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 pro-hibitively 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.Neverthe-less,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 com-pressor 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.