Uncertainty quantification of film cooling effectiveness in gas turbines

Abstract

In this study the effect of uncertainty of velocity ratio on jet in crossflow and particual- rly film cooling performance is studied. Direct numerical simulations have been combined with a stochastic collocation approach where the parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) method. Velocity ratio serves as a bifurcation parameter in a jet in a crossflow and the dynamical system is shown to have several bifurcations. As a result of the bifurcations, the target functional is observed to have low-regularity with respect to the paramteric space. In that sense, ME-gPC is particularly effective in discretizing the parametric space. One particular case of a jet in a crossflow is numerically solved with the velocity ratio variations assumed to have a truncated Gaus- sian distribution with mean of 1.5 and the standard variation of approximately 0.5. Five elements are used to discretize the parametric space using ME-gPC method. Within each element general polynomial chaos of order 3 is used. A fast convergence of the polynomial expansion in the parametric space was observed. Time-dependent Navier-Stokes equations are sampled at Gauss-quadrature points using spectral/hp element method implemented in NEKTAR. Overall due to the low-regularity of the response surface, ME-gPC is observed to be a computationally effective strategy to study the effect of uncertainty in a jet in a crossflow when velocity ratio is the random parameter.