Summary
The existence of the jump in β1=β2 double roots in the three-shock theoretical solutions of steady Mach reflections on the (θ1, M0) plane is determined for the first time, θ1 is flow deflection behind the incident shock, M0 is the incident shock Mach number. This jump behavior of β1=β2 double roots explains the occurrence of newly found α1=β2 double roots of multiple theoretical solutions of steady MR in perfect diatomic and triatomic gases. The critical condition determining the location of M0 of this jump, for gas specific heats ratio of 1.4, is obtained to occur at α1= β1= β2 triple roots where M0=3.41485. There are two findings closely associated with this jump behavior of β1=β2 double roots: 1, the α1 solutions cease to become physically meaningful for M0 > 3.41485; 2, α1=β2 double roots do not exist for M0 < 3.41485.
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© 2009 Springer-Verlag Berlin Heidelberg
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Liu, JJ., Tseng, TI. (2009). α1, β1, β2 - root characteristics of multiply possible theoretical solutions of steady Mach reflections in perfect diatomic gases. In: Hannemann, K., Seiler, F. (eds) Shock Waves. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85181-3_86
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DOI: https://doi.org/10.1007/978-3-540-85181-3_86
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85180-6
Online ISBN: 978-3-540-85181-3
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