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Reflection of a rightward-moving shock wave over a steady oblique shock with post-formed expansion wave

Published online by Cambridge University Press:  02 April 2025

Miaomiao Wang Open the ORCID record for Miaomiao Wang [Opens in a new window]  and
Ziniu Wu Open the ORCID record for Ziniu Wu [Opens in a new window]
Miaomiao Wang*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Ziniu Wu
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
Corresponding author: Miaomiao Wang, [email protected]
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Abstract

Reflection of a rightward-moving shock over a steady oblique shock, equivalent to a shock-on-shock interaction, is typically studied with post-formed shock waves. Law, Felthun and Skews (Shock Waves, vol. 13, 2003, pp. 381–394) reported post-formed expansion fan (PFEF) reflection for second-family incident shock. Here, we show that PFEF reflection also exists for first-family incident shock. We derive the critical condition for PFEF reflection in the shock speed Mach number and incident shock angle plane. Our findings indicate PFEF emergence near type post-I region. Numerical simulations reveal that PFEF with rising incident angle can intersect the incident shock, triple point or Mach stem, echoing the Hillier (J. Fluid Mech., vol. 575, 2007, pp. 399–424) three-type classification of shock–expansion fan interactions. The complex shock reflection pattern is essentially composed of an upstream structure linked to the moving shock wave, and a downstream structure linked to the unperturbed oblique shock wave. Under the conditions investigated, the upstream structure is characterized by a Mach reflection of the incident shock over the wall, potentially featuring a triple point formed within the Mach stem. Below this triple point, there is a curved segment of the Mach stem that is close to the wall. As the inclined angle increases, the curved shock may expand and interact with the incident shock, leading to an asymmetric regular reflection, which is a phenomenon that has not been observed previously. The downstream structure is a double $\lambda$ shock structure, with the lower shock resulting from the generation of recompression shock waves.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A19
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Athira, C., Rajesh, G., Mohanan, S. & Parthasarathy, A. 2020 Flow interactions on supersonic projectiles in transitional ballistic regimes. J. Fluid Mech. 894, A27.Google Scholar
Blankenship, V.D. 1965 Shock–shock interaction on a slender supersonic cone. J. Fluid Mech. 22 (3), 599–615.CrossRefGoogle Scholar
Bramlette, T. 1974 Simple technique for predicting type III and IV shock interference. AIAA J. 12 (8), 1151–1152.Google Scholar
Brown, E. & Mullaney, G. 1965 Experiments on the head-on shock–shock interaction. AIAA J. 3 (11), 2168–2170.Google Scholar
Edney, B. 1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. Tech. Rep., Flygtekniska Forsoksanstalten, Stockholm (Sweden).CrossRefGoogle Scholar
Frame, M.J. & Lewis, M.J. 1997 Analytical solution of the type IV shock interaction. J. Propul. Power 13 (5), 601–609.CrossRefGoogle Scholar
Gao, B. & Wu, Z. 2010 A study of the flow structure for Mach reflection in steady supersonic flow. J. Fluid Mech. 656, 29–50.CrossRefGoogle Scholar
Gentry, R.A., Martin, R.E. & Daly, B.J. 1966 An Eulerian differencing method for unsteady compressible flow problems. J. Comput. Phys. 1 (1), 87–118.Google Scholar
Grasso, F., Purpura, C., Chanetz, B. & Délery, J. 2003 Type III and type IV shock/shock interferences: theoretical and experimental aspects. Aerosp. Sci. Technol. 7 (2), 93–106.Google Scholar
Hillier, R. 2007 Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection. J. Fluid Mech. 575, 399–424.Google Scholar
Inger, G.R. 1966 Blast wave impingement on a slender wedge moving at hypersonic speeds. AIAA J. 4 (3), 428–435.Google Scholar
Ivanov, M., Ben-Dor, G., Elperin, T., Kudryavtsev, A. & Khotyanovsky, D. 2002 The reflection of asymmetric shock waves in steady flows: a numerical investigation. J. Fluid Mech. 469, 71–87.CrossRefGoogle Scholar
Kutler, P. & Sakell, L. 1975 Three-dimensional, shock-on-shock interaction problem. AIAA J. 13 (10), 1360–1367.Google Scholar
Kutler, P., Sakell, L. & Aiello, G. 1974 On the shock-on-shock interaction problem. In 7th Fluid and Plasma Dynamics Conference, p. 524. American Institute of Aeronautics and Astronautics (AIAA).Google Scholar
Kutler, P., Sakell, L. & Aiello, G. 1975 Two-dimensional shock-on-shock interaction problem. AIAA J. 13 (3), 361–367.Google Scholar
Law, C., Felthun, L. & Skews, B. 2003 Two-dimensional numerical study of planar shock-wave/moving-body interactions. Part I: Plane shock-on-shock interactions. Shock Waves 13 (5), 381–394.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1997 Analytical investigation of two-dimensional unsteady shock-on-shock interactions. J. Fluid Mech. 340, 101–128.CrossRefGoogle Scholar
Liou, M.-S. 1996 A sequel to AUSM: AUSM+. J. Comput. Phys. 129 (2), 364–382.Google Scholar
Martínez-Ruiz, D., Huete, C., Martínez-Ferrer, P.J. & Mira, D. 2019 Irregular self-similar configurations of shock-wave impingement on shear layers. J. Fluid Mech. 872, 889–927.CrossRefGoogle Scholar
Merritt, D. & Aronson, P. 1966 Free flight shock interaction studies. AIAA Paper (66-57). i,1–10,10(1)–10(6).Google Scholar
Merritt, D.L. & Aronson, P.M. 1967 Wind Tunnel Simulation of Head-On Bow Wave-Blast Wave Interactions. Vol. United States Naval Ordnance Laboratory.Google Scholar
Smyrl, J. 1963 The impact of a shock-wave on a thin two-dimensional aerofoil moving at supersonic speed. J. Fluid Mech. 15 (2), 223–240.CrossRefGoogle Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.CrossRefGoogle Scholar
Wang, M.-M. & Wu, Z.-N. 2022 Reflection of rightward moving shocks of the first and second families over a steady oblique shock wave. J. Fluid Mech. 936, A18.Google Scholar
Wang, M.-M., Xu, Z.-Z. & Wu, Z.-N. 2024 Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave. J. Fluid Mech. 979, A28.Google Scholar
Windisch, C., Reinartz, B. U. & Müller, S. 2016 Investigation of unsteady Edney type IV and VII shock–shock interactions. AIAA J. 54 (6), 1846–1861.CrossRefGoogle Scholar