Modelling of non-ideal steady detonations

Steady state detonations of rate-stick explosives can be modelled via a streamline based
approach. The Straight Streamline Approximation (SSA) is a method for predicting the
shape of the shock front and sonic surface for an explosive rate-stick. The SSA model
is implemented with different explosives models to verify its ability to accurately match
high resolution Direct Numerical Simulations (DNS) beyond the simple polytropic EOS
(equation of state) and power law reaction rate models. For explosive models using a
reaction rate with an induction zone it shown that the SSA is unable to capture diameter
effect curves when compared with DNS.
The CREST model is implemented into the ZND and Wood-Kirkwood steady-
state detonation models. Implementing the CREST model into the steady-state models
required the development of a thermodynamic relation not published before. Rate-
stick calculations are performed for the SSA model and compared with DNS for various
explosive models. With a realistic equation of state there is a limit on the boundary that
the SSA model can integrate to, beyond this the streamlines begin to converge and the
model equations break down. This places a limit on the SSA’s modelling capabilities
not previously reported.
Equations for the post-shock streamline curvature with a reaction term are devel-
oped. The streamline curvature is calculated for a polytropic EOS with and without
reaction at the shock. It is shown that when reaction is a maximum at the shock the
magnitude of the streamline curvature is reduced and, in some cases, changes the sign
of the curvature. With no reaction at the shock the streamline curvature is signifi-
cantly larger. Moreover DNS shows that the streamlines are more curved for reaction
rates with induction zones when compared to simple power law reaction rates. The
implications for the SSA’s validity are discussed.