Shock dynamics analysis of discontinuity on elliptical converging shock waves

SI Dongxian; LI Zhufei; JI Junze; ZHANG Enlai; YANG Jiming

doi:10.7527/S1000-6893.2021.26093

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2022 , Vol. 43 >Issue 12: 126093 - 126093

DOI: https://doi.org/10.7527/S1000-6893.2021.26093

Fluid Mechanics and Flight Mechanics

Shock dynamics analysis of discontinuity on elliptical converging shock waves

SI Dongxian ,
LI Zhufei ,
JI Junze ,
ZHANG Enlai ,
YANG Jiming

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Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China

Received date: 2021-07-12

Revised date: 2021-07-20

Online published: 2021-08-17

Supported by

National Natural Science Foundation of China (11872356, 11772325, 11621202)

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Abstract

Shock convergence phenomenon generated by an elliptical internal conical model is investigated to reveal the non-uniform effects during the shock convergence process. The three-dimensional steady shock in the elliptical internal conical model is converted into a two-dimensional unsteady elliptical converging shock using the hypersonic equivalence principle. A "shock front-disturbance tracking method" based on the two-dimensional geometrical shock dynamics theory is proposed, which can be used to calculate the positions and parameters of the moving shock and track the disturbances along the shock front simultaneously. With the help of this new method, the non-uniform characteristics of the two-dimensional moving shock during the convergence process is predicted rapidly, and the underlying mechanisms of the formation of discontinuity on the shock front is revealed. The results show that the strength of the elliptical shock whose initial strength is circumferentially uniform but initial curvature is non-uniform becomes increasingly non-uniform during the convergence process with the influence of "Shock-Compression" disturbances generated by the shock front itself. The shock front near the major axis strengthens faster due to its greater shock curvature. As the intensified non-uniformity of the shock strength induces the "Shock-Compression" disturbances to aggregate, discontinuities appear on the shock front. As a result, the originally continuous and smooth shock front is divided into two pairs of shock segments with different strengths. The larger the aspect ratio of the initial elliptical shock is, the faster the non-uniformity of the shock evolves, and the sooner the discontinuity appears. As illustrated in the analyses of elliptical converging shocks, the present "shock front-disturbance tracking method" provides a new approach to solve the non-uniform convergence of three-dimensional internal conical shocks.

Key words： hypersonic; shock dynamics; shock front-disturbance tracking method; non-uniform convergence; discontinuity

Cite this article

SI Dongxian , LI Zhufei , JI Junze , ZHANG Enlai , YANG Jiming . Shock dynamics analysis of discontinuity on elliptical converging shock waves[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(12) : 126093 -126093 . DOI: 10.7527/S1000-6893.2021.26093

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