Shock management in diverging flow passages by blowing/suction, part 1: Quasi-one-dimensional theory

A quasi-one-dimensional compressible-flow theory in the presence of blowing/suction is presented for shock management inside supersonic inlets and supersonic compressor cascades. The theory can predict the amount of flow blowing/suction required to place the shock at a prescribed area ratio in a diverging flow passage as the exit pressure is varied. The formulation is based on classical one-dimensional compressible-flow theories for normal shock waves and flow blowing/suction. Application of the theory to a supersonic nozzle shows that if the exit pressure is higher than the base value, then suction behind the shock or blowing in front of the shock is required to hold the shock stationary. On the other hand, if the exit pressure is lower than the base value, then blowing behind the shock or suction in front of the shock is required. For the case of blowing, the amount required to fix the shock location is a strong function of the stagnation conditions and the angle of the blowing flow. The resulting theory is checked against.