Circular Couette flow with pressure-driven axial flow and a porous inner cylinder

In a rotating filter separator a suspension is introduced at one end of the annulus between a rotating porous inner cylinder and a fixed impermeable outer cylinder. The filtrate is removed through the inner cylinder and the concentrate is removed from the opposite end of the annulus from which the suspension entered. The flow in a rotating filter separator is circular Couette flow with a pressure-driven axial flow and a suction boundary condition at the inner cylinder. Flow visualization was used to determine the effect of the Taylor number, axial Reynolds number, and radial Reynolds number on the types of flows present in the annulus. A rich variety of secondary vortical flows appear, depending upon the flow parameters. The radial inflow at the inner cylinder delays the appearance of supercritical circular Couette flow and prevents the appearance of certain flow regimes that have a helical vortex structure. Nevertheless, the average azimuthal velocity measured using laser Doppler velocimetry indicates that the velocity profile is nearly the same for all supercritical flow regimes.This work was supported by a grant from The Whitaker Foundation     

Numerical study of the generalized cylindrical Couette flow of rarefied gas

We study the cylindrical Couette flow of a rarefied gas between two cylinders in the generalized setup in which the inner of which not only rotates but also slides along its axis. The analysis is based on the numerical solution of the S-model kinetic equation. The influence of ratio of cylinder radiuses, velocities of the inner cylinder and Knudsen number on shear stresses, mass-flow rates as well as macroscopic parameters is investigated in the broad range of Knudsen numbers.     

Large-eddy simulation of counter-rotating Taylor–Couette flow: The effects of angular velocity and eccentricity

In the present work, turbulent flow in the annulus of a counter-rotating Taylor-Couette (CRTC) system is studied using large-eddy simulation. The numerical methodology employed is validated, for both the mean and second-order statistics, with the direct numerical simulation (DNS) data available in the literature, for a range of Reynolds numbers from 500 to 4000. Thereafter, turbulent flow occurring in this system at Reynolds numbers of 8000 and 16000 are studied, and the results obtained are analyzed using mean and second-order statistics, vortical structures, velocity vector plots and power energy spectra. Further, the spatio-temporal variation of azimuthal velocity, extracted near the inner cylinder, shows the existence of herringbone like patterns similar to that observed in the previous studies. The effect of eccentricity of the inner cylinder with respect to the outer cylinder is studied, on the turbulent flow in the CRTC system, for two different eccentricity ratios of 0.2 and 0.5 and for two different Reynolds numbers of 1500 and 4000. The results of the eccentric CRTC are analyzed using contours of pressure, mean and second-order statistics, velocity vectors, vortical structures, and turbulence anisotropy maps. It is observed from the eccentric CRTC simulations that the smaller-gap region seems to contain higher amplitude fluctuations and more vortical structures when compared with the larger-gap region. The mean turbulent kinetic energy contours do not change qualitatively with the Reynolds number, however, quantitatively a higher turbulent kinetic energy is observed in the higher Reynolds number case of 4000.     

Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation

Based on the Bhatnagar–Gross–Krook (BGK) Boltzmann model equation, the unified simplified velocity distribution function equation adapted to various flow regimes can be presented. The reduced velocity distribution functions and the discrete velocity ordinate method are developed and applied to remove the velocity space dependency of the distribution function, and then the distribution function equations will be cast into hyperbolic conservation laws form with non‐linear source terms. Based on the unsteady time‐splitting technique and the non‐oscillatory, containing no free parameters, and dissipative (NND) finite‐difference method, the gas kinetic finite‐difference second‐order scheme is constructed for the computation of the discrete velocity distribution functions. The discrete velocity numerical quadrature methods are developed to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a unified simplified gas kinetic algorithm for the gas dynamical problems from various flow regimes is developed. To test the reliability of the present numerical method, the one‐dimensional shock‐tube problems and the flows past two‐dimensional circular cylinder with various Knudsen numbers are simulated. The computations of the related flows indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

Flow around a cylinder surrounded by a permeable cylinder in shallow water

The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h _w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Re_d?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d.     

Purely tangential flow of a PTT-viscoelastic fluid within a concentric annulus

An analytical solution is presented for the steady state, purely tangential flow of a viscoelastic fluid obeying the Phan-Thien–Tanner (PTT) constitutive equation in a concentric annulus with relative rotation of the inner and outer cylinders. The influence on the velocity distribution within the annulus and on fRe of the Weissenberg number, aspect ratio and an elongational parameter are investigated. The results show that the differences between the radial location of the minimum velocity and of the critical angular velocity compared with their Newtonian counterparts increase as the fluid elasticity increases. The results also show that fRe decreases with increasing Weissenberg number, radius ratio and the elongational parameter in the case of inner-cylinder rotation. In contrast, fRe increases with increasing radius ratio when the outer cylinder is rotating while the inner cylinder is at rest.     

MODELLING AND CALCULATION OF THE TURBULENT BOUNDARY LAYER ON A ROTATING CYLINDER SURFACE WITH STRONG SUCTION 1)

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.     

双柱单锥型液-液旋流管内流场的激光诊断

应用激光测速仪，对一种双柱单锥型液 液旋流管内的流动结构，进行了全场范围内的多工况流动诊断研究．揭示出其切向速度由内旋流区和外旋流区构成，其中内旋流区中的速度分布符合准强制涡关系，外旋流区中的速度分布符合准自由涡关系；轴向速度由上行流动区和下行流动区构成，两者之间在直管段以零速点作分界，在锥体段则以零速区作过渡并伴随有一定的回流出现，且该过渡区或回流区的大小随锥体截面的收缩而减小，直到进入直管段后消失；各湍流量的分布以管芯处最大向外逐渐减小，沿轴向是直管段中的湍流度大于锥体段中的湍流度，而且湍流度在旋流管内具有各向异性的特性．     

强吸气旋转圆筒壁面湍流边界层建模及计算

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.      

The Slip Velocity at the Edge of a Porous Medium: Effects of Interior Resistance and Interface Curvature

Singularity methods are used to analyze creeping planar flow in the annulus between concentric cylinders, when a portion of the annulus is filled with an array of regularly spaced rods adjacent to the inner cylinder. The rods are evenly spaced on concentric circles, and the circles are spaced such that the array resembles a square lattice bent into a circle. The rods and inner cylinder are stationary, and steady rotation of the outer cylinder generates the flow. The quantity of interest is the slip velocity, the mean velocity at the interface between the array and the unfilled portion of the annulus. The primary part of the study concerns the influence of the interior rods on the interfacial velocity, and to this end the velocity is found as successive circles of rods are removed, starting with the circle closest to the inner cylinder. The calculations are carried out for solid volume fractions from 0.0001 to 0.1, and these show that the slip velocity is virtually unchanged as the interior circles of rods are removed, until only one circle remains and then the velocity is of order 10% larger than that for the full array. Hence the velocity at the edge of a sparse porous medium depends minimally on the hydrodynamic resistance of the obstacles in the interior. In the secondary part of the study, it is found that curvature of the interface does not influence the velocity there.     

Experimental investigations on frictional resistance and velocity distribution of rough wall with regularly distributed triangular ribs

The relationship between the flow resistance of a turbulent flow over triangular ribs regularly distributed on a wall surface and the velocity distribution around the ribs was investigated experimentally. A concentric cylinder device composed of an inner test cylinder and an outer cylinder was employed to measure the flow resistance using the torque of the shaft of the inner cylinder and the velocity distribution of the flow around a rib by laser Doppler velocimetry (LDV) simultaneously. We prepared four inner test cylinders having 4, 8, 12 and 16 triangular ribs on the surface with the same interval between them. Each rib had an isosceles right triangle V-shape and a height of 2 mm. To investigate the relationship between flow resistance and velocity distribution, we estimated the frictional drag and pressure drag acting on the surface of the ribs separately using the velocity distribution. Therefore, we could also estimate the total flow resistance using the velocity distribution. As a result of the experiment, the flow resistance and the attachment point downstream of the rib were shown to depend on the distance between ribs. Moreover, the flow resistance estimated using the velocity distribution had good agreement with the flow resistance measured using the torque of the inner cylinder.     

Investigation of slow monatomic gas flows past a circular cylinder

Slow low-Knudsen-number monatomic-gas flow past a circular cylinder is numerically investigated on the basis of a model kinetic equation. The gas flow is described by a new kinetic equation, from which the continuum equations for slow nonisothermal gas flows containing temperature stresses follow rigorously. It is shown that a closed convective-flow region arises near a nonuniformly heated cylinder in a slow gas flow if the flow impinges on the hot side of its surface. Using a new model of the Boltzmann equation makes it possible to study gas flows both in continuum and rarefied flow regimes.     

New exact solution of the problem of rotationally symmetric Couette-Poiseuille flow

An exact solution is obtained for the problem of steady-state viscous incompressible flow under a pressure difference in the gap between coaxial cylinders for the case where the inner cylinder rotates at a constant angular velocity. The solution differs from the classical Couette-Poiseuille result by the presence of radial mass transfer, which provides for interaction between the poloidal and azimuthal circulations. The flow rate is found to depend linearly on the angular velocity of rotation of the inner cylinder. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 71–77, September–October, 2007.     

Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Thermal convection for an incompressible Herschel-Bulkley fluid along an annular duct, whose inner cylinder is rotating and outer is at rest, is analyzed numerically and experimentally. The outer cylinder is heated at constant heat flux density and the inner one is assumed adiabatic. The first part of this study deals with the effect of the rheological behavior of the fluid and that of the rotation of the inner cylinder on the flow field and heat transfer coefficient. All the physical properties are assumed constant and the flow is assumed fully developed. The critical Rossby number Ro_c = (R₁Ω/U_d)_c, for which the dimension of the plug flow is reduced to zero is determined with respect to the flow behavior index, the radius ratio and the Herschel-Bulkley number for axial flow. The rotation of the inner cylinder induces a decrease of the axial velocity gradient at the outer cylinder thereby reducing the heat transfer between the heated wall and the fluid. The second part of this study introduces the variation of the consistency K with temperature and analyzes the evolution of the flow pattern and heat transfer coefficient along the heating zone. Two cases are distinguished depending on the Rossby number: (i) Ro < Ro_c, the plug flow dimension increases along the heating zone; (ii) Ro < Ro_c, the decrease of K with temperature leads to the reappearance of the plug flow. For high angular velocities, it is possible to have a plug zone attached to the outer cylinder. Finally, a correlation is proposed for the Nusselt number. It shows clearly that the effect of thermodependency of K on the heat transfer becomes more important with increasing rotational velocity of the inner cylinder.     

Investigation of the rarefied gas flow around a circular cylinder in stationary and oscillatory regimes

Numerically, on the basis of the Krook kinetic equation, the rarefied gas flow around a circular cylinder is investigated in stationary and oscillatory regimes. The flows around a rotating cylinder and a cylinder with a nonuniformly heated surface are considered. The Knudsen numbers at which the lift force acting on the rotating cylinder changes sign are calculated. It is shown that at low Knudsen numbers a lift force acts on the nonuniformly heated cylinder.     

稀薄流到连续流的气体运动论模型方程算法研究

通过引入碰撞松弛参数和当地平衡态分布函数对BGK模型方程进行修正，确定含流态控制参数可描述不同流域气体流动特性的气体分子速度分布函数的简化控制方程。发展和应用离散速度坐标法于气体分子速度空间，利用一套在物理空间和时间上连续而速度空间离散的分布函数来代替原分布函数对速度空间的连续依赖性。基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式，建立直接求解气体分子速度分布函数的气体运动论有限差分数值方法。推广应用改进的Gauss-Hermite无穷积分法和华罗庚－王元提出的以单和逼近重积分的黄金分割数论积分方法等，对离散速度空间进行宏观取矩获取物理空间各点的气体流动参数，由此发展一套从稀薄流到连续流各流域统一的气体运动论数值算法。通过对不同Knudsen数下一维激波管问题、二维圆柱绕流和三维球体绕流的初步数值实验表明文中发展的数值算法是可行的。     

非稳态不可压缩自由表面粘性流体的三维数值计算

扩展了相对体积算法，计算了变速旋转的敞口圆筒内水的真实非稳态流动。采用了原始变量、交错非等分网格和显式迭代。计算结果与实验现象相吻合。当圆筒长时间等速旋转，其内流体与筒体一起作刚性旋转时，计算自由表面形状与流体力学理论公式的预言吻合得很好。     

基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径.      

An iterative method for the computation of the response of linearised Navier–Stokes equations to harmonic forcing and application to forced cylinder wakes

The central aim of this paper is the development and application of an efficient, iterative methodology for the computation of the perturbation fields induced by harmonic forcing of the linearised Navier–Stokes equations. The problem is formulated directly in the frequency domain, and the resulting system of equations is solved iteratively until convergence. The method is easily implemented to any implicit code that can solve iteratively the steady‐state Navier–Stokes equations. In this paper, it is applied to investigate the flow around a static cylinder with pulsating approaching flow and a cylinder undergoing forced stream‐wise oscillations. All terms of the perturbation kinetic energy equation are computed, and it is shown that perturbations grow by extracting energy from two sources: the underlying base flow field and the externally provided energy that maintains the imposed oscillation. The periodic drag force acting on the cylinder is also computed, and it is demonstrated that Morrison's equation is a simple model that can estimate with good accuracy the amplitude and phase of this force with respect to the approaching flow. The perturbation fields induced by periodic inlet flow (static cylinder) and forced stream‐wise cylinder oscillation are closely related: the velocity fields are identical in the appropriate reference frames, and a simple expression is derived, which links the pressures in the two flow cases. Copyright © 2014 John Wiley & Sons, Ltd.     

开放空腔壳体倾斜入水运动特性试验研究

基于高速摄像试验方法,研究了开放空腔壳体的倾斜入水运动特性,重点分析了开放空腔结构引起的空泡流动特征和壳体运动规律. 通过试验数据分析了开放空腔内气体运动将引起独特的空泡流动和阶段性的运动规律,探讨了初始入水速度、入水姿态对入水弹道和空泡形态等运动特征的影响. 结果表明:开放空腔壳体入水空泡出现阶段波动演化现象,并先后经历两次闭合;入水空泡演化改变流体动力分布,直接影响壳体运动方式,进而改变水下弹道特征;空腔内部形成相对独立流场环境和开放端周期性流动,在重力作用下液体对空腔内下侧壁面作用力较大,加剧壳体偏转,从而改变入水运动过程的稳定性;随着入水速度的增大,空泡波动特征逐渐明显,闭合时间延迟,非对称深闭合引起的横向位移减小,但偏转角度与入水速度无关;随着初始姿态倾角减小,空泡波动程度减弱、闭合时间延迟,偏转角速度增大,闭合引起的横向位移增大.