Numerical modelling of steady detonations with the CREST reactive burn model

Abstract

Watt et al. [J Eng Math 75(1):1-14, 2012] have shown that one can obtain good results for the propagation of detonation waves in cylindrical charges by assuming that the post-shock streamlines are straight. In this paper, we compare this Straight Streamline Approximation (SSA) to high-resolution Direct Numerical Simulations (DNS) for different models of explosives. We find that the SSA is less accurate for realistic explosion models than it is for polytropic equations of state with power-law reaction rates.

Numerical modelling of steady detonations with a variational streamline approach

“…The governing equations in streamline coordinates, ( 7)-( 10) can be reduced to a master equation in the y velocity, v, coupled to the rate law. Following a similar approach outlined in a previous paper [12] the master equation in v is…”

“…First, a power law type which has maximal reaction at the shock, where the SSA has been shown to be predict diameter effect curves with good accuracy compared to DNS [11]. Secondly, the induction type which has zero reaction at the shock and reaches a maximum reaction downstream, this class reaction rate model is more representative of reaction rate models typically used; the SSA was shown to be less accurate compared to DNS for reaction rates of this form [12].…”

“…Pressure dependent rate laws are commonly used to develop detonation models. The choice of x(ψ, y) was guided by the following: exothermic heat release has the effect of curving the streamlines inwards [9]; the power law reaction model has maximal reaction at the shock, therefore its effect on the streamline curvature will be greatest near the shock, and reduce as reaction proceeds; in [11,12] it was shown that for such reaction rate models the streamlines curve immediately behind the shock and then straighten through the reaction zone so any suitable ansatz should have maximal curvature at the shock and straighten through the reaction zone. A convenient form of ansatz which will reproduce those features is…”

“…which match the analytical values obtained from the oblique shock relations at the shock y = y f . In [12] it was shown that, for γ = 3,…”

“…They showed that it can accurately reproduce the velocity-radius curves from high resolution DNS calculations for non-ideal explosives. A follow up study found that for detonation models whose reaction rate models did not have maximal reaction at the shock, the SSA proved to be less accurate [12].…”