Numerical predictions of oblique detonation stability boundaries

Oblique detonation stability was studied by numerically integrating the two-dimensional. one-step reactive Euler equations in a generalized, curvilinear coordinate system. The integration was accomplished using the Roe scheme combined with fractional stepping; nonlinear flux limiting was used to prevent unphysical solution oscillations near discontinuities. The method was verified on oneand two-dimensional flows with exact solutions, and its ability to correctly predict one-dimensional detonation stability boundaries was demonstrated. The behavior of straight oblique detonations attached to curved walls was then considered. Using the exact, steady oblique detonation solution as an initial condition, the numerical simulation predicted both steady and unsteady oblique detonation solutions when a detonation parameter known as the normal overdrive, In, was varied. For a standard test case with a specific heat ratio of '"Y = 1.2, a dimensionless activation energy of e = 50, and dimensionless heat release of q = 50, an oblique detonation with a constant dimensionless component of velocity tangent to the lead shock, VIan = 4.795, underwent transition to unstable behavior at In = 1.77. This is slightly higher than the threshold of In = 1.73 predicted by one-dimensional theory; thus, the two-dimensionality renders the flow slightly more susceptible to instability.