Lift Force Acting on Body in Liquid in the Vicinity of Boundary Executing Tangential Oscillations

The average force acting on a cylindrical or spherical body placed near the boundary of cylindrical cavity filled with liquid and executing rotational vibrations is experimentally studied. The repulsive lift force acting on solid is found and measured using the method of body suspension in the gravity field. In horizontal cavity the repulsive force provides steady state of light cylinder near the upper boundary at a distance comparable with the thickness of the Stokes layer. The heavy sphere which hangs on thread repulses from the wall of vertical cylindrical cavity under torsional vibration. The dependence of the average lift force on the amplitude and frequency of vibrations and on distance between the body and the boundary has been investigated. Results are presented on the plane of dimensionless parameters. In the examined frequency range the lift force acting on cylinder decreases exponentially with distance from the boundary. Lift force acting on sphere decreases with distance and strongly depends on dimensionless frequency of vibration. Conclusion that lift force is generated by body oscillations excited by its viscous interaction with the oscillating boundary is done. The found phenomenon is important for control of inclusions under microgravity conditions.     

Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 1. Creeping flows

Numerical simulations are presented for flows of inelastic non-Newtonian fluids through periodic arrays of aligned cylinders, for cases in which fluid inertia can be neglected. The truncated power-law fluid model is used to define the relationship between the viscous stress and the rate-of-strain tensor. The flow is shown to be dominated by shear effects, not extension. Numerical simulation results are presented for the drag coefficient of the cylinders and the velocity variance components, and are compared against asymptotically valid analytical results. Square and hexagonal arrays are considered, both for crossflow in the plane perpendicular to the alignment vector of the cylinders (flows along the axes of the array as well as off-axis flows), and for flow along the cylinders. It is shown that the observed strong dependence of the drag coefficient on the power-law index (through which the stress tensor is related to the rate-of-strain tensor) can be described at all solid area fractions by scaling the drag on a cylinder with appropriate velocity and length scales. The velocity variance components show only a weak dependence on the power-law index. The results for steady-state drag and velocity variances are used in an approximate theory for flows accelerated from rest. The numerical simulation data for unsteady flows agree very well with the approximate theory.     

Steady viscous flow past a tapered cylinder

The three-dimensional nature of the viscous flow past a linearly tapered circular cylinder is examined at low Reynolds numbers. The numerical solution of the unsteady Navier–Stokes equations converges to a steady state. The primary flow in planes perpendicular to the cylinder axis is practically indistinguishable from the two-dimensional flow past a uniform cylinder. A secondary spanwise flow is observed in the stagnation zone going from the wide end towards the narrow end, whereas a secondary motion on the rear side goes in the opposite direction. In spite of this secondary flow, the length of the separation zone varies linearly with the local Reynolds number.     

Stokes flow through a channel obstructed by horizontal cylinders

Summary The slow viscous flow through a channel obstructed by internal circular tubes is solved by domain decomposition, eigenfunction expansions and matching. The resistance caused by a periodic sequence of cylinders is determined. The interaction between the cylindeers is negligible if the period is more than four times the channel width. An asymptotic formula for the very small cylinder shows an inverse logarithmic singularity.     

Die Abplattung im Kontaktproblem paralleler Zylinder

To calculate the deflection of cylinders with parallel axes contacting under load, i.e. the approach of the two axes, a simple equation of general validity is given. Such an equation was searched for since the fundamental works of Heinrich Hertz in 1881 and 1882 solving the contact problem of elastic bodies under load. The objective of the presented project was to close this gap on the base of theoretical, numerical and experimental investigations. The principal results can be summarized as follows: The deflection of parallel cylinders is directly proportional to the loading force, but reciprocal to the materials stiffness and to the length of the cylinder. Besides this it is independent of the curvature relations, therefore not influenced by the values of the cylinder's radius and the combinations of curvatures which are convex/convex, convex/plane and convex/concave. These statements are explained theoretically and verified experimentally as well as with FEM-calculations. In this form, they are valid for whole cylinders and for bodies with cylindrical surface in the contact region.     

Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

串列双圆柱静止绕流的二维数值仿真分析

利用CFX软件建立二维流场模型,采用有限体积法针对串列双圆柱的静止绕流现象进行了数值模拟计算。首先计算了雷诺数Re=200,不同间距时上下游圆柱的斯托罗哈数,并与参考文献的计算结果进行了对比,证明了该文计算的可靠性。然后分析了不同间距时上下游圆柱的升力系数和阻力系数的变化特点,得出了Re=200时双圆柱绕流的临界间距在3.375D~3.5D之间。最后通过对不同间距下流场变化的研究得出:上下游圆柱的间距小于临界间距时,上游圆柱不存在旋涡脱落;超过临界间距时,上游圆柱出现旋涡脱落;下游圆柱始终存在旋涡脱落现象。研究成果能够为计算流体力学和空气动力学技术的发展提供理论基础。     

Asymptotic analysis of the viscous micro/nano pump at low Reynolds number

The steady viscous parabolic flow past an eccentrically placed rotating cylinder is studied in the asymptotic limit of small Reynolds number. It is assumed that the flow around the rotating cylinder undergoes boundary slip described by the Navier boundary condition. This involves a single parameter to account for the slip, referred to as the slip length ?, and replaces the standard no-slip boundary condition at solid boundaries. The streamlines for ? > 0 are closer to the body than for ? = 0, and it is discovered that the loss of symmetry due to the rotation of the cylinder is significantly reduced by the inclusion of slip. This arises as a result of a balance between the rotation velocity and the slip velocity on that portion of the cylinder which rotates opposite to the free-stream flow. Streamline patterns for nonzero eccentricity partially agree with Navier–Stokes simulations of the viscous pump; the small discrepancy is primarily due to the fact that here wall effects are not explicitly considered. Expressions for the frictional drag and the torque on the cylinder are obtained. The expression for the torque agrees well with the lubrication solution for the flow past a rotating cylinder placed symmetrically in a fully developed channel flow. The results presented here may be used to validate numerical schemes developed to study the viscous pump.     

A rheological interface model and its space–time finite element formulation for fluid–structure interaction

This contribution discusses extended physical interface models for fluid–structure interaction problems and investigates their phenomenological effects on the behavior of coupled systems by numerical simulation. Besides the various types of friction at the fluid–structure interface the most interesting phenomena are related to effects due to additional interface stiffness and damping. The paper introduces extended models at the fluid–structure interface on the basis of rheological devices (Hooke, Newton, Kelvin, Maxwell, Zener). The interface is decomposed into a Lagrangian layer for the solid‐like part and an Eulerian layer for the fluid‐like part. The mechanical model for fluid–structure interaction is based on the equations of rigid body dynamics for the structural part and the incompressible Navier–Stokes equations for viscous flow. The resulting weighted residual form uses the interface velocity and interface tractions in both layers in addition to the field variables for fluid and structure. The weak formulation of the whole coupled system is discretized using space–time finite elements with a discontinuous Galerkin method for time‐integration leading to a monolithic algebraic system. The deforming fluid domain is taken into account by deformable space–time finite elements and a pseudo‐structure approach for mesh motion. The sensitivity of coupled systems to modification of the interface model and its parameters is investigated by numerical simulation of flow induced vibrations of a spring supported fluid‐immersed cylinder. It is shown that the presented rheological interface model allows to influence flow‐induced vibrations. Copyright © 2010 John Wiley & Sons, Ltd.     

低雷诺数下串联双圆柱涡激振动机理的数值研究

利用有限元数值方法求解不可压缩粘性流体的Navier-Stokes方程,结合任意拉格朗日-欧拉（ALE）动网格方法,对低雷诺数下（Re = 150）等直径串联圆柱的涡激振动问题进行了数值模拟研究。其中上游圆柱固定,下游圆柱在弹簧和阻尼作用下允许同时发生顺流向和横流向的运动。在约化速度Ur = 3.0 ~ 12.0的范围内（阻尼比ξ = 0.007）研究了两圆柱圆心间距比（LX / D = 3.0、5.0、8.0）及圆柱质量比（m* = 5.0、10.0、20.0）对下游圆柱的运动响应及受力的影响。数值结果表明,圆柱间距比的变化会导致锁定区间的变化,进而影响到圆柱涡激振动的位移响应和受力特性。这些方面都与尾流区涡旋脱落模式密切相关,体现了双圆柱间干涉作用对涡激振动的影响。进一步的研究表明,圆柱质量比的变化对以约化速度表征的锁定区间、运动响应和尾流模式等都有一定的影响作用。     

Vertical Taylor–Couette flow with free surface at small aspect ratio

The free surface flow between two concentric cylinders with vertical axes is investigated using numerical and experimental approaches. The bottom end wall of the cylinders and the outer cylinder are stationary and fixed, and the inner cylinder is allowed to rotate. In such a case, an odd number of Taylor vortices is usually formed (normal mode). However, we found that anomalous modes with outer flow near the bottom end wall or inner flow at the free surface appear in some conditions. Further, we determined bifurcation diagrams between the normal three-cell mode and normal one-cell mode and between the normal five-cell mode and the normal three-cell mode.     

A velocity-decomposition formulation for the incompressible Navier–Stokes equations

The principle of velocity decomposition is used to combine field discretization and boundary-element techniques to solve for steady, viscous, external flows around bodies. The decomposition modifies the Navier–Stokes boundary-value problem and produces a Laplace problem for a viscous potential, and a new Navier–Stokes sub-problem that can be solved on the portion of the domain where the total velocity has rotation. The key development in the decomposition is the formulation for the boundary condition on the viscous potential that couples the two components of velocity. An iterative numerical scheme is described to solve the decomposed problem. Results are shown for the steady laminar flow over a sectional airfoil, a circular cylinder with separation, and the turbulent flow around a slender body-of-revolution. The results show the viscous potential is obtainable even for massively separated flows, and the field discretization must only encompass the vortical region of the total velocity.     

端部状态对斜拉索节段模型气动特性的影响

为了给实际工程中串列三圆柱结构的风荷载取值提供参考,通过刚性模型测压风洞试验方法,测试了12个不同间距比L/D(L为两圆柱中心之间的距离,D为圆柱的直径)下串列三圆柱的平均风压系数和平均阻力系数,并与单圆柱的平均风压系数和平均阻力系数进行了对比。研究结果表明：串列三圆柱存在临界间距,其临界间距比为3.0≤L/D≤3.5。三个圆柱的平均阻力均小于单圆柱的平均阻力;上游圆柱的平均阻力最大,下游圆柱的平均阻力次之,中游圆柱的平均阻力最小。     

串列多圆柱气动力干扰效应的试验研究

通过刚性模型测压风洞试验,在均匀流场中对比研究了不同数量和不同间距串列多圆柱气动力的干扰效应。串列多圆柱两相邻圆柱的中心距L与圆柱的直径D之比L/D的变化范围为1.2~12.0。圆柱数量的变化范围为1~4。试验的雷诺数为3.4×10⁴。试验结果发现:串列多圆柱发生流态切换的临界间距比(L/D)cr为3.5~4.0,在临界间距附近,前两个圆柱的时均阻力系数和脉动升力系数突升,其余圆柱则突降,所有圆柱的斯托罗哈数均突升;气动干扰对串列多圆柱时均阻力系数和斯托罗哈数的影响主要表现为减小效应;后方干扰圆柱数量的增加对上游第一个圆柱气动力的影响基本可以忽略;前方干扰圆柱数量的增加对下游最后一个圆柱的气动力影响显著。     

Stability of nonisothermal flow of a viscous liquid in an annular channel

In nonisothermal flow of a viscous liquid in an annular channel between coaxial cylinders where the outer cylinder has finite dimensions and is stationary, and the inner cylinder infinitely moves along the axis, the central position of the latter is unstable. When superimposing a thermal field, principally it is possible to create as large a force as required which holds the inner cylinder exactly on center.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 1, pp. 32–37, July, 1992.     

Nonisothermal cross-flow around a cylinder with a square cross section and an impermeable core covered with a porous layer

Nonisothermal cross flow of a viscous incompressible fluid around a porous cylinder with a square cross section is considered. Main attention is paid when an impermeable core of the cylinder is surrounded with a porous layer. The full system of Navier–Stokes and energy equations is integrated numerically by the finite-volume method. The hydrodynamic interaction between the flow and the matrix of the porous layer is described by Darcy’s law. At moderate Reynolds numbers, the influence of the permeability of the porous layer on the nature of the flow and the heat exchange between the cylinder and the flow is studied. It is shown that, with increasing permeability, heat transfer from the cylinder increases mainly on its front side. From the analysis of the data obtained, an approximate formula for the mean Nusselt number as a function of the Reynolds and Darcy numbers is derived. The results of the calculation of hydrodynamic and thermal characteristics of the cross-flow around an impermeable and a fully permeable cylinder are also presented.     

Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t=0) steady and then at t>0 it becomes unsteady. The semi-similar solution of the unsteady Navier–Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier–Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier–Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time.     

Stokes flow past a swarm of porous circular cylinders with Happel and Kuwabara boundary conditions

The problem of creeping flow past a swarm of porous circular cylinders with Happel and Kuwabara boundary conditions is investigated. The Brinkman equation for the flow inside the porous cylinder and the Stokes equation outside the porous cylinder in their stream function formulations are used. The force experienced by each porous circular cylinder in a cell is evaluated. Explicit expressions of stream functions are obtained for both the inside and outside flow fields. The earlier results reported by Happel and Kuwabara for flow past a solid cylinder in Happel’s and Kuwabara’s cell model, have been deduced. Analytical expressions for the velocity components, pressure, vorticity and stresstensor are also obtained     

均匀流场串列双Π型断面涡激振动气动干扰试验研究

针对串列双Π 型断面涡激振动气动干扰效应,对不同间距比、不同阻尼比条件下,上下游Π 型断面在均匀流场中涡激振动气动干扰效应进行风洞试验研究,并将上下游Π 型断面涡激振动锁定区间、涡激振动振幅分别与单幅Π 型断面进行了对比。结果显示：上下游Π 型断面涡激振动锁定区间基本不随间距比、阻尼比变化而变化,上下游Π 型断面的涡激振动振幅则随间距比和阻尼的变化而变化。上游断面涡激振动气动干扰效应主要受间距比D/B 的影响,当间距比D/B=0.5~1.0 时,对上游断面涡激振动干扰效应最为明显;下游断面涡激振动气动干扰效应主要受上游断面涡激振动振幅影响;随着双幅断面间距比增加,这种干扰效应逐渐减弱。     

Vortical flow between rotating ellipsoids

Summary. Experimental results on incompressible viscous flows in the gap between rotating spheroids are presented. Oblate ellipsoids are discussed as a connecting link between a sphere and a disk, while a prolate ellipsoid represents the geometrical intermediate stage between a sphere and a cylinder. The axes ratios of the ellipsoids are A : B=2 : 1 and A : B=1 : 2, respectively. The basic flow field and the occurring instabilities in form of Taylor- and cross-flow vortices have been studied by flow visualization. The common properties and their differences regarding the various flow patterns of the disks, spheres, cylinders as well as of the oblate and prolate ellipsoids are treated. The location of the generation of the different vortex systems at the various rotating bodies is determined. A comparison of the friction torque for these bodies of rotation is given by diagrams. Finally, the theoretically derived curves for the friction torque of the disks, spheres and cylinders are compared with the experimentally obtained data for the oblate and prolate ellipsoids.Dedicated to Prof. Dr.-Ing. Dr. techn. E. h. J. Zierep on the occasion of his 75th birthday.