MODELING FLOWS WITH CURVED DETONATION-WAVES

The nonzero width of a curved detonation front has a significant effec t on its propagation. Physically, the curvature effect is a small but important correction. In numerical simulations, the curvature effect t ends to be greatly exaggerated due to an artificially large width of a n underresolved wave. In the context of reactive fluid flow, a detonat ion wave consists of a lead shock followed by a thin reaction zone. Th e curvature effect is determined by the dynamics within the reaction z one; in particular, the competition between a source term for the rate of chemical energy release and a geometric source term due to front c urvature. When the width of the reaction zone is small compared with t he radius of curvature of the front, the reaction zone can be approxim ated as quasi-steady and be modeled locally by a system of ordinary di fferential equations (ODEs) in which the front curvature enters as a p arameter. Front curvature breaks the Galilean invariance and the quasi -steady approxmation is only valid in a distinguished frame determined by both the front curvature and the tangential velocity divergence ah ead of the front. The quasi-steady ODEs determine the reaction zone pr ofile to leading order and can be viewed as an extension of the ZND mo del. However, the source terms in the ODEs lead to modified Hugoniot j ump conditions that take into account front curvature and reaction zon e width. When the reaction zone is underresolved, a calculation in eff ect reduces to a ''capturing algorithm'' in which the burn model plays an analogous role for detonation waves as artificial viscosity does f or shock waves. In particular, the reaction zone has an unphysically l arge width that is proportional to the cell size. As a consequence of the modified jump conditions, the numerical reaction zone width gives rise to an artificial curvature effect. This causes numerical solution s to depend on the cell size and orientation of a detonation front rel ative to the grid. Two algorithms that:eliminate numerical curvature e ffects are discussed, detonation shock dynamics and front tracking.