Unsteady flow of an elastico-viscous fluid between two coaxial circular cylinders

Unsteady flow of an Oldroyd fluid between two coaxial circular cylinders is investigated, the fluid being set in motion as the inner cylinder moves from rest for a certain period with linearly growing speed and then stops suddenly. The Laplace transform technique is used to derive the solution. For the case when the gap between the cylinders is small, a simplified solution is obtained. The expression for the shear stress on the wall of the outer cylinder is obtained and particular cases are discussed.     

Nonisothermal steady flow of a viscoplastic liquid between two coaxial rotating cylinders

Rotational viscosimeters are widely used to determine liquid viscosity. The technique for processing the experimental data is based fundamentally on the analytic solution of the problem of isothermal flow of a viscous liquid between two rotating cylinders.If in the course of the experiment the heat released due to the internal friction leads to significant heating, then the processing of the experimental results using the equations obtained on the assumption of isothermocity of the flow may lead to large errors. The dissipative heating may be reduced by reducing the angular velocity of rotation of the cylinder; however extensive reduction of the angular velocity is not desirable, since this leads to an increase of the measurement relative error. In addition, there is the possibility of conducting the experiments with a wide variation of the angular velocities in order to identify the structural-rheological peculiarities of the liquid. In the latter case we must be able to separate the purely thermal effects from the influence of the rheological factors. All these questions are discussed in detail in [1]. The authors of [1] obtained the solution of the problem of nonisothermal flow of a Newtonian fluid between two rotating cylinders and gave a technique for processing the experimental data which takes account of the dissipative heating of the fluid. The present paper pursues the same objective for a visco-plastic fluid.An attempt to solve the problem of nonisothermal flow of a viscoplastic fluid was made by Dzhafarov in [2], where the problem was solved in two versions. In the first version it was considered that the viscosity varies hyperbolically with the temperature and the gap between the cylinders is small in comparison with the radius of the inner cylinder. As a result of the linearization of the equations of motion and heat balance, it turned out that in fact the problem of Couette flow of a viscoplastic fluid was solved rather than the original problem. In this case, naturally, such a characteristic of the flow of a viscoplastic fluid in an annular gap as the possibility of the formation of an elastic zone was not covered. In the second version the problem was solved under the assumption that the viscosity is independent of the temperature and the angular velocity is small.In the present study the problem is solved without the limitations discussed above on the angular velocity, the fluid visoosity, and the gap between the cylinders. In this case we consider two types of temperature boundary conditions: a) constant temperatures are specified on the surfaces of the cylinders, which in the general case may be different; and b) a constant temperature is given on the surface of the outer cylinder and the inner cylinder is thermally insulated.     

Viscous dissipation of a power law fluid in axial flow between isothermal eccentric cylinders

We study the temperature distribution of a power law fluid in a pressure-driven axial flow between isothermal eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible and fully developed flow [Eq. (64)]. We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power law exponent n. The temperature is a strong function of the gap between the cylinders. The temperature profiles are flat in the middle of the gap and then, near the wall, suddenly drop to the wall temperature.     

Stability of Couette flow between two rotating cylinders

We investigate the stability in the large of Couette flow between two cylinders rotating in the same direction. For the case of infinitesimally small perturbations, a sufficient condition for stability of the Couette flow (the Synge condition) was obtained in [1, 2]. In [3] for an investigation of the stability in the nonlinear case, to this condition we must add certain constraints on the initial energy and the angular velocities. In the proposed study, using the second method of Lyapunov, sufficient conditions for stability in the large are obtained, which differ little from the Synge condition. In this case these conditions approach the Synge condition as the distance between the cylinders is decreased.     

A numerical study on the flow patterns of two oscillating cylinders

Flow around two oscillating cylinders in a side-by-side arrangement at Reynolds number (Re)=185 is simulated using the immersed boundary method. The purpose of this study is to investigate the combined effects of the gap between the two cylinders and their oscillation in the flow. The cylinders oscillate transversely to a uniform cross-flow with a prescribed sinusoidal function in the opposite direction, with the oscillation amplitude equal to 20% of the cylinder diameter. The gap between the two cylinders and the oscillating frequency are chosen as major variables for the parametric study to investigate their influence on the flow pattern. The ratio of mean gap distance between the two oscillating cylinders to the cylinder diameter is chosen to be 0.6, 1.0, 1.4, and 1.8, and the ratio of oscillating frequencies to the natural vortex shedding frequency of a fixed cylinder is 0.8, 1.0, and 1.2. Wake patterns and the drag and lift coefficients are described and compared with those from a single oscillating cylinder and two stationary cylinders. The wake patterns of two oscillating cylinders can be explained by flow mechanisms of two stationary cylinders, a single oscillating cylinder, and their combinations, and are in agreement with classifications of flow over two stationary cylinders presented in previous studies. In the case of two oscillating cylinders, the modulation phenomenon appears from a lower excitation frequency than in a single oscillating cylinder. Generally, oscillating cylinders have higher drag and root-mean-square (r.m.s.) values of drag coefficients than stationary cylinders.     

Improved delayed detached-eddy simulation of massive separation around triple cylinders

The massively separated flow past triple cylinders(Tri C) in tandem arrangement is simulated using the improved delayed detached-eddy simulation(IDDES)method based on the shear stress transport(SST) model, coupled with the high order adaptive dissipation scheme. The spacing between adjacent cylinders is sub-critical(1.435D).IDDES prediction of two cylinders(TC) with the same spacing is compared to experimental data for validation, and the numerical results agree well with the available measurements, except for the asymmetry in the gap region. The flow past Tri C is investigated using the same method. Generally,the mean flow quantities past Tri C, such as the velocity,pressure, and vorticity, are similar to the corresponding components of TC. However, the pressure fluctuations on the Tri C surface are uniformly larger than those on TC. Meanwhile,the instantaneous flows past Tri C are much more complex.The periodical blockage in the first gap region is found in the Tri C case and leads to the up-and-down movement of shear layer in the second gap region.     

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.     

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

New experimental methods for turbulent spots and turbulent spirals in the Taylor-Couette flow

 The flow between concentrically counter-rotating circular cylinders is investigated experimentally with respect to the appearance of turbulent spots, combining two new methods, based on digital image processing. The simultaneous visualization of the transition to turbulence in the whole flow field in the gap between the two cylinders leads to a qualitative understanding of the phenomenon of turbulent spots. Quantitative results about spiral turbulence are obtained from measurements based on a time-resolved technique introducing a special method of image processing for long sequences of video frames. Variations of the gap width between the cylinders and the investigation of different boundary conditions at the end plates of the rotating cylinders allow conclusions concerning the importance of locally defined parameters of the flow field. Received: 4 December 1995/Accepted: 15 May 1997     

Weissenberg effect and its dependence upon the experimental geometry

The flow of a second-order fluid with a free surface between two coaxially mounted cylinders of finite length, the inner one of which is rotating, is being studied. In the case of slow flow and small shear rates the flow can be divided into a primary flow in the plane perpendicular to the axis of rotation and a secondary flow in the meridional plane. These flow components are numerically calculated and the results are compared with the analytical results for the semi-infinite cylinder approximation. The influence of the finiteness of the cylinders (end effect) upon the free surface deformation is analysed. The numerical results for the secondary flow are compared with results obtained by flow visualisation.     

Experimental and theoretical observations of elastic instabilities in eccentric cylinder flows: local versus global instability

A theoretical and experimental investigation of the stability of the viscoelastic flow of a Boger fluid between eccentric cylinders is presented. In our theoretical study, a local linear stability analysis for the flow of an Oldroyd-B fluid suggests that the flow is elastically unstable for all eccentricities. A global solution to the stability problem is obtained by a perturbation eigenvalue analysis, incorporating the azimuthal variation of the base state flow at the same order as the streamwise variation of the stability function. A comparison between the local and global stability predictions is made. Flow visualization experiments with a solution of high molecular weight polyisobutylene dissolved in a viscous solvent clearly show the transition from a purely azimuthal flow to a secondary toroidal flow. Comparison of these experimental results with the local linear stability theory shows good agreement between the measured and predicted critical conditions for the onset of the non-inertial cellular instability at small δ, where δ is the eccentricity made dimensionless with the average gap thickness. At higher eccentricities, experiment and local linear stability theory cease to agree. Evidence will be given that this disagreement is due to a global affect, i.e. the convection of stress not included the local theory. Specifically, it is suggested that convection of polymeric stresses in the base flow as well as in the disturbance flow can stabilize the instabilities found in this geometry. Finally, the discovery of a new localized purely elastic instability associated with the recirculation flow in the co-rotating eccentric cylinder geometry is presented.     

A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders

The behavior of vortices induced by a pair of side-by-side square cylinders in an oscillating flow is investigated using an in-house numerical model. The study is carried out for various Keulegan–Carpenter numbers, Reynolds numbers, and cylinder gap spacings. For an oscillating flow past a pair of side-by-side cylinders, the gap ratio plays a vital role in the flow pattern. A jet-like structure is observed when fluid flows through the gap. Moreover, the gap promotes the earlier appearance of asymmetric vortex shedding. In-line force and lift force coefficients of two square cylinders are analyzed using spectral analysis. An autocorrelation function is used to determine the relation between flow patterns around two cylinders. These results demonstrate the transition of the flow field from the periodic state to the chaotic state.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

Numerical computation of the flow around two square cylinders arranged side-by-side

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侧柱与串列双柱绕流之间的干扰

本文给出了关于串列双柱与创柱间流动干扰的实验研究结果。当三个圆柱排成等边三角形并靠得很近时，由于三圆柱间强烈的缝隙流动，大大地改变了绕流其中的串列双圆柱的流态。特别，当三圆柱中心距等于二倍圆柱直径时，在串列双柱的前、后柱之间形成了强烈的偏斜的缝隙流，出现了独特的压力分布以及要比单柱高出三倍以上的旋涡脱落频率。     

同心旋转圆柱间粘弹性流的非线性动力学模型

基于小间隙假设,将速度场和应力场有杉Ｆｏｕｒｉｅｒ展开式截断近似,推导了同心旋转圆柱间Ｏｌｄｒｏｙｄ－Ｂ型流体的六维动力系统,探讨了高分子添加对滑动轴承间油膜稳定性的影响。结果表明,少量的高分子添加剂具有推迟流体层流失稳的作用。     

Unsteady pressure in the annular flow between two concentric cylinders,one of which is oscillating: Experiment and theory

The first objective of this paper is to present a series of accurate experimental measurements of the unsteady pressure in the annulus between two concentric cylinders, the outer one of which executes a harmonic planar motion, either transverse translational or rocking motion about a hinge, with and without annular flow. The second objective is the solution of the unsteady Navier–Stokes and continuity equations for the same annular geometry under the same boundary conditions for an incompressible fluid in the laminar regime. The solutions are obtained with a three-time-level implicit integration method in a fixed computational domain by assuming small amplitudes of oscillation of the outer cylinder. A pseudo-time integration method with artificial compressibility is used to advance the solution between consecutive real time levels. The finite difference method is used for spatial discretization on a stretched staggered grid. The problem is reduced to a scalar tridiagonal system, solved by a decoupling procedure which is based on a factored Alternating Direction Implicit (ADI) scheme with lagged nonlinearities. The third objective is the comparison of the experimental results with the theoretical ones. This comparison shows that the two are in good agreement in the case of translational motion, and in excellent agreement in the case of rocking motion. The experimental and theoretical work presented in this paper is useful for fluid–structure interaction and flow-induced vibration analyses in such geometries.     

Numerical simulation of flows around two circular cylinders by mesh‐free least square‐based finite difference methods

In this paper, the mesh‐free least square‐based finite difference (MLSFD) method is applied to numerically study the flow field around two circular cylinders arranged in side‐by‐side and tandem configurations. For each configuration, various geometrical arrangements are considered, in order to reveal the different flow regimes characterized by the gap between the two cylinders. In this work, the flow simulations are carried out in the low Reynolds number range, that is, Re=100 and 200. Instantaneous vorticity contours and streamlines around the two cylinders are used as the visualization aids. Some flow parameters such as Strouhal number, drag and lift coefficients calculated from the solution are provided and quantitatively compared with those provided by other researchers. Copyright © 2006 John Wiley & Sons, Ltd.     

Flow of non-Newtonian fluid contained in a fixed circular cylinder due to the longitudinal oscillation of a concentric circular cylinder

Summary The flow of a Reiner-Rivlin fluid between two coaxial porous circular cylinders has been studied. The inner cylinder performs a steady oscillation while the outer one is fixed.The exact solution of this problem has been obtained and approximate solutions for the two extreme cases, very small and very high frequencies, have been derived.     

FLOW PAST TWO CYLINDERS IN TANDEM: INSTANTANEOUS AND AVERAGED FLOW STRUCTURE

A technique of high-image-density particle image velocimetry is employed to characterize the instantaneous and averaged patterns of velocity, vorticity and Reynolds stress due to flow past two cylinders in tandem. These features of the flow patterns are characterized in the gap region as a function of the distance between the cylinders. In turn, they are related to the patterns in the near-wake of the two-cylinder system. Along the gap between the cylinders, small-scale concentrations of vorticity are formed in the separated shear layers. These concentrations buffet the surface boundary layer on the downstream cylinder, and thereby influence the eventual shedding of large-scale vortices. Within the gap, the instantaneous structure of the recirculation zones can exhibit both symmetrical and asymmetrical patterns. In the near-wake of the downstream cylinder, the form of the vortex shedding, as well as the averaged patterns of the flow structure, are substantially altered, relative to the case of a single cylinder. The width of the near-wake, as represented by averaged patterns of vorticity, is substantially narrower and the magnitudes of the peak Reynolds stress are significantly attenuated. On the other hand, if the gap region is sufficiently large such that Kármán-like vortices form between the cylinders, the near-wake of the downstream cylinder shows distinctive patterns, and both the wake width and the magnitude of the Reynolds stresses become larger, relative to those at smaller gap width.