Instabilities of flows due to rotating disks: preface

There are many flows driven by the rotation of one, or more, disks, and this paper is concerned with the instabilities of such flows, and their laminar–turbulent transition. The original, and most studied, rotating-disk flow is the von Kármán swirling flow produced by an infinite rotating disk in an otherwise still fluid. This flow shares many stability characteristics with three-dimensional boundary layers of engineering interest over aerofoils; most notably, the cross-flow instability giving rise to stationary cross-flow vortices. Various basic flows produced by rotating disks, and their stability, are reviewed, and motivations for assembling this special issue dedicated to the instabilities of rotating-disk flows are presented. The papers appearing in this special issue are discussed and related to major research themes in the field, and to one-another.     

Stability of the boundary layer on a sphere rotating in still fluid

Summary A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear stability analysis. A set of perturbation equations governing the instability of the flow field is derived assuming the perturbations to be consisting of spiral vortices. It is shown that the critical Reynolds numbers obtained in the present analytical study are close to those observed in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere while the streamline-curvature instability overtakes near the equator.     

Study on boundary layer transition of a rotating disk

Summary Behaviour of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail. Through visualizations of the transition regime by using close-up camera, new striped flow patterns originating along the axis of spital vortices are found to be ring-like vortices which occur on the surfaces of each spiral vortices. Mechanism of the spiral vortex is clarified by cutting the vortices by strobo slit light. It is also found out experimentally that the phase velocity of the vortices is zero.     

Behaviour of spiral vortices on a rotating cone in axial flow

Summary The purpose of the present paper is to investigate experimentally in detail the boundary layer transition process and the behaviour of spiral vortices appearing in the transition range of the boundary layer on a 30°-cone, rotating in axial flow. Counterrotating spiral vortices in the transition range are visualized with a white smoke method, and observed the time dependent behaviour of them using a drum camera and a light sheet illumination method with a stroboscope flash light. The light passes a slit in order to illuminate only a thin sheet in the flow. With this method, the time dependent growing up and breaking down process of these spiral vortices is greatly clarified. A hot wire anemometer is also used for measuring in the flow field quantitatively. The results show that the spiral vortices are generated in the thin region of the steep shear velocity gradients near the wall. As the vortices grow up in z-direction, they are strongly distorted by the mean velocity field there, and finally they are teared off.With 7 Figures     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

Typical flow between enclosed corotating disks and its dependence on Reynolds number

Abstract

The flow in an enclosed co‐rotating disk pair is investigated by Laser Doppler Velocimetry (LDV) measurements and flow visualizations. First, the typical flow structure at Re = 5.25 × 10⁵ and S = 0.09 is clarified. The flow fields in the r – θ and the r – z planes are both investigated and then divided into several flow regions based on the distinct flow types observed. The flow regions found in the two different planes are also compared and integrated. Second, with S fixed, the dependence of the flow field structure upon the Reynolds number is discussed. Three regimes of the r – θ plane flow with different Reynolds numbers are identified based on the measured mean velocity and spectral intensity. When Re < 1.6 × 10⁵, no solid body region is found and the flow is in a laminar regime. In the range 1.6 × 10⁵ ≤ Re ≤ 2.0 × 10⁶, the solid body region and the outer region vortices coexist, and an empirical equation is developed to estimate the number of vortices. When Re > 2.0 × 10⁶, the flow becomes turbulent. As Re increases from 9.3 × 104 to 5.25 × 10⁵, the spectral intensity initially increases and then decreases before increasing again to an even higher level, resulting in an increasing sawtooth pattern.     

The flow structure of a puff

From time-resolved stereoscopic particle image velocimetry measurements over the entire circular cross section of a pipe, a first-of-its-kind quasi-instantaneous three-dimensional velocity field of a turbulent puff at a low Reynolds number is reconstructed. At the trailing edge of the puff, where the laminar flow undergoes transition to turbulence, pairs of counterrotating streamwise vortices are observed that form the legs of large hairpin vortices. At the upstream end of the puff, a quasi-periodic regeneration of streamwise vortices takes place. Initially, the vortex structure resembles a travelling wave solution, but as the vortices propagate into the turbulent region of the puff, they continue to develop into strong hairpin vortices. These hairpin vortices extract so much energy from the mean flow that they cannot be sustained. This structure provides a possible explanation for the intermittent character of the puffs in pipe flow at low Reynolds numbers.     

Hydrodynamic structures — elements of the self-sustained oscillation system in the flow

The character of hydrodynamic disturbances in the near-wall shear flow inducing self-oscillations in the channel has been investigated. Experiments have been performed in a small and a large wind tunnel at a flow velocity of 10–40 m / sec. It has been found that excitation of self-oscillations becomes possible as a result of narrow-band acoustic radiation generation by not only vortex formations but also large-scale coherent structures in the region of the laminar-turbulent transition and in the turbulent boundary layer.     

Behaviour of organised disturbances in fully developed turbulent channel flow

In our earlier work we have shown the relevance of stability theory in understanding the sustenance of turbulence in turbulent boundary layers. Here we adopt the same model to study the evolution of organised disturbances in turbulent channel flow. Since the dominant modes are wall modes we find that the stability characteristics in the two flows are nearly identical although the boundary conditions (at the edge of the boundary layer and at the centre of the channel) are different. Comparisons with the experiments of Hussain and Reynolds are also presented.     

不同压力差下微通道尺寸和表面粗糙度对摩擦系数的影响

该文数值模拟液体在圆形和梯形截面微通道内的流动,分析了层流和湍流下液体在微圆管内的流动状态。着重研究不同压力差、微通道尺寸和表面粗糙度下,液体在微通道内的流动摩擦系数,并通过摩擦系数随雷诺数的变化曲线推断微通道流动转捩的雷诺数范围。研究表明:微通道中流动的摩擦系数随雷诺数的增大逐渐减小;通道截面的当量直径会改变过渡状态存在的雷诺数范围;粗糙度会影响湍流状态下流动的摩擦系数,相同雷诺数下,粗糙度越大,摩擦系数越大。     

Flow over compliant rotating disks

Flow over compliant materials and compliant coatings has been studied for decades because of the potential of using such materials for laminar-flow control. Since boundary layers in most flows of engineering interest are three-dimensional the classic rotating-disk flow geometry, the paradigm for studying three-dimensional boundary layers, has been adapted to investigate flow over compliant rotating disks. This paper reviews the literature on the existing experimental and theoretical research on flow over compliant rotating disks. The article concludes by evaluating the status of the available results and their implications as regards future research routes to investigate the capabilities of compliant materials for laminar-flow control.     

微管道内湍流转捩的实验研究

研究旨在确定微管道内流动从层流到湍流转捩的临界雷诺数。利用微观粒子图像测速技术(Micro-PIV)研究了去离子水在内径为230μm的圆形截面玻璃微管道内的流场结构,得到了从层流到充分发展湍流各流动状态下的轴向平均速度分布和湍流度分布,实验雷诺数为1020~3145,同时研究了微管道内的流动阻力特性。平均速度场和脉动速度场的实验结果表明微管道内从层流到湍流的转捩发生在Re=1800~1900左右,与流动阻力的测量结果一致,与宏观流动比较,并未发现微管道内的流动转捩有明显提前。实验结果还显示,当Re>2700时,微管道内的平均流速分布和相对湍流度分布呈现典型的充分发展湍流状态特征。     

Numerical methods for two-fluid hydrodynamics: Application to the Taylor vortex flow of superfluid helium II

We describe the numerical method which we have developed to solve for the first time the fully nonlinear HVBK equations. These equations generalise Landau's two fluid model to take into account the presence of quantised vortices. We apply the method to investigate the flow pattern of helium II between rotating concentric cylinders (Taylor vortex flow) at increasing Reynolds numbers. We compare the results against classical Taylor vortex flow.     

On the interaction of a vortex pair and a vortex ring with a flat shield

The approximate method of calculation of nonstationary flow in the interaction of a vortex pair and a vortex ring with a parallel and respectively perpendicular flat shield is presented. It is shown that these primary vortices induce transverse wall flow on the shield in the ideal-fluid approximation; in this flow, with allowance for the fluid’s viscosity, a boundary layer is generated which represents vortex flow with sign opposite to that of the primary vortices. Boundary-layer separations occur on the portion of the shield with a positive longitudinal pressure gradient. Secondary flows interact with the primary ones due to which the flow is rearranged; the transverse displacement of the initial vortex pair with a loop-shaped trajectory of its motion is observed in the plane problem, whereas the formation of ascending flow along the axis of the vortex ring is observed in the axisymmetric problem. The effect found in the latter case in laminar and turbulent regimes of flow is confirmed for the laminar regime by experiment and by the data of numerical simulation of Navier–Stokes and Reynolds equations.     

Establishing a relation between turbulent stresses and the mean flow parameters for an incompressible fluid with a positive pressure gradient

The isothermal turbulent boundary layer is analyzed which forms during the flow of air through conical or flat diffusers at Reynolds numbers in the 48,850–202,000 range in the entrance. The relation between turbulent stresses and the mean flow parameters in the boundary layer can be established on the basis of the data obtained here.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 21, No. 1, pp. 48–52, July, 1971.     

Dynamics of the viscous interaction of a ring vortex with a flat screen

A separation turbulent flow has been mathematically simulated on the basis of numerical solution of nonstationary Navier-Stokes equations for determining the dynamics of viscous interaction of a ring vortex with a flat screen. The problem was solved for an axisymmetric turbulent flow at Reynolds numbers falling within the range 10⁵–10⁷. On the basis of the calculation data obtained, the interaction of a ring vortex with a turbulent flow induced on the screen and with the secondary ring vortices was investigated. The data obtained are in qualitative agreement with the analogous data obtained by other authors with the use of the discrete-vortex method and the boundary-layer theory as well as with the available experimental and calculation data obtained for a laminar flow. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 184–190, January–February, 2008.     

Primary crossflow vortices,secondary absolute instabilities and their control in the rotating-disk boundary layer

The three-dimensional boundary layer produced by a disk rotating in otherwise still fluid is analytically investigated and its stability properties are systematically established. Using a local parallel flow approximation, finite-amplitude primary travelling vortices governed by a nonlinear dispersion relation are obtained. A secondary stability analysis yields the secondary linear dispersion relation and the secondary absolute growth rate, which determines the long-term stability of the primary nonlinear vortex-trains. By using these local characteristics, spatially developing global patterns of crossflow vortices are derived by employing asymptotic techniques. This approach accounts for both the self-sustained behaviour, exhibiting a sharp transition from laminar to turbulent flow, and the spatial response to external harmonic forcing, for which onset of nonlinearity and transition both depend on the forcing parameters. Based on these results, an open-loop control method is described in detail. Its aim is not to suppress the primary fluctuations but rather to enhance them and to tune them to externally imposed frequency and modenumber, and thereby to delay onset of secondary absolute instability and transition. It is shown that transition can be delayed by more than 100 boundary-layer units.     

Transition from Taylor vortices to cross-flow instabilities

Summary We present experimental results of fluid flow instabilities between different rotating surfaces. We start withcounter-rotating Taylor vortices between two coaxial cylinders. We go over to rotating cones with increasing apex angle. Due to the growing cross-flow we finally end up with spiral vortices allrotating in the same direction between a rotating disk and a housing. Figure 13 gives a complete survey of these results. We discuss the transition from one vortex system to the other in detail.Dedicated to Prof. Dr. Dr. h. c. mult. S. Wittig on the occasion of his 60th birthday     

Numerical experiments on feedback EMHD control of large scale coherent structures in channel turbulence

Summary The current work focusses on the spatio-temporal evolution of large scale coherent structures in the turbulent boundary layer of a plane channel both with and without microtile-based EMHD control. The heuristic concept behind the microtile designs that we have simulated apparently does not yield a successful drag reduction strategy (for the open-loop case [1]). In this work we investigate the flow response when the Lorentz force is applied with feedback conditioned on the advection of large-scale flow structures (e.g. hairpin vortices). We performed a long-time simulation conditioned on the passage of strong ejection events but obtained no reduction in skin friction. Based on short-time simulations we found that the near-wall flow structures undergo merely a spatial phase-shift when advecting above a single Lorentz force actuator: the structures are simply decelerated or accelerated with little change in their appearance, based on flow visualization. During this interaction of the applied Lorentz force with the flow, the Reynolds stress is unchanged.     

Aero-optic effects in turbulent flows

Large-scale vortices and related aero-optic effects in a turbulent boundary layer, a free mixing layer, and an underwater stream have been mathematically simulated. The results are used for the analysis of distortions in the wavefront-phase function of a coherent light beam, which are induced by turbulent fluctuations in the parameters of the medium. The results of numerical calculations are compared to the experimental data and to a solution of the Reynolds equations.