First damkohler parameter for prediction and classification of unsteady combustions around hypersonic projectiles

An effective non-dimensional parameter referred to as the first Damk6hler parameter has been proposed to quantitatively classify the unsteady flow regime of shock-induced combustion around a hypervelocity spherical projectile into a detonable gas mixture. The parameter consists of the ratio of the fluid charac­teristic time scale to the chemical characteristic time scale. The fluid characteristic time is defined as a projectile diameter over a speed of sound behind the normal segment of the steady bow shock. The chemical characteristic time is defined as a temperature behind the normal segment of the steady bow shock over the maximum temperature increase per unit time for the exothermicity. The temperature increase for the exothermicity was estimated by the time-integration of the species equations in zero-dimension in space. The parameter quantitatively distinguished from two distinct flow regimes observed in the experimental and numerical results. Also, features of the transition between two regimes are clarified by changing scale and speed of the projectiles and pressure level of the test gases. The proposed first Damkohler number can predict the unsteady flow regime of shock-induced combustion around the projectile based on the small analytical computations estimating the chemical and fluid characteristics without the bal­listic range apparatus or the simulations on the high performance computer.