Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

非Newton流体的物质点法模拟研究

准确模拟非Newton流体的运动特性具有重要的工程意义.物质点法作为一种相对新兴的粒子型算法,其结合了Lagrange算法和Euler算法的双重优势,已广泛有效地应用于各个工程领域.基于物质点法,结合人工状态方程,分析了两种非Newton流体(cross流体和幂律流体)在平板Poiseuille流和Couette流情况下的流动特性.结果表明:对Newton流体,物质点模拟结果与理论值一致;对非Newton流体,物质点法可准确模拟其剪切稀化和剪切稠化现象.表明了物质点法在模拟非Newton流体流动问题时的适用性,拓展了物质点法的应用范围.     

Influence of power-law index on transitional Reynolds numbers for flow over a semi-circular cylinder

In this work, the governing partial differential equations (continuity and Cauchy’s momentum equations) describing the flow of power-law type non-Newtonian fluids across a semi-circular cylinder (oriented with its curved surface in the upstream direction) have been solved numerically. In particular, consideration has been given to the delineation of the critical Reynolds numbers denoting the onset of flow separation from the surface of the cylinder and the onset of the laminar vortex shedding regime. This information is germane to establish the scaling of the macroscopic characteristics like drag coefficient and Strouhal number on the governing parameters, namely, Reynolds number and power-law index. The present results clearly suggest that the transitional Reynolds numbers show a strong dependence on the type (shear-thinning and shear-thickening) of fluid behavior as well as on the severity of the shear-dependence of the viscosity. With reference to the behavior seen in Newtonian fluids, the flow remains not only attached to the surface up to higher Reynolds numbers, but shear-thinning behavior also delays the onset of the laminar vortex shedding regime. As expected, shear-thickening fluids, of course, display the opposite characteristics.     

速度-涡量法数值求解具有表面吹吸圆柱的绕流问题

用速度-涡量法数值求解了具有表面吹吸圆柱的绕流问题.所得高阶隐式差分方程,采用以修正的不完全LU分解作预处理器的共轭梯度法(MILU-CG),高效解出.研究了雷诺数Re=100时,各种吹吸位置、吹吸强度对圆柱尾流涡旋结构和阻力、升力系数的影响规律.指出,在圆柱肩部的吸气和在圆柱尾部的吹气,可有效地抑制尾流涡旋结构在垂直来流方向上的非对称性,达到减小升力的目的.对在圆柱肩部吸气的情形,合适选择吸气强度,还可有效减小圆柱在来流方向上所受的阻力.     

MILU-CG方法和绕旋转圆柱流动的数值研究

本文采用以修正的不完全LU分解作预处理器的共轭梯度法(MILU-CG),结合高阶隐式差分格式,改进了作者(1992)提出的基于区域分解、有限差分法与涡法杂交的数值方法(HDV).系统地研究了雷诺数Re=1000,200,旋转速度比α∈(0.5,3.25)范围内,绕旋转圆柱从突然起动到充分发展,长时间内尾流旋涡结构和阻力、升力系数的变化规律.计算所得流线与实验流场显示相比,完全吻合.首次揭示了临界状态时的旋涡结构特性,并指出最佳升阻比就在该状态附近得到.     

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract

In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.     

Viscoelastic flow in a curved channel: A similarity solution for the Oldroyd-B fluid

A similarity solution is used to analyse the flow of the Oldroyd fluid B, which includes the Newtonian and Maxwell fluids, in a curved channel modelled by the narrow annular region between two circular concentric cylinders of large radius. The solution is exact, including inertial forces. It is found that the non-Netonian kinematics are very similar to the Newtonian ones, although some stress components can become very large. At high Reynolds number a boundary layer is developed at the inner cylinder. The structure of this boundary layer is asymptotically analysed for the Newtonian fluid. Non-Newtonian stress boundary layers are also developed at the inner cylinder at large Reynolds numbers.     

The effects of vortex breakdown bubbles on the mixing environment inside a base driven bioreactor

The bubble-type vortex breakdown inside a cylinder with flow driven by rotation of the base, has applications in mixing. We investigate this phenomena and its effect on the environment inside an open cylinder, with potential application as a tissue-engineering bioreactor, with tissue-scaffolds of two different geometries immersed in the fluid. Addition of scaffolds induces a blockage effect, hindering the flow in the central vortex core returning to the rotating base. This promotes early onset of vortex breakdown and alters the final shape of vortex breakdown bubbles. Placement of the scaffolds centrally on the cylinder axis yields almost identical levels and distributions of shear stress between the upper and lower surfaces of scaffolds. A change from a disk shaped to an ellipsoidal scaffold, of the same size, reduces the intensity of the maximum shear stresses at the scaffold surface by up to 50%. There is a range of Reynolds numbers where increasing Reynolds number, and hence possibly increasing mixing efficiency, leads to a decrease in the maximum levels of fluid forces at the scaffold surfaces. This is an important conclusion for scaffold based tissue engineering where improved mixing is sought, but often sacrificed in favor of minimizing fluid forces.     

Active control of cylinder wake

The objective of this paper is to develop an efficient active control algorithm for manipulating wake flows past a solid cylinder in an electrically low-conducting fluid (e.g. seawater). The intent is to avoid both vortex shedding and flow separation from the body. It is expected to reduce the mean drag significantly. This is achieved through the introduction of a Lorentz force in the azimuthal direction generated by an array of permanent magnets and electrodes located on the solid structure. With the use of a symmetric and static Lorentz force over the entire surface of the cylinder, the vortex shedding behind the cylinder weakens and eventually disappears completely when the Lorentz force is sufficiently large. The localized Lorentz force along the rear surface of the cylinder was also used to control the vortex shedding behind the cylinder. In this case, numerical results show that the efficiency of the localized Lorentz force in controlling the flow is to that of the Lorentz force distributed over the whole surface.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

Numerical solution of laminar incompressible generalized Newtonian fluids flow

This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian fluids in the branching channel. The generalized Newtonian fluids contain Newtonian fluids, shear thickening and shear thinning non-Newtonian fluids. The mathematical model is the generalized system of Navier-Stokes equations. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t → ∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.     

On Regularity of Incompressible Fluid with Shear Dependent Viscosity

The authors consider a non-Newtonian fluid governed by equations with p-structure in a cubic domain.A fluid is said to be shear thinning(or pseudo-plastic) if 1 < p < 2,and shear thickening(or dilatant) if p > 2.The case p > 2 is considered in this paper.To improve the regularity results obtained by Crispo,it is shown that the secondorder derivatives of the velocity and the first-order derivative of the pressure belong to suitable spaces,by appealing to anisotropic Sobolev embeddings.     

Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.     

Torque on a sphere inside a rotating cylinder

Summary The couple on a sphere in the centre of a finite rotating circular cylinder is measured over a wide range of Reynolds numbers for both Newtonian and non-Newtonian fluids. Wall effects are calculated. Experimental results are compared with Collins' analysis. Secondary flow is made visible. For non-Newtonian fluids the apparatus determines accurately the zero shear rate viscosity.

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Résumé Le couple sur une sphère dans un cylindre circulaire rotatoire est mesuré pour des divers nombres de Reynolds et pour des fluides Newtoniens et non-Newtoniens. L'effet des parois sur le couple est calculé. Les resultats obtenus sont comparés avec l'analyse de Collins. Pour les fluides non-Newtoniens l'appareil determine la viscosité de zéro cisaillement.

     

Unsteady flow and heat transfer in a thin film of Ostwald–de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald–de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller–Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena.     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.     

Global regularity of a class of p-fluid flows in cylinders

We consider the motion of an incompressible non-Newtonian fluid with shear dependent viscosity. We extend and improve the results obtained in the recent paper by Crispo [F. Crispo, Shear thinning viscous fluids in cylindrical domains. Regularity up to the boundary, J. Math. Fluid Mech., in press], concerning the case of the motion between two coaxial cylinders, to the case of a full cylinder. Actually we prove boundary regularity for solutions to the stationary Dirichlet problem with zero boundary data.     

Simulation of Vortex-Induced Oscillations within a Shear Thinning Liquid

The present work discusses the impact of nonlinear shear thinning in a viscous fluid flow on the vibration behavior of an elastic bar. In the process numerical simulations have been performed concerning a well-known FSI benchmark geometry. In contrast to past investigations a non-Newtonian liquid of the Carreau-Yasuda type is used as fluid component. In order to accomplish the coupling between the liquid and the solid domain, an approach using quasi-Newton iterations is applied. In a parameter study material and geometrical parameters are changed. The solutions show distinct deviations compared to results obtained with a Newtonian liquid. These differences emphasize the nonlinearity of the shear thinning material model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flow of a Newtonian Fluid between Eccentric Rotating Cylinders and Related Problems

An incompressible Newtonian fluid is contained in the annular region between two infinite cylinders, one or both of which rotate with constant angular velocities about their respective axes. The first-order inertial correction to the forces exerted by the fluid on the cylinders is obtained in explicit algebraic form. The results are applied to the related problem in which the inner cylinder executes a planetary motion about the axis of the outer cylinder. They are also applied to the problem of the transverse sedimentation of a long cylinder in a half space of fluid bounded by a rigid wall. Certain anomalies which arise in this case are noted.     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise charac-