Correction formula for film-cooling effectiveness considering the influence of thermal radiation in high-temperature environments

Abstract

Film-cooling effectiveness (η) evaluation test of aero-engine turbine blades is usually conducted in a low or medium temperature environment. Through the scaling criteria, it can be approximately equivalent to the η in a real high-temperature environment. However, this method does not consider the influence of thermal radiation and overestimates the cooling effect of the gas film in a high-temperature environment, which in turn affects the design accuracy of turbine blades. In this study, the thermal radiation correction of the film-cooling effectiveness scaling criteria was done by developing a physics-based empirical correlation. Firstly, the radiation correction factor (krad) was defined as the average value of the flow direction of η¯high/η¯low, which is related to gas-to-cold-air temperature ratio (TR), emissivity (εw), and operating temperature ratio (the ratio of the hot gas temperature of the η¯ predicted to that of the known η¯, Tbi). Secondly, based on computational fluid dynamics (CFD) results, the influence of the dimensionless parameters (εw, Tbi, TR) on krad was revealed. Subsequently, the physical relationship and correlation form between the three parameters and krad was preliminarily determined. Moreover, a test dataset (εw, Tbi, TR, krad) of a 3 × 4 × 3 measurement matrices was built. The relationship between (εw, Tbi, TR) and krad was incorporated into the empirical framework of krad, and the empirical coefficient was determined by nonlinear fitting. Finally, the applicable dimensionless parameter range for the current correlation were determined by recording datasets with the coefficients of determination (R2) > 0.8. When the scaling criteria from low to high temperature were satisfied and the influence of the radiation participating medium was ignored, εw was in a range of 0.3–0.8, Tbi was in a range of 1–3, and TR was in a range of 1.5–2.5; any reasonable Reynolds number and blowing ratio were applicable to the thermal radiation correction correlation.