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Second-order curved shock theory

Second-order curved shock theory
Second-order curved shock theory
Second-order curved shock theory is developed and applied to planar and axisymmetric curved shock flowfields. 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 flowfields 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 flowfield 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.
gas dynamics, high-speed flow, shock waves
0022-1120
Shi, Chongguang
965178d8-b039-46e0-abe6-29ea2080682f
Han, Weiqiang
95212bd8-aab7-431a-b9e2-53bfafa82e6b
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Zhu, Chengxiang
844b7998-fb6a-4b7c-a4d1-8ad78ac3ed8e
You, Yancheng
e6ecac38-5fd5-4767-9e6c-f7a1b811c59f
Shi, Chongguang
965178d8-b039-46e0-abe6-29ea2080682f
Han, Weiqiang
95212bd8-aab7-431a-b9e2-53bfafa82e6b
Deiterding, Ralf
ce02244b-6651-47e3-8325-2c0a0c9c6314
Zhu, Chengxiang
844b7998-fb6a-4b7c-a4d1-8ad78ac3ed8e
You, Yancheng
e6ecac38-5fd5-4767-9e6c-f7a1b811c59f

Shi, Chongguang, Han, Weiqiang, Deiterding, Ralf, Zhu, Chengxiang and You, Yancheng (2020) Second-order curved shock theory. Journal of Fluid Mechanics, 891, [A21]. (doi:10.1017/jfm.2020.158).

Record type: Article

Abstract

Second-order curved shock theory is developed and applied to planar and axisymmetric curved shock flowfields. 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 flowfields 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 flowfield 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.

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jfm-0520-Shi - Accepted Manuscript
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Accepted/In Press date: 23 February 2020
e-pub ahead of print date: 27 March 2020
Published date: 25 May 2020
Keywords: gas dynamics, high-speed flow, shock waves

Identifiers

Local EPrints ID: 439360
URI: http://eprints.soton.ac.uk/id/eprint/439360
ISSN: 0022-1120
PURE UUID: cdeff095-2ada-48b9-b386-76e68525e0c5
ORCID for Ralf Deiterding: ORCID iD orcid.org/0000-0003-4776-8183

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Date deposited: 17 Apr 2020 16:30
Last modified: 28 Apr 2022 05:13

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Contributors

Author: Chongguang Shi
Author: Weiqiang Han
Author: Ralf Deiterding ORCID iD
Author: Chengxiang Zhu
Author: Yancheng You

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