Hypersonic flow past a supersonic two-phase source

The interaction of a uniform hypersonic gas flow with a supersonic two-phase gas-particle source is considered. In the symmetry-axis neighborhood between the bow and termination shock waves, an approximate analytical solution for the carrier-phase parameters is found. On the basis of parametric numerical calculations, the behavior of the particle trajectories and the concentration distribution in the shock layers are studied for both continuum and free-molecule flow regimes around the particles. The appearance of regions with multiple intersections of the particle trajectories and the formation of "layer structures" in the particle concentration distributions (particle accumulation regions near the envelopes of the particle trajectories) are indicated. The dependence of the number of the high concentration layers on the governing parameters is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–147, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Foundation for Natural Sciences of China (joint RFBR-NFNS grant No.96-01-00017c).     

Calculation of the flow of an ideal fluid past a wing of finite thickness

The problem of irrotational flow past a wing of finite thickness and finite span can be reduced by Green's formula to the solution of a system of Fredholm equations of the second kind on the surface of the wing [1]. The wake vortex sheet is represented by a free vortex surface. Besides panel methods (see, for example, [2]) there are also methods of approximate solution of this problem based on a preliminary discretization of the solution along the span of the wing in which the two-dimensional integral equations are reduced to a system of one-dimensional integral equations [1], for which numerical methods of solution have already been developed [3–6]. At the same time, a discretization is also realized for the wake vortex sheet along the span of the wing. In the present paper, this idea of numerical solution of the problem of irrotational flow past a wing of finite span is realized on the basis of an approximation of the unknown functions which is piecewise linear along the span. The wake vortex sheet is represented by vortex filaments [7] in the nonlinear problem. In the linear problem, the sheet is represented both by vortex filaments and by a vortex surface. Examples are given of an aerodynamic calculation for sweptback wings of finite thickness with a constriction, and the results of the calculation are also compared with experimental results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 124–131, October–December, 1981.     

Calculation of spatial flow past an inclined flat plate with a detached shock wave

The results of a numerical analysis of a supersonic underexpanded jet impinging on an inclined flat plate are presented. The effects of the angle between the plate and the jet symmetry axis, the distance from the nozzle exit section, the exit Mach number, and the off-design conditions on the distribution of the gasdynamic parameters in the jet flowfield and on the plate surface are demonstrated. Specific features of the compressed layer and obstacle surface flows are revealed. The three-dimensional flow is simulated using the large particle method on the basis of the nonstationary Euler equations written in the cylindrical coordinate system. The calculated results are compared with experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–35, January–February, 1997.     

Viscous flow past an airfoil

Incompressible viscous flow past an airfoil at low Reynolds numbers is investigated on the basis of a numerical solution of the complete Navier-Stokes equations. Steady flow regimes, with and without separation, are obtained and, moreover, periodic regimes with the formation of a vortex trail in the wake. The frequency of vortex formation is determined by the linear dimension of the projection of the airfoil on the normal to the freestream velocity. The relation between the Strouhal and Reynolds numbers, determined from this linear dimension, depends only slightly on the angle of attack and shape of the airfoil and is similar to the experimental dependence for circular cylinders.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 29–36, July–August, 1986.In conclusion the authors wish to express their warm thanks to G. I. Petrov for his interest in their work and valuable discussion of their results, and to V. P. Shkadova for discussing the formulation of the problem and the method of solution and for her constant readiness to advise on the organization of the calculations.     

Calculation of viscous compressible gas flow past a corner

We consider the problem of calculating the parameters for supersonic viscous compressible gas flow past a corner (angle greater than ). The complete system of Navier-Stokes equations for the viscous compressible gas is solved in the small vicinity Q₁. (characteristic dimensionl~1/R) of the corner point. The conditions for smooth matching of the solution of the Navier-Stokes equations and the solution of the ideal gas or boundary layer equations are specified on the boundary of Q₁. All these solutions are a priori unknown, and the conditions for smooth matching reduce to certain differential equations on the boundary of Q₁. Here account is taken of the interaction of the flows near the wall surface and in the so-called outer region [1].We note that no a priori assumptions are made in Q₁ concerning the qualitative behavior of the solution, in contrast with other studies on viscous flow past a corner (for example, [2–4]).The Navier-Stokes system in Q₁ is solved numerically, using the difference scheme suggested in [5]. This scheme permits obtaining the steady-state solution by the asymptotic method for large Reynolds numbers R, and also has an approximation accuracy adequate to account for the effects of low viscosity and thermal conductivity.     

Calculation of inviscid radiating gas flow past a blunt body

During hypersonic gas flow past a blunt body with a velocity on the order of the escape velocity or more, the gas radiation in the disturbed region behind the shock wave becomes the primary mechanism for aerodynamic heating and has a significant effect on the distribution of the gasdynamic parameters in the shock layer. This problem has been considered from different points of view by many authors. A rather complete review of these studies is presented in [1–4].In earlier studies [5, 6] the approximation of bulk emission was used. In this approximation, in order to account for the effect of radiative heat transfer a term is added in the energy equation which is equivalent to the body efflux, whose magnitude depends on the local thermodynamic state of the gas. However, the use of this assumption to solve the problem of inviscid flow past a blunt body leads to a singularity at the body [7, 8]. To eliminate the singularity, account is taken of the radiation absorption in a narrow wall layer [7], or the concept of a viscous and heat-conductive shock layer is used [8]. A further refinement was obtained by Rumynskii, who considered radiation selectivity and studied the flow of a radiating and absorbing gas in the vicinity of the forward stagnation point of a blunt body.In the present paper we study the distribution of the gasdynamic parameters in the shock layer over the entire frontal surface of a blunt body in a hypersonic flow of a radiating and absorbing gas with account for radiation selectivity.     

Cavitation flow past an arbitrarily-shaped airfoil

The problem of two-dimensional inviscid incompressible flow past an arbitrarily-shaped airfoil in the presence of developed cavitation is studied in an accurate nonlinear formulation.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 86–90, September–October, 1995.     

Field-aligned flow of a conducting fluid past a source of magnetism

Summary A prescribed source of magnetism moves at constant speed through a viscous conducting incompressible fluid with an aligned uniform magnetic field. The velocity and magnetic fields induced at a distance from the source are calculated. The induced fields are also calculated for the case in which the applied field is absent. Although no special symmetry or alignment is assumed, the source is ideal in the sense that enclosures (wires or magnets) are infinitesimal in at least two dimensions. Dynamical interactions will occur in a viscous fluid and their effect in the far field is estimated.As a consequence of finite conductivity and viscosity, the usual wakes are present which trail or lead the source depending upon the sign of (1–A ²), where A is the ratio of the source speed to the Alfvén speed in the undisturbed fluid. Outside the wake the total perturbation magnetic field due to the source is the static field plus a monopole field, divided by (1–A ²).An estimate is also made of the rate at which energy is dissipated as a consequence of viscous interactions and ohmic heating throughout the fluid, outside the immediate vicinity of the source.Geo-Astrophysics Laboratory.Plasma Physics Laboratory.     

Simulation of the hypervelocity regime of flow past bodies in wind tunnels

The main features of the hypervelocity regime of flow past aircraft due to the influence of the real properties of an airstream and some criteria for simulating this regime in aerodynamic facilities of various types are considered. A comparative analysis reveals that there are definite advantages (from the point of view of reproducing the real flight conditions) of using facilities with the actual flow velocities, for example, wind tunnels with magnetogasdynamic acceleration of the gas. The development of rocket and space technology confronts experimental aerodynamics with the problem of reproducing more accurately the parameters of hypervelocity flow past bodies under laboratory conditions. The present paper considers the main requirements and some criteria for simulating the hypervelocity regime in aerodynamic facilities of various types.     

Calculation of supersonic equilibrium-dissociating air-xenon mixture flow past a blunt body

The flow of an equilibrium-reacting multicomponent three-element air-xenon mixture is numerically investigated. The effect of multicomponent diffusion on the convective heat transfer to the body surface is examined. The dependence of the convective heat transfer to the body surface and the total shock-layer spectral radiation flux P_m on the xenon concentration is obtained. A comparison of the calculated data for P_m and the experimental data of [2] gives good agreement. A simple approximation for the convective heat flux at the stagnation point as a function of xenon concentration is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 156–164, July–August, 1991.In conclusion the authors wish to thank I. A. Sokolova for supplying data on the resistance coefficients of the various mixtures and S. A. Yunitskii for discussing the numerical method.     

Transonic flow past an airfoil with mini-flaps

The effect of mini-flaps located on either the lower or upper side of an airfoil near its trailing edge on the flow around the trailing edge and the global flow past the airfoil is numerically investigated. The flow pattern near the trailing edge is compared with that on which the Chaplygin-Joukowski hypothesis is based. The mini-flap effect on the aerodynamic characteristics of the airfoil is studied.     

Calculation of transverse flow of a stream of rarefied gas past a plate

We give the results of a calculation by the Monte Carlo method of the coefficient of resistance and the field of flow past a plate placed perpendicular to a stream of rarefied gas at Mach numbers M = 2–20 and Reynolds numbers Re₀27. The calculations were carried out for two forms of the law governing the variation of the coefficient of viscosity as a function of temperature (T, T). The results are compared with available calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1976.