Showing papers on "Fluid dynamics published in 1996"

Computational methods for fluid dynamics

Abstract: Preface. Basic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.- Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flow.- Efficiency and Accuracy Improvement. Special Topics.- Appendeces.

A finite point method in computational mechanics. applications to convective transport and fluid flow

Abstract: The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non-self adjoint equations typical of convective-diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.

Two-phase binary fluids and immiscible fluids described by an order parameter

Abstract: A unified framework for coupled Navier-Stokes/Cahn-Hilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two space dimensions.

On boundary conditions in lattice Boltzmann methods

Abstract: A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two‐dimensional Poiseuille flow, unsteady Couette flow, lid‐driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.

Tortuous flow in porous media

Abstract: The concept of tortuosity of fluid flow in porous media is discussed. A lattice-gas cellular automaton method is applied to solve the flow of a Newtonian uncompressible fluid in a two-dimensional porous substance constructed by randomly placed rectangles of equal size and with unrestricted overlap. A clear correlation between the average tortuosity of the flow paths and the porosity of the substance has been found. \textcopyright{} 1996 The American Physical Society.

A Brief Introduction to Fluid Mechanics

Abstract: Fluid Statics. Elementary Fluid DynamicsThe Bernoulli Equation. Fluid Kinematics. Finite Control Volume Analysis. Differential Analysis of Fluid Flow. Similitude, Dimensional Analysis, and Modeling. Viscous Flow in Pipes. Flow Over Immersed Bodies. Open-Channel Flow. Turbomachines. Appendices. Answers. Index.

Chemical engineering fluid mechanics

Abstract: Basic concepts dimensional analysis and scale-up fluid properties in perspective fluid statics conservation principles pipe flow internal flow applications pumps and compressors compressible flows flow measurement and control externalflows fluid-solid separations by free settling flow in porous media fluidization and sedimentation two-phase flow appendices.

Diffusion in a multicomponent lattice Boltzmann equation model.

Abstract: Diffusion phenomena in a multiple component lattice Boltzmann equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is found to have correct diffusion behavior and the multiple diffusion coefficients are obtained analytically. The analytical results are further confirmed by numerical simulations in a few solvable limiting cases. The LBE model is established as a useful computational tool for the simulation of mass transfer in fluid systems with external forces. \textcopyright{} 1996 The American Physical Society.

Review and classification of structural controls on fluid flow during regional metamorphism

Abstract: Mechanisms for kilometre-scale, open-system fluid flow during regional metamorphism remain problematic. Debate also continues over the degree of fluid flow channellization during regional metamorphism, and the mechanisms for pervasive fluid flow at depth. The requirements for pervasive long-distance fluid flow are an interconnected porosity and a large regional gradient in fluid pressure and hydraulic head (thermally or structurally controlled) that dominates over local perturbations in hydraulic head due to deformation. In contrast, dynamic or transient porosity interconnection and fluid flow accompanying deformation of heterogeneous rock suites should result in moderately to strongly channellized flow at a range of scales, of which there are many examples in the literature. Classification of fluid flow types based on scale and degree of equilibration between fluid and rock, wallrock permeability, and mode of fluid transport contributes to an understanding of key factors that control fluid flow. Closed-system fluid behaviour, with restricted fluid flow in microcracks or cracks and limited fluid–rock interaction, occurs over a range of strains and crustal depths, but requires low permeabilities and/or small fluid fluxes. Long-distance, open-system fluid flow in channels is favoured in heterogeneous rocks at high strains, moderate (but variable) permeabilities, and moderate to high fluid fluxes. Long-distance, broad, pervasive fluid flow during regional metamorphism requires that the rocks are not accumulating high strains and have high permeabilities, low permeability contrasts, and high fluid fluxes. The ideal situation for such fluid flow is in situations where the rocks are undergoing stress relaxation immediately after a major deformation phase. In the mid-crust, fairly specific conditions are thus required for pervasive fluid flow. During active orogenesis, structurally controlled fluid flow (with focused open systems surrounding regions of closed-system behaviour) predominates in most, but not all, regional metamorphic situations, at a range of scales.

Hydrodynamics of Fractal Aggregates with Radially Varying Permeability

Abstract: Hydrodynamic properties of fractal aggregates with radially varying permeability are investigated in terms of two parameters: radius of equivalent solid sphere experiencing the same drag as the aggregate (Ω*radius of aggregate) and fluid collection efficiency (η) of the aggregate. Resistance to the fluid flow through the aggregate is predicted to increase with increasing fractal dimension, while the fluid collection efficiency is expected to decrease. It is shown that a reasonable estimate of the fluid drag force on a fractal aggregate may be obtained by assigning a constant volume-averaged porosity to the aggregate and using any of the expressions available in the literature for aggregates with uniform permeability. The two hydrodynamic parameters, Ω and η, are used to modify the existing expressions for interactions between solid spheres to account for the porous nature of aggregates and thus calculate the collision rate kernels for interacting aggregates. The ratio of hydrodynamic radius of an aggregate to its radius of gyration predicted by the proposed model was in reasonable agreement with an experimental value reported in the literature.

An approximate projection scheme for incompressible flow using spectral elements

Abstract: SUMMARY An approximate projection scheme based on the pressure correction method is proposed to solve the NavierStokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is Mer validated by simulating the laminar flow over a backward-facing step. The solution of the Navier-Stokes equations for unsteady incompressible fluid flow is still a major challenge in the field of computational fluid dynamics. An overview of the most important aspects with respect to the solution of the incompressible Navier-Stokes equations can be found in References 1-5. The Navier-Stokes equations form a set of coupled equations for both velocity and pressure (or, better, the gradient of the pressure). One of the main problems related to the numerical solution of these equations is the imposition of the incompressibility constraint and consequently the calculation of the pressure. The pressure is not a thermodynamic variable, as there is no equation of state for an incompressible fluid. It is an implicit variable which instantaneously 'adjusts itself' in such a way that the velocity remains divergence-free. The gradient of the pressure, on the other hand, is a relevant physical quantity: a force per unit volume. The mathematical importance of the pressure in an incompressible flow lies in the theory of saddle-point problems (of which the steady Stokes equations are an example), where it acts as a Lagrangian multiplier that constrains the velocity to remain divergence-free. There are numerous approaches to solve the Navier-Stokes equations. For the solution of unsteady Navier-Stokes flow perhaps one of the most successful approaches to date is provided by the class of projection methods.&' Projection methods have been developed as a useful way of obtaining an efficient solution algorithm for unsteady incompressible flow. In this paper, projection methods are considered that are applied to the set of continuous equations, yielding very efficient and simple-toimplement algorithms. By decoupling the treatment of velocity and pressure terms, a set of easier-tosolve equations arises: a convectiondiffusion problem for the velocity, yielding an intermediate velocity which is not divergence-free; and a Poisson equation for the pressure (or a related quantity).

Coarse‐grained description of thermo‐capillary flow

Abstract: A mesoscopic or coarse‐grained approach is presented to study thermo‐capillary induced flows. An order parameter representation of a two‐phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn–Hilliard equation with advective transport. A modified Navier–Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier–Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo‐capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient.

Hybrid Multifluid Algorithms

Abstract: Extensions of many successful single-component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components. A new algorithm based on the compressible Euler equations for multicomponent fluids augmented by the pressure evolution equation is presented. The extended set of equations offers two alternative ways to update the pressure field: (i) using the equation of state or (ii) using the pressure evolution equation. In a numerical implementation, these two procedures generally yield different answers. The former is a standard conservative update, but may produce oscillations near material interfaces; the latter is nonconservative, but becomes exact near interfaces and automatically maintains pressure equilibrium. A hybrid scheme which selects from the two pressure update procedures is presented. The scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite (very small) number of grid cells. Computed solutions exhibit oscillation-free interfaces and have {\em negligible} relative conservation errors in total energy even for very strong shocks. The proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one's favourite scheme to solve multifluid dynamics.

Dynamics of fluid flow inside carbon nanotubes

Abstract: The dynamics of fluid flow through nanomachines is different from in other systems in that the flow is granular (no continuum assumption) and that the `walls' move. We have performed molecular dynamics simulations of the flow of helium and argon inside carbon (graphite) nanotubes of several sizes. The fluid was started at some initial velocity; fluid particles were allowed to recycle axially through the tube via minimum image boundary conditions. Argon slowed down more quickly than helium. In addition, the behaviour of the fluid strongly depended on the rigidity of the tube; a dynamic tube slowed down the fluid far more quickly than one in which the tube was held frozen. It also depended on the fluid density and tube diameter. It did not, however, depend on the tube length, because fluid flow tended to prevent the development of strong longitudinal modes, whose behaviour is length dependent.

Steady flow in an aneurysm model: correlation between fluid dynamics and blood platelet deposition.

Abstract: Laminar and turbulent numerical simulations of steady flow in an aneurysm model were carried out over Reynolds numbers ranging from 300 to 3600. The numerical simulations are validated with Digital Particle Image Velocimetry (DPIV) measure­ ments, and used to study the fluid dynamic mechanisms that characterize aneurysm deterioration, by correlating them to in vitro blood platelet deposition results. It is shown that the recirculation zone formed inside the aneurysm cavity creates condi­ tions that promote thrombus formation and the viability of rupture. Wall shear stress values in the recirculation zone are around one order of magnitude less than in the entrance zone. The point of reattachment at the distal end of the aneurysm is charac­ terized by a pronounced wall shear stress peak. As the Reynolds number increases in laminar flow, the center of the recirculation region migrates toward the distal end of the aneurysm, increasing the pressure at the reattachment point. Under fully turbulent flow conditions (Re = 3600) the recirculation zone inside the aneurysm shrinks considerably. The wall shear stress values are almost one order of magnitude larger than those for the laminar cases. The fluid dynamics mechanisms inferred from the numerical simulation were correlated with measurements of blood platelet deposition, offering useful explanations for the different morphologies of the platelet deposition curves.

Diascalar flux and the rate of fluid mixing

Abstract: We define the rate at which a scalar 0 mixes in a fluid flow in terms of the flux of θ across isoscalar surfaces. This flux Φ d is purely diffusive and is, in principle, exactly known at all times given the scalar field and the coefficient of molecular diffusivity. In general, the complex geometry of isoscalar surfaces would appear to make the calculation of this flux very difficult. In this paper, we derive an exact expression relating the instantaneous diascalar flux to the average squared scalar gradient on an isoscalar surface which does not require knowledge of the spatial structure of the surface itself. To obtain this result, a time-dependent reference state θ(t, z * ) is defined. When the scalar is taken to be density, this reference state is that of minimum potential energy. The rate of change of the reference state due to diffusion is shown to equal the divergence of the diffusive flux, i.e. (∂/∂z * )Φ d . This result provides a mathematical framework that exactly separates diffusive and advective scalar transport in incompressible fluid flows. The relationship between diffusive and advective transport is discussed in relation to the scalar variance equation and the Osborn-Cox model. Estimation of water mass transformation from oceanic microstructure profiles and determination of the time-dependent mixing rate in numerically simulated flows are discussed.

Implantable device and method for removing fluids from the blood of a patient method for implanting such a device and method for treating a patient experiencing renal failure

Abstract: An implantable ultrafiltration device for removing low to medium molecular weight solutes and fluids from the blood of a patient experiencing renal failure, the device including: a pump having an inlet and an outlet; a first component for forming a first fluid flow path between the patient's vascular system and the pump inlet; a filter interposed in the first fluid flow path, the filter being permeable to water and substantially impermeable to blood cells and proteins; and a second component for forming a second fluid flow path between the pump outlet and the patient's bladder, wherein the pump, the first and second components, and the filter are all constructed to be surgically implanted in the patient's body For removing unwanted fluids from the blood of a patient experiencing renal failure the first component is connected in the vascular system of the patient and the second component is implanted in the patient's bladder or ureter; and the pump is then operated to cause fluid to flow through the filter at a controlled rate in order to maintain the volume of the blood in the vascular system and total body volume at a selected value The infusion of peritoneal solution free of osmotic agents can also be carried out in conjunction with conventional hemodialysis or with operation of the implanted device

Fluid Dynamics of the Heart and its Valves

Abstract: Blood is a viscous incompressible fluid which is propelled through the arteries, capillaries, and veins of the circulation by a collection of elastic and contractile fibers known as the heart. The left side of the heart receives bright red oxygenated blood from the lungs, and it pumps this blood into the aorta through which it is distributed to all of the tissues of the body, including the heart muscle (via the coronary arteries). As it flows through these various tissues, part of the oxygen is removed, and the color changes from bright red to bluish red. At the same time, carbon dioxide that has been generated by tissue metabolism is picked up by the blood. The deoxygenated blood returns to the right side of the heart, which pumps it through the pulmonary arterial tree to the lungs, where the carbon dioxide is removed and the blood becomes once more saturated with oxygen. Each side of the heart has two chambers, an atrium and a ventricle. Each ventricle has an inflow (atrioventricular) and an outflow (arterial) valve. The valves are primarily passive structures that move in response to the flow of blood, although the atrioventricular valves are supported by muscles that prevent prolapse when those valves are closed. Both types of valves are constructed in such a way that they open freely to allow forward flow but close to prevent backflow. When the ventricles are relaxed (diastole), their inflow valves are open and their outflow valves are closed: during this time period the ventricular pressures are low, and each ventricle fills with blood from the corresponding atrium. When the ventricles contract (systole), the inflow valves close first, and then the outflow valves open as the ventricular pressures rise. Once the outflow valves are open, each ventricle ejects blood into its corresponding artery. The familiar heart sounds are associated with the closure of the valves and the subsequent vibration of the cardiac and arterial chambers. The lower pitch “Lub” is associated with the nearly synchronous closure of the two atrioventricular valves, and the higher pitched “Dup” is associated with the nearly synchronous closure of the two arterial valves. Valve opening is normally silent but may produce sounds in disease states. Heart murmurs are associated with turbulence that may be generated by jets of fluid that form when valves fail to open fully or fail to close properly. For further detail concerning the physiology of the heart, see Guy-

A stable penalty method for the compressible navier-stokes equations. i. open boundary conditions

Abstract: The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier--Stokes equations in three spatial dimensions The treatment uses the conservation form of the Navier--Stokes equations and utilizes linearization and localization at the boundaries based on these variables The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder