Abstract
The flow downstream of an axisymmetric conical shock wave, with a downstream pointing apex, can be predicted by solving the Taylor-Maccoll equations. Previous research, however, has suggested that these theoretical flowfields are not fully realisable in practice, and that a Mach reflection forms towards the centreline of the flow. This phenomenon is investigated for the case where the freestream Mach number is 3.0 and the shock angle is 150\(^\circ \). A range of complementary prediction techniques that include the solution to the Taylor-Maccoll equations, the method of characteristics, curved shock theory and CFD, are used to gain insight into this flow. The case where a cylindrical centrebody is placed along the axis of symmetry is studied for several values of centrebody radius that are expected to produce regular reflection at the centrebody surface. An analysis of pressure gradients suggests that the flowfield downstream of the reflected shock does not contribute to the process of transition from regular to Mach reflection at these conditions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Courant, R., Friedrichs, K.O.: Supersonic flow and shock waves. Interscience (1948)
Grozdovskii, G.L.: Supersonic axisymmetric conical flows with conical shocks adjacent to uniform parallel flows. Prikl Mat. Mekh. 23(2), 379–383 (1959)
Isakova, N.P., Kraiko, A.N., P’yankov, K.S., Tillyayeva, N.I.: The amplification of weak shock waves in axisymmetric supersonic flow and their reflection from an axis of symmetry. J. Appl. Math. Mech. 76, 451–465 (2012)
Kraiko, A.N., Tillyayeva, N.I.: Axisymmetric-conical and locally conical flows without swirling. J. Appl. Mech. Tech. Phy. 55(2), 282–298 (2014)
Rylov, A.I.: On the impossibility of regular reflection of a steady-state shock wave from the axis of symmetry. Appl. Math. Mech. 54(2), 245–249 (1990)
Mölder, S., Gulamhussein, A., Timofeev, E., Voinovich, P.A.: Focusing of conical shocks at the centerline of symmetry. In: Proceedings of the 21th ISSW, Vol. 2, pp. 875–880, Panther Publishing (1997)
Timofeev, E., Mölder, S., Voinovich, P., Hosseini, S.H.R., Takayama, K.: Shock wave reflections in axisymmetric flow. In: Lu, F. (ed) Shock Waves, CD-ROM Proc of the 23th International Symp on Shock Waves, Fort Worth, USA, 22–27 July, 2001, University of Texas at Arlington, pp. 1486–1493 (2001)
Mölder, S.: Internal axisymmetric conical flow. AIAA J. 5(7), 1252–1255 (1967)
Mölder, S.: Curved aerodynamic shock waves. PhD Thesis, McGill University (2012)
Masterix, ver. 3.40, RBT Consultants, Toronto, Ontario, Canada (2003–2015)
Savchuk, A., Timofeev, E.: On further development of an unstructured space-marching technique. AIAA Paper 2011–3690 (2011)
Délery, J.: Handbook of compressible aerodynamics. Wiley (2010)
Mölder, S.: Curved shock theory. Shock Waves 26(4), 337–353 (2015)
Saito, T., Voinovich, P., Timofeev, E., Takayama, K.: Development and application of high-resolution adaptive numerical techniques in Shock Wave Research Center. In: Toro, E.F. (ed) Godunov Methods: Theory and Applications, pp. 763–784. Kluwer Academic/Plenum Publishers, New York, USA (2001)
Mölder, S., Timofeev, E., Emanuel, G.: Shock detachment from curved surfaces. In: Kontis, K. (ed) Proc of the 28th International Symposium on Shock Waves, Manchester, UK, 17-22 July, 2011, Springer, Vol. 2, pp. 593–598 (2011)
Mölder, S., Timofeev, E.: Regular-to-Mach reflection transition on curved surfaces. In: Book of Papers, XXIV ICTAM, 21–26 August 2016, Montreal, Canada (2016)
Acknowledgements
The present research of B.S. and E.T. is supported by the Fonds de recherche du Quèbec - Nature et technologies (FRQNT) via the Team Research Project program and the National Science and Engineering Research Council (NSERC) via the Discovery Grant program. B.S. gratefully acknowledges the McGill Engineering Doctoral Award (MEDA) funded in part by the Faculty of Engineering, McGill University. Rabi Tahir’s support regarding Masterix code is greatly appreciated.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Shoesmith, B., Mölder, S., Ogawa, H., Timofeev, E. (2018). Shock Reflection in Axisymmetric Internal Flows. In: Kontis, K. (eds) Shock Wave Interactions. RaiNew 2017. Springer, Cham. https://doi.org/10.1007/978-3-319-73180-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-73180-3_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73179-7
Online ISBN: 978-3-319-73180-3
eBook Packages: EngineeringEngineering (R0)