On the flow of a Bingham fluid passing through an electric field

We study the action of an electric field on a Bingham fluid from the point of view of existence and uniqueness of solutions. We also give an upper bound for the stopping time.     

Mathematical Models for Waxy Crude Oils

In this paper we review a series of mathematical models formulated for the flow of waxy crude oils, that is, of mineral oils with a high content of paraffinic hydrocarbons (with the generic name of waxes) which may be dissolved or segregated as solid crystals at sufficiently low temperatures. The flow takes place in a laboratory test loop. The crystals have a tendency to form aggregates, producing a gel-like structure. The resulting product can be modeled as a Bingham fluid, but its rheological parameters (yield stress and viscosity) depend on the amount and state of the segregated phase, whose evolution is in turn influenced by the flow. Of course temperature plays a key role. Wax can form a solid deposit at the pipe wall, reducing the pipe radius and this phenomenon is also taken into account. The models presented have a different degree of complexity, depending on which phenomena they include. In presenting each of them we discuss their expected range of validity.     

An implicit solution of bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow

1.IntroductionItisamajordiffct.encefi-omtheNewtonnuidflowthattheBinghammodelofNonNewtonfluidflowischaracterizedbytwoparameters:ayieldstressandaviscosity.WhenthestressoftheBinghalnmaterialbelowtheyieldstress,materialisrigidotherwisethequasiNewtolliannowresultstll:'71.Hence,therearesomeofthefloating"rigidcores"involvedintheBinghamfluidfloworsomeofthe'rigidcores"attachedtotheboundaries,inwhichthelocationsalldshapesofthese"rigidcores"maychangeforthetransientBinghamfluid,flow.ThisBingllammodelh…     

Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria

We present new results on the nonlinear stability of Bingham fluid Poiseuille flows in pipes and plane channels. These results show that the critical Reynolds number for transition, Re_c, increases with Bingham number, B, at least as fast as Re_cB^1/2 as B→∞. Estimates for the rate of increase are also provided. We compare these bounds and existing linear stability bounds with predictions from a series of phenomenological criteria for transition, as B→∞, concluding that only Hanks [AIChE J. 9 (1963) 306; 15 (1) (1963) 25] criteria can possibly be compatible with the theoretical criteria as B→∞. In the more practical range of application, 0≤B≤50, we show that there exists a large disparity between the different phenomenological criteria that have been proposed.     

离心泵叶轮内宾汉流体湍流流场的数值计算

考虑宾汉流体本构关系特点,建立了任意曲线坐标系（ζ,η）下宾汉流体湍流流动的基本方程,应用压力加权校正算法,实现了速度场和压力场的关联,采用交错网格技术,解决了非物理压力振荡问题,在此基础上,对离心泵叶轮内回转面上宾汉流体湍流流动进行了数值模拟,并分析探讨了离心泵叶轮内宾汉流体湍流流动机理。     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

尾矿颗粒沉降和分选规律研究1)

开展了尾矿颗粒在流体中沉降和分选规律研究。首先,对尾矿颗粒在流体中受力特征和各种力作用效果进行分析;其次,对牛顿流体中尾矿颗粒沉降和分选进行研究;再次,对宾汉浆液中尾矿颗粒沉降和分选进行研究;最后,对理论公式进行了讨论和结果验证。论文确定了尾矿颗粒在不同流体中的沉降特点,提出在浆体流动中不沉的最大粒径,推导出球形颗粒的沉降微分方程,推导出颗粒最终沉速和沉降距离,求得了颗粒水平运移距离,结果讨论验证了理论公式的正确性。     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

THE ANALYSIS OF STABILITY OF BINGHAM FLUID FLOWIGN DOWN AN INCLINED PLANE

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Lattice-Boltzmann model for compressible perfect gases

We present an adaptive lattice Boltzmann model to simulate supersonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the measured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection. The project supported by the National Natural Science Foundation of China (Grant Nos. 19672030 and 19972037) and by the Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry     

内通道式磁流变阻尼器研究

设计制作了一种新型的内通道式磁流变液阻尼器,该阻尼器的流场通道位于线圈内部,磁流变效应发生在两层固定的平板区域之间,并能保持磁流变液的流向与磁感应方向垂直,即保证磁流变液的大面积成链,产生大的可控阻尼力,又具备失效安全性;根据宾汉模型,建立了阻尼器的准静态力学模型;最后对研制的阻尼器进行动力学实验研究,并与理论结果进行比较,二者吻合较好。     

A numerical study of bingham turbulent flow in sudden-expansion straight circular pipe

I.IntroductionBinghamfluidisonebranchofnon-Newtonianfluid,suchascrudeparaffinoil,highsediment--ladenwaterflow,highconcentrationmudandthelikewhicharetransportedinpipelinesinmanyindustries,soit'sofgreatsignificancetostudytheflowmechanismsofBinghamfluid.Tsaietal.II]studiedthelinkagebetweenBinghamfluidandpluggedflow.Wangetal.I2]measuredtheturbulencestructureofBinghammud.Mengetal.[3]researchedthekineticenergycorrectionfactorofBinghamfluidinacircularpipe.However,thestudyofBinghamfluidsofarisn't…     

Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.     

宾汉流体物性参数对湍流强度影响的研究

考虑宾汉流体本构关系的特点，建立了适用于宾汉流体的修正动量方程和Ｋτ－ετ模型方程。采用压力耦合半隐式ＳＩＭＰＬＥ算法，通过流场的数值计算研究，指出了宾汉流体本身的物性参数（如屈服应力、塑性粘度）对其湍流强度有着重要影响。     

Bingham流体在旋转圆盘上流动的数值解

导出了描述Ｂｉｎｇｈａｍ流体在旋转圆盘上流动的基本方程，用差分方法数值解薄膜厚度分布方程，得到二种类型的厚度分布。数值解分别和计算机磁盘的厚度分布，Ｊｅｎｅｋｈｅ等的实验结果定性一致。     

Instability of Bingham fluids in Taylor-Dean flow between two concentric cylinders at arbitrary gap spacings

Stability of Bingham fluids is investigated numerically in azimuthal pressure-driven flow between two infinitely long concentric cylinders. An infinitesimal perturbation is introduced to the basic flow and its time evolution is monitored using normal mode linear stability analysis. An eigenvalue problem is obtained which is solved numerically using pseudo-spectral collocation method. Numerical results are obtained for two different cases: (i) the inner cylinder is rotating at constant velocity while the outer cylinder is fixed (i.e., the Taylor-Dean flow) and (ii) both cylinders are fixed (i.e., the Dean flow). The results show that the yield stress always has a stabilizing effect on the Taylor-Dean flow. But, for the Dean flow the effect of the yield stress is predicted to be stabilizing or destabilizing depending on the magnitude of the Bingham number and also the gap size.     

The analysis of stability of Bingham fluid flowing down an inclined plane

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Displacement of yield-stress fluids in a fracture

We consider a displacement of several yield-stress fluids in a Hele-Shaw cell. The topic is relevant to the development of a model for the flow of multiple phases inside a narrow fracture with application to hydraulically fracturing a hydrocarbon-bearing underground formation. Existing models for fracturing flows include only pure power-law models without yield stress, and the present work is aimed at filling this gap. The fluids are assumed to be immiscible and incompressible. We consider fluid advection in a plane channel in the presence of density gradients. Gravity is taken into account, so that there can be slumping and gravitational convection. We use the lubrication approximation so that governing equations are reduced to a 2D width-averaged system formed by the quasi-linear elliptic equation for pressure and transport equations for volume concentrations of fluids. The numerical solution is obtained using a finite-difference method. The pressure equation is solved using an iterative algorithm and the Multigrid method, while the transport equations are solved using a second-order TVD flux-limiting scheme with the superbee limiter. This numerical model is validated against three different sets of experiments: (i) gravitational slumping of fluids in a closed Hele-Shaw cell, (ii) viscous fingering of fluids with a high viscosity contrast due to the Saffman–Taylor (S–T) instability in a Hele-Shaw cell at microgravity conditions, (iii) displacement of Bingham fluids in a Hele-Shaw cell with the development of fingers due to the S–T instability. Good agreement is observed between simulations and laboratory data. The model is then used to investigate the joint effect of fingering and slumping. Numerical simulations show that the slumping rate of yield-stress fluid is significantly less pronounced than that of a Newtonian fluid with the same density and viscosity. If a low-viscosity Newtonian fluid is injected after a yield-stress one, the S–T instability at the interface leads to the development of fingers. As a result, fingers penetrating into a fluid with a finite yield stress locally decrease the pressure gradient and unyielded zones develop as a consequence.     

Finite element analysis of the duct flow of Bingham plastic fluids: an application of the variational inequality

The duct flow of Bingham plastic fluids is analysed with the variational inequality-based finite element method. The problem of tracking the yield surface is solvable through the regularization technique which can be easily incorporated into the existing finite element code. The existence theorem of this method was established through the theory of variational inequalities. A small positive constant is added to the second shear rate invariant, resulting in an apparent viscosity of finite magnitude in the unyielding plug zone. This makes the minimization of the non-differential variational integral possible. In order to achieve convergence at small regularization parameter, a zero-order continuation is employed. It is also shown that a fine tessellation of the flow domain is necessary for tracking the yield surfaces unambiguously. Two classes of duct flow, namely axial flows in eccentric annuli and in an L-shaped duct, were investigated. In both cases it was easy to show the presence of the mobile plugs around the duct centres from the axial velocity profiles; however, the stagnant plugs at the narrow side in eccentric annuli with large eccentricity and near the apex of right-angled corners in an L-shaped duct could only be identified from the calculation of the distributions of the second shear rate or shear stress invariant. © 1997 John Wiley & Sons, Ltd.