Flow of a viscoelastic fluid between eccentric cylinders: impact on flow stability

The flow of an elastic fluid between eccentric cylinders was experimentally and theoretically examined. A purely elastic flow instability in the eccentric cylinder flow geometry has been discovered 1, 2. The focus of this paper is an investigation of how the characteristics of the base flow ultimately influence the flow stability. The velocity profiles of a Boger fluid between eccentric cylinders was measured by Laser Doppler velocimetry and compared to the theoretical predictions from a lubrication analysis. The base flow stress profiles between eccentric cylinders were calculated by integrating the polymeric stresses along streamlines. It is shown that the convection of polymeric stresses alter the hoop stresses in the flow. Implications of this observation to the flow stability are discussed.     

正方形排列四圆柱体绕流特性及互扰效应研究

基于计算流体动力学理论,运用大涡模拟方法对雷诺数Re=3900三维正方形排列四圆柱体结构群的绕流问题进行数值计算,主要分析来流攻角与间距比两个参数对四圆柱体结构群流体参数及流场模态的影响。结果表明:来流攻角与间距比均对四圆柱体结构群绕流特性有较强的影响;来流攻角θ=0°、22.5°、45°下,临界间距比分别为3.5、4.0、3.0;间距比的变化会导致下游圆柱表面压力系数分布发生改变;另一方面,间距比较小时,四圆柱体结构之间的互扰作用均以临近效应为主;随间距比增大,上游圆柱尾流对下游圆柱有显著影响,其互扰作用会转变尾激效应。     

涡激诱导并列双圆柱碰撞数值模拟研究

圆柱类结构物的涡激振动是工程中较为常见的一种现象,如果圆柱结构物之间的距离较小, 就会产生涡激诱导碰撞现象,而涡激碰撞会比涡激振动对结构物疲劳破坏产生更严重的威胁.采用浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时出现数值求解不稳定问题,采用有限元方法对圆柱的运动和碰撞进行求解,通过数据回归方法建立了流体流动条件下的润滑模型,对不同间隙比下涡激诱导并列双圆柱振动及碰撞过程进行了数值模拟, 数值结果表明,如果两圆柱产生了碰撞将会有连续的碰撞发生, 碰撞时出现了多阶频率,振动主频率要比无碰撞时大, 两圆柱碰撞时的相对速度比自由来流速度小;当两圆柱相互接近时, 随着涡环分离角度的逐渐倾斜, 横向流体力先逐渐减小,当两圆柱间涡环开始相互影响发生挤压时, 横向流体力开始逐渐增大;当两圆柱开始反弹时, 两圆柱间形成了低压区, 改变了横向流体阻力的方向,使两圆柱又产生了接近运动,如此反复从而产生了碰撞后横向流体力和圆柱速度的振荡现象.      

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.     

Numerical predictions for unsteady viscous flow past an array of cylinders

The unsteady two-dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analysed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The centre-to-centre distance between adjacent cylinders is fixed at three diameters, and the rows are staggered. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder. Two cases, for Reynolds numbers of 1000 and 10,000, are presented.     

Lattice Boltzmann simulation of non-Newtonian flows past confined cylinders

A second-order lattice Boltzmann algorithm is used for Power-Law non-Newtonian flow simulation. The shear dependent behavior of the fluid is implemented through calculating the shear locally from the lattice distribution functions. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The flow past a series of tandem arrangement of two cylinders is computed in a confined domain. The effects of Reynolds number, the Power-Law index, and the distance between two cylinders on both the flow field and the drag coefficients of the cylinders are examined in detail.     

Fluid trapping by two partially shrouded rotating cylinders

In this paper we examine the prospect of using localized flow control for biomimetic fluid trapping. The problem is of interest for applications that call for guided transport of fluid volumes.The study shows that trapping can be achieved with the help of two partially shrouded rotating cylinders in a side-by-side arrangement. Secondary flows that manifest successful trapping resemble recirculation zones forming under the crests of peristaltic deformation waves, in particular with respect to their response to increasing incident flow velocity. Varying the rotation speed of the cylinders provides means to control the amount of trapped fluid.Numerical calculations to support these conclusions are presented in the paper for 0≤Re≤100 and h≈2, where Re and h are, respectively, the Reynolds number and the center-to-center distance between two cylinders divided by the cylinder diameter. Experimental validation of numerical results is performed for 0≤Re≤4.     

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.     

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

A computer model of the two-roll mill for generalised Newtonian flow

We investigate the flow of a generalised Newtonian liquid between two contra-rotating cylinders of equal size — the so called two-roll mill problem. A finite element method is used to obtain solutions for the case of a Carreau model and for a power law model. Consideration is given to the influence of shearthinning on the flow pattern around the cylinders. Results are presented for different speeds of rotation of the cylinders and for various values of fluid parameters. A comparison is made with the analytical solution of Jeffrey.     

A computer simulation of elastic effects in the two-roll mill problem

In a previous paper consideration was given to the flow of a generalised Newtonian liquid between contra-rotating cylinders — the so-called two-roll mill problem. We present here an extension to that work in which we consider the effect of elasticity on the flow. An Oldroyd three-constant model is used to characterize the fluid properties and a finite-element method used to solve the relevant equations. Results are presented for different speeds of rotation of the cylinders and for various values of the fluid parameters. A comparison is made between the effects of elasticity and of shear-thinning on the flow patterns around the cylinders.     

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.     

A study on laminar motion of a viscous incompressible fluid between two parallel eccentric cylinders

The flow of incompressible viscous fluid between two eccentric cylinders under the action of a difference between the pressures imposed at the ends of the cylinders is analyzed. Using bipolar coordinates, the resulting boundary value problem is solved analytically, and the average flux velocity is calculated for various values of the geometric parameters of the problem.     

Plane flow of a second-order fluid past submerged boundaries

We consider the plane flow of a second-order fluid past submerged obstacles such as circular and elliptical cylinders in situations where inertia effects cannot be neglected. The effect of the short memory of the fluid upon the flow features is analyzed in detail. In particular, it is found that the viscoelasticity of the fluid reduces the drag coefficient for very low Reynolds numbers, while the opposite is true for large Reynolds numbers.     

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.     

Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects

A detailed analysis is carried out of the flow of a Newtonian fluid in the annular region between two infinitely long circular cylinders with parallel axes, resulting from the uniform rotation of one, or both, of the cylinders about their axes. No restriction is placed on the geometry of the system and results are obtained both with the neglect of inertial effects and for the linearized inertial approximation. In both cases, the resultant of the forces exerted by the fluid on the cylinders and the distribution of their normal and tangential components over the cylinders are calculated, and the stream-line patterns are analyzed in some detail. A number of conditions, under which stagnation points, separation points and eddies can exist, are established.     

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.     

Viscous flow between two rotating nonconcentric cylinders for small eccentricity

The flow of a viscous and incompressible fluid between two rotating nonconcentric cylinders is investigated. An approximate solution of the Navier-Stokes equations is obtained by a perturbation method for the case of small eccentricity. A second solution of the basic flow is obtained by imposing the additional geometric restriction of small gap between the two cylinders and employing the asymptotic expansion of Bessel functions by Meissel's series. This second solution is also obtained by formulating a small gap boundary value problem. The transverse velocity profiles are presented for the case when the eccentricity and gap are small and the outer cylinder is stationary.     

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 + , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.     

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

The interaction between two circular cylinders was studied in the slow flow of a Bingham viscoplastic fluid in an infinite medium without any inertia effects. The configuration studied is that in which the flow direction is parallel to the centre line of the cylinders. Finite-element numerical simulations were used with an approximation by Papanastasiou's regularisation method. The case of high yield stress effect was particularly examined. The convergence of the solutions was examined in detail. Changes in the rigid zones, kinematics and stresses were determined in relation to the degree of interaction, which is a function of the distance between the cylinders and the effect of yield stress. The results compared with the case of a single cylinder show that yield stress reduces interaction effects. The transition between configurations with interacting cylinders and configuration with isolated cylinders was examined as a function of the effect of yield stress. Correlations were proposed for the drag coefficient and the stability criterion when the cylinders are interacting.