Shock formation in overexpanded flow: a study using the hydraulic analogy

Tests were performed to study the mechanism of shock formation in supersonic flow in long orifices to gain insight into the leakage flow of turbine tip gaps. The flow was modeled on a water table using a sharp-edged rectangular channel. The hydraulic analogy between free surface water flows and compressible gas flows was used to study the implications of the water table flow on tip leakage flows.

The flow on the water table exhibited oblique hydraulic jumps starting on the channel sidewall near the channel entrance. This flow was analyzed using the oblique hydraulic jump relations developed by classical hydraulic theory. The results of this analysis suggested a model for the formation of the jump. As the flow accelerates around the corner of the channel entrance, supercritical free stream flow is turned as it intersects the sidewall. The abrupt change in flow direction results in the formation of the oblique hydraulic jump.

An acceptable hydraulic analogy of compressible gas flows with shocks was obtained by reducing the surface tension of the water and using a large model size. The modified analogy for non-isentropic flow then allowed quantitative evaluation of the modeled shock structure in a compressible flow field. The predicted shock formation in such a flow has possible implications for both the efficiency of a gas turbine and the useful life of the turbine blade.