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 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 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 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.     

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.     

Supersonic nonuniform viscous gas flow past a blunt body with supply of gas from the surface

The problem of axisymmetric nonuniform gas flow past smooth blunt bodies at high Mach numbers is investigated. The approach stream is a parallel axisymmetric flow in which the velocity and temperature depend on the radial distance from the axis of symmetry and the pressure is constant. On the axis of symmetry the velocity has a minimum and the temperature a maximum. A characteristic feature of this flow is the existence of two qualitatively different flow regimes: separated [1-4], when in the shock layer on the front of the body there is a closed region of reverse-circulating flow, and unseparated [5, 6], when there is no such zone. In this study the case of unseparated flow is investigated. The equations of a thin viscous shock layer with generalized Rankine-Hugoniot conditions at the shock and boundary conditions on the body that take into account the supply of gas from the surface are solved numerically. The effect of the gas supply on the conditions of unseparated flow is analyzed in relation to the Reynolds number, and the critical values of the nonuniformity parameter a = a_k [5] are obtained. It is shown that at high Reynolds numbers the supply of gas from the surface has practically no effect on a_k, while at low and intermediate Reynolds numbers it reduces the region of unseparated flow. For high Reynolds numbers and an intense supply of gas from the surface an asymptotic solution of the problem is obtained for the neighborhood of the stagnation point. This is compared with the numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–129, July–August, 1988.The authors wish to thank G. A. Tirskii for useful discussions of the results.     

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.     

Supersonic flow over elongated blunt bodies with a cross section of elliptical shape

Up to now computational algorithms have been developed for, and systematic studies have been made of, supersonic flow over axisymmetric bodies both by a stream of ideal gas and by an air stream with equilibrium and nonequilibrium physicochemical transformations [1–6]. Conical flows around bodies having cross sections of different shapes and in a wide range of angles of attack have been studied in detail [7–11]. With the further development of numerical methods the next problem has become the analysis of supersonic flow over blunt bodies of large elongation having cross sections of sufficiently arbitrary shape. The effects of essentially three-dimensional flow (without planes of symmetry) over bodies whose cross sections represent ellipses with a constant or variable ratio of axes along the length of the body are discussed in the present paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 155–159, November–December, 1976.     

Investigation of three-dimensional boundary layers on blunt bodies with permeable surface

Numerical and approximate analytic methods are used to investigate three-dimensional laminar boundary layers on blunt bodies with permeable surface in a supersonic gas stream. In the first approximation of the integral method of successive approximation an analytic solution is obtained to the problem for an impermeable surface, small values of the blowing parameter, and arbitrary suction. For large parameters of the blowing (or suction), whose velocity vector in the general case is directed at a certain angle to the vector of the outer normal to the body, asymptotic expressions are derived for the components of the frictional stress and the heat flux. A numerical solution is obtained to the equations of the three-dimensional boundary layer in a wide range of variation of the blowing (or suction) parameter. The accuracy and region of applicability of the analytic solutions is estimated by comparison with the numerical solutions. On the basis of the solutions obtained in the present paper and the work of other authors an expression is proposed for calculating the heat fluxes to a perfectly catalytic surface of a body in a three-dimensional supersonic flow of dissociated or ionized air. The present paper continues earlier work of the authors [1, 2] on boundary layers in the neighborhood of a symmetry plane and on sweptback wings of infinite span.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 49–58, May–June, 1982.     

Numerical investigation of flow of a viscous reacting gas past blunt bodies

Numerical solution of the Navier—Stokes equations is used to estimate the limits of applicability of simplified models used to describe the laminar nonequillbrium flow of a viscous multicomponent reacting gas past blunt bodies moving at hypersonic velocity in air.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–23, September–October, 1982.     

Effect of angle of attack on supersonic flow past axisymmetric blunt bodies with surface injection

The effect of angles of attack in the interval 0 40° on the flow pattern and the aerodynamic characteristics of a body of power-law shape (equation of the generator in the cylindrical coordinate system r=zⁿ, n=0.125) is investigated for supersonic flow without injection and with intense subsonic localized injection from the surface. As a result of numerical calculations it is established that the use of Newton's theory for determining the coordinates of the gas stagnation point behind the shock in flow past an impermeable body of the shape in question leads to serious errors, and an expression for determining the location of this point is given. It is shown that for three-dimensional flow the flow pattern and the surface pressure distribution are sharply different from the case=0. It is established that on the parameter interval in question intense injection considerably reduces the aerodynamic drag without loss of static stability, which is important in connection with the solution of the problem of gas-stable aircraft control.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–101, September–October, 1987.     

Flow past blunt bodies with nose spikes and surface injection

Axisymmetric supersonic ideal-gas flow past a blunt body with a forward-projecting spike is numerically investigated with allowance for injection from the surface. The effect of the length and shape of the spike, the parameters of the injected gas and the position of the permeable zone on the flow pattern and drag is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–133, July–August, 1987.