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Improvement of the eN method for predicting hypersonic boundary-layer transition in case of modal exchange

存在模态转换时高超声速边界层转捩预测eN方法的改进

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A Correction to this article was published on 04 May 2023

A Correction to this article was published on 04 May 2023

This article has been updated

Abstract

In hypersonic boundary layers, a disturbance may first manifest itself as a first mode wave and subsequently evolves into a second mode wave. Under such condition, the rationality of the traditional eN method, which is based on linear stability theory with a local parallel assumption, contains uncertainties. This paper evaluates the efficacy of the eN method in the presence of modal exchange by investigating the linear amplification of disturbance in a Mach 6 flat plate boundary layer. It is shown that the eN method significantly underestimates the N factor when the modal exchange from the first mode to the second mode occurs. Furthermore, under certain circumstances, linear stability theory fails to track the second mode when following a first mode from upstream to downstream, resulting in an inaccurate prediction of the eN method. A new strategy of computing the disturbance amplification is proposed. Results show that by neglecting the disturbance decay between the two instability modes, the proposed strategy provides more accurate results than existing strategies. This investigation provides a theoretical foundation for developing automatic and robust transition prediction tools based on the eN method.

摘要

在高超声速边界层中, 扰动可能先以第一模态波的形式出现, 之后又演化为第二模态波. eN方法以局部平行的线性稳定性理论为基础, 在这种情况下, 其合理性是受到质疑的. 本文通过研究马赫数为6的平板边界层中不稳定波的线性演化来考察eN方法在存在模态转换时的有效性. 研究发现, 当存在第一模态到第二模态的模态转换时, eN方法会明显低估扰动波放大的N值. 此外, 在特定情况下,线性稳定性理论还存在从上游的第一模态出发, 无法捕捉到向下游的第二模态的问题, 从而使eN方法无法给出准确的预测结果. 为此,本文提出了一种新的计算扰动增长的策略. 结果表明, 忽略第一模态和第二模态不稳定波之间的衰减区, 该策略得到的结果比现有的计算扰动演化方法更准确. 本文的研究为发展基于eN方法的自动化、可靠的转捩预测工具提供了理论支撑.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 91952202). The authors thank Heng Zhou of Tianjin University for fruitful discussions and insights.

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Authors and Affiliations

  1. Laboratory of High-Speed Aerodynamics, Tianjin University, Tianjin, 300072, China

    Shasha Tao  (陶莎莎), Caihong Su  (苏彩虹) & Zhangfeng Huang  (黄章峰)

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  1. Shasha Tao  (陶莎莎)
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  2. Caihong Su  (苏彩虹)
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  3. Zhangfeng Huang  (黄章峰)
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Contributions

Author contributions Caihong Su designed the overarching research goals and aims, obtained financial support, and provided the programing. Zhangfeng Huang designed the methodology and created the model. Shasha Tao performed the program test and data organization and wrote the first draft of the manuscript. Caihong Su helped organize the manuscript. Shasha Tao and Caihong Su revised and edited the final version.

Corresponding author

Correspondence to Caihong Su  (苏彩虹).

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Tao, S., Su, C. & Huang, Z. Improvement of the eN method for predicting hypersonic boundary-layer transition in case of modal exchange. Acta Mech. Sin. 39, 122416 (2023). https://doi.org/10.1007/s10409-022-22416-x

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