Scaling Flat Plate, Low Temperature Adiabatic Effectiveness Results Using the Advective Capacity Ratio

Effective design of film cooled engine components requires the ability to predict behavior at engine conditions. This is commonly accomplished through low temperature testing on scaled up geometries. The adiabatic effectiveness, η, is one indicator of the performance of a film cooling scheme. Performing an experiment to measure η in a low temperature wind tunnel requires appropriate selection of the coolant flow rate. Perhaps the most common flow rate parameter that is used to characterize the coolant flow relative to the freestream is the mass flux ratio, or blowing ratio, M. This is usually used in lieu of the velocity ratio to account for the fact that the density of the coolant is typically much larger than that of the hot freestream gas. Numerous studies have taken place evaluating the ability of M to properly scale the effects of density ratio and its performance has produced mixed results. The momentum flux ratio, I, is an alternative that is also found to have mixed success, leading some to recommend matching the density ratio to allow simultaneous matching of M and I. Nevertheless, widely varying results in the literature regarding the efficacy of these coolant flow rate parameters to scale the density ratio suggests there may be other largely ignored effects playing a role in the thermal physics. In the present work, thermal experiments were performed to measure adiabatic effectiveness on a flat plate with a single 7-7-7 shaped hole. Various coolant gases were used to give a large range of thermodynamic property variations. It is shown that a relatively new coolant flow rate parameter that accounts for not only density variations but also specific heat variations, the advective capacity ratio (ACR), far exceeds the ability of either M or I to provide matched adiabatic effectiveness between the various coolant gases that exhibit extreme property differences. Particularly considering that the specific heat of the coolant in an engine is significantly lower than the specific heat of the freestream gas, ACR is shown to be appropriate for characterizing non-separating coolant flow situations.