Method for Determining Adiabatic Film Effectiveness in Presence of Thermal Boundary Layer

Abstract

In this paper, we present a new method for determining adiabatic film effectiveness in film cooling experiments with nonuniform inlet temperature distributions, in particular the situation of an inlet thermal boundary layer. This might arise in a quasi-steady experiment due to loss of heat from the mainstream flow to the inlet contraction walls, for example. In this situation, the thermal boundary layer would be time-varying. Adiabatic film effectiveness is generally normalized by the difference between mainstream and coolant gas temperatures. Most importantly, these temperatures are generally assumed to be spatially—and, possibly temporally—uniform at the system inlet. In experiments with nonuniform inlet temperature, the relevant hot gas temperature for a particular point of interest on a surface is not easily determined, being a complex function of both the inlet temperature profile and the flow field between the inlet and the point of interest. In this situation, adiabatic film effectiveness cannot be uniquely defined using conventional processing techniques. We solve this problem by introducing the concept of equivalent mainstream effectiveness, a nondimensional temperature for the mainstream that can be used to represent the thermal boundary layer profile at the inlet plane, or the effective temperature of the mainstream gas—which we refer to as the equivalent mainstream temperature—entrained into the mixing layer affecting the wall temperature at a particular point of interest. By using data from two or more time instants during an experiment, we simultaneously solve for equivalent mainstream effectiveness and true adiabatic film effectiveness, that is, the adiabatic film effectiveness that we would measure in an experiment with both steady and uniform inlet temperature. This is an important transformation because the true adiabatic effectiveness has a clear physical interpretation and is a more transportable quantity between systems (comparisons between different experiments, between experiment and computational fluid dynamics (CFD), etc.). The proposed method is experimentally demonstrated using full-surface infrared (IR) thermography measurements of a cooled rotor blade platform, operated in a transonic linear cascade facility at matched engine conditions. Film effectiveness measurements processed in the conventional way suffer from inlet thermal boundary layer effects, rendering them both time-varying (as heat is released to the walls of the tunnel) and, in certain regions, nonphysical in magnitude. The proposed technique renders the same data insensitive to time, and everywhere within physically reasonable limits. By demonstrating independence to the particular (time-varying) inlet temperature profile, we demonstrate the advantages of the proposed technique.