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 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.     

Three-dimensional hypersonic rarefied gas flow round bodies of revolution

A proposed method of studying three-dimensional rarefied gas flow around a body of revolution is based on the numerical solution of model kinetic equations. By way of example, the problem is considered of hypersonic flow round an ellipsoid of revolution whose velocity vector forms an angle of ₀ with the axis of symmetry of the body and is located in the plane of symmetry. A study is made of the effect of the angle of attack, surface temperature and Knudsen number on the aerodynamic characteristics of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti 1 Gaza, No. 1, pp. 184–186, January–February, 1986.     

Estimates of nonequilibrium radiative heating of blunt bodies in a hypersonic flow of carbon dioxide gas

The solution to the problem of hypersonic nonequilibrium flow over cones with rounded noses [1, 2] is used to estimate the radiative heating of the surfaces of the bodies.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 158–160, November–December, 1979.     

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.     

Supersonic flow of a rarefied gas around a wire grid

The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a number of infinite parallel wires. Characteristic features of the shock disturbance formation of in the interaction of a supersonic flow with a permeable grid are revealed. Particular attention is paid to studying the influence of geometrical parameters of the wire target on the number of particles colliding with the surface of the wires.     

Hypersonic similarity in the flow of an imperfect gas around slender blunt bodies of complex shape

The hypersonic similarity laws for flow around slender blunt bodies [1–3] are generalized to bodies with nonsmooth lateral surface, in particular, those having corners (under the condition of unseparated supersonic flow). The similarity conditions are considered for a gas which is imperfect throughout the entire disturbed region.     

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.     

Asymptotic solutions of the thin viscous shock layer equations near the symmetry plane of blunt bodies in hypersonic rarefied gas flow

The hypersonic rarefied gas flow over blunt bodies near the symmetry plane is investigated for the regime transitional from continuum to free-molecular. Three rarefied gas flow regimes are considered depending on the relationship between the determining parameters of the problem. For all regimes, at small Reynolds numbers, asymptotic solutions of the thin viscous shock layer equations near the symmetry plane of blunt bodies are obtained in the form of simple analytical expressions for the heat transfer, skin friction and pressure coefficients as functions of the gas-dynamic parameters of the free-stream flow and the geometric parameters and temperature of the body. With decrease in the Reynolds number these coefficients approach their values in free-molecular flow (with the accommodation coefficient equal to unity). From comparison with the data calculated using the direct simulation Monte Carlo method, the accuracy and applicability limits of the analytical solution are estimated.