A computationally efficient hybrid leakage model for positive displacement compressors and expanders

An empirical frictional correction factor to the isentropic nozzle model has been developed for application to refrigerant leakage modeling in scroll, rotary and other similar compressors and expanders. This correction factor is derived by calculating the leakage mass flow rate with a compressible, variable area, real gas properties model and referencing the results to an isentropic nozzle model. The ratio of flows is correlated to the Reynolds number, a characteristic length and the leakage gap width. A representative selection of fluids and geometries are employed. For all the correlations, at least 93% of the points are predicted within an absolute error band of 20%.