Prediction method of unsteady combustion around hypersonic projectile in stoichiometric hydrogen-air

An effective nondimensional parameter, referred to as the first Damköhler parameter, is proposed to quantitatively classify the unsteady flow regime of shock-induced combustion around a hypervelocity spherical projectile in the stoichiometric hydrogen-air mixture. The parameter consists of the ratio of the fluid characteristic timescale to the chemical characteristic timescale. The fluid characteristic time is defined as a projectile diameter divided by 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 tune for the exothermicity. The temperature increase for the exothermicity is estimated by the time integration of the species equations in the zero dimension in space. The proposed first Damköhler number can be analytically computed by the chemical and fluid characteristics only, without ballistic range experiments or expensive simulations on high-performance computers. The parameter is quantitatively characterized from the two distinct flow regimes observed in the experimental and numerical results. Also, features of the transition between two regimes are clarified by changing the projectile diameter, the projectile speed, and the test gas pressure.