Unsteady convective diffusion in a pulsatile flow through a channel

Summary The paper presents an exact analysis of the streamwise dispersion of passive contaminant molecules released in an incompressible viscous fluid flowing through a channel under the influence of a periodic pressure gradient. Using the Aris-Barton method of moments which is valid for all time after the injection of the solute, the dispersion coefficients of a passive contaminant cloud are obtained separately for three different cases: steady, periodic and for comparison the combined effect of steady and periodic currents. Here it is shown how the injected material disperses due to the shear effect caused by the combined effects of flow (steady or periodic) and lateral diffusion about its mean position, and how the centre of gravity of mass moves, when the initial distribution of contaminant is uniform over the cross-section of the channel. The comparison reveals that for all cases the dispersion coefficient asymptotically reaches a stationary state after a certain time, but it changes cyclically with dispersion time even in the stationary state for the case of oscillatory flows. The analysis leads to the interesting result that the dispersion coefficient consists of a steady part and a fluctuating part due to the pulsatility of the flow.     

Dispersion of a solute in pulsatile non-Newtonian fluid flow through a tube

The unsteady dispersion of a solute by an imposed pulsatile pressure gradient in a tube is studied by modeling the flowing fluid as a Casson fluid. The generalized dispersion model is applied to study the dispersion process, and according to this process, the entire dispersion process is expressed in terms of two coefficients, the convection and the dispersion coefficients. This model mainly brings out the effects of yield stress and flow pulsatility on the dispersion process. It is observed that the dispersion phenomenon in the pulsatile flow inherently differs from the steady flow, which is due to a change in the plug flow radius during a cycle of oscillation. Also, it was found that the dispersion coefficient fluctuates due to the oscillatory nature of the velocity. It is seen that the dispersion coefficient changes cyclically, and the amplitude and magnitude of the dispersion coefficient increases initially with time and reaches a non-transient state after a certain critical time. It is also seen that this critical time varies with Womersley frequency parameter and Schmidt number and is independent of yield stress and fluctuating pressure component. It is observed that the yield stress and Womersley frequency parameter inhibit the dispersion of a solute. It is also observed that the dispersion coefficient decreased approximately 4 times as the Womersley frequency parameter increases from 0.5 to 1. The study can be used in the understanding of the dispersion process in the cardiovascular system and blood oxygenators.     

Oscillatory non-Newtonian flow in tubes of slowly varying radius

Summary The paper studies low Reynolds number flow of a non-Newtonian fluid in an axisymmetric tube of slowly varying radius which is subjected to an axial oscillatory pressure gradient. It is observed that the leading approximation is affected by the visco-elastic coefficient. In the higher approximation particular attention is centered around the steady streaming components for both small and large values of the frequency of oscillation. On the overall the combined effect of visco-elast c and cross viscosity parameter is to induce a radial pressure gradient. For the velocity components the Newtonian and non-Newtonian effects are of the same magnitude when the frequency is small; but when this frequency is large the non-Newtonian effects swamp the flow velociites. When the results are applied to a locally constricted tube, flow reversal is possible downstream of this constriction. The most striking feature however is the condition of zero velocity at a locally constricted tube for the steady streaming velocities—upstream of this constriction the velocity is positive while downstream it is negative. In pathophysiology thrombus formation in constrictions is believed to be caused by aggregation of platelets due to endothelium damage. The condition of zero steady streaming velocity at the constriction is another possible explaination of platelet accumulation and possible blood cloting.With 2 Figures     

MHD flow between two parallel plates with heat transfer

Summary In the present paper, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied. The upper plate is given a constant velocity while the lower plate is kept stationary. The viscosity of the fluid is assumed to vary with temperature. The effect of an external uniform magnetic field as well as the action of an inflow perpendicular to the plates together with the influence of the pressure gradient on the flow and temperature distributions are reported. A numerical solution for the governing non-linear ordinary differential equations is developed.     

Unsteady shear flow of fluids with pressure-dependent viscosity

We study the unsteady shear flow of fluids with pressure-dependent viscosity, situated between two parallel horizontal plates with the upper plate moving while the flow is subjected to an oscillating pressure gradient. The dimensionless form of the momentum equation is solved numerically using a central difference approximation for the spatial derivative terms and a forward difference approximation for the time derivative term. In addition to providing the velocity profiles at the midsection between the two plates, the values of shear stress at the lower (stationary) plate for various values of the dimensionless numbers are also plotted.     

一种基于冯卡门尺度的湍流模式在模拟稳态和非稳态流动问题中的应用

采用尺度自适应模型(SAS)对稳态和非稳态流动进行了数值仿真。SAS模型有效解决了传统脱体涡数值模拟(DES)方法在网格加密过程中引发的“附面层速度型偏离对数率”的问题;同时,SAS模型的尺度自解效应也赋予了该方法类LES特征,可以在不出现非物理解的前提下有效地释放当地脉动。通过高雷诺数平板边界层模拟,SAS方法在附面层内模拟的速度型分布与理论值贴合得很好,说明该方法对于稳态流动的求解并未偏离RANS模型;同时,在串联双圆柱算例中,SAS方法对于圆柱表面压力分布的预测精度高于其他稳态和非稳态模型,Q云图也显示出该方法的类LES特征。算例结果证明了SAS方法有着一定的工程使用价值。     

Magnetohydrodynamic stability of boundary layers along a flat plate with pressure gradient

Summary The purpose of the paper is to consider theoretically the characteristics of steady two-dimensional magnetohydrodynamic boundary layer flow past a flat plate with pressure gradient in the presence of transverse magnetic field and its stability problem. The boundary layer equation is transformed into a non-similar one and numerical solutions are obtained by the difference-differential method. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity profiles obtained above. Numerical results for the magnetic parameter and pressure gradient parameter are given for the velocity profiles, coefficient of skin friction, displacement thickness and the critical Reynolds number.With 10 Figures     

Effect of uniform suction or injection on a magnetohydrodynamic boundary layer flow along a flat plate with pressure gradient

Summary The effect of uniform suction or injection on the flow of an incompressible electrically conducting fluid past a flat plate with pressure gradient in the presence of a transverse magnetic field was theoretically investigated. The boundary layer equations were transformed into non-similar ones, and the numerical calculations of the resulting equations were performed by the difference differential method. The velocity profiles, the coefficient of skin friction, and the displacement thickness were given for various values of the pressure gradient, the magnetic and suction/injection parameters. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type and the critical Reynolds numbers were then presented for the velocity profiles obtained above.With 13 Figures     

横板型稳压罐气液两相流场数值模拟及流量稳定性研究

依据湍流模式理论中的标准k-ε湍流模型及流体体积函数多相流模型,实现了水流量标准装置中横板型稳压罐多相湍流流场的数值研究,采用PISO方法求解离散控制方程,并使用UDF编写入口速度脉动信号。获得稳压罐压力场、速度场、流线等关键信息,分析了入口脉动频率、气液比、竖隔板位置因素对流量稳定性的影响,并通过实验验证了计算结果的有效性。结果表明:低频脉动对稳定性影响较大,当泵出口脉动5Hz时,气液比1:3,竖板位于罐体D/3处,稳定性最好,流量波动系数为0.058%。     

翼型动态风洞试验洞壁效应研究

翼型动态失速导致气动非线性特征突出,与洞壁效应耦合给风洞试验数据带来极大的不确定性,该文通过试验和数值手段揭示了翼型动态试验洞壁效应产生机理和影响规律,结果表明：相比于静态试验,由于洞壁的存在,动态试验翼型的尾流区的总压和静压分布更不均匀,动态试验翼型在相同迎角下的洞壁干扰更严重,表现为翼型在大迎角段,洞壁干扰导致模型中间截面附近和端部截面附近的速度分布和压力分布差异更明显,且相比于压力面,吸力面流动的二维性变得较差。侧壁干扰抑制了翼型中间截面附近的流向分离,诱导了端部附近的展向分离流。上洞壁和下洞壁的非定常压力系数随翼型实时迎角变化也呈迟滞环曲线,迟滞环方向相反,且脉动一阶主频率与翼型俯仰振荡频率一致。风洞洞壁干扰下,翼型动态失速三维涡结构呈“Ω”型。风洞上下壁干扰使得翼型线性段的升力系数和升力线斜率均增加,诱导翼型提前失速;在负行程,则使得翼型升力系数降低。侧壁干扰在负行程诱导了翼型表面的展向流动、减小了翼型弦向流动速度,引起翼型升力系数减小,正行程范围则影响较小,且翼型失速延迟。FL-11风洞翼型动态试验的上下壁干扰效应为主导因素;但是侧壁干扰不可忽略,特别是在翼型振荡周期的大迎角和负行程范围。     

Shear flow over a particulate or fibrous plate

Simple shear flow over a porous plate consisting of a planar array of particles is studied as a model of flow over a membrane. The main objective is to compute the slip velocity defined with reference to the velocity profile far above the plate, and the drift velocity induced by the shear flow underneath the plate. The difference between these two velocities is shown to be proportional to the thickness of the plate. When the geometry of the particle array is anisotropic, the directions of the slip and drift velocity are generally different from the direction of the overpassing shear flow. An integral formulation is developed to describe flow over a plate consisting of a periodic lattice of particles with arbitrary shape, and integral representations for the velocity and pressure are developed in terms of the doubly-periodic Green's function of three-dimensional Stokes flow. Based on the integral representation, asymptotic expressions for the slip and drift velocity are derived to describe the limit where the particle size is small compared to the inter-particle separation, and numerical results are presented for spherical and spheroidal particles of arbitrary size. The asymptotic results are found to be accurate over an extended range of particle sizes. To study the limit of small plate porosity, the available solution for shear flow over a plane wall with a circular orifice is used to describe flow over a plate with a homogeneous distribution of circular perforations, and expressions for the slip and drift velocity are derived. Corresponding results are presented for axial and transverse shear now over a periodic array of cylinders arranged distributed in a plane. Streamline pattern illustrations confirm that a negative drift velocity is due to the onset of eddies between closely-spaced particles.     

人字形波纹板式蒸发器数值模拟

本文根据两相流动换热理论,提出了一个板式换热器的稳态分布参数模型.在此模型基础上,利用分布参数法求解各控制方程,得出了制冷剂的温度、压力、气液相速度以及冷冻水温度、压力沿通道方向上的分布情况.此模型可用于分析换热器的整体性能,为板式换热器的优化设计、制冷系统的匹配提供依据.     

Oscillating cascade unsteady aerodynamics including separated flow effects

A mathematical model is developed to predict the effect of flow separation on the unsteady aerodynamic lift and moment acting on a two-dimensional flat plate cascade which is harmonically oscillating in a subsonic flow field. The unsteady flow is considered to be a small perturbation to the uniform steady flow, with the steady flow assumed to separate at a specified fixed position on the airfoil suction surface. This formulation does not require the difference in the upwash velocity across the airfoil in the separated flow region to be determined before calculating the unsteady pressure difference across the chordline of the airfoils, thereby eliminating the assumption that the upwash difference is zero at the trailing edge when the steady flow is separated. Results obtained demonstrate that although flow separation decreases bending mode stability, it does not result in bending mode flutter. However, flow separation can result in torsion mode flutter, with this instability being a function of the location of both the separation point and the elastic axis.     

On the effectiveness of variation in the physical variables on the steady MHD flow between parallel plates with heat transfer

The influence of variation in physical variables on the steady Hartmann flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal and electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing non‐linear coupled equations of motion and the energy equation is obtained. The effect of magnetic field, the temperature dependent viscosity, thermal conductivity, and electric conductivity on both the velocity and temperature distributions is examined. Copyright © 2005 John Wiley & Sons, Ltd.     

平行圆盘间电流变液的挤压流研究

采用双粘度本构模型研究了两平行圆盘间电流变液的挤压流特性,壁面边界上采用Navier滑移模型.流场根据其特性被分为两个区域:对称轴附近的牛顿区以及远离对称轴的双粘区;双粘区存在屈服面.本文在牛顿区和双粘区分别求解出其速度场和压力梯度场.壁面上的滑移速度与当地的压力梯度成正比;而压力梯度在牛顿区与r成正比,在双粘区r值较大的地方与r近似成线性关系.通过将压力梯度在双粘区近似为r的线性函数,可积分出流场的压力分布与作用在圆盘上的挤压力.此外,本文还通过计算,考察了速度场的分布特点,分析了滑移系数对速度场、压力梯度场、屈服面位置以及挤压力的影响.     

Interaction of peristaltic flow with pulsatile magneto-fluid through a porous medium

Summary The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid under the effect of a transverse magnetic field through a porous medium between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier-Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first-order steady flow is found to exist, as contrasted to a second-order effect in the absence of the imposed periodic pressure gradient. The effect of the magnetic parameter, permeability parameter and the various parameters included in the problem are discussed numerically.     

MHD compressible turbulent boundary-layer flow with adverse pressure gradient

Summary The effects of the magnetic field and localized suction on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied. The magnetic field is constant and applied transversely to the direction of the flow (global or local). The fluid flow is subjected to a constant velocity of localized suction, and there is no heat transfer between the fluid and the plate (adiabatic plate). The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner-Skan transformation. The resulting coupled and nonlinear system of PDEs is solved using the Keller’s box method. For the eddy-kinematic viscosity the turbulent models of Cebeci-Smith and Baldwin-Lomax are employed. For the turbulent Prandtl number the extended Kays-Crawford’s model is used. The flow is subjected to an adverse pressure gradient. The obtained results show that the flow field can be controlled by the applied magnetic field as well as by localized suction.     

Analytical solution of time periodic electroosmotic flows: analogies to Stokes' second problem.

Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large kappa values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.     

Effect of pressure gradient on MHD boundary layer over a flat plate

Summary The magnetohydrodynamic (MHD) boundary layer flow over a flat plate is examined here for two cases, viz. a uniform free-stream velocity and a uniform hydrostatic pressure. The nonlinear boundary layer equations are solved using a reliable finite-difference method. The boundary layer physical parameters such as skin-friction coefficient, displacement, momentum and energy thicknesses of the boundary layer are determined. It is found that the normal surface velocity gradient decreases with the local magnetic interaction parameter for the cases of a uniform hydrostatic pressure, whereas in the case of a uniform free-stream volocity it increases with the interaction parameter.     

Combined effect of thermal dispersion and radiation on free convection in a fluid saturated, optically thick porous medium

The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.