Accuracy of asymptotic solutions for nonuniform supersonic flow past a blunt body

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 61–66, January–February, 1994.     

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.     

Calculation of supersonic viscid flow near stagnation line of a blunt body

A numerical study is made of supersonic flow of a viscous gas in the vicinity of the stagnation line of plane and axisymmetric blunt bodies (cylinder, sphere). As in [1–5], which consider the compressed layer of a viscous gas in the vicinity of the stagnation point, use is made of the locally self-similar approximation, which is used to transform the Navier-Stokes equations into a system of ordinary differential equations. In the present paper the solution is sought with the simplifications of [5] and with more general conditions, which makes it possible to study a broad class of flows. The proposed numerical algorithm permits obtaining the structure of the compressed layer near the stagnation line, including the shock wave and the boundary layer. The calculations made on a computer for different flow conditions are illustrated by graphs.The author wishes to thank G. I. Petrov, G. F. Telenin, and L. A., Chudov for their interest in the study and for their helpful discussions. discussions.     

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.     

Combustible mixture flow ahead of a blunt body

A solution is given in [1] for the problem of the supersonic flow of a combustible gas mixture past a sphere, using one of the simplest models of the combustion zone structure. The entire flow behind the shock wave in this model consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of combustion products-separated by the combustion front. Mixture passage through the front is accompanied by instantaneous combustion. The solution is given only for the subsonic and transonic regions.In the following the same problem is solved under the assumption that the reactions behind the combustion front proceed in equilibrium. The model used is that of a two-component mixture of the initial and combustion products with a single first-order chemical reaction taking place. This model is used to illustrate the effect of nonequilibrium on the flow pattern and the distribution of the functions in the shock layer. The solution may be used in the vicinity of the axis of symmetry for the case of combustible mixture flow past a blunt body of arbitrary shape.In conclusion the author wishes to thank G. G. Chernyi for his guidance in performing this study.     

Heat transfer at the nose of a blunt body in a rarefied supersonic flow of a nitrogen-hydrogen mixture

The temperature-recovery factor and specific heat flux have been measured at the nose of a spherically blunted body in a low-density supersonic stream of a nitrogen-hydrogen mixture. The experiments were carried out in the transition flow regime from continuous to free-molecular flow. The measurements show that the values of the recovery factor and heat flux in the mixture are larger than in the pure gases.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 88–91, November–December, 1973.The authors are grateful to I. F. Zavarzina and P. G. Itin for assistance.     

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.     

Magnetohydrodynamic interaction in hypersonic air flow past a blunt body

Hypersonic MHD air flow past a blunt body in the presence of an external magnetic field is considered. The MHD effect on the flow consists in a significant increase in the shock wave stand-off from the body surface and a significant reduction in the heat flux to the wall (up to 50%). It is shown that even in the presence of a strong Hall effect the intensity of the magnetohydrodynamic interaction in the plasma behind the shock wave remains at a high level commensurable with the ideal case of the absence of a Hall effect.     

Flow of a supersonic low-density jet of nitrogen and nitrogen-hydrogen mixture over a blunt body

This paper gives the results of electron-beam measurements of the rotational temperature of nitrogen and its concentration in front of a spherically blunt cylinder situated on the axis of a supersonic rarefied jet of nitrogen and nitrogen-hydrogen mixture.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 50–55, November–December, 1972.     

Effect of blowing on supersonic dust-laden gas flow round a blunt body

One of the main problems which arise in the design of high-speed aircraft is the protection of the streamline surfaces against the erosion effect of solid particles and drops occurring in the free stream. For this purpose it is possible to use the device of blowing cold gas. This leads to the formation of a boundary layer of high density in which the particles are decelerated [1]. The present study investigates the effectiveness of this method of erosion protection in the example of supersonic flow round a sphere.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–181, March–April, 1986.     

Mechanism of transverse structure formation in supersonic flow past a body

Direct numerical simulation within the framework of the Navier-Stokes equations is applied to study the mechanism of the generation of transverse structures (streamwise vortices) in the problem of supersonic M = 6 flow over a flat plate, when a shock wave is incident on it. The vortices formed at the lateral edges of the plate are shown to be the sources of streamwise streaky structures in the zone of separation of the boundary layer from the plate. Their interaction with the Kelvin-Helmholtz vortices in the region of incidence of the shock on the plate leads to the formation of mushroom-shaped structures (streamwise vortices) similar with the azimuthal Λ-structures in subsonic jets. The plate width effect on the formation and turbulization of the mushroom-shaped structures is considered.     

Asymptotic study of viscous compressible gas flow past a blunt body

Supersonic viscous gas flow past a blunt body is examined. A method is proposed which permits constructing the asymptotic expansion of any order in the small parameter , which characterizes the viscosity and thermal conductivity coefficients. The asymptotic solution is constructed, including terras of zero, first, and second orders of . Acomparison is made with results of other authors who have studied various particular aspects of the subject problem using the method of inner and outer expansions [1–3].     

On the transient regime in nonstationary supersonic flow past a body

The transient regime in gas flow past a stepwise accelerated body is analyzed by the method of singular perturbations at small Froude numbers. A marked effect of the initial conditions on the shock layer gas flow is demonstrated. The problem of flow past a wedge is solved in quadratures. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–121, January–February, 1997.     

Non-stationary effects in hypersonic nonuniform dusty-gas flow past a blunt body

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found. The project supported by the Russian Foundation for Basic Research (project No. 96-01-00313) and the National Natural Science Foundation of China (joint RFBR-NSFC grant No. 96-01-00017c)