Time Averaged Net Heat Flux Reduction for Unsteady Film Cooling

Film cooling flow for reduction in heat flux to a gas turbine engine hot gas path component is generally assumed to be steady. However, unsteady film cooling may occur due to naturally occurring flow unsteadiness or may be induced intentionally. Analysis of pulsed or otherwise unsteady film coolant flow necessitates a reformulation of the existing steady-state technique for net heat flux reduction (NHFR). We show that addition of a cross-coupled term to the traditional steady form of the NHFR equation with time averaged quantities accounts for the unsteady effects. In the experimental technique to determine the time averaged NHFR, we present a new parameter $γ$ to capture the combined influence of the average adiabatic effectiveness and the coupling between $η′$ and $h′$⁠. Measurement of $γ$ is shown to be straightforward but requiring careful considerations beyond those required to measure $η$ with steady film cooling.