MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction

This work provides a comprehensive theoretical analysis of MHD unsteady free convection viscoelastic fluid flow through a porous medium. The medium is treated as incompressible and optically transparent. The flow of the fluid is initiated by shearing action of the moving wall with time dependent suction. Radiative heat flow is considered in temperature equation. The coupled nonlinear problem has been solved asymptotically. Approximate solutions have been obtained for the mean velocity, mean temperature using multi parameter perturbation technique. The originality of the present study is to investigate the effect of viscoelastic property of the fluid(Walters B? model) on the flow and heat transfer phenomena when the flow is permeated through a porous medium with uniform porous matrix subject to transverse magnetic field and time dependent fluctuative suction at the boundary surface. The case of viscous flow has been discussed as a particular case on comparison with the result reported earlier and it is in good agreement. Flow reversal is indicated incase of viscoelastic fluid with high heat capacity in the presence of magnetic field. The higher cooling of the plate in case of viscoelastic flow also causes a flow reversal.     

Application of binding theory for seepage of viscoelastic fluid in a variable diameter capillary

The polymer solution for polymer flooding is a viscoelastic fluid. There exist both shear flow and elongational flow when the polymer solution flows in a porous medium, where an additional dissipation is involved. The additional dissipation caused by elongational deformation is often ignored while studying the flow of the fluid in a porous medium. For a complex polymer solution, the generated elongational pressure drop cannot be ignored. In a capillary of fixed diameter, the polymer solution is only impacted by the shear force, and its rheological property is pseudoplastic. Therefore the variable diameter capillary and the converging-diverging flow model with different cross sections are required to describe the flow characteristics of the polymer solution in porous media more accurately. When the polymer solution flows through the port, we have the elongational flow and the polymer molecules undergo elongational deformation elastically. By using the mechanical energy balance principle and the minimum energy principle, a mathematical model of non-Newtonian fluid inlet flow was established by Binding. On the basis of the Binding theory, with the application of the theory of viscoelastic fluid flow in the circular capillary and the contraction-expansion tube, the relations between the viscoelastic fluid flow rate and the pressure drop are obtained.     

UNSTEADY FLOW OF NON-NEWTONIAN VISCO-ELASTIC FLUID IN DUAL-POROSITY MEDIA WITH THE FRACTIONAL DERIVATIVE

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest's inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.     

A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW

In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the twodimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.     

粘弹性流体平面收缩流动的数值模拟

在石油、化工、轻纺和材料等工业中，有大量粘弹性液体的流动问题。如原油升举过程和管道输送中的流动；聚合物溶液和纸浆的流动等。由于粘弹性具有复杂的流变性，实验模拟和解析求解都较困难，随着计算机和计算流体力学的发展，粘弹性流体流动的数值研究日益活跃，成为非牛顿流体研究的一个重要方向。粘弹性流体运动数值模拟的主要困难在于：当Ｒｅｙｎｏｌｄｓ数和Ｗｅｉｓｓｅｎｂｅｒｇ数达到一定值以后，方程组在求解域内是混合型的，既有椭圆型区又有双曲型区［１］，已有数值计算方法只是得到小Ｒｅ数（Ｒｅ≤８）和小Ｗｅｉｓｓｅｎｂｅｒｓ数（Ｗｅ≤０．４）的结果［２］，因此，探讨这类问题的数值方法有重要的实用意义。本文在二维Ｍａｘｗｅｌｌ流体控制方程组类型分析基础上，采用类型相关格式求解原始变量方程，对粘弹性流体二维流动进行了数值模拟，得到收缩通道在Ｒｅ＝０～２０００和Ｗｅ＝０～０．８的流动结果。和已有算例比较，扩大了线性粘弹性流体的可计算范围，为进一步研究粘弹性流体三维流动的数值方法打下了基础。     

Thermal instability and heat transfer of viscoelastic fluids in bounded porous media with constant heat flux boundary

A numerical simulation is performed for thermal instability and heat transfer of viscoelastic fluids in bounded porous media under the bottom constant heat flux boundary condition. The results for six different combinations of relaxation and retardation times demonstrate the existence of the thermal instability induced flow bifurcation. It is found that the increase of the relaxation time can enhance the heat transfer efficiency by disturbing the fluid flow and facilitating the bifurcation. The increase of the retardation time can stabilize the flow and postpone the bifurcation, leading to simpler flow pattern and lower heat transfer rate.     

The viscoelastic effects on thermal convection of an Oldroyd-B fluid in open-top porous media

The effects of two viscoelastic parameters on the thermal convection of a viscoelastic Oldroyd-B fluid in an open-top porous square box with constant heat flux are investigated. The results show that the increase of relaxation time is able to destabilize the fluid flow leading to a higher heat transfer rate, while the increase of retardation time tends to stabilize the flow and suppress the heat transfer. The flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time, resulting in more complicated flow patterns in the porous medium.     

MECHANISM FOR VISCOELASTIC POLYMER SOLUTION PERCOLATING THROUGH POROUS MEDIA

The pore throat of porous media is modeled as a constricted channel or expanded channel. The flow of viscoelastic polymer solution in pore throat model is studied by numerical method. Relationship between pressure drop and flow rate is developed,viscoelasticity and throat size are found to be two main factors in high flow resistance. According to pore throat model,2-D stochastic channel bundle is put forward to model porous media,which is composed of pore throat models in series -parallel connection with size and length accord to Haring -Greenkorn stochastic distribution. Percolation model of viscoelastic fluid is developed on the basis of Darcy equation and pressure drop vs. flow rate relation in 2-D stochastic channel bundle. Results indicate that the seepage ability of viscoelastic polymer solution decreases with the increase of viscoelasticity,injection rate,and heterogeneity as well as the decrease of mean pore size of porous media. The high pressure drop of viscoelastic fluid at the connection of pore to throat plays a great role in its anomalous high flow resistance through porous media.     

Electro-osmotic flow and heat transfer of a non-Newtonian fluid in a hydrophobic microchannel with Navier slip

In this paper, we investigate the implications of electro-osmosis on electrohydrodynamic transport of a non-Newtonian fluid on a hydrophobic micro-channel by developing a suitable analytical method. Velocity-slip and temperature-jump conditions are paid due attention. An attempt has been made to examine the effects of rheological and electro-osmotic parameters on the kinematics of the fluid. The nonlinear Poisson-Boltzmann equation governing the formation of the electrical double layer and the body force that is generated by the applied potential are accounted for in the study. Perturbation solutions are presented. In order to exhibit the applicability of the analysis, the problem of electro-osmotic flow and heat transfer of blood in an arteriole has been taken up as an illustrative example of a real-life problem. An intensive quantitative study has been made through numerical computation of the physical variables involved in the analysis, which are of special interest in the study. The computational results are presented graphically. The study reveals that the temperature of blood can be controlled by increasing/decreasing the Joule heating parameter.     

Stability of fluid flow in a Brinkman porous medium–A numerical study

The stability of fluid flow in a horizontal layer of Brinkman porous medium with fluid viscosity different from effective viscosity is investigated. A modified Orr-Sommerfeld equation is derived and solved numerically using the Chebyshev collocation method. The critical Reynolds number cRe, the critical wave number αc and the critical wave speed cc are computed for various values of porous parameter and ratio of viscosities. Based on these parameters, the stability characteristics of the system are discussed in detail. Streamlines are presented for selected values of parameters at their critical state.     

Lifting of a large object from a rigid porous seabed

This study investigates the flow field induced by the tilting lift of a large object from a rigid porous seabed and the induced force acting on the object using an analytical approach. In the corners between the object and the seabed, we assume the flow is a corner flow with a low Reynolds number, and the porous media flow in the seabed obeys Brinkman equations. The complete boundary conditions for viscous flow, including the continuity of velocities and stresses, are utilized at the seabed-water interface. The Helmholtz decomposition theorem, which decomposes the flow field into irrotational and rotational parts, and a perturbation expansion are employed to solve the boundary-value problem. Leading-order analytical solutions for the flow in the water and in the porous seabed are presented, indicating that the flow inside the corners is not a parallel flow, and the porous media flow inside the seabed is a Stokes boundary layer flow that does not obey Darcy’s law.

     

多孔介质内非牛顿流体沿垂直平板的混合对流

本文研究了非牛顿流体在多孔介质内沿垂直等温平板的混合自然和强迫对流。以幂律型渗流规律和边界层近似为数学模型的主要理论依据,得到了问题的精确相似解和近似积分解。对于同向混合对流,近似解与相似解的误差只有3％;对于反向混合对流,两者之间的误差也不超过10％。本文还发现,流体的非牛顿特性对温度场、速度场及多孔介质内的流态转变范围等均有相当显著的影响。     

Numerical Simulation of Unsteady Flow for Visco-Elastic Fluid in An Eccentric Annulus with Inner Rod Reciprocation

The equation governing the unsteady flow of viscoelastic fluids in an eccentric annulus was derived by using the common conversion Maxwell fluid constitutive equation and then discretized by the control volume method. The velocity distribution of flow field was computed by using the ADI method. The influences of the pressure gradient, eccentricity, stroke length, and stroke frequency on the velocity and flow capacity in the flow field was analyzed. The foundation for further research of the eccentric wear problem of the pumping rod in polymer-flood well was laid.     

任意平面流场中的湍流临界准则数

作者应用涡量对流及扩散(传输)的概念和理论建立了对任意平面流场中发生湍流流动的湍流临界准则数。这个准则数不同于熟知的雷诺数。如果应用此准则数在接近直管壁和平板边界层固壁处表明流动会诱发“猝发”现象;对毛细管内的流动而言它也会指出无论管中平均流速多大、它总不会发生湍流;而对多孔介质中的流动,湍流会出现。所有这些预示颇令人感兴趣和关注。     

Numerical analysis of a magnetohydrodynamic duct flow with flow channel insert under a non-uniform magnetic field

This study performs a numerical analysis of three-dimensional liquid metal(LM) magnetohydrodynamic(MHD) flows in a square duct with an FCI in a non-uniform magnetic field. The current study predicts detailed information on flow velocity, Lorentz force, pressure, current and electric potential of MHD duct flows for different Hartmann numbers. Also, the effect of the electric conductivity of FCI on the pressure drop along the main flow direction in a non-uniform magnetic field is examined. The present study investigates the features of LM MHD flows in consideration of the interdependency among the flow variables.     

一类非牛顿流体非线性渗流的压力波解析求解方法及波形分析

一类非牛顿流体渗流的视粘度依赖于压力梯度,且在不同的压力梯度区间内变化规律不同。其具有既不同于牛顿流体渗流,也不同于幂律流体渗流和宾汉流体渗流的非线性渗流特征。建立了该流体在多孔介质内部渗流的数学模型并利用行波法推导出了压力波的解析解。通过一系列算例分析了渗流方程控制参数对压力波形的影响,对比了该类流体与牛顿流体渗流的压力波差异。     

Numerical simulation of thermal convection of viscoelastic fluids in an open-top porous medium with constant heat flux

This paper makes a numerical study of the buoyancy-driven convection of a viscoelastic fluid saturated in an open-top porous square box under the constant heat flux boundary condition. The effects of the relaxation and retardation times on the onset of the oscillatory convection, the convection heat transfer rate and the flow pattern transition are investigated. It is shown that a large relaxation time can destabilize the fluid flow leading to an early onset of the thermal convection and a high heat transfer rate, while a large retardation time tends to stabilize the flow and suppress the convection onset and the heat transfer. After the convection sets in, the flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time, resulting in more complicated flow patterns in the porous medium. Furthermore, with the increase of the ratio of the relaxation time to the retardation time, the fluid may be blocked from flowing through the open-top boundary, which may be caused by the viscoelastic effect. Finally, the comparison of our results with those under isothermal heating boundary conditions reveals that the heat transfer rate corresponding to a constant heat flux boundary is always higher.     

悬沙冲淤问题的湍流两相模型

在双流体模型框架内统一二阶矩两相湍流模型的基础上，建立了改进的悬沙冲淤问题的湍流两相模型-湍流代数应力模型，这一模型不仅能反映两相湍流的各向异性特征，并且更深刻揭示了悬沙颗粒与流体的湍流相互作用的机理，以及浮力、回流及旋流等的影响。适用于河口悬沙冲淤及水库泥沙异重流等工程问题的模拟计算。     

Numerical investigation of Reynolds number and scaling effects in microchannels flows

Compared with conventional channels, experiments of microchannel often exhibit some controversial findings and sometimes even opposite trends, most notably the effects of the Reynolds number and the scaled channel height on the Poiseuille number. The experimental method has still been constrained by two key facts, firstly the current ability to machine microstructures and secondly the limitation of measurement of parameters related to the Poiseuille number. As a consequence, numerical method was adopted in this study in order to analyze a flow in two-dimensional rectangular microchannels using water as working fluid. Results are obtained by the solution of the steady laminar incompressible Navier-Stokes equations using control volume finite element method(CVFEM) without pressure correction. The computation was made for channel height ranging from 50 ?m to 4.58 ?m and Reynolds number varying from 0.4 to 1 600. The effect of Reynolds number and channel heights on flow characteristics was investigated. The results showed that the Poiseuille numbers agree fairly well with the experimental measurements proving that there is no scale effect at small channel height. This scaling effect has been confirmed by two additional simulations being carried out at channel heights of 2.5 ?m and 0.5 ?m, respectively and the range of Reynolds number was extended from 0.01 up to 1 600. This study confirm that the conventional analysis approach can be employed with confidence for predicting flow behavior in microchannels when coupled with carefully matched entrance and boundary conditions in the dimensional range considered here.     

The inception cavitating flows over an axisymmetric body with a blunt head-form

The inception cavitating flows around a blunt body are studied based on flow visualizations and velocity field measurements. The main purpose of the present work is to study the incipient cavity evolution and the interplay between the inception cavitation and the local turbulent flows. A high-speed video camera is used to visualize the cavitating flow structures, and the particle image velocimetry(PIV) technique is used to measure the velocity field, the vorticity, and the Reynolds stresses under non-cavitating and inception cavitating flow conditions. It is found that the appearance of visible cavities is preceded by the formation of a cluster of micro-bubbles not attached to the body surface and in a hairpin-shaped vortex structure. During its evolution, the cavity moves downstream with a lower speed. The effect of the incipient cavity is significant on the local vortical structures but slight on the timeaveraged velocity distribution. The mean Reynolds stress distributions in the turbulent shear flow can be substantially altered by the incipient cavities. The presence of the incipient cavities can lead to the production of turbulent fluctuations.