Slip flow due to a stretching cylinder

The slip flow due to a stretching cylinder is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations. Asymptotic solutions for large Reynolds number and small slip show the problem can be related to the existing two-dimensional stretching cases. Due to algebraic decay, the equations are further transformed through a compressed variable, and then integrated numerically. It is found that slip greatly reduces the magnitudes of the velocities and the shear stress.     

Numerical simulation of an isolated vortex and shear flow interaction

A numerical solution for the Navier-Stokes equations in the unbounded region is considered for the interaction of an isolated vortex and shear flow. A Chebyshey collocation method in space and finite-difference method for temporal discretization are used. The results of the numerical experiments for the interaction are discussed. It is shown that shear flow can both increase and decrease the vortex dissipation rate.     

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study.The disk impinges the oncoming flow with a time-dependent axial velocity.The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations.The governing equations are solved numerically,and two distinct similarity solution branches are obtained.Both solution branches exhibit different flow patterns.The upper branch solution exists for all values of the impinging parameter β and the rotating parameter.However,the lower branch solution breaks down at some moderate values of β.The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β.The results of the velocity profile,the skin friction,and the stream lines are demonstrated through graphs and tables for both solution branches.The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.     

Variational iteration method for two-dimensional steady slip flow in micro-channels

In this paper, the two-dimensional steady slip flow in microchannels is investigated. Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). The Navier-Stokes equations for two-dimensional steady slip flow in microchannels are reduced to a nonlinear third-order differential equation by using similarity solution. The variational iteration method (VIM) is used to solve this nonlinear equation analytically. Comparison of the result obtained by the present method with numerical solution reveals that the accuracy and fast convergence of the new method.     

Finite element computations of two-dimensional arterial flow in the presence of a transverse magnetic field

A finite element solution of the Navier-Stokes equations for steady flow under the magnetic effect through a double-branched two-dimensional section of a three-dimensional model of the canine aorta is discussed. The numerical scheme involves transforming the physical co-ordinates to a curvilinear boundary-fitted co-ordinate system. The shear stress at the wall is calculated for a Reynolds number of 1000 with the branch-to-main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and found to be in reasonable qualitative agreement. The steady flow, shear stress and branch flow under the effect of a magnetic field have been discussed in detail.     

广义Stokes方程的完全边界积分表示式及其在求解N-S方程中的应用

为了分解N-S方程组各变量相互偶合,本文采用Peaceman-Rachford算子分裂法,将时间相依的N-S方程组分解成不存在上述偶合特性的线性和非线性的子问题。线性子问题具有广义Stokes方程类型。本文采用多重互易法,即采用多阶拉普拉斯算子基本解逐步变换,将其解表示成完全边界积分形式,从而使问题的计算维数降低一维。广义Stokes方程的算例以及二维圆柱在剪切流中的Stokes绕流解,都表明多重互易算法具有高效特点,而且后者与文[3]解析解吻合得非常好。     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.     

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.     

Unsteady magnetohydrodynamic stagnation point flow — closed-form analytical solutions

This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic(MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes(NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation,and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.     

Computational technique for flow in blood vessels with porous effects

IntroductionThehemodynamicsofflowsthroughbloodvesselsisofgreatinterest,becausethesevesselspresentasubstantialhealthriskandareamajorcauseofmortalityandmorbidityintheindustrializedworld .Researchpapersonthebloodflowhaveappearedbutmostofthemhaveneglectedtheporosityeffectsduetovesselwalls.Inthisstudyweareinterestedintheflowthroughabloodvesseltakingintoaccounttheporosityeffectsofthevessels.Fluidflowthroughaporousmediumisoffundamentalimportancetowiderangeofdisciplinesinthevariousbranchesofnaturalsci…     

高雷诺数流动的基本控制方程体系和扩散跑物化Navier-Stokes方程组的意义和用途

在计算机发达的时代, 高雷诺($Re$)数绕流计算中有无必要使用简化NS方程组, 本文讨论这个问题. 主要内容如下: (1)高$Re$数绕流包含3种基本流动: 所有方向对流占优流动、所有方向对流扩散竞争流动和部分方向对流占优部分方向对流扩散竞争流动(简称干扰剪切流动), 3个基本流动的特征彼此不同且在流场中所占领域大小彼此相差悬殊, NS方程区域很小,它们的最简单控制方程组Euler、Navier-Stokes (NS)和扩散抛物化(DP) NS方程组的数学性质彼此不同, 因此利用Euler-DPNS-NS方程组体系分析计算高$Re$数绕流流动就是一个合乎逻辑的选择, 该法与利用单一NS方程组的常用方法可以彼此检验和补充. (2)流体之间以及流体与外界的动量、能量和质量交换, 流态从层流到湍流的演化主要发生在干扰剪切流动中, 干扰剪切流及其最简单控制方程------DPNS方程组具有基础意义; DPNS方程组笔者在1967年已提出. (3)诸简化NS方程组: DPNS、抛物化(P)NS、薄层(TL)NS、黏性层(VL)NS方程组的发展、相互关系, 它们的历史贡献和今后的用途; 它们的数学性质均为扩散抛物型, 但它们包含的黏性项彼此有所不同; 从流体力学角度来看, 它们中只有DPNS方程组能够准确描述干扰剪切流动. 提出把诸简化NS方程组统一为DPNS方程组的建议. (4)干扰剪切流------DPNS方程组与无干扰剪切流------边界层方程组之间的关系以及进一步研究干扰剪切流的意义.      

Study on forced shear flow by a oscillating spoiler

In the present paper, numerical solution of the two-dimensional unsteady Navier-Stokes equations is used to study the forced shear flow induced by a spoiler's periodical up and down oscillation on a flat plate. The paper studies the evolution of growing, shedding, merging and decaying of vortices due to the spoiler's oscillation, particularly the dependence of the forced shear flow on the reduced frequency. Results show that the reduced frequency is a key factor in controlling the growing and the shedding of vortices in the shear layer. The instantaneous streamlines and the equi-vorticity contours, as well as the surface pressure distributions, have also been investigated. Numerical results agree well with corresponding experimental ones. The study is helpful for understanding the physical mechanism of shear flow control.     

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.     

Comparative analysis of viscous flows in cavities and channels containing axisymmetric obstacles

The flow past axisymmetric bodies of various shapes in expanding cavities and cylindrical channels is studied on the basis of a numerical solution of the Navier-Stokes equations. For each body shape velocity, pressure and shear stress distributions are obtained. These data are then used for the purposes of a comparative flow analysis in terms of body shape and Reynolds number. The properties characteristic of flows around bodies in channels and cavities with moving boundaries are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–66, May–June, 1988.     

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed.The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection.The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form velocity equations.Making use of this solution,analytical formulas for the angular velocity components as well as for the permeable wall shear stresses are derived.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation.The temperature field is shown to accord with the dissipation and the Joule heating.As a result,exact formulas are obtained for the temperature field which take different forms corresponding to the condition of suction or injection imposed on the wall.     

Homotopy analysis and differential quadrature solution of the problem of free-convective magnetohydrodynamic flow over a stretching sheet with the Hall effect and mass transfer taken into account

This paper presents an analytical solution of the problem of free-convective magnetohydrodynamic flow over a stretched sheet with the Hall effect and mass transfer taken into account. A similarity transform reduces the Navier-Stokes, energy, Ohm law, and mass-transfer equations to a system of nonlinear ordinary differential equations. The governing equations are solved analytically using an analytical method for solving nonlinear problems, namely, the homotopy analysis method. The results are compared with the results of a promising numerical method of differential quadrature developed by the authors. It is shown that there is very good agreement between analytical results and those obtained by the differential quadrature method. The differential quadrature method was validated, and the effects of non-dimensional parameters on the velocity, temperature and concentration profiles were studied.     

Stagnation flow towards a shrinking sheet

The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.     

Obtaining the exact solutions of the Navier-Stokes equations

The Navier-Stokes equations of two-dimensional, steady, incompressible flow are studied using the unknown streamlines as one of the coordinates. The solution of the equations for in-plane motion is obtained, which corresponds to the well known solution of Couette flow, radial flow, spiral flow and the flow between two concentric cylinders. Possibilities of obtaining other solutions by this approach are also discussed.     

Calculation of laminar recirculating flows using a local non-staggered grid refinement system

A grid-embedding technique for the solution of two-dimensional incompressible flows governed by the Navier-Stokes equations is presented. A finite volume method with collocated primitive variables is employed to ensure conservation at the interfaces of embedding grids as well as global conservation. The discretized equations are solved simultaneously for the whole domain, providing a strong coupling between regions of different refinement. The formulation presented herein is applicable to uniform or non-uniform Cartesian meshes. The method was applied to the solution of two scalar transport equations, to cavity flows driven by body and shear forces and to a sudden plane contraction flow. The numerical predictions are compared with the exact solutions when available and with experimental data. The results show that neither the convergence rate nor the stability of the method is affected by the presence of embedded grids. Embedded grids provide a better distribution of grid nodes over the computational domain and consequently the solution accuracy was improved. The grid-embedding technique proved also that significant savings in computing time could be achieved.     

Magnetohydrodynamic oblique stagnation-point flow

Laminar two-dimensional stagnation flow of a viscous and electrically conducting fluid obliquely impinging on a flat plate in the presence of a uniform applied magnetic field is formulated as a similarity solution of the Navier-Stokes equations. The relative importance of this flow is measured by the dimensionless strain rate and magnetohydrodynamic parameters γ and M. The viscous problem is reduced to a coupled pair of ordinary differential equations governed by γ and M. It is found that the parameter M causes a shift in the position of the point of zero skin friction along the wall.