Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method

Manufactured blades are inevitably different from their design intent, which leads to a deviation of the performance from the intended value. To quantify the associated performance uncertainty, many approaches have been developed. The traditional Monte Carlo method based on a Computational Fluid Dynamics solver (MC-CFD) for a three-dimensional compressor is prohibitively expensive. Existing alternatives to the MC-CFD, such as surrogate models and second-order derivatives based on the adjoint method, can greatly reduce the computational cost. Nevertheless, they will encounter ‘the curse of dimensionality’ except for the linear model based on the adjoint gradient (called MC-adj-linear). However, the MC-adj-linear model neglects the nonlinearity of the performance function. In this work, an improved method is proposed to circumvent the low-accuracy problem of the MC-adj-linear without incurring the high cost of other alternative models. The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade, subject to prescribed geometric variability with industrial relevance. It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost, showing the great potential for fast uncertainty quantification.