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-degree 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. A fast convergence of the polynomial expansion in the random space was observed. 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 standard deviation of 15% was observed in the region within a four-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. Overall the computational strategy is shown to be very effective with the total computational cost being equivalent to solving twenty independent direct numerical simulations that are performed concurrently.