Supersonic flow over energy-releasing sources

The problem of supersonic flow over three-dimensional axisymmetric heat-releasing sources is solved within the framework of the linear theory. The dependence of the distribution of the parameters in the flow on the shape of the heat-releasing source is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 179–182, September–October, 1992.The author is grateful to V. A. Levin for supervising the work.     

Supersonic flow past a blunt wedge

A study is made of the asymptotic solution of the problem of flow past a blunt wedge by a uniform supersonic stream of perfect gas. By separation of variables it is shown that at large distances the disturbance of the flow is damped exponentially. In the case of subsonic flow behind the shock wave the exponent of the leading correction term in the expansion of the shock front is calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1984.     

Supersonic flow past axisymmetric flared cones

Systematic data on the determination of the aerodynamic characteristics of axisymmetric bodies with a break in the generating line (Fig. 1a, b) in supersonic flow at zero angle of attack are presented in [1, 2, and others]. A characteristic feature of the flow past such bodies is the appearance of an extensive separation zone dec in the region of the break in the generator when the break angle exceeds some minimum value _min, which for a turbulent boundary layer depends basically on the Mach number M at the body surface ahead of the separation zone. In this case, compression waves which change into the oblique compression shocks dc and cc, emanate both from the beginning of the separation zone (point c) and from the end of it (point d). These shocks, intersecting at the point c, form the triple shock configuration acd and acc for which we introduce the notationac[c, d]. The maximum value (_max) of the generator break angle is limited by the possibility of the existence of an attached compression shock, dc. According to these data a change in the generator break angle for the range _minmax of the angle does not disrupt the nature of the flow in the separation zone, but only alters the size of this zone.We shall examine the flow past cones with values of the generator break angles (_max) for which the attached shock dc cannot exist.     

Supersonic radial flow past sharp-nosed cones

Axisymmetric and three-dimensional gas flows past sharp cones are studied both analytically and numerically for the case in which the supersonic oncoming stream is of source type. The effect of the governing parameters, such as the distance from the source to the cone, the specific heat ratio, the cone angle, and the angle of attack, on the flow is studied. Asymptotic laws governing the flow at large distances from the cone vertex are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 112–120, March–April, 1994.     

Supersonic swirling flow past a blunt body

The problem of supersonic swirling flow past a blunt body is studied numerically on the basis of the complete Navier-Stokes equations.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1994.     

Supersonic flow past a body with transverse jets

The results of an experimental study of the flow past a body with transverse jets are presented. The gas jets flowed out simultaneously from several nozzles arranged on the body's lateral surface. Various flow regimes were considered to such parameters as the relative jet momentum, the angle of incidence, etc. The experimental results were generalized on the basis of an approximate similarity law.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 75–80, July–August, 1995.     

Supersonic transverse rarefied gas flow past a strip

The supersonic flow of a monatomic gas consisting of hard spherical particles past a flat strip normal to the flow is investigated using the direct simulation Monte-Carlo (DSMC) method. The calculations are performed over the Knudsen and Mach number ranges 0.015–5 and 1.8–15, respectively. The structure of the compressed layer and the aerodynamic characteristics are systematically studied for the Mach number 5 and various Knudsen numbers. The dependences of the compressed-layer thickness in molecular free paths are found. The nonequilibrium processes in the neighborhood of the strip are described on the basis of the data on the temperature anisotropy with respect to three coordinates.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 159–167. Original Russian Text Copyright © 2005 by Maltsev and Rebrov.     

Supersonic flow past a step downstream of longitudinal grooves

Supersonic flow past a step preceded by longitudinal grooves cut in the plane surface upstream of it is studied experimentally in the presence of a turbulent boundary layer. It is shown that the grooves affect both the shape and the size of the flow separation zone and generate longitudinal vortex cores in the latter.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 201–206, September–October, 1996.     

Supersonic flow past obstacles on the edges of dihedrals

Supersonic flow with M=3 and P₀=1.2 MPa past cylindrical obstacles located in the plane of symmetry at the edges of exterior and interior dihedrals at a distance ₀=140 mm from the leading edge of a model consisting of two intersecting flat sharp-edged plates is investigated in the presence of a turbulent boundary layer on the faces of the dihedral. The linear angle of the model dihedral was varied discretely from 45 to 310°. Interchangeable cylinders with diameters d=16 and 10 mm and variable height h=0–64 mm were used. The models were tapped along the axis of symmetry and rays starting from the center of the cylinder base and inclined to the edge of the model at angles = 30, 60, and 90°. The pressure was measured with IKD transducers. The results of the measurements were processed on a IVK-1 computer system. The flow past the model was photographed with a Töpler schlieren instrument. Before the experiment the surface of the model was coated with a carbon-oil solution. After the experiment the distribution of the visualizing composition was photographed and the dimensions of the region of separated flow near the obstacle were measured.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–184, September–October, 1989.     

Supersonic flow past blunt bodies involving fast nonequilibrium processes

In the numerical integration of the system of equations of relaxation gasdynamics the solution may become unstable. Instability arises in those cases when the characteristic time for the nonequilibrium process becomes less than the characteristic flow time. To ensure stability it is necessary to reduce the integration step. With approach to equilibrium conditions, when the process rate increases, the step reduction may lead to excessive computational time. Preceding studies have overcome the difficulty in solving the one-dimensional [1–3] and two dimensional [4] problems by various techniques, the basic idea being the use of implicit difference schemes for approximating the relaxation equations.In the present paper analogous considerations are used to develop a scheme for calculating supersonic flow past blunt bodies with fast non-equilibrium processes within the framework of [5]. The basic coordinate system , is used to approximate the equations, just as in [5]. However the relaxation equation is solved along a streamline element. Calculations are presented for the air flow past a sphere with account for the oxygen dissociation reaction. The validity of the binary similarity law for this model is verified. As an example of the applicability of the technique, a calculation is made of the flow of a chemically reacting mixture with heat release about a sphere.     

Supersonic flow past a cylinder with a fluid flare

The aerodynamic parameters and the pressure distribution over the surface of a cylinder in a steady axisymmetric supersonic flow is studied within the framework of the inviscid perfect gas model in the absence and the presence of combined intense air injection fromthe flat face and the lateral surface into the shock layer. The purpose of the study is to investigate the effect of gas blowing from different regions of the cylindrical surface on the supersonic axisymmetric flow past the body.     

Supersonic viscous perfect gas flow past a circular cylinder

The complete Navier-Stokes equations are used to calculate supersonic perfect gas flow past a circular isothermal cylinder by the method described in [1]. The effects of the Mach number M=2.5–10 and the Reynolds number Re=30-10⁵ on the flowfield structure and heat transfer to the cylinder wall are investigated. Special attention is paid to the study of the near wake and the local characteristics on the leeward side of the cylinder.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 107–115, November–December, 1993.     

Supersonic flow past a slender cone with asymmetric nosetip

Supersonic flow of an inviscid gas that does not conduct heat past a slender cone with asymmetric nosetip has been investigated at zero and nonzero angle of attack. The flow is calculated by the Babenko-Voskresenskii numerical method. It is shown that the asymmetry of the nosetip has a strong influence on the distribution of the parameters of the gas over the surface of the slender cone even at a large distance from the nosetip. The results of the calculations are compared with experimental data.     

Supersonic flow past circular cones at large angles of attack

Flow past sharp-nosed circular cones is investigated for a broad range of freestream Mach numbers M>1 and cone half-angles _c at angles of attack from zero to the value at which conical flow breaks down. Several new results are obtained with regard to the position of the Ferri point, the shape of the local supersonic zones and internal shock wave, and the nonmonotonicity of the windward shock slope as a function of the angle of attack. The existence of flow regimes in which the radial velocity on the windward side is directed toward the apex of the cone is demonstrated. The investigation is carried out numerically with relaxation of the solution in a fictitious time coordinate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 6, pp. 79–84, November–December, 1973.     

Supersonic flow of a combustible gas mixture past a sphere

In recent years considerable interest has developed in the problems of steady-state supersonic flow of a mixture of gases about bodies with the formation of detonation waves and slow combustion fronts. This is due in particular to the problem of fuel combustion in a supersonic air stream.In [1] the problem of supersonic flow past a wedge with a detonation wave attached to the wedge apex is solved. This solution is based on using the equation of the detonation polar obtained in [2]-the analog of the shock polar for the case of an exothermic discontinuity. In [3] a solution is given of the problem of cone flow with an attached detonation wave, and [4] presents solutions of the problems of supersonic flow past the wedge and cone with the formation of attached adiabatic shocks with subsequent combustion of the mixture in slow combustion fronts. In the two latter studies two different solutions were also found for the problem of flow past a point ignition source, one solution with gas combustion in the detonation wave, the other with gas combustion in the slow combustion front following the adiabatic shock. These solutions describe two different asymptotic pictures of flow of a combustible gas mixture past bodies.In an experimental study of the motion of a sphere in a combustible gas mixture [5] it was found that the detonation wave formed ahead of the sphere splits at some distance from the body into an ordinary (adiabatic) shock and a slow combustion front. Arguments are presented in [6] which make it possible to explain this phenomenon and in certain cases to predict its occurrence.The present paper presents examples of the calculation of flow of a combustible gas mixture past a sphere with a detonation wave in the case when the wave does not split. In addition, the flow near the point at which the detonation wave splits is analyzed for the case when splitting occurs where the gas velocity behind the wave is greater than the speed of sound. This analysis shows that in the given case the flow calculation may be carried out without any particular difficulties. On the other hand, the calculation of the flow for the case when the point of splitting is located in the subsonic portion of the flow behind the wave (or in the region of influence of the subsonic portion of the flow) presents difficulties. This flow case is similar to the problem of the supersonic jet of finite width impacting on an obstacle.