Uncertainty quantification and sensitivity analysis of aerothermal performance for the turbine blade squealer tip

Abstract

In this paper, an uncertainty quantification (UQ) method is proposed using the non-intrusive polynomial chaos expansion method and Smolyak sparse grids. Then coupled with three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solutions, an uncertainty quantification procedure is carried out for aerodynamic and heat transfer performance of GE-E3 rotor blade squealer tip. A parameter sensitivity analysis using the Sobol Indice method is carried out to identify the key parameters for aerothermal performance of the squealer tip. Wherein, the inlet total pressure and the inlet flow angle are considered as flow condition uncertainty parameters and cavity depth is considered as geometrical uncertainty parameters. The uncertainty analysis results showed that under the influence of the uncertain geometry and operating conditions, the heat flux of squealer tip basically conforms to the normal distribution and the statistical mean value of it increased by 28.30% relative to the design value and the probability of it deviating from the design value by 10% is as high as 86.59%. The statistical average of the squealer tip film cooling effectiveness is reduced by 23.89% compared to the design value, and the probability of it deviating from the design value by 10% is as high as 85.08%. The result of sensitivity analysis reveals that the uncertainty of the aerodynamic characteristics of the squealer tip is almost entirely caused by the inlet flow angle which accounts for 94.01% of the variance of the leakage flow rate. And it is also the dominant variable for the uncertainty of the heat transfer performance considering that its variance indexes for tip heat flux QTip and film cooling effectiveness η are 67.71% and 54.42% respectively. Compared with the main effects, the influence of the interaction effects among the variables on the squealer tip aerothermal performance is almost negligible.