Abstract
An increasingly common experimental technique allows measurement of overall effectiveness by matching the Biot number between experimental and engine conditions. The measured overall effectiveness distribution correlates to the expected turbine component temperature distribution. While a good deal of work has been devoted to determining the appropriate flow conditions necessary to scale adiabatic effectiveness, very little attention has been paid to the subtleties beyond matching the Biot number that arise when performing experiments on a conducting model to determine overall effectiveness. Notably, the ratio of the internal and external heat transfer coefficient must be matched. The density ratio and more recently, the specific heat ratio, have been shown to play important roles in scaling adiabatic effectiveness; however, in the present work, we demonstrate the requirements for the coolant and freestream flow conditions required to conduct an appropriately scaled overall effectiveness experiment. Since the viscosity and thermal conductivity of the fluids (in addition to density and specific heat) play significant roles that influence heat transfer coefficient behavior, this gives rise to an additional nondimensional parameter that should, in theory, be matched to properly execute an overall effectiveness experiment.
In this paper, we demonstrate that this new nondimensional parameter will be matched provided that Pr∞, Prc, and Rec are matched in addition to the freestream Reynolds number and the advective capacity ratio. We demonstrate the validity of this requirement through computational fluid dynamics simulations, which are well-suited for this since the over-constrained requirements can be overcome by altering gas properties from the real values. Simulations of an internally cooled wall exposed to a hot freestream were performed with various gases to show the sensitivity of the overall effectiveness to these previously ignored requirements. An additional set of simulations on a film cooled plate reveals additional complexities when coolant mixes with the freestream gas.