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

Design of film-cooled engine components requires the ability to predict behavior at engine conditions through low-temperature testing. The adiabatic effectiveness, η, is one indicator film cooling performance. An experiment to measure η in a low-temperature experiment requires appropriate selection of the coolant flowrate. The mass flux ratio, M, is usually used in lieu of the velocity ratio to account for the fact that the coolant density is larger than that of the hot freestream at engine conditions. Numerous studies have evaluated the ability of M to scale η with mixed results. The momentum flux ratio, I, is an alternative also found to have mixed success, leading some to recommend matching the density ratio to allow simultaneous matching of M and I. Nevertheless, inconsistent results in the literature regarding the efficacy of these coolant flowrate parameters to scale the density ratio suggest other properties also play a role. Experiments were performed to measure η on a flat plate with a 7-7-7-shaped hole. Various coolant gases were used to give a large range of property variations. We show that a relatively new coolant flowrate parameter that accounts for density and specific heat, the advective capacity ratio, far exceeds the ability of either M or I to provide matched η between the various coolant gases that exhibit extreme property differences. With the specific heat of coolant in an engine significantly lower than that of the freestream, advective capacity ratio (ACR) is appropriate for scaling η with non-separating coolant flow.