Geometrical Uncertainty and Film Cooling: Fillet Radii

This study presents an investigation of the impact of filleted edge variations on heat transfer. In real gas turbines, sharp edges are an approximation because of manufacturing tolerances and/or geometrical modifications occurring during operation. The value of fillet radius is not exactly known a priori. It can be assumed that a specific radius occurs with a probability following a probabilistic distribution. For this reason, the effect of variation of the filleted edge on internal channel of a film cooling configuration has been studied numerically using an in house solver. The hole exit is fanshaped and the feeding duct axis and the main stream are perpendicular to each other. A response surface has been generated, varying the internal Mach number of coolant and the pressure ratio range between coolant and main gas. Four fillet radii for the internal duct have been analyzed, $r/D=0.0–5%$⁠. A Gaussian distribution for the fillet radius has been assumed. Using the overmentioned distributions, it is possible to obtain the probabilistic functions of corresponding discharge coefficient Cd and adiabatic effectiveness $η$⁠. The overall variation of Cd and $η$ can be more than 10% the value without fillet. Furthermore, the differences on Cd due to the uncertainties on fillet radius are bigger than those obtained due to modifying the exit duct shape (i.e., from cylindrical to fanshaped). This paper shows that the effect of variation of fillet radii must be included in numerical simulations. This has direct consequences on LES and DNS simulations, which normally include sharp corners or mean radii. A probabilistic approach must be included in the analysis of the results and the equivalent fillet radius must be assumed instead.