Numerical study on the two-phase flow distribution in a T-junction

The main objective of this paper is to investigate the ability of a two-dimensional two-fluid computer code to predict the phase separation in a T-junction. A new semi-implicit numerical scheme is developed for solving the two-fluid model equations. Special attention is directed to the modelling of the constitutive for the interfacial friction term. Detailed distribution of void fraction, pressure and velocities are obtained for an air–water mixture in a vertical tee. Good agreement was obtained between the computer code results and the experimental data for the phase separation in the T-junction.     

Numerical study of laminar fluid flow in a curved elliptic duct with internal fins

The fully developed laminar incompressible flow inside a curved duct of elliptical cross-section with four thin, internal longitudinal fins is studied using the improved CVP method. We present numerical results for the friction factor and an investigation of the effect of the fin height and the Dean number on the flow. It is found that the friction factor increases for large fins and for high Dean numbers and that in some cases, it has a strong dependence on the cross-sectional aspect ratio. The thermal results show that the heat transfer rate is enhanced by the internal fins and that it depends on the aspect ratio.     

A numerical study of bifurcation in laminar flow in curved ducts

The bifurcation phenomenon whereby multiple-vortex secondary flow occurs in place of the normal two-vortex flow in laminar flow in curved ducts has previously been studied numerically by several researchers. However, the various results have been conflicting on many points. The present paper describes a set of numerical experiments conducted to study the effect of numerical accuracy on the solution. The results show that the transition from two- to four-vortex structure depends strongly on the differencing scheme and to a lesser extent on the grid size. The study also shows that as the Reynolds number of the flow increases, a two-vortex structure is re-established via a path which involves strongly asymmetric secondary flow patterns. These results are in agreement, at least qualitatively, with recent experimental theoretical and numerical results.     

Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

This article studies the three-dimensional boundary layer flow of an elasticoviscous luid over a stretching surface. Velocity of the stretching sheet is assumed to be ime-dependent. Effect of mass transfer with higher order chemical reaction is further onsidered. Computations are made by the homptopy analysis method (HAM). Convergence f the obtained series solutions is explicitly analyzed. Variations of embedding arameters on the velocity and concentration are graphically discussed. Numerical computations f surface mass transfer are reported. Comparison of the present results with he numerical solutions is also given.     

Time-dependent three-dimensional flow and mass transfer of elastico-viscous fluid over unsteady stretching sheet

This article studies the three-dimensional boundary layer flow of an elasticoviscous fluid over a stretching surface. Velocity of the stretching sheet is assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction is further considered. Computations are made by the homptopy analysis method (HAM). Convergence of the obtained series solutions is explicitly analyzed. Variations of embedding parameters on the velocity and concentration are graphically discussed. Numerical computations of surface mass transfer are reported. Comparison of the present results with the numerical solutions is also given.     

Effects of the side walls on unsteady flow of a second grade fluid over a plane wall

The effects of the side walls on unsteady flow of a second grade fluid over a plan wall are considered. The solution of the governing equation for velocity is obtained by the sine transform method. This gives a correct result for the shear stress at the bottom wall. The shear stress at the bottom wall is minimum at the middle of the plate and it increases near the side walls. It is shown that the mean thickness of the layer of the liquid over the plate increases with time and the ratio of the mean thickness to the distance between the side walls becomes ultimately 0.2714.     

Effective equations for two-phase flow in porous media: the effect of trapping on the microscale

In this article, we consider a two-phase flow model in a heterogeneous porous column. The medium consists of many homogeneous layers that are perpendicular to the flow direction and have a periodic structure resulting in a one-dimensional flow. Trapping may occur at the interface between a coarse and a fine layer. Assuming that capillary effects caused by the surface tension are in balance with the viscous effects, we apply the homogenization approach to derive an effective (upscaled) model. Numerical experiments show a good agreement between the effective solution and the averaged solution taking into account the detailed microstructure.     

Interstitial fluid flow: simulation of mechanical environment of cells in the interosseous membrane

In vitro experiments have shown that subtle fluid flow environment plays a significant role in living biological tissues,while there is no in vivo practical dynamical measurement of the interstitial fluid flow velocity.On the basis of a new finding that capillaries and collagen fibrils in the interosseous membrane form a parallel array,we set up a porous media model simulating the flow field with FLUENT software,studied the shear stress on interstitial cells’ surface due to the interstitial fluid flow,and analyzed the effect of flow on protein space distribution around the cells.The numerical simulation results show that the parallel nature of capillaries could lead to directional interstitial fluid flow in the direction of capillaries.Interstitial fluid flow would induce shear stress on the membrane of interstitial cells,up to 30 Pa or so,which reaches or exceeds the threshold values of cells’ biological response observed in vitro.Interstitial fluid flow would induce nonuniform spacial distribution of secretion protein of mast cells.Shear tress on cells could be affected by capillary parameters such as the distance between the adjacent capillaries,blood pressure and the permeability coefficient of capillary’s wall.The interstitial pressure and the interstitial porosity could also affect the shear stress on cells.In conclusion,numerical simulation provides an effective way for in vivo dynamic interstitial velocity research,helps to set up the vivid subtle interstitial flow environment of cells,and is beneficial to understanding the physiological functions of interstitial fluid flow.     

A finite element analysis of the steady laminar entrance flow in a 90° curved tube

A standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier–Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser–Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.     

Slip effects and heat transfer analysis in a viscous fluid over an oscillatory stretching surface

In this study, we investigate the heat transfer problem in a viscous fluid over an oscillatory infinite sheet with slip condition. The sheet is moved back and forth in its own plane. The derived problem involves a dimensionless parameter indicating the relative magnitude of frequency to sheet stretching rate. A system of non‐linear partial differential equations is solved numerically using the finite‐difference scheme, in which a coordinate transformation is employed to transform the semi‐infinite physical space to a bounded computational domain. The physical features of interesting parameters on the velocity and temperature distributions are shown graphically and discussed. The values of the skin‐friction coefficient and the local Nusselt number are given in tabular form. Copyright © 2008 John Wiley & Sons, Ltd.     

The numerical solution of Stokes flow in a domain with re-entrant boundaries by the boundary element method

Numerical solutions are presented for two-dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re-entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.     

An analytical solution and analysis of characters for viscoelastic fluid flow in annular pipe

I.Introducti0nLuiCiqunandHuangJunqiI'I(l989),ZhuWeihuiandLuiCiquri1'l(l992)sequentiallystudiedtheaxialflowofsecondorderandMaxwellfluidsandanalyzedtheflowcharactersofthesefluids.Thispaperwillstudyunsteadyrotat0ryflowofsecondorderandMaxwellfluidsinannularpi…     

Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study

This paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non‐linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non‐Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear‐thinning and shear‐thickening characteristics of the non‐Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid. Copyright © 2009 John Wiley & Sons, Ltd.     

Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.     

Numerical solution of the turbulent flow of an incompressible fluid in curved planar and axially symmetrical channels

The governing equations for axially symmetric flow, where the Reynolds stresses are expressed by scalar turbulent viscosity, are the Reynolds equations. The turbulence model k, ? is used in the well-known form for fully developed turbulent flow.The numerical method, a continuation of the MAC system¹, is adapted so that even for high Reynolds cell numbers precision (δx²) can be achieved for the steady flow. Irregular cells join the rectangular network on the curved surface. Von Neumann's stability condition of the linearised numerical system is investigated. Special problems concerning the numerical solution of the turbulence model equations are stated and a special procedure is worked out to ensure that the fields k, ? do not converge to physically meaningless values. The program for the computer is universal in that the boundary problems can be assigned by input data.As an example, an axially symmetrical diffuser with an area ratio of widening 1.40 is computed. Fields of velocity and pressure at the wall as well as fields v_T and k are assessed. The results are compared with an experiment. The conclusion is that this method is suitable for the problems mentioned in this study as well as for unsteady flow.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Combined effects of heat and chemical reactions on the peristaltic flow of carreau fluid model in a diverging tube

The study of peristaltic flow of a Carreau fluid in a non‐uniform tube under the consideration of long wavelength in the presence of heat and mass transfer is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Two types of analytical solutions have been evaluated (i) perturbation method (ii) homotopy analysis method for velocity, temperature and concentration field. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Copyright © 2010 John Wiley & Sons, Ltd.