Hypersonic Limit for Steady Compressible Euler Flows Passing Straight Cones

Hypersonic Limit for Steady Compressible Euler Flows Passing Straight Cones

Year:    2024

Author:    Qianfeng Li, Aifang Qu, Xueying Su, Hairong Yuan

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 2 : pp. 136–167

Abstract

We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the measures associated with the weak entropy solution containing an attached shock ahead of the cone converge vaguely to the measures associated with a Radon measure solution to the conical hypersonic-limit flow. This justifies the Newtonian sine-squared pressure law for cones in hypersonic aerodynamics. For Chaplygin gas, assuming that the Mach number of the incoming flow is less than a finite critical value, we demonstrate that the vertex angle of the leading shock is independent of the conical body’s vertex angle and is totally determined by the incoming flow’s Mach number. If the Mach number exceeds the critical value, we explicitly construct a Radon measure solution with a concentration boundary layer.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmaa.2024-0008

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 2 : pp. 136–167

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Compressible Euler equations shock wave conical flow hypersonic limit Radon measure solution.

Author Details

Qianfeng Li

Aifang Qu

Xueying Su

Hairong Yuan