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Second-order curved shock theory

Published online by Cambridge University Press:  27 March 2020

Chongguang Shi Open the ORCID record for Chongguang Shi [Opens in a new window] ,
Weiqiang Han ,
Ralf Deiterding Open the ORCID record for Ralf Deiterding [Opens in a new window] ,
Chengxiang Zhu Open the ORCID record for Chengxiang Zhu [Opens in a new window]  and
Yancheng You Open the ORCID record for Yancheng You [Opens in a new window]
Chongguang Shi
Affiliation:
School of Aerospace Engineering, Xiamen University, Xiamen, Fujian, 361005, China
Weiqiang Han
Affiliation:
School of Aerospace Engineering, Xiamen University, Xiamen, Fujian, 361005, China
Ralf Deiterding
Affiliation:
School of Engineering, University of Southampton, SouthamptonSO16 7QF, UK
Chengxiang Zhu
Affiliation:
School of Aerospace Engineering, Xiamen University, Xiamen, Fujian, 361005, China
Yancheng You*
Affiliation:
School of Aerospace Engineering, Xiamen University, Xiamen, Fujian, 361005, China
*
†Email address for correspondence: yancheng.you@xmu.edu.cn
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Abstract

Second-order curved shock theory is developed and applied to planar and axisymmetric curved shock flow fields. Explicit equations are given in an influence coefficient format, relating the second-order gradients of pre-shock and post-shock flow parameters to shock curvature gradients. Two types of applications are demonstrated. First, the post-shock flow fields behind known curved shocks are solved using the second-order curved shock equations. Compared with the first-order curved shock equations, the second-order equations give better agreement with solutions obtained using the method of characteristics. Second, the second-order theory is applied to capture the curved shock shape with limited flow field information. In terms of the residual sum of squares of the curved shock, the second-order curved shock equations give a value one order of magnitude better than those given by the Rankine–Hugoniot equations and the first-order equations. This improved accuracy makes the second-order theory a good candidate for solving shock capture problems in computational fluid dynamics algorithms.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Shock waves Compressible Flows: Gas dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A21
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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