Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T05:58:36.414Z Has data issue: false hasContentIssue false
  • English
  • Français

Converging near-elliptic shock waves

Published online by Cambridge University Press:  21 December 2020

Enlai Zhang Open the ORCID record for Enlai Zhang [Opens in a new window] ,
Zhufei Li Open the ORCID record for Zhufei Li [Opens in a new window] ,
Junze Ji ,
Dongxian Si  and
Jiming Yang
Enlai Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Zhufei Li*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Junze Ji
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Dongxian Si
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
Jiming Yang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei230026, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper characterizes the geometry of converging near-elliptic shock waves at a Mach number of 6. The converging shocks are produced by elliptic conical surfaces with shapes made up from adjacent straight generators, each deflected a constant angle from the free-stream direction. Combined shock tunnel experiments and numerical analyses are conducted to depict the evolution of the converging shock waves for several elliptic entry aspect ratios $AR$s (i.e. the ratio of the major axis to the minor axis). It is revealed that the deviation from axial symmetry is amplified as the shock front approaches the centreline, which results in different shock interaction types compared with the axisymmetric case. Three typical shock interaction types are classified depending on various ARs. For a small AR, faster shock strengthening in the major plane dominates, although a Mach reflection (type A) that resembles the axisymmetric flow field is formed. However, for a sufficiently large AR, the shock strengthening is eventually terminated by the intersection of the weaker shocks in the minor plane owing to their smaller off-centre distances, which results in a regular reflection (type B). Between these two interaction patterns, there is a critical AR for which both the shock fronts in the major and minor planes intersect at the centreline coincidentally, and this critical intersection (type C) exhibits an extreme case of a shock front converging to a singular point. This study indicates that deviation from axial symmetry affects the evolution of the shock structures in converging flow.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A2
Check for updates
Copyright
© The Author(s), 2020. 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

REFERENCES

Barth, T. & Jespersen, D. 1989 The design and application of upwind schemes on unstructured meshes. AIAA Paper 89–0366. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena, 2nd edn. Springer.Google Scholar
Ben-Dor, G., Ivanov, M., Vasilev, E. I. & Elperin, T. 2002 Hysteresis processes in the regular reflection$\leftrightarrow$Mach reflection transition in steady flows. Prog. Aerosp. Sci. 38 (4–5), 347–387.CrossRefGoogle Scholar
Courant, R. & Friedrichs, K. O. 1999 Supersonic Flow and Shock Waves. Springer Science and Business Media.Google Scholar
Emanuel, G. 2018 Analytical extension of curved shock theory. Shock Waves 28 (2), 417–425.CrossRefGoogle Scholar
Ferri, A. 1946 Application of the method of characteristics to supersonic rotational flow. NACA Rep. 841. National Advisory Committee for Aeronautics.Google Scholar
Filippi, A. A. & Skews, B. W. 2017 Supersonic flow fields resulting from axisymmetric internal surface curvature. J. Fluid Mech. 831, 271–288.CrossRefGoogle Scholar
Filippi, A. A. & Skews, B. W. 2018 Streamlines behind curved shock waves in axisymmetric flow fields. Shock Waves 28 (4), 785–793.CrossRefGoogle Scholar
Gounko, Y. P. 2017 Patterns of steady axisymmetric supersonic compression flows with a Mach disk. Shock Waves 27 (3), 495–506.CrossRefGoogle Scholar
Hornung, H. G. 2000 Oblique shock reflection from an axis of symmetry. J. Fluid Mech. 409, 1–12.CrossRefGoogle Scholar
Hornung, H. G. & Schwendeman, D. W. 2001 Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity. J. Fluid Mech. 438, 231–245.CrossRefGoogle Scholar
Isakova, N. P., Kraiko, A. N., Pyankov, K. S. & Tillyayeva, N. I. 2012 The amplification of weak shock waves in axisymmetric supersonic flow and their reflection from an axis of symmetry. J. Appl. Math. Mech. 76 (4), 451–465.CrossRefGoogle Scholar
Li, H., Chpoun, A. & Ben-Dor, G. 1999 Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows. J. Fluid Mech. 390, 25–43.CrossRefGoogle 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.CrossRefGoogle Scholar
Li, Z.-F., Huang, R., Li, Y.-M. & Yang, J.-M. 2018 Sliding-plug approach for inlet self-starting ability test in shock tunnel. AIAA J. 56 (9), 3785–3790.CrossRefGoogle Scholar
Mölder, S. 2012 Curved aerodynamic shock waves. PhD thesis, McGill University.Google Scholar
Mölder, S. 2017 a Flow behind concave shock waves. Shock Waves 27 (5), 721–730.CrossRefGoogle Scholar
Mölder, S. 2017 b Reflection of curved shock waves. Shock Waves 27 (5), 699–720.CrossRefGoogle Scholar
Mölder, S. 2017 c Shock detachment from curved wedges. Shock Waves 27 (5), 731–745.CrossRefGoogle Scholar
Roe, P. L. 1981 Approximate riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (2), 357–372.CrossRefGoogle Scholar
Rylov, A. I. 1990 On the impossibility of regular reflection of a steady-state shock wave from the axis of symmetry. J. Appl. Math. Mech. 54 (2), 201–203.CrossRefGoogle Scholar
Shoev, G. & Ogawa, H. 2019 Numerical study of viscous effects on centreline shock reflection in axisymmetric flow. Phys. Fluids 31 (2), 026105.CrossRefGoogle Scholar
Smart, M. K. 1999 Design of three-dimensional hypersonic inlets with rectangular-to-elliptical shape transition. J. Propul. Power 15 (3), 408–416.CrossRefGoogle Scholar
Toponogov, V. A. 2006 Differential Geometry of Curves and Surfaces, A Concise Guide. Springer.Google 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, 086102.CrossRefGoogle 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, 026110.CrossRefGoogle Scholar
Zuo, F.-Y., Memmolo, Antonio, Huang, G.-P. & Pirozzoli, Sergio 2019 Direct numerical simulation of conical shock wave-turbulent boundary layer interaction. J. Fluid Mech. 877, 167–195.CrossRefGoogle Scholar
Zuo, F.-Y. & Mölder, S. 2019 Hypersonic wavecatcher intakes and variable-geometry turbine based combined cycle engines. Prog. Aerosp. Sci. 106, 108–144.CrossRefGoogle Scholar