Stochastic variations of the operation conditions and the resultant variations of the aerodynamic performance in Low-Pressure Turbine (LPT) can often be found. This paper studies the aerodynamic performance impact of the uncertain variations of flow parameters, including inlet total pressure, inlet flow angle, and turbulence intensity for an LPT cascade. Flow simulations by solving the Reynolds-averaged Navier–Stokes equations, the SST turbulence model, and $\gamma -{\widetilde{Re}}_{\theta t}$ transition model equations are first carried out. Then, a Gaussian process (GP) based on an adaptive sampling technique is introduced. The accuracy of adaptive GP (ADGP) is proven to be high through a function experiment. Using ADGP, the uncertainty propagation models between the performance parameters, including total pressure-loss coefficient, outlet flow angle, Zweifel number, and the uncertain inlet flow parameters, are established. Finally, using the propagation models, uncertainty quantifications of the performance changes are conducted. The results demonstrate that the total pressure-loss coefficient and Zweifel number are sensitive to uncertainties, while the outlet flow angle is almost insensitive. Statistical analysis of the flow field by direct Monte Carlo simulation (MCS) shows that flow transition on the suction side and viscous shear stress are rather sensitive to uncertainties. Moreover, Sobol sensitivity analysis is carried out to specify the influence of each uncertainty on the performance changes in the turbine cascade.

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.

The impact of inlet flow variations on turbomachines is common in the real world, resulting in undesirable performance deteriorations in engineering. The origin of performance changes and how to evaluate the changes require to be investigated. On use of a polynomial chaos based surrogate model method and Monte Carlo simulation (MCS), performance impact considering the stochastic variations of the inlet flow angle for a transonic compressor rotor blade is studied, and the impact mechanisms are investigated by MCS-based statistical flow analysis. A detailed grid-independent study assisted by Richardson extrapolation is first presented to illustrate the reliability of numerical solutions. Then, the implementations of non-intrusive polynomial chaos employing an adaptive sparse grid are introduced. Uncertainty quantifications of adiabatic efficiency and mass flow rate changes of NASA Rotor 67 are achieved, and the effects of different distributions of inlet flow angle variation (IFAV) and different ranges of IFAV on the performance changes under different operation conditions are investigated. Finally, statistical analysis of flow solutions is performed by MCS. The spanwise distributions of the changes in adiabatic efficiency and mass flow rate at the outlet are presented. Moreover, the flow solutions on the blade-to-blade stream surfaces at different spans are statistically analyzed, and discussions are given to demonstrate the impact mechanisms of IFAV on performance changes.