Stability of a supersonic boundary layer on a permeable surface with heat transfer

The effect of cooling of a permeable surface on the stability of a supersonic boundary layer on it is investigated. As distinct from the case of an impermeable surface, deep cooling can reduce the critical Reynolds number. Common points of the continuous and discrete spectra are found in the region of the disturbance parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 41–46, January–February, 1977.The work was carried out at the Department of Applied Mathematics of the University of Western Ontario in Canada. I am grateful to the Head of the Department Professor J. Blackwell for suggesting the investigation of this problem.     

Recovery factors for a permeable surface and a gas surface film in a supersonic turbulent boundary layer

The recovery factor on a permeable surface has been experimentally determined at various rates of injection of air into a supersonic turbulent boundary layer. On the basis of an analysis of the solutions of the integral momentum and energy equations for a turbulent boundary layer an expression is obtained for the recovery factor. The recovery factor in the region of a protective gas surface film in a supersonic external flow has been experimentally determined.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 131–136, March–April, 1972.     

Hypersonic jet issuing into resting medium or a co-flowing supersonic stream

The calculation of supersonic ideal thermodynamically perfect gas jets discharging from a nozzle has been carried out previously in many studies (for example, [1, 2]) on the basis of the numerical method of characteristics. Here we give an approximate analytic solution of the problem of a supersonic jet discharging into a medium at rest or into a supersonic co-flowing stream.The author wishes to express his gratitude to G. G. Chernyi for his continued interest in this study.     

Base pressure of bodies of revolution when gas is blown through their surface into a supersonic flow

One of the most important problems of high-velocity aerodynamics is the investigation of the base pressure and the wake flow behind bodies of revolution under the conditions of surface mass transfer. The present paper reports careful experimental investigations of the flow past bodies of revolution in the presence on their surface of a transverse mass flux, especially at a low blowing intensity. These investigations have yielded new data on the dependence of the base pressure on the main determining parameters, extending and making more accurate the modern picture of the mechanism by which surface mass transfer influences the base pressure and its connection with the state of the boundary layer.     

Mixing of a supersonic stream and a transverse jet injected through a circular hole in a plate

An experimental investigation is conducted of the propagation and mixing of a transverse sonic jet injected into a supersonic gas stream through a circular hole in a plate. The picture of the interaction at the initial section of the injected jet is examined in the majority of papers devoted to this question [1–3]. The aim of this paper is to investigate the mixing of the injected jet with the free stream, and to establish criteria governing the jet insertion and mixing processes.     

Equilibrium of a flexible permeable shell in a supersonic gas flow

The plane steady-state regime of uniform supersonic ideal-gas flow around a uniaxial absolutely flexible open permeable shell is investigated numerically [1]. The effect of the angle of attack and the degree of nonuniformity of the permeability distribution on the aerodynamic characteristics and the equilibrium shape of the shell is determined for various methods of shell attachment. Approximate localization relations, which take into account the dependence of the distributed load on a concave permeable screen on its degree of permeability and the free-stream parameters, are formulated. An example of the application of these relations to the solution of three-dimensional problems of the equilibrium of permeable shells of the circular dome type in a supersonic flow [2] is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 152–158, September–October, 1989.     

Stokes flow through a permeable tube

Pressure-driven Stokes flow through a circular tube with a permeable wall is considered as a model of blood flow through a capillary vessel. Fluid penetrates the tube wall over a test section according to Starling law relating the normal fluid velocity to the transmural pressure defined as the difference between the wall and the uniform ambient pressure. The problem is formulated using the integral representation for Stokes flow, and the solution is computed with high accuracy using a boundary-element method for specified values of the wall permeability and percentage of fluid escaping through the walls. The results illustrate the structure of the flow and validate the predictions of a model based on the assumption of locally unidirectional flow for sufficiently small permeability.     

Axisymmetric flow through a permeable near-sphere

An analytical approach is described for the axisymmetric flow through a permeable near-sphere with a modification to boundary conditions in order to account permeability. The Stokes equation was solved by a regular perturbation technique up to the second order correction in epsilon representing the deviation from the radius of nondeformed sphere. The drag and the flow rate were calculated and the results were evaluated from the point of geometry and the permeability of the surface. An attempt also was made to apply the theory to the filter feeding problem. The filter appendages of small ecologically important aquatic organisms were modeled as axisymmetric permeable bodies, therefore a rough model for this problem was considered here as an oblate spheroid or near-sphere.     

Flow in a viscous jet escaping through a supersonic nozzle into a semi-infinite ambient space

The problem of an axisymmetric gas flow in a supersonic nozzle and in the jet escaping from the nozzle to a quiescent gas is solved within the framework of Navier-Stokes equations. The calculated pressure distribution is compared with that measured in the jet by a Pitot tube. The influence of the jet pressure ratio, Reynolds number, and half-angle of the supersonic part of the nozzle on nozzle flow and jet flow parameters is studied. It is shown that the distributions of gas-dynamic parameters at the nozzle exit are nonuniform, which affects the jet flow. The flow pattern for an overexpanded jet shows that jet formation begins inside the nozzle because of boundary-layer displacement from the nozzle walls. This result cannot be obtained with the inviscid formulation of the problem.     

Spectroscopic study of the properties of a supersonic plasma stream

A plasma diagnosis has been carried out by spectroscopic methods. The behavior of temperature and concentration of charged particles was measured along the stream as a function of polarity for a stream with a shock wave and a stream with periodic structure. An explanation of the observed phenomena is given. The physical processes occuring in a supersonic plasma stream are quite distinctive [1], Spectroscopic investigations are necessary since they provide more detailed information on the physical state of the plasma. It is also of interest to study wave processes taking place in the stream from the point of view of the additional plasma heating thus obtained.We take this opportunity to express our sincere thanks to M. A. El'yashevich for discussing the results.     

Investigation by experiment and calculation of a supersonic stream adjacent to a wall in an accompanying supersonic flow

In well-known papers devoted to the investigation of supersonic streams adjacent to a wall, the authors, as a rule, restrict themselves to the case of a subsonic blast. In the present paper we determine the velocity field and the concentration field of an admixture of helium in a plane supersonic stream of air (M₁=2.18), propagating along a surface in an accompanying supersonic flow of air (M₂=2.7 and 3.8). In the boundary layer approximation a numerical calculation is made of the non-self-similar isobaric flow, using the equation for the turbulent viscosity [1] as the closing relationship. Results of the calculation are compared with experimental data.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 25–32, July–August, 1972.