A Method for Correlating the Influence of External Crossflow on the Discharge Coefficients of Film Cooling Holes

An empirical means of predicting the discharge coefficients of film cooling holes in an operating engine has been developed. The method quantifies the influence of the major dimensionless parameters, namely hole geometry, pressure ratio across the hole, coolant Reynolds number, and the freestream Mach number. The method utilizes discharge coefficient data measured on both a first-stage high-pressure nozzle guide vane from a modern aero-engine and a scale (1.4 times) replica of the vane. The vane has over 300 film cooling holes, arranged in 14 rows. Data was collected for both vanes in the absence of external flow. These noncrossflow experiments were conducted in a pressurized vessel in order to cover the wide range of pressure ratios and coolant Reynolds numbers found in the engine. Regrettably, the proprietary nature of the data collected on the engine vane prevents its publication, although its input to the derived correlation is discussed. Experiments were also conducted using the replica vanes in an annular blowdown cascade which models the external flow patterns found in the engine. The coolant system used a heavy foreign gas (SF₆ /Ar mixture) at ambient temperatures which allowed the coolant-to-mainstream density ratio and blowing parameters to be matched to engine values. These experiments matched the mainstream Reynolds and Mach numbers and the coolant Mach number to engine values, but the coolant Reynolds number was not engine representative (Rowbury, D. A., Oldfield, M. L. G., and Lock, G. D., 1997, “Engine-Representative Discharge Coefficients Measured in an Annular Nozzle Guide Vane Cascade,” ASME Paper No. 97-GT-99, International Gas Turbine and Aero-Engine Congress & Exhibition, Orlando, Florida, June 1997; Rowbury, D. A., Oldfield, M. L. G., Lock, G. D., and Dancer, S. N., 1998, “Scaling of Film Cooling Discharge Coefficient Measurements to Engine Conditions,” ASME Paper No. 98-GT-79, International Gas Turbine and Aero-Engine Congress & Exhibition, Stockholm, Sweden, June 1998). A correlation for discharge coefficients in the absence of external crossflow has been derived from this data and other published data. An additive loss coefficient method is subsequently applied to the cascade data in order to assess the effect of the external crossflow. The correlation is used successfully to reconstruct the experimental data. It is further validated by successfully predicting data published by other researchers. The work presented is of considerable value to gas turbine design engineers as it provides an improved means of predicting the discharge coefficients of engine film cooling holes.