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Three-dimensional supersonic flow past blunt bodies with contour discontinuities, with account for equilibrium and frozen state of the gas in the shock layer

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Abstract

An algorithm is devised for calculating by the finite difference method the supersonic flow region for three-dimensional steady-state flow of a viscous gas past a blunted body with many contour discontinuities. The state of this gas at high hypersonic flight speeds can be characterized by equilibrium or frozen physicochemical processes.

Generally speaking, any arbitrary number and sequence of either compression or expansion discontinuities is permitted. The computational scheme adopted provides identification of the vortex layers, regions with different equations of state, and so on.

We use a flow model that is either frozen throughout the entire shock layer or only in the portion of the layer adjacent to the body surface. The pressure at certain points on the surface of spherically blunted cones with half-angles θ⪝10° may differ by a factor of 2 or more in equilibrium and frozen flows.

Example calculations are presented, and the results are analyzed.

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Abbreviations

R:

spherical nose radius

xR,ϕ, and rR:

coordinates of a space point in the body cylindrical coordinate system (x is measured along the body axis from the plane where the nose joins,ϕ is measured counterclockwise from the upwind direction of the plane of the angle of attackα)

uU∞, vU∞, wU∞ :

projections of the velocity vector V on the x,ϕ, and r axes, respectively

n:

the unit vector of the inward normal to the surface r(x,ϕ)

pρ ∞U∞ 2 :

pressure

cU∞ :

local speed of sound

iU∞ 2 :

enthalpy

s:

entropy (or entropy function)

ρρ ∞ :

density

γ:

adiabatic exponent for perfect gas

∞:

quantities relating to the uniform approaching stream

b:

quantities at the body surface

s:

quantities at the shock wave

f :

quantities on a surface between the body and the shock wave.

Literature cited

  1. K. I. Babenko and G. P. Voskresenskii, “Numerical calculation of three-dimensional supersonic gas flow past bodies”, Zh. vychislit. matem. i matem. fiz., vol. 1, no. 6 (1961).

  2. O. M. Belotserkovskii, Calculation of Flow past Axisymmetric Bodies with Detached Shock Wave: Computational Formulas and Flow-Field Tables [in Russian], Moscow (1961).

  3. S. M. Gilinskii, G. F. Telenin, and G. P. Tinyakov, “Method for calculating supersonic flow over blunted bodies with detached shock wave”, Izv. AN SSSR, Mekhanika i mashinostroenie, no. 4 (1964).

  4. K. I. Babenko and V. V. Rusanov, “Difference methods for solving three-dimensional gas-dynamic problems”, collection: Proceedings of 2nd Ail-Union Congress on Theoretical and Applied Mechanics, 1964; summary report [in Russian], no. 2, Nauka, Moscow (1965).

  5. V. V. Lunev, K. M. Magomedov, and V. G. Pavlov, Hypersonic Flow past Blunted Cones with Account for Equilibrium Physicochemical Transformations (Table) [in Russian], Moscow (1968).

  6. S. G. Sinchenko, “Approximation of the thermodynamic functions of air”, Zh. vychislit, matem. i matem. fiz., vol. 8, no. 4 (1968).

  7. A. S. Predvoditelev, E. V. Stupochenko, and A. S. Pleshanov, Tables of the Thermodynamic Functions of Air: For Temperatures from 200 to 6000° K and Pressures from 0.00001 to 100 atm [in Russian], VTs AN SSSR, Moscow (1962, 1963).

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  8. Yu. N. D'yakonov, V. B. Minostsev, G. F. Telenin, and G. P. Tinyakov, “Supersonic three-dimensional flow past blunted bodies”, in: Problems of Continuum Hydrodynamics and Mechanics [in Russian] (1968).

  9. R. Vaglio-Laurin and M. H. Bloom, “Chemical Effects in External Hypersonic Flows”, in: Hypersonic-Flow Research [in Russian] (1964).

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Authors and Affiliations

  1. Moscow

    A. V. Antonets

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  1. A. V. Antonets
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Additional information

Translated from Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, No. 2, pp. 178–181, March–April, 1970.

In conclusion, the author thanks V. V. Lunev for posing the problem and for his scientific guidance and also I. N. Murzinov, K. M. Magomedov, V. G. Pavlov, V. G. Voronkin, S. G. Sinchenko, and others for their assistance.

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Antonets, A.V. Three-dimensional supersonic flow past blunt bodies with contour discontinuities, with account for equilibrium and frozen state of the gas in the shock layer. Fluid Dyn 5, 324–328 (1970). https://doi.org/10.1007/BF01080252

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  • DOI: https://doi.org/10.1007/BF01080252

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