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An analytic solution on hypersonic flow over an arbitrary slender body with near power-law profile

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Abstract

On the basis of a self-similar solution as well as of the assumption of the “Transverse Motion” a general linear theory on hypersonic flow over a general slender body is set up in this paper. By means of this theory, the problem concerned can be put into a universal system of O.D.Eqs. which can be integrated numerically in advance.

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Abbreviations

r, 0, t :

polar coordinates, time

v τ,v θ, ρ,p :

radial and circumferential velocity component, density, pressure

n ε :

index and coefficient of a piston with power-law dialation

λ :

variable of self-similar motion (λ=λ, at piston. λ=1 at shock wave) shock wave velocity of self-similar motion

f, g, h :

non-dimensional velocity. density and pressure of the self-similar motion

ϕ1ϕ1 :

perturbations of the motion of the piston and the shock wave

n θ :

circumferential project of the unit normal vecter of the shock wave

ΔD :

perturbation velocity of the shock wave

f 1 c 1,g 1,h 1 :

non-dimensional perturbations of radial and circumferential velocity, density and pressure

F(λ),E(λ),G(λ),H(λ):

pertubation functions of the seperation of variables

m, β :

indexes of the separation of variables

v :

adiabatic index of the gas

Sub-index “2”:

shock wave parameters of the self-similar motion

Super-index “*”:

updating parameters in the entropy layer

References

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  7. Sychev, V.V., On the theory of hypersonic gas flow with a power-law shock wave, PMM Jour. Appl. Math. and Mech.24, 3 (1960). (in Russian)

  8. Zhou Guang-yuan, Supersonic flow over an arbitrary cone which is wearly normal. (to be published)

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Authors and Affiliations

  1. Dept. of Mechanics, Peking Univ., Beijing

    Chen Yao-song & Chen Yong-ze

Authors
  1. Chen Yao-song
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  2. Chen Yong-ze
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Communicated by Tsai Shu-tang

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Yao-song, C., Yong-ze, C. An analytic solution on hypersonic flow over an arbitrary slender body with near power-law profile. Appl Math Mech 10, 1063–1080 (1989). https://doi.org/10.1007/BF02014553

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  • DOI: https://doi.org/10.1007/BF02014553

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