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Shock-wave reflections over double-concave cylindrical reflectors

  • V. Soni (a1), A. Hadjadj (a1), A. Chaudhuri (a2) and G. Ben-Dor (a3)

Abstract

Numerical simulations were conducted to understand the different wave configurations associated with the shock-wave reflections over double-concave cylindrical surfaces. The reflectors were generated computationally by changing different geometrical parameters, such as the radii of curvature and the initial wedge angles. The incident-shock-wave Mach number was varied such as to cover subsonic, transonic and supersonic regimes of the flows induced by the incident shock. The study revealed a number of interesting wave features starting from the early stage of the shock interaction and transition to transitioned regular reflection (TRR) over the first concave surface, followed by complex shock reflections over the second one. Two new shock bifurcations have been found over the second wedge reflector, depending on the velocity of the additional wave that appears during the TRR over the first wedge reflector. Unlike the first reflector, the transition from a single-triple-point wave configuration (STP) to a double-triple-point wave configuration (DTP) and back occurred several times on the second reflector, indicating that the flow was capable of retaining the memory of the past events over the entire process.

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Corresponding author

Email address for correspondence: hadjadj@coria.fr

References

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Ben-Dor, G. 1980 Analytical solution of double-Mach reflection. AIAA J. 18, 10361043.
Ben-Dor, G. 1987 A reconsideration of the three-shock theory for a pseudo-steady Mach reflection. J. Fluid Mech. 181, 467484.
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena, 2nd edn. Springer.
Ben-Dor, G., Dewey, J. M. & Takayama, K. 1987 The reflection of a plane shock wave over a double wedge. J. Fluid Mech. 176, 483520.
Ben-Dor, G. & Elperin, T. 1991 Analysis of the wave configuration resulting from the termination of an inverse Mach reflection. Shock Waves 1 (3), 237241.
Ben-Dor, G. & Glass, I. I. 1979 Domains and boundaries of non-stationary oblique shock-wave reflexions. Part 1. Diatomic gas. J. Fluid Mech. 92, 459496.
Ben-Dor, G. & Takayama, K. 1985 Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges. J. Fluid Mech. 158, 365380.
Ben-Dor, G., Takayama, K. & Kawauchi, T. 1980 The transition from regular to Mach reflexion and from Mach to regular reflexion in truly non-stationary flows. J. Fluid Mech. 100, 147160.
Bryson, A. E. & Gross, R. W. F. 1961 Diffraction of strong shocks by cones, cylinders, and spheres. J. Fluid Mech. 10, 116.
Chaudhuri, A., Hadjadj, A. & Chinnayya, A. 2011a On the use of immersed boundary methods for shock/obstacle interactions. J. Comput. Phys. 230 (5), 17311748.
Chaudhuri, A., Hadjadj, A., Chinnayya, A. & Palerm, S. 2011b Numerical study of compressible mixing layers using high-order WENO schemes. J. Sci. Comput. 47, 170197.
Colella, P. & Glaz, H. M. 1984 Numerical calculation of complex shock reflections in gases. In 4th Mach Reflection Symposium, pp. 154158. Sendai.
Drikakis, D., Ofengeim, D., Timofeev, E. & Voionovich, P. 1997 Computation of non-stationary shock-wave/cylinder interaction using adaptive-grid methods. J. Fluids Struct. 11 (6), 665692.
Geva, M., Ram, O. & Sadot, O. 2013 The non-stationary hysteresis phenomenon in shock wave reflections. J. Fluid Mech. 732, R1.
Gruber, S.2012 Weak shock wave reflections from concave curved surfaces. MSc thesis, University of Witwatersrand, South Africa.
Gvozdeva, L. G., Lagutov, Yu. P. & Fokeev, V. P. 1982 Transition from mach reflection to regular reflection when strong shock waves interact with cylindrical surfaces. Fluid Dyn. 17 (2), 273278.
Hadjadj, A. & Kudryavtsev, A. 2005 Computation and flow visualization in high-speed aerodynamics. J. Turbul. 6, 125.
Heilig, W. H. 1969 Diffraction of a shock wave by a cylinder. Phys. Fluids 12 (5), I154I157.
Henderson, L. F. & Lozzi, A. 1975 Experiments on transition of Mach reflexion. J. Fluid Mech. 68, 139155.
Hornung, H. 1986 Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18, 3358.
Hornung, H. G. & Taylor, J. R. 1982 Transition from regular to Mach reflection of shock-waves. Part 1. The effect of viscosity in the pseudosteady case. J. Fluid Mech. 123, 143153.
Itoh, S., Okazaki, N. & Itaya, M. 1981 On the transition between regular and Mach reflection in truly non-stationary flows. J. Fluid Mech. 108, 383400.
Izumi, K., Aso, S. & Nishida, M. 1994 Experimental and computational studies focusing processes of shock waves reflected from parabolic reflectors. Shock Waves 3 (3), 213222.
Kaca, J.1988 An interferometric investigation of the diffraction of a planar shock wave over a semicircular cylinder. UTIAS Technical Note 269.
Kleine, H., Timofeev, E., Hakkaki-Fard, A. & Skews, B. W. 2014 The influence of Reynolds number on the triple point trajectories at shock reflection off cylindrical surfaces. J. Fluid Mech. 740, 4760.
Mach, E. 1878 Über den verlauf von funkenwellen in der ebene und im räume. Sitz.ber. Akad. Wiss. Wien 78, 819838.
von Neumann, J. 1963 Collected Works of John von Neumann, 2nd edn. Pergamon.
Ram, O., Geva, M. & Sadot, O. 2015 High spatial and temporal resolution study of shock wave reflection over a coupled convex–concave cylindrical surface. J. Fluid Mech. 768, 219239.
Shadloo, M. S., Hadjadj, A. & Chaudhuri, A. 2014 On the onset of postshock flow instabilities over concave surfaces. Phys. Fluids 26 (7), 076101.
Skews, B. & Blitterswijk, A. 2011 Shock wave reflection off coupled surfaces. Shock Waves 21 (6), 491498.
Skews, B. W. & Kleine, H. 2007 Flow features resulting from shock wave impact on a cylindrical cavity. J. Fluid Mech. 580, 481493.
Smith, L. G.1945 Photographic investigation of the reflection of plane shocks in air Tech. Rep. OSRD Rep. 6271. Off. Sci. Res. Dev., Washington DC, USA.
Soni, V., Roussel, O. & Hadjadj, A. 2016 On the accuracy and efficiency of point-value multiresolution algorithms for solving scalar wave and Euler equations. J. Comput. Appl. Maths; (under review).
Takayama, K. & Ben-Dor, G. 1983 A reconsideration of the hysteresis phenomenon in the regular ↔ Mach reflection transition in truly nonstationary flows. Israel J. Tech. 21(1/2), 197204.
Takayama, K. & Sasaki, M. 1983 Effects of radius of curvature and initial angle on the shock transition over concave and convex walls. Rep. Inst. High-Speed Mech. 46, 130.
White, D. R.1951 An experimental survey of the Mach reflection of shock waves. Tech. Rep. II–10. Deptartment of Physics, Princeton University, Princeton, USA.
Whitham, G. B. 1999 Linear and Nonlinear Waves. Wiley.
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