On the spatio-temporal structure of cylinder wakes

The wake of a short aspect ratio cylinder placed in a uniform flow is experimentally investigated. After having characterized the temporal behavior of the Bénard–Von Kàrmàn vortex shedding by the use of a classical hot-wire anemometer, an ultrasound anemometry technique is applied to study the spatial critical behavior of the envelope of the transverse velocity of the wake. It is shown that this envelope which represents the spatial form of the global mode of the wake, follows universal scaling laws which are in agreement with a second order phase transition. In a second set of experiments, the behavior of the longitudinal velocity fluctuations is also investigated. It is discovered that there is a special point several diameters behind the cylinder, which plays a role of a wave maker. Finally, for very small aspect ratio cylinders, symmetric vortex shedding is reported and interpreted using a system of coupled oscillators. Received: 15 May 1997/Accepted: 20 January 1998     

Evolution of the turbulent wakes of spherical bodies in stably stratified media

A turbulent wake model, based on the Reynolds, energy and turbulence dissipation equations together with the closing relations for the turbulent transport coefficients, is proposed. A comparative investigation of swirled momentumless wakes with zero and nonzero angular momentum is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 13–22, January–February, 1994.     

The structure of subsonic air wakes behind a flat plate

 Acetone vapor planar laser-induced fluorescence has been used to visualize the structure of a subsonic air wake behind a flat plate. Longitudinal and transversal wavelengths have been directly measured from the acquired images. The ratio between them has been calculated to be 2/5. Received: 29 September 1998/Accepted: 15 December 1998     

On the shape of bodies ablating in a supersonic gas stream

When objects move at a high velocity in a dense medium, their front surfaces undergo intense heating. There can then be a strong interaction between the oncoming flow and the surface of the body in which the body is not merely subject to the thermal and force effect of the stream but also significantly changes the flow field itself due to the intense blowing of ablation products from its surface and the change in the geometry of the front surface. Experimental and numerical investigations into the various regimes of strong interaction have established how stable shapes are adopted by bodies ablating in a supersonic gas stream.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 18–21, January–February, 1981.     

Inverse problems of determining the shape of incompressible bodies under finite strains

Transformations preserving the volume under finite strains are given for some classes of two-dimensional problems. Several settings of nonlinear elasticity problems meant for determining the shape of mechanical rubber objects from a given configuration in a strained state are proposed on the basis of these transformations. Two axisymmetric problems are solved as an example. In the first problem, we determine the shape of a rubber bushing in a combined rubber-metal joint which has a prescribed configuration in the assembled state. In the second problem, we determine the shape of the rubber element of a cylindrical compression damper in working state.     

Problem of the optimum shape of carrying bodies in a Newtonian flow

The Ritz method is employed in order to determine the shapes of the upper and lower surfaces of a carrying body which will exhibit the maximum aerodynamic quality at hypersonic flight velocities in the presence of blunted leading edges, the thickness of these being determined by the limited temperature to which they may be raised.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 171–174, May–June, 1975.     

The effect of submergence on the scattering by the interface between two semi-infinite sheets

This paper considers the reflection and transmission of a flexural-gravity wave within ice sheets floating on water as it propagates through a series of abrupt changes in ice sheet characteristics. The canonical problem involves one such junction at which two semi-infinite ice sheets of different properties are either frozen together or separated by a crack. Unlike most mathematical approaches to problems involving ice sheets, we allow the ice sheets to adopt a variable submergence according to their thickness. The problem is solved using integral equations formulated through the matching of eigenfunction expansions.     

Measurements of the flow over a low-aspect-ratio cylinder mounted on a ground plane

The flow over a finite-height cylinder of aspect ratio 1, with one end mounted on a ground plane and the other end free, has been studied by means of surface flow visualisation, particle image velocimetry (PIV) and surface pressure measurements. The diameter-based Reynolds number was 200,000. The mean flow topology has been identified in three areas: the horseshoe vortex system, the separated flow over the free-end and the wake region. Evidence is shown for the existence of a three-horseshoe vortex system, while the mean flow over the free-end consists of an arch vortex with its bases on the forward half of the free-end. There are two tip vortices coming off the free-end. The wake region is found to be highly unsteady, with considerable variation from the mean flow.     

The influence of relative velocity on the eddy structure between two spheres in Stokes flow

Davis et al. (1976) have shown that if two solid spheres move together in an axisymmetric Stokes flow, then provided they are sufficiently close, a body of fluid becomes trapped between the spheres. Here it is shown how the small eddy motions induced in this trapped fluid are significantly disrupted when one sphere moves relative to the other.     

Effect of leading-edge tubercles on the flow over low-aspect-ratio wings at low Reynolds number

Two-dimensional time-resolved particle image velocimetry (TR-PIV) and stereographic particle image velocimetry (SPIV) techniques were used to investigate the effect of leading-edge tubercles on the flow over low-aspect-ratio wing models. The angle of attack is fixed at 10°, and the Reynolds number based on chord length is 5.8 × 10³. It is shown that the leading-edge tubercles can effectively mitigate flow separation in the model and also reduce the contribution of wake vortex to the fluctuating energy of flow. Counter-rotating vortex pairs (CVPs) initiated from the peak of leading-edge tubercles can promote nearby momentum exchange, enhance mixing of the flow and increase the energy contained in the boundary layer, which results in resisting the larger adverse pressure gradient. Therefore, it is concluded that CVPs play an important role in mitigating the flow separation for wings with leading-edge tubercles.     

On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].     

Mathematical modeling of laminar and turbulent supersonic flow round bodies of convex-concave shape

Tomsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 138–145, September–October, 1988.     

On the effects of free-stream turbulence on axisymmetric disc wakes

Wind tunnel experiments have been used to study the effects of free-stream turbulence on the axisymmetric wake behind a disc. The disc and its wake were introduced to various turbulent streams having various levels of turbulence intensity and length scale. It was found that the presence of free-stream turbulence enhances the body??s drag and hence wake momentum deficit, if it is of sufficient strength, changes the far wake??s decay rate and prevents the appearance of self-similarity. The external turbulence causes a significant transformation in the wake??s turbulence structure. This gradually evolves towards the character of the free-stream turbulence itself and thus is characterised by much weaker turbulence (cross-stream) transport processes and a consequent dominance of shear stress production, which acts to maintain the shear stress and mean velocity profiles.     

Effects of notches on the surface pressure field downstream of a wall-mounted spoiler

Notched spoilers have been observed to be more effective than uniform spoilers to suppress the flow-induced cavity resonance of vehicles with open sunroofs. In this study, a few mechanisms possibly involved in buffeting suppression from notched spoilers were investigated experimentally and numerically. One objective was to investigate the spatial coherence and phase of the wall pressure fluctuations downstream of notched spoilers in comparison with the same quantities for uniform spoilers. Another objective was to gather detailed measured data to allow the verification of computer simulations of the flow over the notched spoiler. Experiments were performed to measure the velocity and wall pressure fields downstream of spoilers mounted on the rigid floor of a closed test section wind tunnel. Efforts were made to reproduce the spoiler and wind tunnel geometry and boundary conditions of the experimental setup in the numerical simulations. The numerical investigation used the Lattice Boltzmann Method (LBM), with the so-called Very Large Eddy Simulation (VLES) viscosity turbulence model. The results of the numerical investigation were in satisfactory agreement with measured data at low frequencies, where buffeting is expected to occur. The results suggested that the notches break down the homogeneity of the leading edge cross-stream vortices predominantly responsible for the cavity excitation. This decreased the cross-stream coherence of the surface pressure field, thereby reducing the magnitude of the net equivalent excitation force acting over the surface downstream.     

Flow structures and dynamics in the wakes of sliding bubbles

An experimental investigation is reported for the flow structures in the wake of an air bubble sliding under an inclined surface in quiescent water. Time-resolved particle image velocimetry (PIV) is used to study the wakes of sliding bubbles for a range of measurement planes, bubble diameters and surface inclination angles. Additionally, key aspects of the bubble’s motion are measured simultaneously using a novel method that accounts for the motion of the bubble’s interface. Thus, vortex shedding may be linked to changes in the bubble shape and path.Analysis of the measured velocity and vorticity fields reveals a wake structure consisting of a near wake that moves in close proximity to the bubble, shedding vorticity at the inversion points of the bubble path. Downstream of the bubble in the far wake, these structures evolve into asymmetrical, oppositely-oriented hairpin vortices that are generated in the near wake. These hairpin vortices bear similarities to those observed behind freely rising bubbles and near-wall bluff bodies and are found to cause significant motion of the bulk fluid. This bulk fluid motion has the potential to offer significant convective cooling of adjacent heated surfaces, such as submerged electronics components.