Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-01T00:56:12.099Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of Reynolds number on the triple point trajectories at shock reflection off cylindrical surfaces

Published online by Cambridge University Press:  10 January 2014

H. Kleine ,
E. Timofeev ,
A. Hakkaki-Fard  and
B. Skews
H. Kleine*
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
E. Timofeev
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada
A. Hakkaki-Fard
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada
B. Skews
Affiliation:
Flow Research Unit, School of Mechanical, Industrial & Aeronautical Engineering, University of the Witwatersrand, Johannesburg 2050, South Africa
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In the unsteady process of shock reflection off convexly curved surfaces, the Reynolds number can have an influence on the development of the irregular reflection pattern. Time-resolved visualizations of the reflection process and high-resolution numerical simulation are used in this investigation to quantify this influence, which manifests itself in a delayed growth of the shock pattern with decreasing Reynolds number. In order to conduct reliable and unambiguous measurements, the present study concentrates on observing the development of the established irregular reflection pattern rather than attempting to determine the transition point directly. It can be seen that the influence of the Reynolds number is highly nonlinear and that changes of two orders of magnitude or more are required to produce a reliably measurable difference in the triple point trajectories, which is considerably more than what has so far been reported in the literature. The results allow one to make inferences regarding the transition process and they help to clarify previously reported discrepancies between predicted and experimentally determined transition angles.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 740 , 10 February 2014 , pp. 47 - 60
Copyright
©2014 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

Bazhenova, T. V., Gvozdeva, L. G., Lagutov, Yu. P., Lyakhov, V. N., Faresov, Yu. M. & Fokeev, V. P.Unsteady Interactions of Shock and Detonation Waves in Gases. 1977 Nauka, (in Russian).Google Scholar
Bazhenova, T. V., Gvozdeva, L. G. & Nettleton, M. A. 1984 Unsteady interactions of shock waves. Prog. Aerosp. Sci. 21, 249–331.Google Scholar
Ben-Dor, G. 2007 Shock Wave Reflection Phenomena. Springer.Google Scholar
Ben-Dor, G. & Takayama, K. 1981 Streak camera photography with curved slits for the precise determination of shock wave transition phenomena. Can. Aeronaut. Space J. 27 (2), 128–134.Google Scholar
Ben-Dor, G., Takayama, K. & Kawauchi, T. 1980 The transition from regular to Mach reflection and from Mach to regular reflection in truly nonstationary flows. J. Fluid Mech. 100, 147–160.CrossRefGoogle Scholar
Drikakis, D., Ofengeim, D., Timofeev, E. & Voinovich, P. 1997 Computation of non-stationary shock-wave/cylinder interaction using adaptive-grid methods. J. Fluids Struct. 11 (6), 665–691.Google Scholar
Geva, M., Ram, O. & Sadot, O. 2013 The non-stationary hysteresis phenomenon in shock wave reflections. J. Fluid Mech. 732 (R1), 1–11.Google Scholar
Glazer, E., Sadot, O., Hadjadj, A. & Chaudhuri, A. 2011 Velocity scaling of a shock wave reflected off a circular cylinder. Phys. Rev. E 83, 066317.Google Scholar
Hakkaki-Fard, A. 2011 Study on the sonic point in unsteady shock reflections via numerical flow field analysis. PhD thesis, McGill University. http://digitool.library.mcgill.ca/R/-?func=dbin-jump-full&object_id=106502&silo_library=GEN01.Google Scholar
Hakkaki-Fard, A. & Timofeev, E. 2012a Determination of the sonic point in unsteady shock reflections using various techniques based on numerical flow field analysis. In Proceedings of 28th International Symposium on Shock Waves (ed. Kontis, K.), vol. 2, pp. 643–648. Springer.Google Scholar
Hakkaki-Fard, A. & Timofeev, E. 2012b On numerical techniques for determination of the sonic point in unsteady inviscid shock reflections. Intl J. Aerosp. Innovations 4 (1–2), 41–52.Google Scholar
Heilig, W. H. 1969 Diffraction of a shock wave by a cylinder. Phys. Fluids 12, I-154–I-157.Google Scholar
Henderson, L. F., Takayama, K., Crutchfield, W. Y. & Itabashi, S. 2001 The persistence of regular reflection during strong shock diffraction over rigid ramps. J. Fluid Mech. 431, 273–296.Google Scholar
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, 143–153.Google Scholar
Itoh, S., Okazaki, N. & Itaya, M. 1981 On the transition between regular and Mach reflection in truly nonstationary flows. J. Fluid Mech. 108, 383–400.CrossRefGoogle Scholar
Kleine, H., Tetreault-Friend, M., Timofeev, E., Gojani, A. & Takayama, K. 2007 On the ongoing quest to pinpoint the location of RR-MR transition in blast wave reflections. In Proceedings 26th International Symposium on Shock Waves (ed. Hannemann, K. & Seiler, F.), vol. 2, pp. 1455–1460. Springer.Google Scholar
Takayama, K. & Sasaki, M. 1983 Effects of radius of curvature and initial angle on the shock transition over concave and convex walls. In Rep. Inst. High Speed Mech, vol. 46, pp. 1–30. Japan, Tohoku University.Google Scholar
Timofeev, E. & Merlen, A. 2007 Unsteady Navier–Stokes simulations of regular-to-Mach reflection transition on an ideal surface. In Proceedings 26th International Symposium Shock Waves (ed. Hannemann, K. & Seiler, F.), vol. 2, pp. 1543–1548. Springer.Google Scholar
Timofeev, E., Skews, B. W., Voinovich, P. A. & Takayama, K. 1999 The influence of unsteadiness and three-dimensionality on regular-to-Mach reflection transitions: a high-resolution study. In Proceedings of 22th International Symposium on Shock Waves (ed. Ball, G. J., Hillier, R. & Roberts, G. T.), vol. 2, pp. 1231–1236. University of Southhampton.Google Scholar