On the propagation and reflection of curved shock waves
Date
2015-04
Authors
Gray, Brendan James
Journal Title
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Abstract
Curved shock waves, particularly converging shock waves, have applications in a wide variety
of elds, yet they are severely under-represented in the literature. Shock re
ection is typically
categorised in terms of the shock Mach number and incident angle, but these parameters both
vary with time for a curved shock wave.
A facility capable of producing shock waves with an arbitrary two-dimensional pro le was
designed and manufactured. A planar shock from the end of a conventional shock tube is
passed through a narrow slit and turned through a 90 bend, generating a shock with an
initial shape matching the pro le of the slit.
The facility was rst used to study the propagation of shock waves of arbitrary shape. This
included a brief computational
uid dynamics (CFD) study of the interaction between straight
and concave segments on a shock front, followed by CFD and experimental studies into the
propagation of shock waves consisting of both concave and convex segments, with initially
sharp and rounded pro les. Shocks with Mach numbers between 1.2 and 1.45 were generated,
and the behaviour of the shock waves produced by the experimental facility agreed favourably
with the CFD simulations, particularly for the higher Mach numbers.
A detailed study into the re
ection of converging cylindrical shock wave segments was then
carried out. CFD simulations for Mach numbers at the apex of the wedge varying from 1.2
to 2.1, for wedge angles between 15 and 60 , and experiments with apex Mach numbers
between 1.5 and 2.1 and wedge angles between 15 and 50 were carried out. The sonic
condition usually used for predicting the planar shock re
ection con guration was successful
at predicting the initial re
ection con guration. If the initial re
ection was regular, then the
shock was cleanly re
ected o the surface, with no discontinuities in the re
ected shock front.
However, if the initial re
ection was a Mach re
ection, this would inevitably transition into
a transitioned regular re
ection, with the residual Mach stem and shear layer still present
behind the re
ection point. Collision of the Mach stem with the corner at the end of the
wedge generated a small region of very high pressure, which lasted for several microseconds.
A simple theoretical model was developed for estimating the Mach stem height and transition
point for a converging cylindrical shock segment encountering a straight wedge. The model
gives reasonable predictions for shocks of moderate strength and wedge angles below 40 , but
deviates from experimental results for wedges at 40 and above.