Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

Magnetoconvection in a vertical channel with heat source or sink

The problem of steady, laminar mixed convective flow and heat transfer of an electrically conducting fluid through a vertical channel with heat source or sink is analyzed. The effects of viscous and Ohmic dissipations are included in the energy equation. Both walls are kept either at the same or different temperatures such as isothermal-isothermal, isoflux-isothermal and isothermal-isoflux conditions. Analytical solutions are found using regular perturbation technique and numerical solutions are found using finite difference method. A selected set of graphical results illustrating the effects of various parameters involved in the problem on the flow as well as flow reversal situation and Nusselt numbers are presented and discussed. It is also found that both the analytical and numerical solutions agree very well for small values of the perturbation parameter.     

A numerical method for subcritical and supercritical open channel flow calculation

A marching finite volume method is presented for the calculation of two-dimensional, subcritical and supercritical, steady open channel flow including the usually neglected terms of slope and bottom friction. The channel flow will be assumed to be homogeneous, incompressible, two-dimensional and viscous with wind and Coriolis forces neglected. A hydrostatic pressure distribution is assumed throughout the flow field. The numerical technique used is a combination of the finite element and finite difference methods. A transformation is introduced through which quadrilaterals in the physical domain are mapped into squares in the computational domain. The governing system of PDEs is thus transformed into an equivalent system applied over a square grid network. Comparisons with other numerical solutions as well as with measurements for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique.     

Mixed convection of magneto hydrodynamic and viscous fluid in a vertical channel

Mixed convective flow and heat transfer in a vertical channel with one region filled with conducting fluid and another region with non-conducting fluid is analyzed. The viscous and Ohmic dissipation terms are included in the energy equation. Three types of thermal boundary conditions such as isothermal-isothermal, isoflux-isothermal and isothermal-isoflux for the left-right walls of the channel are prescribed. Analytical solutions are found for the governing equations using the regular perturbation method. A selected set of graphical results illustrating the effects of various parameters involved in the problem are presented and discussed.     

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.     

基于格子-波尔兹曼法的流体能耗求解

格子-波尔兹曼法是近年来新兴的一种计算流体力学数值方法。随着这种方法的不断发展,人们将它用于流体的仿真、优化等不同场合。与此同时,一些与流场流速和压强相关的物理量(如能耗)的求解也成为关注的焦点。本文介绍了能耗这一流体宏观量的格子-波尔兹曼法求解及其实现。与传统的有限差分法不同,本文在求解有关的速度梯度时使用了格子-波尔兹曼-矩法,这种方法不但能够避免有限差分法在边界处失效的缺点,而且计算简单,算法局部性好,适合大规模并行计算。本文在分析其数值解精度的基础上,使用这种方法进行了以能耗极小为目标的直通道内椭圆挡块的参数优化。这些分析和算例分别定量和定性地说明了本文算法的准确性。     

二维定常不可压缩粘性流动N-S方程的数值流形方法

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.     

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 .     

On high‐resolution schemes for solving unsteady compressible two‐phase dilute viscous flows

A high‐resolution numerical scheme based on the MUSCL–Hancock approach is developed to solve unsteady compressible two‐phase dilute viscous flow. Numerical considerations for the development of the scheme are provided. Several solvers for the Godunov fluxes are tested and the results lead to the choice of an exact Riemann solver adapted for both gaseous and dispersed phases. The accuracy of the scheme is proven step by step through specific test cases. These simulations are for one‐phase viscous flows over a flat plate in subsonic and supersonic regimes, unsteady flows in a low‐pressure shock tube, two‐phase dilute viscous flows over a flat plate and, finally, two‐phase unsteady viscous flows in a shock tube. The results are compared with well‐established analytical and numerical solutions and very good agreement is achieved. Copyright © 1999 John Wiley & Sons, Ltd.     

A complete boundary integral formulation for compressible Navier–Stokes equations

A complete boundary integral formulation for compressible Navier–Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two‐dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd.     

注塑成型三维流动的数值模拟

建立了非等温、粘性、不可压缩、非牛顿流体流动的控制方程。为了避免同时求解耦合的压力场、速度场,本文通过修改Galerkin方法的变分方程,导出了关于压力场的拟Poisson方程,用迭代法独立地求解连续性方程、动量方程,并进行速度一粘度迭代求出最终的压力场、速度场。由于直接使用Galerkin方法求解能量方程容易引起温度场的振荡,本文采用隐式格式及“上风”法离散能量方程,用超松驰迭代法求解温度场的代数方程组。比较了模拟结果与等温管道流动的解析解及法兰的实际注射结果,算例表明本文方法可以预测注射成型流动过程中的一些重要特征。与传统Galerkin方法相比,本文方法可以减少内存,提高数值方法的稳定性。     

A singular perturbation problem of laminar flow in a uniformly porous channel with large injection and with an applied transverse magnetic field

Summary The problem of the steady flow of an electrically conducting viscous fluid through porous walls of a channel in the presence of an applied transverse magnetic field is considered. A solution for the case of small M ²/R (where M = Hartmann number, R = suction Reynolds number) with large blowing at the walls has been given by Terrill and Shrestha [3]. Their solution, on differentiating three times, is found to become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and Terrill and Shrestha are neglecting the shear layer. In this paper the solution given by Terrill and Shrestha is extended by obtaining an extra term of the series of expansion and the method of inner and outer expansion is used to obtain the complete solution which includes the viscous layer. The resulting series solutions are confirmed by numerical results.     

A distributed Lagrange multiplier/fictitious domain method for flows around moving rigid bodies: Application to particulate flow

This article discusses the application of a Lagrange multiplier‐based fictitious domain method to the numerical simulation of incompressible viscous flow modeled by the Navier–Stokes equations around moving rigid bodies; the rigid body motions are due to hydrodynamical forces and gravity. The solution method combines finite element approximations, time discretization by operator splitting and conjugate gradient algorithms for the solution of the linearly constrained quadratic minimization problems coming from the splitting method. The study concludes with the presentation of numerical results concerning four test problems, namely the simulation of an incompressible viscous flow around a NACA0012 airfoil with a fixed center but free to rotate, then the sedimentation of 200 and 1008 cylinders in a two‐dimensional channel, and finally the sedimentation of two spherical balls in a rectangular cylinder. Copyright © 1999 John Wiley & Sons, Ltd.     

Spectral element method for viscoelastic flows in a planar contraction channel

A new algorithm, which combines the spectral element method with elastic viscous splitting stress (EVSS) method, has been developed for viscoelastic fluid flows in a planar contraction channel. The system of spectral element approximations to the velocity, pressure, extra stress and the rate of deformation variables is solved by a preconditioned conjugate gradient method based on the Uzawa iteration procedure. The numerical approach is implemented on a planar four‐to‐one contraction channel for a fluid governed by an Oldroyd‐B constitutive equation. The behaviour of the Oldroyd‐B fluids in the contraction channel is investigated with various Weissenberg numbers. It is shown that numerical solutions obtained here agree well with experimental measurements and other numerical predictions. Copyright © 2003 John Wiley & Sons, Ltd.     

Unsteady conjugate problem of a dissipative fluid in a horizontal channel with a periodic variation temperature

The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness, Péclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary, while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or integrated transport variables at any point or section of the medium.     

A Direct theory of viscous fluid flow in channels

This paper deals with an Eulerian formulation of the theory of directed fluid sheets appropriate for incompressible, linear viscous fluid flow in channels with arbitrary shapes for their major boundaries which may be moving or fixed. Special cases of the theory are applied to a number of two-dimensional fluid flow problems and these solutions are in general discussed for unsteady flow. Specific applications include fluid flow in a channel whose boundaries are symmetric with respect to a middle plane in the channel, subjected to time-dependent pressure gradient at one end; and to lubrication problems in a general shaped channel when one of the channel walls is a fixed plane while the other is moving with a constant velocity. Flow of a viscous fluid with a free surface over a fixed boundary is also discussed.Dedicated to J. L. Ericksen on the occasion of his Sixtieth Birthday     

Flow field calculation and its experimental verification for inertia stage of marine gas turbine air intake filter

A numerical method is presented in this paper for the solution of flow field in marine gas turbine air intake filtration channel. The flow field was successfully calculated by this method, and aerodynamic characteristics were obtained for various types of filtration channels. This work is expected to be of practical importance for the design of such filters. Upstream difference was adopted to discretize the non-conservative type N-S equation for two-dimensional, time-dependnet, viscous and incompressible flow, and the stability, convergence, accuracy and artificial viscosity of the resulting difference equation were examined. This equation can be used to calculate viscous flows with Reynolds number up to tens of thousands. Also presented in this paper is a calculation method for treating wall vortex at boundary inflection points. Careful studies show that calculation based on the difference equational and wall vortex treatment proposed here are in good agreement with experimental results.     

Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low Reynolds numbers

Numerical simulation and flow visualization were performed to study the dynamical behavior of vortices generated in channels with two different geometries, i.e., a periodically converging–diverging channel and serpentine channel, both having sinusoidal wavy walls. This system for pulsatile flow is used to enhance heat and mass transfer in very viscous liquids. The numerical results predict well the dynamical behavior of vortices and agree with the flow visualizations. For both channels, the vortex expands in each furrow of the channel walls during the deceleration phase and shrinks during the acceleration phase, which leads to fluid exchange between the vortex and the mainstream. The time-averaged vortex strength and wall shear stresses increase, as the frequency of fluid oscillation increases under a fixed oscillatory fraction of the flow rate. However, above a certain value of the frequency, they reversely decrease due to viscous effects. This frequency for the serpentine channel is smaller than that for the converging–diverging channel. The channel geometries are found to have an important effect of the flow characteristics.     

船用燃气轮机进气滤清器惯性级内的流场计算和实验验证

本文提出了一套求解船用燃气轮机进气滤清器流道流场的数值方法,成功地计算了流道内流场的状态,给出了各种不同型号流道的气动特性,对指导滤清器的设计有较大的现实意义, 在这套方法中,我们应用上风差分来逼近二维、非定常、粘性、不可压缩流体非守恒型的N-S方程,提出了一种可计算雷诺数高达上万的粘性流的差分方程,考察了这种差分方程的稳定性,收敛性、精度和人工粘性,本文还提出了处理一些边界拐点处壁涡的计算方法,实际算例表明,使用本文提出的差分方程和壁涡处理方法给出的计算结果和实验吻合良好。     

Flow of viscoelastic fluids through a porous channel—I

The flow of viscoelastic fluids through a porous channel with one impermeable wall is computed. The flow is characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. Three solutions are developed: (i) an exact numerical solution, (ii) a perturbation solution for small R, the cross-flow Reynold's number and (iii) an asymptotic solution for large R. The results from exact numerical integration reveal that the solutions for a non-Newtonian fluid are possible only up to a critical value of the viscoelastic fluid parameter, which decreases with an increase in R. It is further demonstrated that the perturbation solution gives acceptable results only if the viscoelastic fluid parameter is also small. Two more related problems are considered: fluid dynamics of a long porous slider, and injection of fluid through one side of a long vertical porous channel. For both the problems, exact numerical and other solutions are derived and appropriate conclusions drawn.