Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness

In this study, the effect of randomness of blowing ratio on film cooling performance is investigated by combining direct numerical simulations with a stochastic collocation approach. The geometry includes a 35-deg inclined jet with a plenum attached to it. The blowing ratio variations are assumed to have a truncated Gaussian distribution with mean of 0.3 and the standard variation of approximately 0.1. The parametric space is discretized using multi-element general polynomial chaos (ME-gPC) with five elements where general polynomial chaos of order 3 is used in each element. Direct numerical simulations were carried out using spectral element method to sample the governing equations in space and time. The probability density function of the film cooling effectiveness was obtained and the standard deviation of the adiabatic film cooling effectiveness on the blade surface was calculated. A maximum of 20% of variation in film cooling effectiveness was observed at 2.2 jet-diameter distance downstream of the exit hole. The spatially-averaged adiabatic film cooling effectiveness was 0.23 ± 0.02. The calculation of all the statistical properties were carried out as off-line post processing. A fast convergence of the polynomial expansion in the random space is observed which shows that the computational strategy is very cost-effective.