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Notes on the hypersonic boundary layer transition


A brief discussion is given in this note to clarify the transition path of the hypersonic boundary layer. The first mode plays an important role in the hypersonic boundary layer transition and should not be ignored. The second mode may enhance the boundary layer transition, but it is not the decisive factor affecting the transition.

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We note a recent publication by Zhao et al. [1] in Advances in Aerodynamics. The citation of our work (Reference 5 in the article by Zhao et al. [1]) is stated as “The first mode is dominant at low Mach numbers, but as the Mach number increases, the Mack second mode leads to the transition”. We feel the need to clarify our views and have a benifical discussion in the future. In fact, the research group at Peking University believes that the first mode plays a dominant role in the boundary layer transition at both low and high Mach numbers [2, 3].

The Mack second mode belongs to the family of trapped acoustic waves, propagating between the relative sonic line and the wall [4]. At high Mach numbers, the second mode grows rapidly due to the existence of a relatively supersonic region within the boundary layer. The research group at Peking University identified that the first mode leads to the transition directly in the hypersonic boundary layer, and the second mode decays before transition, although it obtains a high amplitude. The boundary layer transition is closely related to the first mode, which has also been observed in previous experiments [5, 6] and numerical simulations [7].

Transition refers to the process in which the flow changes from regular laminar flow to disorderly turbulent flow. A notable feature of this process is the significant growth of nonlinear disturbances, and the flow becomes three-dimensional. In the hypersonic wind tunnel experiments, the research group at Peking University showed that the second mode grows, saturates and decays before the transition, while the first mode keeps growing in the hypersonic boundary layer [8, 9]. Theoretical results show that the rapid growth of the low-frequency mode is due to the rapid growth of linear terms from the meanflow, rather than being caused by the second mode directly. The second mode only enhances the ability of low-frequency modes to obtain energy from the meanflow by changing their perturbation profile [10]. Further analysis showed that the first mode is related to the viscous force and inertial force and the shear of the fluid; the second mode in the hypersonic boundary layer is related to the compression and expansion of the fluid [11, 12]. It was shown that heat generation within the hypersonic boundary layer is comprised of dilatation and shear processes. Dilatation heating, due to pressure, dominates the early transitional high-temperature region. Shear-induced heating is the dominant process creating the latter hightemperature region, where the transition is almost complete [13].

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  1. Zhao R, Liu X, Wen CY, Wang XY (2022) Broadband design of acoustic metasurfaces for the stabilization of a Mach 4 boundary layer flow. Adv Aerodyn 4:15

    Article  Google Scholar 

  2. Lee CB, Jiang XY (2019) Flow structures in transitional and turbulent boundary layers. Phys Fluids 31:111301

    Article  Google Scholar 

  3. Lee CB, Chen SY (2019) Recent progress in the study of transition in the hypersonic boundary layer. Natl Sci Rev 6(1):155–170

    Article  Google Scholar 

  4. Fedorov A (2011) Transition and stability of high-speed boundary layers. Annu Rev Fluid Mech 43:79–95

    MATH  Google Scholar 

  5. Stetson K, Thompson E, Donaldson J, Siler L (1983) Laminar boundary layer stability experiments on a cone at Mach 8. I - sharp cone. AIAA paper 1983–1761

  6. Bountin DA, Sidorenko AA, Shiplyuk AN (2001) Development of natural disturbances in a hypersonic boundary layer on a sharp cone. J Appl Mech Tech Phys 42:57–62

    Article  Google Scholar 

  7. Huang ZF, Cao W, Zhou H (2005) The mechanism of breakdown in laminar-turbulent transition of a supersonic boundary layer on a flat plate-temporal mode. Sci China Ser G Phys Ast 48:614–625

    Article  Google Scholar 

  8. Zhang CH, Tang Q, Lee CB (2013) Hypersonic boundary-layer transition on a flared cone. Acta Mech Sinica 29:48–54

    Article  Google Scholar 

  9. Zhu YD, Zhang CH, Chen X, Yuan HJ, Wu JZ, Chen SY, Lee CB, Gad-el-Hak M (2016) Transition in hypersonic boundary layers: role of dilatational waves. AIAA J 54:3039–3049

    Article  Google Scholar 

  10. Chen X, Zhu YD, Lee CB (2017) Interactions between second mode and low-frequency waves in a hypersonic boundary layer. J Fluid Mech 820:693–735

    MathSciNet  Article  Google Scholar 

  11. Zhu YD, Chen X, Wu JZ, Chen SY, Lee CB, Gad-el-Hak M (2018) Aerodynamic heating in transitional hypersonic boundary layers: role of second-mode instability. Phys Fluids 30:011701

    Article  Google Scholar 

  12. Zhu YD, Lee CB, Chen X, Wu JZ, Chen SY, Gad-el-Hak M (2018) Newly identified principle for aerodynamic heating in hypersonic flows. J Fluid Mech 855:152–180

  13. Smith CR (2021) Aerodynamic heating in hypersonic flows. Physics Today 74:66–67

    Article  Google Scholar 

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This work was supported by the National Natural Science Foundation of China (grant nos. 109103010062, 10921202, 11372009, 11602005 and 11632002) and the National Key Project GJXM92579.

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Wenkai Zhu contributes all the contents in this paper. The author read and approved the final manuscript.

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Correspondence to Wenkai Zhu.

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Zhu, W. Notes on the hypersonic boundary layer transition. Adv. Aerodyn. 4, 23 (2022).

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  • Boundary layer
  • Hypersonic
  • Transition