Shock Formation in Overexpanded Tip Leakage Flow

Shock formation due to overexpansion of supersonic flow at the inlet to the tip clearance gap of a turbomachine has been studied. The flow was modeled on a water table using a sharp-edged rectangular channel. The flow exhibited an oblique hydraulic jump starting on the channel sidewall near the channel entrance. This flow was analyzed using hydraulic theory. The results suggest a model for the formation of the jump. The hydraulic analogy between free surface water flows and compressible gas flows is used to predict the location and strength of oblique shocks in analogous tip leakage flows. Features of the flow development are found to be similar to those of compressible flow in sharp-edged orifices. Possible implications of the results for high-temperature gas turbine design are considered.