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Quantitative measure and visualization for local shock strength in two-dimensional flow

二维流动中当地激波强度的定量测量及可视化

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Abstract

The concept of local shock strength and a quantitative measure index str of local shock strength are proposed, derived from the oblique shock relation and the monotonic relationship between total pressure loss ratio and normal Mach number. Utilizing the high density gradient characteristic of shock waves and the oblique shock relation, a post-processing algorithm for two-dimensional flow field data is developed. The objective of the post-processing algorithm is to obtain specific shock wave location coordinates and calculate the corresponding str from flow filed data under the calibration of the oblique shock relation. Validation of this post-processing algorithm is conducted using a standard model example that can be solved analytically. Combining the concept of local shock strength with the post-processing algorithm, a local shock strength quantitative mapping approach is established for the first time. This approach enables a quantitative measure and visualization of local shock strength at distinct locations, represented by color mapping on the shock structures. The approach can be applied to post-processing numerical simulation data of two-dimensional flows. Applications to the intersection of two left-running oblique shock waves (straight shock waves), the bow shock in front of a cylinder (curved shock wave), and Mach reflection (mixed straight and curved shock waves) demonstrate the accuracy, and effectiveness of the mapping approach in investigating diverse shock wave phenomena. The quantitative mapping approach of str may be a valuable tool in the design of supersonic/hypersonic vehicles and the exploration of shock wave evolution.

摘要

本研究基于斜激波关系式和总压损失与法向马赫数的单调关系提出了当地激波强度的概念及其定量测量指标str. 为了实现从流场数据中获得具体的激波位置坐标并计算出对应的当地激波强度, 本研究基于激波的高密度梯度特性并利用斜激波关系式, 发展了一种二维流场数据的后处理算法, 并利用可以解析求解的标模算例验证了该后处理算法的准确性. 结合当地激波强度的概念和流场数据后处理算法, 本研究开创了当地激波强度的定量映射方法, 实现了全流场激波不同位置处当地激波强度的定量测量和可视化, 并通过超声速双楔绕流(斜激波)、超声速圆柱绕流(弯曲激波)和马赫反射算例(斜激波与弯曲激波)验证了其有效性和准确性. 当地激波强度的定量映射方法研究对探索复杂波系激波强度演变机制具有学术价值和应用前景.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12372233), the Fund of NPU-Duke China Seed Program (Grant No. 119003067), and the “111 Project” of China (Grant No. B17037-106).

Author information

Authors and Affiliations

  1. Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing, 100871, China

    Jiashuo Li  (李家硕)

  2. School of Aeronautics, NPU-Duke Aerodynamics and Aeroelasticity, Northwestern Polytechnical University, Xi’an, 710072, China

    Jiashuo Li  (李家硕) & Aiming Shi  (史爱明)

  3. National Key Laboratory of Aircraft Configuration Design, Xi’an, 710072, China

    Aiming Shi  (史爱明)

  4. Department of Mechanical Engineering and Materials Science, NPU-Duke Aerodynamics and Aeroelasticity, Duke University, Durham, 27708-0300, USA

    Earl H. Dowell

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  1. Jiashuo Li  (李家硕)
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  2. Aiming Shi  (史爱明)
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  3. Earl H. Dowell
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Contributions

Author contributions Jiashuo Li: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing–original draft, Writing–review & editing. Aiming Shi: Conceptualization, Data curation, Funding acquisition, Methodology, Project administration, Resources, Supervision, Validation, Writing–original draft, Writing–review & editing. Earl H. Dowell: Conceptualization, Methodology, Writing–original draft, Writing–review & editing.

Corresponding author

Correspondence to Aiming Shi  (史爱明).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Li, J., Shi, A. & Dowell, E.H. Quantitative measure and visualization for local shock strength in two-dimensional flow. Acta Mech. Sin. 41, 324255 (2025). https://doi.org/10.1007/s10409-024-24255-x

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