 3 2 2 Aliasing Removal by Padding or Truncation.- 3.2.3. Aliasing Removal by Phase Shifts.- 3.2.4. Convolution Sums in Chebyshev Methods.- 3.2.5. Relation Between Collocation and Pseudospectral Methods.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.4.1. Polar Coordinates.- 3.4.2. Spherical Polar Coordinates.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.2.1. The First-Derivative Operator.- 4.2.2. The Second-Derivative Operator.- 4.3. Some Standard Schemes.- 4.3.1. Multistep Schemes.- 4.3.2. Runge-Kutta Methods.- 4.4. Special Purpose Schemes.- 4.4.1. High Resolution Temporal Schemes.- 4.4.2. Special Integration Techniques.- 4.4.3. Lerat Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.1.1. Fourier Approximations.- 5.1.2. Chebyshev Tau Approximations.- 5.1.3. Schur-Decomposition and Matrix-Diagonalization.- 5.2. Fundamentals of Iterative Methods.- 5.2.1. Richardson Iteration.- 5.2.2. Preconditioning.- 5.2.3. Non-Periodic Problems.- 5.2.4. Finite-Element Preconditioning.- 5.3. Conventional Iterative Methods.- 5.3.1. Descent Methods for Symmetric, Positive-Definite Systems.- 5.3.2. Descent Methods for Non-Symmetric Problems.- 5.3.3. Chebyshev Acceleration.- 5.4. Multidimensional Preconditioning.- 5.4.1. Finite-Difference Solvers.- 5.4.2. Modified Finite-Difference Preconditioners.- 5.5. Spectral Multigrid Methods.- 5.5.1. Model Problem Discussion.- 5.5.2. Two-Dimensional Problems.- 5.5.3. Interpolation Operators.- 5.5.4. Coarse-Grid Operators.- 5.5.5. Relaxation Schemes.- 5.6. A Semi-Implicit Method for the Navier-Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier-Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.2.1. A Spectral Galerkin Solution Technique.- 7.2.2. Treatment of the Nonlinear Terms.- 7.2.3. Refinements.- 7.2.4. Pseudospectral and Collocation Methods.- 7.3. Inhomogeneous Flows.- 7.3.1. Coupled Methods.- 7.3.2. Splitting Methods.- 7.3.3. Galerkin Methods.- 7.3.4. Other Confined Flows.- 7.3.5. Unbounded Flows.- 7.3.6. Aliasing in Transition Calculations.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.4.1. Choice of Mesh.- 7.4.2. Coupled Methods.- 7.4.3. Splitting Methods.- 7.4.4. Other Methods.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.5.1. Potential Flow.- 8.5.2. Ringleb Flow.- 8.5.3. Astrophysical Nozzle.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. Fourier Approximation.- 9.1.1. Inverse Inequalities for Trigonometric Polynomials.- 9.1.2. Estimates for the Truncation and Best Approximation Errors.- 9.1.3. Estimates for the Interpolation Error.- 9.2. Sturm-Liouville Expansions.- 9.2.1. Regular Sturm-Liouville Problems.- 9.2.2. Singular Sturm-Liouville Problems.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.4.1. Inverse Inequalities for Algebraic Polynomials.- 9.4.2. Estimates for the Truncation and Best Approximation Errors.- 9.4.3. Estimates for the Interpolation Error.- 9.5. Chebyshev Approximations.- 9.5.1. Inverse Inequalities for Polynomials.- 9.5.2. Estimates for the Truncation and Best Approximation Errors.- 9.5.3. Estimates for the Interpolation Error.- 9.5.4. Proofs of Some Approximation Results.- 9.6. Other Polynomial Approximations.- 9.6.1. Jacobi Polynomials.- 9.6.2. Laguerre and Hermite Polynomials.- 9.7. Approximation Results in Several Dimensions.- 9.7.1. Fourier Approximations.- 9.7.2. Legendre Approximations.- 9.7.3. Chebyshev Approximations.- 9.7.4. Blended Fourier and Chebyshev Approximations.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.1.1. A Fourier Galerkin Method for the Wave Equation.- 10.1.2. A Chebyshev Collocation Method for the Heat Equation.- 10.1.3. A Legendre Tau Method for the Poisson Equation.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.4.1. Galerkin Methods.- 10.4.2. Tau Methods.- 10.4.3. Collocation Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.5.1. Conditions for Stability and Convergence: The Parabolic Case.- 10.5.2. Conditions for Stability and Convergence: The Hyperbolic Case.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.1.1. Legendre Methods.- 11.1.2. Chebyshev Methods.- 11.1.3. Other Boundary Value Problems.- 11.2. Advection-Diffusion Equation.- 11.2.1. Linear Advection-Diffusion Equation.- 11.2.2. Steady Burgers Equation.- 11.3. Navier-Stokes Equations.- 11.3.1. Compatibility Conditions Between Velocity and Pressure.- 11.3.2. Direct Discretization of the Continuity Equation: The \"inf-sup\" Condition.- 11.3.3. Discretizations of the Continuity Equation by an Influence-Matrix Technique: The Kleiser-Schumann Method.- 11.3.4. Navier-Stokes Equations in Streamfunction Formulation.- 11.4. The Eigenvalues of Some Spectral Operators.- 11.4.1. The Discrete Eigenvalues for Lu = ? uxx.- 11.4.2. The Discrete Eigenvalues for Lu = ? vuxx + bux.- 11.4.3. The Discrete Eigenvalues for Lu = ux.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.1.1. Periodic Boundary Conditions.- 12.1.2. Non-Periodic Boundary Conditions.- 12.1.3. Hyperbolic Systems.- 12.1.4. Spectral Accuracy for Non-Smooth Solutions.- 12.2. Heat Equation.- 12.2.1. Semi-Discrete Approximation.- 12.2.2. Fully Discrete Approximation.- 12.3. Advection-Diffusion Equation.- 12.3.1. Semi-Discrete Approximation.- 12.3.2. Fully Discrete Approximation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.2.1. Notation.- 13.2.2. Discretization.- 13.2.3. Solution Techniques.- 13.2.4. Examples.- 13.3. Variational Methods.- 13.3.1. Formulation.- 13.3.2. The Spectral-Element Method.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.5.1. Patching Methods.- 13.5.2. Equivalence Between Patching and Variational Methods.- 13.6. Some Stability and Convergence Results.- 13.6.1. Patching Methods.- 13.6.2. Variational Methods.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi-Gauss-Lobatto Roots.- References.

3,753 citations


ReportDOI
01 May 1991
TL;DR: TOUGH2 as mentioned in this paper is a numerical simulation program for nonisothermal flows of multicomponent, multiphase fluids in porous and fractured media, designed for geothermal reservoir engineering, nuclear waste disposal, and unsaturated zone hydrology.
Abstract: TOUGH2 is a numerical simulation program for nonisothermal flows of multicomponent, multiphase fluids in porous and fractured media. The chief applications for which TOUGH2 is designed are in geothermal reservoir engineering, nuclear waste disposal, and unsaturated zone hydrology. A successor to the TOUGH program, TOUGH2 offers added capabilities and user features, including the flexibility to handle different fluid mixtures, facilities for processing of geometric data (computational grids), and an internal version control system to ensure referenceability of code applications. This report includes a detailed description of governing equations, program architecture, and user features. Enhancements in data inputs relative to TOUGH are described, and a number of sample problems are given to illustrate code applications. 46 refs., 29 figs., 12 tabs.

780 citations


Journal ArticleDOI
TL;DR: In this paper, low-dimensional dynamical models for two-dimensional unsteady flows in complex geometries that are characterized by simple (low-dimensional) dynamical behavior are considered.
Abstract: Two‐dimensional unsteady flows in complex geometries that are characterized by simple (low‐dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low‐dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short‐ and long‐term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.

547 citations


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

526 citations


Journal ArticleDOI
TL;DR: In this article, a series of applications demonstrate that the lattice Boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes, ranging from laminar to fully turbulent flows in two and three dimensions.

517 citations


Journal ArticleDOI
TL;DR: In this article, the incompressible Navier-Stokes equations were derived from a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of Hilbert or Chapman-Enskog.
Abstract: The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of Hilbert or Chapman-Enskog. The moment formalism shows that the limit leading to the incompressible Navier-Stokes equations, like that leading to the compressible Euler equations, is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible Navier-Stokes equations. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution of the classical Boltzmann equation and the Leray solution of the Navier-Stokes equations is discussed.

499 citations


Journal ArticleDOI
TL;DR: In this article, an algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented, which can be used to compute both steady-state and time-dependent flow problems.
Abstract: An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The equations are solved with a line-relaxation scheme that allows the use of very large pseudotime steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. The steady-state solution of flow through a square duct with a 90-deg bend is computed, and the results are compared with experimental data. Good agreement is observed. Computations of unsteady flow over a circular cylinder are presented and compared to other experimental and computational results. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

422 citations


Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations that govern fluid flow are reduced to the more tractable Reynolds equation, which is valid for low Reynolds numbers and under certain restrictions on the magnitude of the roughness.

319 citations


Journal ArticleDOI
TL;DR: In this paper, a cell volume fraction field is obtained by integrating the advected area underneath the interface line-segment and a criterion is developed for identifying the line segment orientation by inspecting the cell volume fractions.

285 citations


Journal ArticleDOI
TL;DR: In contrast to the case of mantle convection, only very small lateral variations in core density are necessary to drive the flow; these density variations are, by several orders of magnitude, too small to be imaged seismically; therefore, the geomagnetic secular variation is utilized to infer the flow as discussed by the authors.
Abstract: This review examines the recent attempts at extracting information on the pattern of fluid flow near the surface of the outer core from the geomagnetic secular variation. Maps of the fluid flow at the core surface are important as they may provide some insight into the process of the geodynamo and may place useful constraints on geodynamo models. In contrast to the case of mantle convection, only very small lateral variations in core density are necessary to drive the flow; these density variations are, by several orders of magnitude, too small to be imaged seismically; therefore, the geomagnetic secular variation is utilized to infer the flow. As substantial differences exist between maps developed by different researchers, the possible underlying reasons for these differences are examined with particular attention given to the inherent problems of nonuniqueness.

276 citations


Journal ArticleDOI
TL;DR: In this article, a new approximation scheme for the convective term of the species equations was proposed, which relies on some properties of the exact solution of the Riemann problem for the multi-component system, and applies when an upwind Godunov-type scheme is used for the Euler equations.

Journal ArticleDOI
TL;DR: In this article, three-dimensional flows of an incompressible fluid and an inviscid subsonic compressible gas are considered and how the WKB method can be used for investigating their stability.
Abstract: Three‐dimensional flows of an inviscid incompressible fluid and an inviscid subsonic compressible gas are considered and it is demonstrated how the WKB method can be used for investigating their stability. The evolution of rapidly oscillating initial data is considered and it is shown that in both cases the corresponding flows are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. Analyzing the corresponding transport equations, a number of classical stability conditions are rederived and some new ones are obtained. In particular, it is demonstrated that steady flows of an incompressible fluid and an inviscid subsonic compressible gas are unstable if they have points of stagnation.

Journal ArticleDOI
TL;DR: In this paper, the extinction limits of methane-air flames at different equivalence ratios in the stationary case were derived for different levels of methane oxidation chemistry and the influence of temporally periodical change of the strain rate on the flame front behavior.

Journal ArticleDOI
TL;DR: In this article, a finite difference model to study the simultaneous movement of a dense, nonaqueous phase liquid and water in heterogeneous porous media is developed, which is well suited for the simulation of ground water contamination problems involving the advance of immiscible liquids into previously uncontaminated groundwater systems.
Abstract: A two-dimensional finite difference model to study the simultaneous movement of a dense, nonaqueous phase liquid and water in heterogeneous porous media is developed. A distinctive feature of the solution is that the primary variables solved for, wetting phase pressure and wetting phase saturation, are both existent throughout the solution domain regardless of whether the nonwetting phase is present. This eliminates the need to specify small, fictitious saturations of nonwetting fluid ahead of the advancing front where only wetting fluid is present, as is often required in conventional simulators. The model is therefore well suited for the simulation of ground water contamination problems involving the advance of immiscible liquids into previously uncontaminated groundwater systems. The finite difference equations are solved fully implicitly using Newton-Raphson iteration. In order to minimize computer storage and execution time a Dupont-Kendall-Rachford iterative solver utilizing Orthomin acceleration has been incorporated. The numerical model is verified against an exact analytical solution which incorporates fully the effects of both relative permeability and capillary pressure. The model is validated through comparison to a parallel-plate laboratory experiment involving the infiltration of tetrachloroethylene into a heterogeneous sand pack.

Journal ArticleDOI
TL;DR: Numerical results are presented for axial and secondary flow velocity and wall shear stresses with special emphasis on the fluid dynamics in the carotid sinus, of major interest because it is affected preferentially by lesions.

Book
01 Jun 1991
TL;DR: In this article, D'Alember's Principle and Lagrange Equations of Motion are combined with the concept of virtual work, and the first integral integral of the Equation of Motion is presented.
Abstract: 1. Kinematics.- 2. Statics, Systems of Forces, Hydrostatics.- 3. Mechanical Work, Power, Potential Energy.- 4. Constitutive Equations.- 5. Principle of Virtual Work.- 6. Selected Topics of Elastostatics.- 7. Dynamics of Solids and Fluids, Conservation of Momentum of Material and Control Volumes.- 8 First Integrals of the Equations of Motion, Kinetic Energy.- 9. Stability Problems.- 10. D'Alember's Principle and Lagrange Equations of Motion.- 11. Some Approximation Methods of Dynamics and Statics.- 12. Impact.- 13. Elementary Supplements of Fluid Dynamics.- 14. Selected Problems.- Table A. Some Average Values of Mechanical Material Parameters.- Table B. U.S. (Basic) Customary Units and Their SI Equivalents.

Journal ArticleDOI
TL;DR: In this article, a mathematical model of the hydrocyclone based on the physics of fluid flow is developed, and the model equations are solved in a computer code that takes as input the hydrocyclone dimensions and feed slurry characteristics.
Abstract: A mathematical model of the hydrocyclone, based on the physics of fluid flow, has been developed. The model equations are solved in a computer code that takes as input the hydrocyclone dimensions and feed slurry characteristics. The output of the computer code is the velocity profiles of the fluid and the separation efficiency curve. To validate the model, an LDV was used to measure the velocity profiles inside a 75-mm hydrocyclone. Pure water and glycerol-water mixture were used as the working media to simulate the increase of slurry viscosity in the presence of solid particles. The predicted velocity profiles agree well with the experimental measurements. Dilute limestone slurry was also classified with the same hydrocyclone, and predicted the separation efficiency curve shows good agreement with experimental observation.

Journal ArticleDOI
TL;DR: In this paper, numerical simulations with high spatial resolution (up to 96cubed gridpoints) are used to study three-dimensional, compressible convection, and a sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent.
Abstract: Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. 39 refs.

Journal ArticleDOI
TL;DR: The RIPPLE model as mentioned in this paper obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology, which represents surface tension as a localized volume force.
Abstract: A new free surface flow model, RIPPLE, is summarized. RIPPLE obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology. The key innovation is the continuum surface force model which represents surface tension as a (strongly) localized volume force. Other features include a higher-order momentum advection model, a volume-of-fluid free surface treatment, and an efficient two-step projection solution method. RIPPLE's unique capabilities are illustrated with two example problems: low-gravity jet-induced tank flow, and the collision and coalescence of two cylindrical rods.

Journal ArticleDOI
Jie Shen1
TL;DR: In this paper, a numerical simulation of the incompressible flow in the unit cavity is performed by using a Chebyshev-Tau approximation for the space variables, and it is found that the flow converges to a stationary state for Reynolds numbers (Re) up to 10,000.

Proceedings ArticleDOI
Jakub Wejchert1, David Haumann1
01 Jul 1991
TL;DR: Methods based on aerodynamics are developed to simulate and control the motion of objects in fluid flows and are applied to an animation that involves hundreds of flexible leaves being blown by wind currents.
Abstract: Methods based on aerodynamics are developed to simulate and control the motion of objects in fluid flows. To simplify the physics for animation, the problem is broken down into two parts: a fluid flow regime and an object boundary regime. With this simplification one can approximate the realistic behaviour of objects moving in liquids or air. It also enables a simple way of designing and controlling animation sequences: from a set of flow primitives, an animator can design the spatial arrangement of flows, create flows around obstacles and direct flow timing. The approach is fast, simple, and is easily fitted into simulators that model objects governed by classical mechanics. The methods are applied to an animation that involves hundreds of flexible leaves being blown by wind currents.

Journal ArticleDOI
01 Mar 1991-Geology
TL;DR: In this paper, a general model that relates fluid flow along a temperature gradient to chemical reaction in rocks can be used to quantitatively interpret petrologic and geochemical data on metasomatism from ancient flow systems in terms of flow direction and time-integrated fluid flux.
Abstract: A general model that relates fluid flow along a temperature gradient to chemical reaction in rocks can be used to quantitatively interpret petrologic and geochemical data on metasomatism from ancient flow systems in terms of flow direction and time-integrated fluid flux. The model is applied to regional metamorphism, quartz veins, and a metasomatized ductile fault zone.

Journal ArticleDOI
TL;DR: In this paper, the authors used Kullback entropy for Young measures to define statistical equilibrium states for a two-dimensional incompressible flow of a perfect fluid, which gave a concentration property about the equilibrium state in the phase space.
Abstract: We use Kullback entropy for Young measures to define statistical equilibrium states for a two-dimensional incompressible flow of a perfect fluid. This approach is justified, as it gives a concentration property about the equilibrium state in the phase space. It might give a statistical understanding of the appearance of coherent structures in two-dimensional turbulence.

Journal ArticleDOI
TL;DR: In this paper, the role of anisotropic surface roughness on fluid flow, solute transport, and electrical current flow in fractures is investigated, and the results show that the directional characteristics of the surfaces are more important in determining fracture transport properties than is the degree of roughness.
Abstract: The topography of natural fracture surfaces has a strong influence on the flow and transport properties of fractures. In this paper we investigate the role of anisotropic surface roughness on fluid flow, solute transport, and electrical current flow in fractures. Our results show that the directional characteristics of the surfaces are more important in determining fracture transport properties than is the degree of roughness. Roughness oriented parallel to the primary flow direction substantially enhances fluid and solute transport rates through fractures, with the effect becoming more apparent as the amount of contact area between the surface increases. Roughness oriented transverse to the flow direction inhibits flow rates and delays the movement of solute through the fracture.

Journal ArticleDOI
TL;DR: In this article, a lid-driven cavity (LDC) with a small amount of throughflow reveals multiple steady states at low cavity Reynolds numbers, which suggest that multiple stable steady states may also exist in closed LDCs.
Abstract: Flow visualization studies of a lid‐driven cavity (LDC) with a small amount of throughflow reveal multiple steady states at low cavity Reynolds numbers. These results show that the well‐known LDC flow, which consists of a primary eddy and secondary corner eddies, is only locally stable, becomes globally unstable, and competes with at least three other steady states before being replaced by a time‐periodic flow. The small amount of throughflow present in this system seems to have no qualitative effect on the fluid flow characteristics. These observations suggest that multiple stable steady states may also exist in closed LDC’s. Since stability properties of the closed LDC flows are virtually unexplored, we interpret our flow visualization results by first proposing an expected behavior of an idealized (free‐slip end walls) LDC and then treating the problem at hand as a perturbation of the ideal case. The results also suggest that there are nonunique and competing sequences of transitions that lead the flow in a LDC from laminar steady state toward turbulence.

Journal ArticleDOI
TL;DR: A geometric estimate from below on the growth rate of a small perturbation of a three-dimensional steady flow of an ideal fluid is presented and thus effective criteria for local instability for Euler's equations are obtained.
Abstract: We present a geometric estimate from below on the growth rate of a small perturbation of a three-dimensional steady flow of an ideal fluid and thus we obtain effective criteria for local instability for Euler's equations. We use these criteria to demonstrate the instability of several simple flows and to show that any flow with a hyperbolic stagnation point is unstable.

Journal ArticleDOI
TL;DR: In this paper, the movement of fluids up growth faults is proposed to be periodic; when faults are active they can concentrate fluid flow, but when inactive, flow is restricted Higher flow rates are predicted to be caused by fault-zone permeabilities and fluid potentials increasing at shear stresses close to the shear strength of the rock.
Abstract: The movement of fluids up growth faults is proposed to be periodic; when faults are active they can concentrate fluid flow, but when inactive, flow is restricted Higher flow rates are predicted to be caused by fault-zone permeabilities and fluid potentials increasing at shear stresses close to the shear strength of the rock In this way, significant flow is confined to the most active sections of moving faults Since fault activity is related to sediment accumulation rates, the volume of fluid flowing up faults should be greatest when accumulation rates are high

Journal ArticleDOI
01 Jan 1991
TL;DR: In this article, a model for the surface-to-volume ratio of a turbulent premixed flame is proposed, valid in the laminar flamelet regime, in a form suitable for incorporation into an existing model of turbulent combustion, and a parametric study shows that correct trends are observed.
Abstract: A model is proposed, valid in the laminar flamelet regime, for the surface-to-volume ratio of a turbulent premixed flame. The new model is in a form suitable for incorporation into an existing model of turbulent premixed combustion. Exact equations are derived which describe the dynamics of the constant-property surface representing the flame interface. Unknown terms in the exact equations are modelled for the simplified case of constant-density combustion in a specified turbulence field. Numerical solutions of the modelled equations are carried out for a one-dimensional test case. Preliminary results indicate that the model is capable of predicting effects present in turbulent flame propagation, and a parametric study shows that correct trends are observed.

Journal ArticleDOI
TL;DR: In this article, the effect of fluid flow on mixed-volatile reactions in metamorphic rocks is described by an expression derived from the standard equation for coupled chemical reaction and fluid-flow in porous media.
Abstract: The effect of fluid flow on mixed-volatile reactions in metamorphic rocks is described by an expression derived from the standard equation for coupled chemical-reaction and fluid-flow in porous media. If local mineral-fluid equilibrium is assumed, the expression quantitatively relates the time-integrated flux at any point in a flow-system to the progress of devolatilization reactions and the temperature- and pressure-gradients along the direction of flow. Model calculations indicate that rocks are generally devolatilized by fluids flowing uptemperature and/or down-pressure. Flow down-temperature typically results in hydration and carbonation of rocks. Time-integrated fluid fluxes implied by visible amounts of mineral products of devolatilization reactions are on the order of 5·102–5·104 mol/cm2. The model was applied to regionally metamorphosed impure carbonate rocks from south-central Maine, USA, to obtain estimates of fluid flux, flow-direction, and in-situ metamorphic-rock permeability from petrologic data. Calculated time-integrated fluxes are 104–106 cm3/cm2 at 400°–450° C, 3,500 bars. Fluid flowed from regions of low temperature to regions of high temperature at the peak of the metamorphic event. Using Darcy's Law and estimates for the duration of metamorphism and hydrologic head, calculated fluxes are 0.1–20·10-4 m/year and minimum permeabilities are 10-10–10-6 Darcy. The range of inferred permeability is in good agreement with published laboratory measurements of the permeability of metamorphic rocks.

Patent
08 Jul 1991
TL;DR: In this paper, a computer-controlled apparatus and method for perfusing a biological organ, such as a heart, kidney, liver, etc., is described, which comprises a plurality of fluid reservoirs and an organ container for holding the biological organ.
Abstract: A computer-controlled apparatus and method for perfusing a biological organ, such as a heart, kidney, liver, etc. The apparatus comprises a plurality of fluid reservoirs and an organ container for holding the biological organ. A first fluid flow path is defined as a loop from the plurality of reservoirs to necessary sensors and temperature conditioning means and back to the plurality of reservoirs. The reservoirs are selectively connectable to the first fluid flow path. Pump means are interposed in the first fluid flow path for pumping fluid from the first fluid flow path to a second fluid flow path. The organ container is located in this second fluid flow path. Pump means may also be included in the second fluid flow path for pumping fluid from the organ container to one or more of the reservoirs or to waste. One or more sensors are interposed in the fluid flow paths for sensing at least one of the concentration, temperature, pH, and pressure of the fluid flowing in the first and second fluid flow paths. Measuring means are interposed in the first and second fluid flow paths for measuring concentration and temperature differences between the upstream and downstream sides, in the fluid flow direction, of the organ container. The sensor(s) and the measuring means are connected to a programmable computer for providing a continuous information stream from the sensor(s) to the computer. The computer is coupled to the selection means and the pump means to continuously selectively control (a) the flow of fluid from each of the reservoirs individually to the fluid flow paths, and (b) at least one of the concentration, temperature, pressure and pH of the fluid flowing in the second fluid flow path, in accordance with a predetermined computer program without operator intervention.