Theoretical Considerations for Scaling Convection in Overall Effectiveness Experiments

Abstract

An increasingly common experimental technique allows measurement of overall effectiveness by matching the Biot number between experimental and engine conditions. While much work has been devoted to determining the appropriate flow conditions necessary to scale adiabatic effectiveness, little attention has been paid to subtleties beyond matching the Biot number that arises when performing overall effectiveness experiments. Notably, the ratio of the internal and external heat transfer coefficients must be matched. The density ratio and the specific heat ratio have been shown to play important roles in scaling adiabatic effectiveness; however, now 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 influence heat transfer coefficient behavior, this gives rise to an additional nondimensional parameter that should be matched to properly perform 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 Re∞ and the advective capacity ratio. We demonstrate the validity of this requirement through computational fluid dynamics simulations, which are well-suited for this since over-constrained requirements can be overcome by altering gas properties. 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.