A Resistive Model to Characterize Overall Effectiveness Influenced by Multiple Coolant Temperatures

Abstract

The surface temperature of a film cooled turbine hot gas path component is typically nondimensionalized according to the overall effectiveness. This nondimensionalization scheme takes advantage of the fact that the surface temperature must be bounded by the coolant temperature and the freestream recovery temperature. Additional complexity arises when the surface temperature is influenced by the addition of a second coolant stream. While the surface temperature remains bounded by the cooler of the two coolant streams, the presence of the warmer stream means that the resulting overall effectiveness is now a function not only of the appropriately nondimensionalized coolant and freestream flowrates, but an additional nondimensional parameter that describes the relative difference in the two coolant temperatures. Previously, it was thought that experiments or computational fluid dynamics simulations would be required to discern this effect. In the present work, however, we introduce a linear resistive model that is based upon the exact solution to the energy equation and which accounts for the effect of any number of independent sources that influence the surface temperature. The model’s efficacy was demonstrated using experimental data acquired on conducting models in which two rows of holes ejected coolant from two independent plenums at two different temperatures.