Combined adaptive meshing technique and characteristic-based split algorithm for viscous incompressible flow analysis

A combined characteristic-based split algorithm and an adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented.The method uses the three-node triangular element with equal-order interpolation functions for all variables of the velocity components and pressure.The main advantage of the combined method is that it improves the solution accuracy by coupling an error estima- tion procedure to an adaptive meshing technique that generates small elements in regions with a large change in solution gradients,and at the same time,larger elements in the other regions.The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder,for their transient and steady-state flow behaviors.     

Interaction between compressibility and particulate suspension on peristaltically driven flow in planar channel

The peristaltic pumping of a viscous compressible liquid mixed with rigid spherical particles of the same size in a channel is theoretically investigated.The momentum equations for the compressible flow are solved with a perturbation analysis.The analysis is carried out by duly accounting for the nonlinear convective acceleration terms for the fluid part on the wavy wall.The zeroth-order terms yield the Poiseuille flow,and the first-order terms give the Orr-Sommerfeld equation.The explicit expression for the net axial velocity is derived.The effects of the embedded parameters on the axial fluid velocity are studied through different engineering applications.The features of the flow characteristics are analyzed and discussed in detail.The obtained results are evaluated for various parameters associated with the blood flow in the blood vessels with diameters less than 5 500 μm,whereas the particle diameter has been taken to be 8 μm.This study provides a scope to evaluate the effect of the theory of two-phase flow characteristics with compressible fluid problems,and is helpful for understanding the role of engineering applications of pumping solid-fluid mixture by peristaltically driven motion.     

Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t~he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.     

A CALCULATION METHOD FOR BLOOD FLOW VELOCITY DISTRIBUTION IN SMALLER BLOOD VESSELS

The calculative method presented in this paper is based on animprovement of boundary conditions for a micro-continuum fluidmodel with blood flow assuming that the blood cell velocity atblood vessel wall is unequal to zero.As for steady state floodflow equation (flow in vitre-a rigid circular tube) presentedby Exingen,the magnitude of the blood cell gyroscopic velocityat blood vessel wall and the slope of the blood cell gyroscopicvelocity distribution curve at the axis of the blood vessel areassumed.From the above-mentioned assumptions the calculatingmethod of velocity distribution curve in blood vessel is deri.ved.The curve calculated by this method is compared with thetest curve measured by Bugliarello and Hayden.The results ob-tained by Turk,Sylvester and Ariman as well as with this me-thod are compared with each other,too.     

Theoretical analysis on hydraulic transient resulted by sudden increase of inlet pressure for laminar pipeline flow

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.     

MHD non-Newtonian micropolar fluid flow and heat transfer in channel with stretching walls

A study is presented for magnetohydrodynamics （MHD） flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.     

UNSTEADY／STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. 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 numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.     

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system.The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES.In Part 2 of this two-part paper,the influence of DC on the time-averaged flow field was systematically studied.Several time-averaging computations were conducted with various boundary conditions and DC for the downstream stator in a transonic compressor stage,by employing the CFD solver developed in Part 1 of this two-part paper.These results were compared with the time-averaged unsteady flow field and the steady one.The study indicated that the circumferentialaveraged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compressors.Furthermore,it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.     

ON FLOW IN POROUS MEDIA

渗流是流体在多孔介质中的流动，渗流现象广泛地存在于自然界、工程材料、动物、植物中。多孔介质种类繁多，包括岩石(含各类矿藏)、土壤、生物材料和人工多孔介质材料等。渗流理论已经成为人类开发地下水、地热、石油、天然气、煤炭与煤层气等诸多地下资源的重要理论基础。本文从渗流的基本概念、渗流的分类、渗流的影响因素、渗流的特征以及渗流的研究意义等方面进行了阐述。     

Nonlinear fluid flow laws for orthotropic porous media

Nonlinear fluid flow laws for orthotropic porous media are written in invariant tensor form. As usual in the theory of fluid flow through porous media [1, 2], the equations contain the flow velocity up to the second power. Expressions that determine the nonlinear resistances to fluid flow are presented and it is shown that, on going over from linear to nonlinear flow laws, the asymmetry effect may manifest itself, that is, the fluid flow characteristics may differ along the same straight line in the positive and negative directions. It is shown that, as compared with the linear fluid flow law for orthotropic media when for three symmetry groups a single flow law is sufficient, in nonlinear laws the anisotropy manifestations are much more variable and each symmetry group must be described by specific equations. A system of laboratory measurements for finding the nonlinear flow characteristics for orthotropic porous media is considered.     

Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.     

Numerical and analytical study to estimate the effect of two length scales upon the permeability of a fibrous porous medium

A fibrous porous medium with two length scales is modeled as a bed of porous cylinders aligned perpendicular to the flow of viscous fluid. The flow behavior is described using Stokes and Darcy flow equations in the regions around (higher length scale) and within the cylinders (lower length scale) respectively. The typical ratio of higher and lower length-scale regions enable us to invoke lubrication approximation and simplify the equations to develop a closed form solution for the overall permeability of this dual-scale porous medium. A parametric analysis is performed to explore the dependence of permeability on factors such as the volumetric ratio of higher and lower length-scale regions, permeability and size of inclusions in the smaller length-scale region. The analytical model is compared with the numerical results and the trend is compared with the experiments.     

A Computational Method for Free-Surface Viscous Flows Through Porous Media

In this paper we have investigated free-surface unsteady viscous flow through porous media using a finite difference technique via primitive formulation. A transformation has been used to convert the irregular flow domain into a rectangular domain. Two illustrations have been presented in case of a standing wave problem and a cavity flow problem with a free surface. The method is found satisfactory for numerical solution for Reynolds number upto 200.     

Finite Element Analysis of Convection Flow Through a Porous Medium in a Horizontal Channel

We analyse the convection flow of a viscous fluid through a horizontal channel enclosing a fully saturated porous medium. The Galerkin finite element analysis is used to discuss the flow and heat transfer through the porous medium using serendipity elements. The velocity, the temperature distributions and the rate of heat transfer are analysed for variations in the governing parameters. The profiles at different vertical levels are asymmetric curves, exhibiting reversal flow everywhere except on the midplane. In a given porous medium, for fixed G or N, the temperature in the fluid region at any position in fluids with a higher Prandtl number, is much higher than in fluids with a lower Prandtl number. Likewise, other parameters being fixed, lesser the permeability of the medium, lower the temperature in the flow field. Nu reduces across the flow at all axial positions, while it enhances along the axial direction of the channel. Nu reduces with decrease in the Darcy parameter D, and thus lesser the permeability of the medium, lesser the rate of heat transfer across the boundary at any axial position of the channel.     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.     

Magnetohydrodynamics convective flow in a vertical slot through a porous medium

An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.     

The Flow Problem of Fluids Flow in a Fractal Reservoir with Double Porosity

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