Supersonic flow past blunt bodies screened by a permeable surface

A study is made of a steady flow of supersonic gas past the front part of blunt bodies with allowance for the screening effect of a thin perforated surface, whose presence is simulated by the introduction of a supplementary hydrodynamic discontinuity (an active surface [1, 2]).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 139–144, March–April, 1986.     

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.     

Numerical investigation of the structure of nonequilibrium three-dimensional hypersonic flow past blunt bodies

Three-dimensional dissociating air flow past blunt bodies is investigated within the framework of the parabolized Navier-Stokes equations in the thin layer approximation. Multicomponent diffusion, barodiffusion and homogeneous chemical reactions, including dissociation-recombination and exchange reactions, are taken into account. The boundary conditions are assigned in the free stream and at the surface of the body with allowance for heterogeneous catalytic reactions and slip effects. The problem of flow at zero angle of attack past blunt bodies possessing two planes of symmetry is investigated numerically for flow patterns varying from smeared layer structure to almost ideal flow (Re=50-10⁵). The flow conditions corresponded to the motion of a body with lift along a re-entry trajectory [1]. The contribution of the chemical reactions in the shock wave as compared to the diffusion flux at the edge of the shock wave was estimated. The edge of the shock wave is assumed to correspond to the point at which the density profile has the greatest slope. The influence of slip effects and barodiffusion on the flow characteristics is demonstrated. The results of the calculations are compared with calculations based on the thin viscous shock layer model [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 143–150, September–October, 1987.The author wishes to express his thanks to G. A. Tirskii and V. V. Lunev for useful discussions and valuable advice.     

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 nonequilibrium flow past segmental bodies of a mixture simulating the atmosphere of venus

Calculations of the flow of the mixture 0.94 CO₂+0.05 N₂+0.01 Ar past the forward portion of segmentai bodies are presented. The temperature, pressure, and concentration distributions are given as a function of the pressure ahead of the shock wave and the body velocity. Analysis of the concentration distribution makes it possible to formulate a simplified model for the chemical reaction kinetics in the shock layer that reflects the primary flow characteristics. The density distributions are used to verify the validity of the binary similarity law throughout the shock layer region calculated.The flow of a CO₂+N₂+Ar gas mixture of varying composition past a spherical nose was examined in [1]. The basic flow properties in the shock layer were studied, particularly flow dependence on the free-stream CO₂ and N₂ concentration.New revised data on the properties of the Venusian atmosphere have appeared in the literature [2, 3] One is the dominant CO₂ concentration. This finding permits more rigorous formulation of the problem of blunt body motion in the Venus atmosphere, and attention can be concentrated on revising the CO₂ thermodynamic and kinetic properties that must be used in the calculation.The problem of supersonic nonequilibrium flow past a blunt body is solved within the framework of the problem formulation of [4].Notation V body velocity - shock wave standoff - universal gas constant - ratio of frozen specific heats - hRt/m enthalpy per unit mass undisturbed stream P pressure - density - T temperature - m molecular weight - c_p specific heat at constant pressure - (X) concentration of component X (number of particles in unit mass) - R body radius of curvature at the stagnation point - _j rate of j-th chemical reaction shock layer P V ² pressure - density - TT temperature - mm molecular weight Translated from Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, No. 2, pp. 67–72, March–April, 1970.The author thanks V. P. Stulov for guidance in this study.     

Hypersonic flow of nonequilibrium air over blunt bodies

A numerical method is described for computing nonequilibrium three-dimensional supersonic flow of a gas in the shock layer over the forward surface of blunt bodies with discontinuities of shape. The basic idea is to divide the original system of differential equations into two subsystems, which are solved in succession: first for the gasdynamic variables, the velocity components and the pressure, and then for the relaxation parameters and the enthalpy. To calculate the velocity components and the pressure we use the iterative marching method [1, 2] in the form given in [3]. The relaxation equations and the enthalpy equation are integrated numerically along the stream lines. A discussion is given of the effect of nonequilibrium of physical and chemical reactions on the distribution of parameters in the inviscid shock layer and on the aerodynamic coefficients of blunt bodies in hypersonic air flow. The unsteady aerodynamic coefficients are calculated by the curved body method [4]. The computational algorithm takes the form of a program in “ALGOL-60” for the BéSM-6 computer.     

Supersonic flow of dusty gas over blunt bodies

The results are given of a numerical investigation of the flow of dusty gas over the complete front surface of a sphere. The flow conditions are varied over a wide range in which the state of the gas suspension in the shock layer changes from a frozen to an equilibrium state. The phenomenological approach [5] is used to derive the system of equations describing the behavior of the two-phase medium. The system of conservation equations for the gas—solid-particle mixture is closed by means of relations that generalize the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 73–77, May–June, 1982.     

Computation of unsteady flow past blunt bodies

In accordance with the recent experimental research for flow visualization,theunsteady behavior of the starting period is investigated numerically for flow past bluntbodies.Finite difference methods are employed to solve the unsteady two-dimensionalincompressible Navier-Stokes equations.A short discussion is presented of explicit,implicit and ADI methods.Finally,the explicit and ADI schemes are used to study the flowfield in the starting period for flow past mountain-shaped and rectangular bodies.     

Hypersonic flow past ducted blunt bodies of revolution

Chernyi [1, 2] has examined the problem of hypersonic flow past a ducted cone with sharp leading edge. In the following we present an analysis of the characteristic features of this problem in the case of a blunt leading edge. We use hypersonic theory for flow past slender bodies with nose blunting of relatively small dimensions [1, 3, 4], based on replacing the nose by a concentrated force and use of the nonsteady analogy. It has been shown in [4, 5] that within the framework of this theory the effect of the violation of the law of plane sections and also the effect of the chemical and physical transformations of the gas in the high-entropy layer is qualitatively equivalent to a change in the drag coefficient of the nose. This approach makes it possible to establish useful similarity laws. The development of these ideas in the direction of the study of the flow structure behind the bow shock wave and analysis of the parameters defining this structure is given in [6–8] in which, in particular, the role of the entropy distribution with respect to the streamlines in the transitional section between the nose and the side surface was clarified and the important practical empirical result was established that this distribution is universal for noses of any form for given flow conditions. In the following these results are extended to blunt bodies of revolution with a duct in the nose. We examine the flow region which is external to the duct under the assumption that the external flow regime corresponds to maximum flow rate through the duct. A characteristic feature of the problem is associated with the additional characteristic linear dimension r₀, which determines the gas mass lost through the duct.     

Influence of nonequilibrium radiation on rarefied gas flow around blunt bodies

The hypersonic nonequilibrium rarefied gas flow is investigated in the neighborhood of the stagnation streamline ahead of a blunt body by taking into account nonequilibrium radiation due to electron excitation for air and carbon dioxide. The analysis is on the basis of a numerical solution of the Navier—Stokes equations simplified under the assumption of local self-similarity of the flow with the Shockwave structure taken into account. It is shown that at low densities, when the shock wave and shock layer thicknesses are of the same order of magnitudes, the two-layer Cheng model becomes inapplicable in the presence of radiation. In this case, the governing process is diffusion of the electronically excited molecules from the shock layer into the forward part of the shock front. The mechanism of the formation of a second luminous plateau on the diagram of the nonequilibrium radiation intensity density is discussed. The combined influence of the limit in collisions and the diffusion transport processes on the intensity of molecular band radiation is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–87, November–December, 1974.The author is grateful to V. V. Lunev for discussion and remarks during performance of the research.     

Supersonic axisymmetric flow past a blunt cone executing longitudinal low-frequency oscillations

The aerodynamic parameters of an oscillating cone in unsteady axisymmetric supersonic flow are investigated on the basis of the inviscid perfect gas model both in the absence and in the presence of strong air injection from its flat end into the shock layer.     

Numerical investigation of supersonic flow past blunt bodies with protruding spikes

A procedure for the calculation of a supersonic flow of ideal gas near axisymmetric blunt bodies with protruding spikes is developed. The flow past a frustum of a cone with a protruding spherically blunt cylindrical spike as a dependence on the ratio K of the spike length1 to the diameter D of the flat end of the body and the Mach number M of the oncoming flow is studied. Several steady flow regimes are obtained, including the formation of circulation zones and internal shock waves in the shock layer. It is shown that mounting a spike in front of the frustum of a cone can lead to a 40–50% reduction in its drag. A full investigation of the variation of the drag coefficient as a dependence on K is carried out for M = 3.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 119–127, May–June, 1986.The authors express their gratitude to V. A. Levin for the formulation of the problem and his constant attention to the work.