Flow past a rotating cylinder translating at different gap heights along a wall

The flow past a rotating circular cylinder translating parallel to a wall at different heights is investigated for Reynolds numbers up to 400 for three discrete rotation rates. In particular, the various wake transitions that occur as a function of gap height are quantified for the three cases examined: non-rotation, and forward and reverse rotations. At low gap heights, only a single steady three-dimensional mode is found to become unstable on the steady base flow. As the gap height is increased, several new three-dimensional modes are observed, of which one attains large amplitudes in the near wake and another preferentially in the far wake. At still larger gap heights, the transition sequence resembles that observed in a rotating cylinder wake, for which the wake first undergoes transition to a periodic state, prior to the onset of three-dimensional flow. Parameter space maps showing the neutral stability curves and regions of instability for each mode are presented for each rotation rate, together with a discussion of the spatio-temporal characteristics and spatial distributions of the new modes. Finally, the force coefficients for the steady and periodic two-dimensional base flows are presented.     

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.     

Magnetic fluid motion driven by a high-frequency rotating magnetic field

The problem of the circulating flow of a nonisothermal magnetic fluid in a long vertical cylinder placed in a rotating magnetic field is solved in the weak vorticity approximation.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–22, January–February, 1996.     

Flow produced in a conical container by a rotating endwall

Numerical calculations have been carried out for flow in a truncated cone generated by rotation of one endwall. For both convergent (radius increasing with approach to the rotating endwall) and divergent geometries, vortex breakdown is suppressed beyond a certain angle of inclination of the sidewall. At the same time Moffat eddies of increasing strength and extent appear in the corner between the sidewall and the non-rotating endwall. For the divergent geometry, a zone of recirculation appears on the sidewall and eventually merges with the Moffat eddies. The flow phenomena identified from streamline patterns are consistent with the calculated variation of pressure around the periphery of the computational domain.     

Convection of a heat-generating fluid in a rotating horizontal cylinder

Thermal convection of a fluid in a horizontal cylinder rotating about its own axis with uniformly volume-distributed internal heat sources is experimentally investigated. The enclosure boundary temperature was kept constant. The threshold of the excitation of convective flows and their structure are studied as functions of the heat-release intensity and the rotation velocity. The experiments are performed with water and water-glycerin solutions. It is shown that rapidly rotating fluid is in a stable quasiequilibrium state, namely, the temperature distribution is axisymmetric and has a maximum at the center of the enclosure. It is found that with decrease in the rotation velocity a convective flow arises thresholdwise, in the form of vortex cells periodically arranged along the axis. The thermal convection in the rotating enclosure is shown to be determined by the effects of two different mechanisms. One of these is due to the centrifugal force of inertia and plays the stabilizing role, while the other, thermovibrational mechanism is connected with nonisothermal fluid oscillations under the action of gravity in the enclosure-fitted reference frame and is responsible for the occurrence of mean thermal convection. The boundaries of the convection generation are plotted in the plane of the governing dimensionless parameters and the heat transfer in the supercritical region is studied.     

Thermal stresses in a rotating non-homogeneous orthotropic hollow cylinder

 In this paper the radial deformation and the corresponding stresses in a non-homogeneous hollow elastic cylinder rotating about its axis with a constant angular velocity is investigated. The material of the cylinder is assumed to the non-homogeneous and cylindrically orthotropic. The system of fundamental equations is solved by means of a finite difference method and the numerical calculations are carried out for the temperature, the components of displacement and the components of stress with the time t and through the thickness of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Received on 21 December 2000     

Turbulent flow around a rotating cylinder in a quiescent fluid

 Hot-wire measurements have been carried out in the turbulent flow around a rotating circular cylinder in still air for Reynolds numbers Re=∣U _w ∣D/ν=1.5×10⁴ to 10⁵. The experimental results confirm the analysis derived by asymptotic theory for high Reynolds numbers. Two different ways of deriving the friction law from the experiments (via shear stress and via velocity distribution) resulted practically in the same law. It is shown, that in spite of the curvature of the streamlines the universal logarithmic velocity distribution is still valid near the wall. Received: 8 August 1996/Accepted: 24 April 1998     

旋转载体驱动硅微机械陀螺幅频特性

介绍了一种安装在旋转体上,用于旋转体姿态控制的新型微机械陀螺.陀螺利用旋转载体的滚转获得角动量,当载体发生偏航或俯仰,敏感质量块受到周期性哥氏力的作用,从而敏感载体的偏航或俯仰角速度.飞行试验中舵机的舵偏打容易使陀螺发生共振,陀螺输出信号无法满足旋转载体姿态控制的要求.针对这一问题,需精确测量陀螺的固有频率.首先基于陀螺运动方程分析了其幅频特性和固有频率,并利用数值计算软件进行了仿真,最后提出了一种对该陀螺幅频特性的测量方法,得到了幅频特性曲线,确定了固有频率70 Hz.实际测量的幅频特性曲线和仿真曲线一致,测量的固有频率相对于舵偏打产生的共振频率点误差为2.1%,通过避开测得的70 Hz 固有频率,获得了符合姿态控制要求的陀螺输出信号.     

Drag reduction using surfactants in a rotating cylinder geometry

Turbulent Couette flow between two circular cylinders has been used for drag reduction experiments using surfactants. In the experiments presented here, only the outer cylinder rotates, the inner cylinder remains at rest and accurate measurements of the torque at the inner cylinder are measured. Water is used as a reference fluid. A drag reducing surfactant called Arquad S-50 (Akzo Nobel Surface Chemistry LLC, Chicago, Ill., USA) (5 mM)+NaSal (12.5 mM) was used as the drag reduction agent. This surfactant can reduce the drag up to 70% (a Reynolds number of about 70,000–150,000) as measured by pressure drop in a pipe flow. Experiments in Couette flow also show drag reduction in the turbulent range. Two arrangements were used, (1) one small trip-wire on the inner cylinder, and (2) four larger trip-wires on the outer cylinder. These trips reduce the critical Reynolds number for transition from laminar to turbulent flow. In case (1), we obtained 18% drag reduction at 5,000<Re<15,000 and in case (2), we obtained an average reduction of about 20% at 2,000<Re<10,000, increasing up to 30% at Re=15,000. The paper also discusses two important problems. First, the shear rate is not constant in the radial gap in circular Couette flow. For non-Newtonian fluids, where the molecular viscosity is a function of the shear rate, this effect must be considered. Second, which viscosity should be used in the Reynolds number? For pipe flow measurements, most authors use the viscosity of the solvent (generally water and Newtonian). For measurements in the Couette flow, we use a different approach, which is described in this paper. We conclude that Couette flow is a useful method for drag reduction investigations. Its advantage is the much smaller geometry in comparison to those of conventional test facilities such as wind tunnels, water, or oil channels or in tubes.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Flow near a vibrating cylinder

The results are given of experimental investigations into the change in the structure of the secondary steady flows near a circular cylinder vibrating in a fluid at rest in the direction perpendicular to its axis in a wide range of vibration amplitudes at high Reynolds numbers. For vibration amplitudes less than the cylinder diameter, not only viscous waves but also four vortices are generated near the surface of the cylinder and four steady flows at some distance from it. During a period of the vibration, the vortices near the cylinder change their shape and position. At vibration amplitudes comparable with the cylinder diameter, the vortices become separated and form two vortex streets. If the vibration amplitude is increased further, the streets bifurcate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 190–192, July–August, 1982.     

Formation of azimuthal flows driven by a mass source-sink system in a rotating paraboloid

The process of formation of azimuthal flows generated by a mass source-sink system in a shallow water layer on the surface of a rotating paraboloid is investigated theoretically and experimentally. The calculations are carried out within the framework of the shallow-water equations with allowance for bottom friction. Asymptotic solutions describing the process of establishment of steady-state azimuthal flows which takes place after instantaneous initiation of the source-sink system are constructed. It is shown that theory and experiment are in satisfactory agreement.     

The boundary layer on a rapidly rotating cylinder

The study considers plane steady flow of an incompressible fluid around a circular cylinder rotating in a homogeneous free stream. On the basis of an asymptotic analysis of the Navier-Stokes equations for high Reynolds numbers, it is shown that at a certain value of the angular velocity of the cylinder an interaction arises between the flow in the boundary layer and the external potential flow. A solution is obtained numerically which describes the flow in the region of interaction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 36–45, September–November, 1987.     

Theory of gravitational stability of a rotating cylinder

The stability of a rotating dust cylinder against perturbations located in the plane perpendicular to the axis of rotation is investigated. It is shown that a homogeneous rotating cylinder containing a weak inhomogeneity is stable against such perturbations. A weakly inhomogeneous cylinder with opposite streams of equal density is unstable for thel=2 mode in the case of a perturbation of the form_ei(l–t), when the density increases radially. The instability of a system consisting of a homogeneous rotating dust cylinder in a hot homogeneous medium is determined. It is shown that the maximum growth rate corresponds tol = 2 when the density of a cold cylinder is not negligible in comparison with the density of the medium. In the opposite case, the maximum growth rate shifts toward l=3. An attempt is made to associate the existence of the maximum growth rate for l=2 with the presence of two spiral arms in most galaxies. It is shown that, when the longitudinal temperature is high enough, a rotating cylinder which is bounded in the radial direction is stable against arbitrary perturbations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol.10, No. 3, pp. 3–11, May–June, 1969.     

Three-dimensional gas flow in a rotating cylinder with a retarding cover

The study of rotating flows is of interest due to both the development of the centrifugal method of separation of gas and isotope mixtures and the possibility of astrophysical applications. An analytical nonlinear model for calculating the hydrodynamic characteristics of the viscous incompressible fluid flow in a rotating cylinder in the presence of a retarding cover is presented. The cases of stationary and rotating covers are considered. The analysis is performed on the basis of the system of hydrodynamic Navier-Stokes equations. The flow domain is divided up into the main flow and end boundary layers at the cylinder bottom and at the rotating cover. In its turn, the main flow is divided up into an inviscid quasi-rigid core and a lateral layer within which almost the entire upward circulatory flow is concentrated. The equations of the boundary layers at the end surfaces are analyzed by the approximate Slezkin-Targ method. The solutions in the boundary and lateral layers are “stitched” together with the velocity distribution in the main flow core. The unknown angular velocity ω ₁ and radial boundary R ₁ of the core are determined from the balance of the moments of the friction forces acting on the main rotating flow and the continuity condition for the circulatory flow. The experimental and calculated data are compared.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.