Thrust loss due to supersonic mixing

The maximum thrust developed by a device in which two streams mix in a parallel configuration at supersonic velocities is estimated. Total pressure profiles in a two-dimensional, compressible shear layer are calculated by assuming turbulent Prandtl and Lewis numbers of unity. As the convective Mach number Mc rises, the total pressure acquires a defect that becomes large for Mc > 1. For shear layers with equal freestream total pressures, an analytical relation for the defect vs Mc is found. The extent and magnitude of the defect agrees well with experimental data. The loss in total pressure is connected to the loss in thrust of a simplified model of a scramjet. The thrust loss is about 30% for Mc = 2 and 50% for Mc 3. The trends are insensitive to details of the shear-layer velocity profile and to the ratios of freestream quantities. The role of turbulent-energy dissipation in the reduction of total pressure is discussed.