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Supersonic air flow past a sphere with account for vibrational relaxation

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Abstract

A numerical solution is obtained for the problem of air flow past a sphere under conditions when nonequilibrium excitation of the vibrational degrees of freedom of the molecular components takes place in the shock layer. The problem is solved using the method of [1]. In calculating the relaxation rates account was taken of two processes: 1) transition of the molecular translational energy into vibrational energy during collision; 2) exchange of vibrational energy between the air components. Expressions for the relaxation rates were computed in [2]. The solution indicates that in the state far from equilibrium a relaxation layer is formed near the sphere surface. A comparison is made of the calculated values of the shock standoff with the experimental data of [3].

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Abbreviations

uVmax, vVmax :

velocity components normal and tangential to the sphere surface

Vmax :

maximal velocity

Pρ ∞V 2max :

pressure

ρρ ∞ :

density

TT∞ :

temperature

eviRT∞ :

vibrational energy of the i-th component per mole (i=−O2, N2)

ε=rγb−1:

shock wave shape

a f :

the frozen speed of sound

HRT∞/m:

gas total enthalpy

References

  1. V. P. Stulov and G. F. Telenin “Nonequilibrium supersonic air flow past a spheres”, Izv. AN SSSR, Mekhanika, no. 1, 1965.

  2. N. A. Generalov, S. A. Losev, and A. I. Osipov, “Relaxation of vibrational energy of air molecules behind a normal shock front”, DAN SSSR, vol. 159, no. 5, 1964.

  3. V. G. Maslennikov, I. G. Parilskii, S. I. Rozov, and A. M. Studenkov, “Experimental investigation of Shockwave detachment in real gases”, PMTF [Journal of Applied Mechanics and Technical Physics], no. 1, 1965.

  4. L. I. Turchak, “Exchange of vibrational energy between components of air behind a normal shock”, Izv. AN SSSR, Mekhanika zhidkosti i gaza [Fluid Dynamics], no. 4, 1966.

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Authors and Affiliations

  1. Institute of Mechanics, Moscow State University, USSR

    V. P. Stulov & L. I. Turchak

Authors
  1. V. P. Stulov
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  2. L. I. Turchak
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Stulov, V.P., Turchak, L.I. Supersonic air flow past a sphere with account for vibrational relaxation. Fluid Dyn 1, 1–3 (1966). https://doi.org/10.1007/BF01022140

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  • DOI: https://doi.org/10.1007/BF01022140

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