Investigations on the Aerothermal Performance Uncertainty Quantification of the Turbine Blade Squealer Tip

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Abstract The first-stage rotor squealer tip is a key area in the gas turbine for both aerodynamic performance and heat transfer characteristics, which should be carefully designed. However, harsh operating conditions near the rotor squealer tip can cause the geometry of the squealer tip to degrade, and manufacturing inaccuracies can also cause the squealer tip geometry to deviate from the ideal design. In this work, an uncertainty quantification (UQ) method is proposed using the non-intrusive polynomial chaos expansion method and Smolyak sparse grids. Then coupled with three dimensional (3D) 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 temperature and the blowing ratio are considered as flow condition uncertainty parameters and tip clearance is considered as geometrical uncertainty parameters. The uncertainty analysis results show 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 13.56% relative to the design value and the probability of it deviating from the design value by 10% is as high as 65.68% The statistical average of the squealer tip film cooling effectiveness is reduced by 29.52% compared to the design value, and the probability of it deviating from the design value by 10% is as high as 91.83%. The result of sensitivity analysis reveals that the uncertainty of the aerodynamic characteristics of the squealer tip is almost entirely caused by the tip clearance which accounts for 88.02% of the variance of the leakage flow rate. The inlet total temperature has almost no effect on the uncertainty of the aerodynamic performance. However, it is 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 84.87% and 24.87% respectively. Compared with the main effects, the influence of the interaction effects among the variables on the squealer tip aerothermal performance is almost negligible.