Internal waves generated by the turbulent wake of a sphere

Internal waves generated by the turbulent wake of a sphere travelling horizontally through a linearly stratified fluid were studied using shadowgraph and particle-streak photography. The Reynolds and internal Froude number ranges considered were 2,000 Re 12,900 and 2.0 Fi 28.0, respectively. Two quite distinct flow regimes based on the structure of the turbulent wake were identified. In one, the wake is characterized by large-scale coherent structures. In the other, the wake, as viewed on a side-view shadowgraph, grows in a roughly symmetric fashion to a maximum height and then collapses slowly; such flows are termed the smallscale structures regime.Wave lengths and maximum wave heights of the internal waves were measured as functions of Nt and Fi, where N is the Brunt-Väisälä frequency and t the time. It was found that the wave lengths scale well with the streamwise dimension of the spiralling coherent structures. The maximum amplitude of the internal waves were found to scale with the vertical dimension of the turbulent wake, upon varying the internal Froude number.     

Vortex systems in the stratified wake of a sphere

The fine structure of the flow and the characteristics of the principal types of vortex structures in the wake of a sphere moving uniformly and horizontally in an exponentially stratified fluid have been experimentally investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–90, July–August, 1991.The authors are grateful to G. Yu. Stepanov for his careful analysis of the first version of this article and his valuable comments.     

An aerodynamic wake in a hypersonic free-molecular gas flow

An experimental investigation was made of the form of an aerodynamic wake and the flow in it for the case where the flow is set up using a point source and is propagated in a motionless residual gas. It is shown that the geometry of the wake is determined by the mutual arrangement of the source and model, that the ground pressure is negligibly small, and that the flow in the wake is part of the oncoming flow, scattered by the residual gas. The value of the transverse velocity ratio exceeds by several orders of magnitude the value of the longitudinal ratio.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 183–186, January–February, 1976.     

Flowfield characterisation in the wake of a low-velocity heated sphere anemometer

Heated sphere anemometers (HSA) are the most widely used instruments for low-velocity measurements in the heating, ventilation and air-conditioning industry. Experiments were conducted to characterise the flowfield around the spherically shaped sensor and upper probe assembly of a HSA. Particle image velocimetry was the main quantitative experimental technique. Measurements of the flowfield around a HSA probe and a 2:1 scaled-up model were performed in a uniform isothermal axisymmetrical jet air flow at Re around 350, based on sensor diameter, for different pitch angle incident flows. Additionally, extensive flow visualisation studies around scaled-up models of the HSA probe were performed. Received: 24 April 2001/Accepted: 16 December 2001     

Mixed convection around a liquid sphere in an air stream

 A linearized finite-difference scheme has been used to investigate the mixed convection boundary-layer flow about a liquid sphere subjected to an air stream. For Prandtl number = 0.7, velocity and temperature profiles are obtained for a wide range of the other controlling parameters: Reynolds number, interior-to-exterior (liquid- to-air) viscosity ratio and Grashof number. Both aiding and opposing natural convections are considered in this study. The effect of the controlling parameters on engineering quantities such as the shear stress and the Nusselt number is also presented. Received on 27 September 2000 / Published online: 29 November 2001     

Vortex dynamics of a sphere wake in proximity to a wall

Toward getting the vortex dynamics characteristics and wake structure of a sphere in proximity to a wall, the effect of a proximal flat plate on the wake of a stationary sphere is investigated via direct numerical simulation. The vortex shedding process and the significant variation of the wake structure are described in detail. The drag coefficient reduces and the wake structure of the sphere becomes complex due to the combined effect of the wake flow and the wall. A jet flow forms between the sphere and the flat plate, which suppresses the vortex separation on the bottom of the sphere. The asymmetric distributions of the coherent structures and the recirculation region behind the sphere are discussed. Besides vortex shedding patterns, the time-averaged velocity distribution, vortex dynamics, distribution regularities of turbulent kinetic energy and enstrophy are investigated.     

Internal waves generated by a moving sphere and its wake in a stratified fluid

The internal gravity waves and the turbulent wake of a sphere moving through stratified fluid were studied by the fluorescent dye technique. The Reynolds number Re=U·2a/v was kept nearly constant at about 3 · 10³ and the Froude number F;U/a N ranged from 0.5 to 12.5. It is observed that waves generated by the body are dominant only when F<4 and are replaced by waves generated by the large scale coherent structures of the wake when F>4.     

Laminar near wake of a sharp wedge in hypersonic perfect-gas flow

The laminar near wake behind a sharp wedge with the semi-vertex angle of 10° and a flat base section placed at zero incidence in a Mach 6 uniform perfect-gas flow with the specific heat ratio 1.4 at Reynolds numbers ranging from 3 × 10² to 10⁵ is considered. The study is carried out on the basis of the numerical solution of the Navier-Stokes equations. The results on the base pressure and the pressure and local stagnation temperature distributions along the plane of symmetry and in several cross-sections in the near wake are compared in detail with the data [1].     

Circulation flow at the front surface of a sphere in a supersonic wake

Several theoretical and experimental studies of supersonic flow past a blunt body located in the wake behind another body have been made [1–7]. It has been shown that a reverse-circulation flow can occur in the shock layer at the front surface. The possibility of such a flow forming depends on the nonuniformity of the freestream flow and the Reynolds number. This paper presents new results of the theoretical study of the structure of the shock wave at the front surface of such a sphere, obtained on the basis of numerical solution of Navier-Stokes equations. It is shown that for a fixed nonuniformity of the freestream flow, an increase in the Reynolds number and cooling of the surface of the body lead to the formation of a secondary vortex in the region where the contour of the body intersects the axis of symmetry. A study is made of the variations of the drag and heat transfer parameters over the front surface of a cooled and thermally insulated sphere. The possibility of numerical simulation of the flow on the basis of the Euler equations is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–148, May–June, 1985.     

Similarity with the outflow of strongly unexpanded jets into a hypersonic wake

The article discusses the outflow of a nonviscous gas from a strongly unexpanded supersonic nozzle into a supersonic wake. Under the assumption that the radius of the outlet cross section of the nozzle is negligibly small in comparison with the characteristic dimensions of the jet, expressions are obtained for the transverse and longitudinal dimensions of the jet, as well as similarity criteria determining the dimensionless gasdynamic functions. The satisfaction of the similarity criteria was verified by comparison with numerical calculations. Similarity with the outflow of strongly unexpanded jets was discussed in [1–3], where, specifically, the characteristic dimension of the flow was determined. In [4] it was demonstrated that the experimentally observed structure of the jet can be best described with the introduction of two characteristic dimensions, longitudinal and transverse. The effective construction of these two characteristic dimensions for the case of nonviscous outflow into a flooded space was carried out in [5], in which it was shown that using the longitudinal and transverse dimensions the geometries of the flow and the gasdynamic parameters are found to depend on the adiabatic index of the outflowing gas and on a parameter formed from the integral characteristics of the nozzle. The present work is a generalization of the results of [5] for the outflow of a jet into a hypersonic wake.     

Experimental study of density fluctuations in a hypersonic laminar wake behind a cone

The characteristics of natural fluctuations of density in a laminar near wake behind a sharp cone in a hypersonic flow of nitrogen at zero incidence are studied by the method of electronbeam fluorescence at Mach numberM=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹. The distributions of the mean density, integral fluctuations, and spectra of density fluctuations are obtained, the longitudinal and azimuthal phase velocities of perturbations are determined, and the growth rates of perturbations in the wake are found. The results are compared with the measurement data in the shock layer on a flat plate. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 111–117, May–June, 2000