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Shock interactions on a V-shaped cowl lip at supersonic and hypersonic speeds

Published online by Cambridge University Press:  30 July 2025

Jun Wang ,
Zhongchen Liu  and
Zhufei Li Open the ORCID record for Zhufei Li [Opens in a new window]
Jun Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhongchen Liu
Affiliation:
AVIC Aerodynamics Research Institute, Shenyang, 110034, PR China
Zhufei Li*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
Corresponding author: Zhufei Li, lizhufei@ustc.edu.cn
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Abstract

Shock interactions on a V-shaped blunt leading edge (VBLE) that are commonly encountered at the cowl lip of an inward-turning inlet are investigated at freestream Mach numbers ($ M_\infty$) 3–6. The swept blunt leading edges of the VBLE generate a pair of detached shocks with varying shapes due to the changes in $ M_\infty$ and $L/r$ (i.e. the ratio of the leading-edge length $L$ to the leading-edge blunt radius $r$), which causes intriguing shock interactions at the crotch of the VBLE. Three subtypes of regular reflection (RR) and a Mach reflection (MR) are produced successively with increasing $ M_\infty$ for a given $L/r$, which appear in the opposite order to those with increasing $L/r$ for a given $ M_\infty$. These shock interactions identified in numerical simulations are verified in supersonic and hypersonic wind tunnel experiments. It is demonstrated that the relative position of the shocks is crucial in determining the transitions of shock interactions by varying either $L/r$ or $ M_\infty$. Transition criteria between subtypes of RR and from RR to MR are theoretically established in the parameter space $(M_\infty,L/r)$ by analysing the shock structures, showing good agreement with the numerical and experimental results. Interactions between either immature or fully developed detached shocks are embedded in these criteria. Specifically, the transition criteria asymptotically approach the corresponding critical $ M_\infty$ when $L/r$ is sufficiently large. These transition criteria provide guidelines for improving the design of the cowl lip of an inward-turning inlet in supersonic and hypersonic regimes.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A15
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© The Author(s), 2025. Published by Cambridge University Press

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References

Anderson, J.D. 2006 Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics.10.2514/4.861956CrossRefGoogle Scholar
Bai, C.Y. & Wu, Z.N. 2022 Type IV shock interaction with a two-branch structured transonic jet. J. Fluid Mech. 941, A45.10.1017/jfm.2022.340CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Bisek, N.J. 2016 High-fidelity simulations of the HIFiRE-6 flow path. In 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1115, pp. 1115. American Institute of Aeronautics and Astronautics.Google Scholar
Cao, S.B., Hao, J., Klioutchnikov, I., Olivier, H., Heufer, K.A. & Wen, C.Y. 2021 Leading-edge bluntness effects on hypersonic three-dimensional flows over a compression ramp. J. Fluid Mech. 923, A27.10.1017/jfm.2021.552CrossRefGoogle Scholar
Durna, A.S., Barada, M.E.H.A. & Celik, B. 2016 Shock interaction mechanisms on a double wedge at Mach 7. Phys. Fluids 28 (9), 096101.10.1063/1.4961571CrossRefGoogle Scholar
Edney, B. 1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. FFA Report No. 115, Aeronautical Research Institute of Sweden.10.2172/4480948CrossRefGoogle Scholar
Fan, J.H., Hao, J. & Wen, C.Y. 2022 Nonlinear interactions of global instabilities in hypersonic laminar flow over a double cone. Phys. Fluids 34 (12), 126108.10.1063/5.0130901CrossRefGoogle Scholar
Gao, L.J., Qian, Z.S., Wang, L. & Xin, Y.N. 2020 Theroretical and technical challenges of wide speed range hypersonic aerothermal wind tunnel. Aeronaut. Sci. Technol. 31 (11), 66–73 (in Chinese).Google Scholar
Gollan, R.J. & Smart, M.K. 2013 Design of modular shape-transition inlets for a conical hypersonic vehicle. J. Propul. Power 29 (4), 832–838.10.2514/1.B34672CrossRefGoogle Scholar
Guan, X.K., Bai, C.Y. & Wu, Z.N. 2020 Double solution and influence of secondary waves on transition criteria for shock interference in pre-Mach reflection with two incident shock waves. J. Fluid Mech. 887, A22.10.1017/jfm.2020.3CrossRefGoogle Scholar
Hu, Z.M., Gao, Y.L., Myong, R.S., Dou, H.S. & Khoo, B.C. 2010 Geometric criterion for RR $\leftrightarrow$ MR transition in hypersonic double-wedge flows. Phys. Fluids 22, 016101.10.1063/1.3276907CrossRefGoogle Scholar
Kang, D., Yan, C., Li, Z., Li, S. & Jiang, Z. 2023 a Shock interactions and heating predictions on a V-shaped blunt leading edge at Mach 6–12. Phys. Fluids 35 (12), 126105.10.1063/5.0174327CrossRefGoogle Scholar
Kang, D., Yan, C., Liu, S., Wang, Z. & Jiang, Z. 2023 b Modelling and shock control for a V-shaped blunt leading edge. J. Fluid Mech. 968, A15.10.1017/jfm.2023.447CrossRefGoogle Scholar
Li, S., Jiang, Z., Kang, D., Yin, T. & Yan, C. 2024 Investigation of the heat flux reduction scheme on a V-shaped blunt leading edge based on secondary recirculation jets. Acta Astronaut. 215, 1–19.10.1016/j.actaastro.2023.11.042CrossRefGoogle Scholar
Li, S., Yan, C., Kang, D.K., Liu, S.J. & Jiang, Z.H. 2023 Investigation of flow control methods for reducing heat flux on a V-shaped blunt leading edge under real gas effects. Phys. Fluids 35 (3), 036113.10.1063/5.0142156CrossRefGoogle Scholar
Li, X., Zhang, Y., Tan, H.J., Jin, Y. & Li, C. 2022 Comparative study on single-incident and dual-incident shock wave/turbulent boundary layer interactions with identical total deflection angle. J. Fluid Mech. 940, A7.10.1017/jfm.2022.211CrossRefGoogle Scholar
Li, Y.M., Li, Z.F. & Yang, J.M. 2021 Tomography-like flow visualization of a hypersonic inward-turning inlet. Chinese J. Aeronaut. 34 (1), 44–49.10.1016/j.cja.2020.10.012CrossRefGoogle Scholar
Li, Z.F., Gao, W.Z., Jiang, H.L. & Yang, J.M. 2013 Unsteady behaviors of a hypersonic inlet caused by throttling in shock tunnel. AIAA J. 51 (10), 2485–2492.10.2514/1.J052384CrossRefGoogle Scholar
Li, Z.F., Zhang, Z.Y., Wang, J. & Yang, J.M. 2019 Pressure-heat flux correlations for shock interactions on V-shaped blunt leading edges. AIAA J. 57 (10), 4588–4592.10.2514/1.J058538CrossRefGoogle Scholar
Lin, M.Y., Yang, F., Hu, Z.M., Wang, C. & Jiang, Z.L. 2023 Transitional criterion and hysteresis of multiple shock–shock interference. Phys. Fluids 35 (4), 046110.Google Scholar
Liu, S.J., Yan, C., Kang, D.K., Jiang, Z.H. & Sun, M. 2023 Opposing jets for heat flux reduction and uncertainty analysis on a V-shaped blunt leading edge. Aerosp. Sci. Technol. 138, 108353.10.1016/j.ast.2023.108353CrossRefGoogle Scholar
Meng, Z.W., Fan, X.Q., Xiong, B. & Tao, Y. 2019 Investigation of aerodynamic heating in V-shaped cowl-lip of the inward turning inlet. Proc. Inst. Mech. Engnrs G: J. Aerosp. Engng 233 (8), 2792–2801.10.1177/0954410018787137CrossRefGoogle Scholar
Mohan, J.A. & Skews, B.W. 2013 Three-dimensional supersonic internal flows. Shock Waves 23 (5), 513–524.10.1007/s00193-013-0441-zCrossRefGoogle Scholar
Roe, P.L. 1981 Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (2), 357–372.10.1016/0021-9991(81)90128-5CrossRefGoogle Scholar
Russell, M.C. & Thomas, E.M. 2012 Hypersonic Ludwieg tube design and future usage at the US Air Force Academy. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2012-0734. American Institute of Aeronautics and Astronautics.Google Scholar
Sinclair, J. & Cui, X. 2017 A theoretical approximation of the shock standoff distance for supersonic flows around a circular cylinder. Phys. Fluids 29 (2), 026102.10.1063/1.4975983CrossRefGoogle Scholar
Spalart, P. & Allmaras, S. 1992 A one-equation turbulence model for aerodynamic flows. In 30th Aerospace Sciences Meeting and Exhibit, AIAA Paper 1992-0439, pp. 439. American Institute of Aeronautics and Astronautics.Google Scholar
Surujhlal, D. & Skews, B.W. 2019 Three-dimensional shock wave reflection transition in steady flow. J. Fluid Mech. 858, 565–587.10.1017/jfm.2018.747CrossRefGoogle Scholar
Sziroczak, D. & Smith, H. 2016 A review of design issues specific to hypersonic flight vehicles. Prog. Aerosp. Sci. 84, 1–28.10.1016/j.paerosci.2016.04.001CrossRefGoogle Scholar
Tumuklu, O., Levin, D.A. & Theofilis, V. 2018 Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach. Phys. Fluids 30 (4), 046103.10.1063/1.5022598CrossRefGoogle Scholar
Urzay, J. 2018 Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annu. Rev. Fluid Mech. 50 (1), 593–627.10.1146/annurev-fluid-122316-045217CrossRefGoogle Scholar
Wang, D.X., Li, Z.F., Zhang, Z.Y., Liu, N.S. & Yang, J.M. 2018 Unsteady shock interactions on V-shaped blunt leading edges. Phys. Fluids 30 (11), 116104.10.1063/1.5051012CrossRefGoogle Scholar
Wang, J., Li, Z.F. & Yang, J.M. 2021 a Shock-induced pressure/heating loads on V-shaped leading edges with nonuniform bluntness. AIAA J. 59 (3), 1114–1118.10.2514/1.J059990CrossRefGoogle Scholar
Wang, J., Li, Z.F., Zhang, Z.Y. & Yang, J.M. 2020 Shock interactions on V-shaped blunt leading edges with various conic crotches. AIAA J. 58 (3), 1407–1411.10.2514/1.J059067CrossRefGoogle Scholar
Wang, J., Li, Z.F., Zhang, Z.Y. & Yang, J.M. 2021 b Effects of geometry parameters on aerothermal heating loads of V-shaped blunt leading edges. Chinese J. Theor. Appl. Mech. 53 (12), 3274–3283 (in Chinese).Google Scholar
Wang, M.M. & Wu, Z.N. 2021 Transition study for asymmetric reflection between moving incident shock waves. J. Fluid Mech. 929, A26.10.1017/jfm.2021.856CrossRefGoogle Scholar
Wieting, A.R. & Holden, M.S. 1989 Experimental shock-wave interference heating on a cylinder at Mach 6 and 8. AIAA J. 27 (11), 1557–1565.10.2514/3.10301CrossRefGoogle Scholar
Xiao, F.S., Li, Z.F., Zhang, Z.Y., Zhu, Y.J. & Yang, J.M. 2018 Hypersonic shock wave interactions on a V-shaped blunt leading edge. AIAA J. 56 (1), 356–367.10.2514/1.J055915CrossRefGoogle Scholar
Zhang, E.L., Li, Z.F., Li, Y.M. & Yang, J.M. 2019 a Three-dimensional shock interactions and vortices on a V-shaped blunt leading edge. Phys. Fluids 31 (8), 086102.10.1063/1.5101031CrossRefGoogle Scholar
Zhang, T., Cheng, J., Shi, C., Zhu, C. & You, Y. 2023 Mach reflection of three-dimensional curved shock waves on V-shaped blunt leading edges. J. Fluid Mech. 975, A45.10.1017/jfm.2023.866CrossRefGoogle Scholar
Zhang, Y.J., Li, Z.F., Zhang, Z.Y., Huang, R., Wang, J., Yang, J.M., Wu, L.L., Liu, K.W. & Cao, X.L. 2022 a Effects of sideslip angle on shock oscillations of V-shaped blunt leading edge. J. Propul. Technol. 43 (11), 210520 (in Chinese).Google Scholar
Zhang, Y.J., Wang, J. & Li, Z.F. 2022 b Shock-induced heating loads on V-shaped leading edges with elliptic cross section. AIAA J. 60 (12), 6958–6962.10.2514/1.J062013CrossRefGoogle Scholar
Zhang, Z.Y., Li, Z.F., Huang, R. & Yang, J.M. 2019 b Experimental investigation of shock oscillations on V-shaped blunt leading edges. Phys. Fluids 31 (2), 026110.10.1063/1.5084184CrossRefGoogle Scholar
Zhang, Z.Y., Li, Z.F. & Yang, J.M. 2021 Transitions of shock interactions on V-shaped blunt leading edges. J. Fluid Mech. 912, A12.10.1017/jfm.2020.1117CrossRefGoogle Scholar
Zhang, Z.Y., Xiao, F.S., Li, Z.F., Zhu, Y.J. & Yang, J.M. 2019 c Shock interaction on a V-shaped blunt leading edge. In 31st International Symposium on Shock Waves 1: ISSW 2017 (ed. A. Sasoh, T. Aoki and M. Katayama), pp. 799–806. Springer.10.1007/978-3-319-91020-8_95CrossRefGoogle Scholar
Zhou, B.K., Li, Z.F., Li, Y.M., Xu, Z.N., Shang, J.K. & Yang, J.M. 2022 Surface pressure characteristics on V-shaped plates with blunt leading edges at high Mach number. J. Propul. Technol. 43 (7), 210205 (in Chinese).Google Scholar
Zuo, F.Y. & Mölder, S. 2019 Hypersonic wavecatcher intakes and variable-geometry turbine based combined cycle engines. Prog. Aerosp. Sci. 106, 108–144.10.1016/j.paerosci.2019.03.001CrossRefGoogle Scholar