椭圆内聚激波面间断化过程的激波动力学分析

司东现; 李祝飞; 姬隽泽; 张恩来; 杨基明

doi:10.7527/S1000-6893.2021.26093

航空学报 >

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

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

流体力学与飞行力学

椭圆内聚激波面间断化过程的激波动力学分析

司东现 ,
李祝飞 ,
姬隽泽 ,
张恩来 ,
杨基明

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中国科学技术大学近代力学系, 合肥 230027

收稿日期: 2021-07-12

修回日期: 2021-07-20

网络出版日期: 2021-08-17

基金资助

国家自然科学基金（11872356，11772325，11621202）

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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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摘要

针对椭圆内锥几何约束下激波的非均匀汇聚问题，利用高超声速等价原理，将三维定常椭圆内锥激波转化为二维非定常椭圆内收缩运动激波。根据激波动力学原理，发展出一种既能得到非定常激波面演变过程及参数分布，又能沿着激波面追踪扰动传播过程的"波面-扰动追踪法"。该方法不仅具有快速预测激波非均匀汇聚及其演变过程的特点，而且有助于揭示激波面从连续弯曲演变出间断的内在机理。研究表明：初始沿周向强度均匀，而几何形状偏离轴对称的椭圆内聚激波受到自身产生的非均匀"Shock-Compression"扰动，在向中心汇聚的过程中，激波强度非均匀性出现且不断加剧。由于长轴附近的激波面曲率大，激波强度增长得更快。而激波强度的非均匀性会导致扰动的聚集，使得原本连续光滑的激波面出现间断，进而将初始长、短轴附近的激波面分割为强、弱两对激波段。增大长短轴比，椭圆激波的非均匀性演化更快，激波面更早地出现间断。利用"波面-扰动追踪法"对椭圆激波汇聚过程进行分析，为解决三维定常内锥激波的非均匀汇聚问题提供了新的途径。

关键词： 高超声速; 激波动力学; 波面-扰动追踪法; 非均匀汇聚; 间断化

本文引用格式

司东现 , 李祝飞 , 姬隽泽 , 张恩来 , 杨基明 . 椭圆内聚激波面间断化过程的激波动力学分析[J]. 航空学报, 2022 , 43(12) : 126093 -126093 . DOI: 10.7527/S1000-6893.2021.26093

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

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