Statistical investigations of profile error impact on flow and performance of a low-pressure turbine cascade

Abstract

Profile error impacts on turbomachinery flow and blade performance have been attracting widespread attention. In the study, the characteristics of profile error of about one thousand real low-pressure turbine blades are extracted. Sensitivities of total pressure loss coefficient (ζ), outflow angle (β), and Zweifel lift coefficient (zw) of the blade to the basis modes of profile error are calculated. Flow solutions of the blades considering specified basis modes with high sensitivities illustrate that profile error contributes much to the variations of transition onset and flow acceleration on the suction side and flow mixing intensity in the wake. Uncertainty quantification of performance changes is then implemented by the method of moment (MM) using second-order sensitivities. With only 5% computational cost of that by Monte Carlo simulation (MCS), the MM-based statistical results are close to MCS ones with maximum relative error not exceeding 1.07%. The statistical results reveal that the variations of both β and zw are linearly dependent, whereas the variation of ζ is nonlinearly dependent on profile error. As the variation range of profile error increases, the standard deviation and skewness increase, indicating that the performance is more dispersive and the nonlinear dependence of ζ on profile error is intensified. Finally, the MCS flow fields are analyzed. Statistical shear stress near the leading edge and transition onset, statistical boundary layer momentum thickness near transition onset, statistical intermittency near transition onset, and statistical entropy in the wake are more considerable. The impact mechanisms of profile error on turbine flow and performance changes are demonstrated.