The Delta Phi Method of Evaluating Overall Film Cooling Performance

Film cooling designs are often evaluated experimentally and characterized in terms of their spatial distributions of adiabatic effectiveness, η, which is the nondimensionalized form of the adiabatic wall temperature, T_aw. Additionally, film cooling may alter the convective heat transfer coefficient with the possibility of an increase in h that offsets the benefits of reduced T_aw. It is therefore necessary to combine these two effects to give some measure of the benefit of film cooling. The most frequently used method is the net heat flux reduction (NHFR), which gives the fractional reduction in heat flux that accompanies film cooling for the hypothetical case of constant wall temperature. NHFR is imperfect in part due to the fact that this assumption does not account for the primary purpose of film cooling—to reduce the metal temperature to an acceptable level. In the present work, we present an alternative method of evaluating film cooling performance that yields the reduction in metal temperature, or in the nondimensional sense, an increase in ϕ that would be predicted with film cooling. This Δϕ approach is then applied using experimentally obtained η and h/h₀ values on a simulated turbine blade leading edge region. The delta-phi approach agrees well with the legacy NHFR technique in terms of the binary question of whether the film cooling is beneficial or detrimental, but provides greater insight into the temperature reduction that a film cooling design would provide an actual turbine component. For example, instead of giving an area-averaged NHFR = 0.67 (indicating a 67% reduction in heat flux through film cooling) on the leading edge region with M = 0.5, the Δϕ approach indicates an increase in ϕ of 0.061 (or a 61 K surface temperature decrease with a notional value of T_∞−T_c = 1000 K). Alternatively, the technique may be applied to predict the maximum allowable increase in T_∞ against which a film cooling scheme could protect.