Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-29T16:26:38.731Z Has data issue: false hasContentIssue false
  • English
  • Français

Shock reflection with incident shock–wedge trailing-edge expansion fan interaction

Published online by Cambridge University Press:  04 August 2023

Chen-Yuan Bai Open the ORCID record for Chen-Yuan Bai [Opens in a new window]
Chen-Yuan Bai*
Affiliation:
Ministry of Education Key Laboratory of Fluid Mechanics, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: baicy@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady shock reflection where the incident shock is free of interaction with other waves has been well studied. In this paper, we consider the less studied shock reflection problem where the incident shock interacts with the wedge trailing-edge expansion fan, which occurs when the wedge trailing-edge height surpasses a threshold. The influence of this interaction on the advance of transition from Mach reflection to regular reflection is quantified in terms of the wedge trailing-edge height ratio. The wave pattern, including primary and reflected Mach waves, for Mach reflection with interaction is clarified using computational fluid dynamics (CFD) and the method of characteristics. Those reflected Mach waves having an important effect on Mach reflection are identified. A simplified Mach stem model that accounts for the direct role of the interaction on the incident shock and its indirect role on the reflected shock and slipline is built up on a past model without interaction. Both theory and CFD show that the Mach stem height decreases nonlinearly with increasing trailing-edge height.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Supersonic flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A21
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Azevedo, D.J. & Liu, C.S. 1993 Engineering approach to the prediction of shock patterns in bounded high-speed flows. AIAA J. 31, 83–90.CrossRefGoogle Scholar
Bai, C.Y. & Wu, Z.N. 2017 Size and shape of shock waves and slipline for Mach reflection in steady flow. J. Fluid Mech. 818, 116–140.CrossRefGoogle Scholar
Bai, C.Y. & Wu, Z.N. 2021 A study of the dependence of the Mach stem height on the trailing edge height. Fluids 6, 313.CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena, 2nd edn. Springer.Google Scholar
Ben-Dor, G. & Takayama, K. 1992 The phenomena of shock wave reflection – a review of unsolved problems and future research needs. Shock Waves 2 (4), 211–223.CrossRefGoogle Scholar
Gao, B. & Wu, Z.N. 2010 A study of the flow structure for Mach reflection in steady supersonic flow. J. Fluid Mech. 656, 29–50.CrossRefGoogle 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.CrossRefGoogle Scholar
Hayes, W.D. & Probstein, R.F. 2004 Hypersonic Inviscid Flow, chap 7.2, 2nd edn. Dover.Google Scholar
Hillier, R. 2007 Shock-wave/expansion-wave interactions and the transition between regular and Mach reflection. J. Fluid Mech. 575, 399–424.CrossRefGoogle Scholar
Holt, M. 1956 The method of characteristics for steady supersonic rotational flow in three dimensions. J. Fluid Mech. 1 (4), 409–423.CrossRefGoogle Scholar
Hornung, H.G. & Robinson, M.L. 1982 Transition from regular to Mach reflection of shock waves. Part 2. The steady-flow criterion. J. Fluid Mech. 123, 155–164.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101–125.CrossRefGoogle Scholar
Liepmann, H.W. & Roshko, A. 1957 Elements of Gas Dynamics. Wiley.Google Scholar
Mouton, C.A. & Hornung, H.G. 2007 Mach stem height and growth rate predictions. AIAA J. 45 (8), 1977–1987.CrossRefGoogle Scholar
Shoesmith, B. & Timofeev, E. 2021 Modelling of Mach reflections in internal axisymmetric steady supersonic flow. Shock Waves 31, 945–957.CrossRefGoogle Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconstruction of oblique shock wave reflection in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.CrossRefGoogle Scholar