Author:
HENDERSON LE ROY F.,MENIKOFF RALPH
Abstract
For a convex equation of state, a general theorem on shock waves
is proved: a
sequence of two shocks has a lower entropy than a single shock to the same
final
pressure. We call this the triple-shock entropy theorem. This
theorem has important
consequences for shock interactions. In one dimension the interaction of
two shock
waves of the opposite family always results in two outgoing shock waves.
In two
dimensions the intersection of three shocks, such as a Mach configuration,
must have
a contact. Moreover, the state behind the Mach stem has a higher entropy
than
the state behind the reflected shock. For the transition between a regular
and Mach
reflection, this suggests that the von Neumann (mechanical equilibrium)
criterion
would be preferred based on thermodynamic stability, i.e. maximum entropy
subject
to the system constraint that the total specific enthalpy is fixed. However,
to explain
the observed hysteresis of the transition we propose an analogy with phase
transitions
in which locally stable wave patterns (regular or Mach reflection) play
the role of
meta-stable thermodynamic states. The hysteresis effect would occur only
when the
transition threshold exceeds the background fluctuations. The transition
threshold is
affected by flow gradients in the neighbourhood of the shock intersection
point and
the background fluctuations are due to acoustic noise. Consequently, the
occurrence of
hysteresis is sensitive to the experimental design, and only under special
circumstances
is hysteresis observed.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
46 articles.
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