Search

Manufactured compressor blades deviate from their intended design, leading to a shift in the mean and scattering of aerodynamic performance. To mitigate performance deterioration without increasing manufacturing costs, an accurate and efficient evaluation of aerodynamic uncertainty, known as uncertainty quantification (UQ), is crucial. The high cost of three-dimensional computational fluid dynamics (CFD) simulations has prompted UQ studies to predominantly target two-dimensional cases or extend to three dimensions with a limited number of geometric variables. Since geometric deviations exist at various positions on three-dimensional blades, accurately describing them would necessitate a high-dimensional geometric deviation space. To investigate high-dimensional uncertainty problems, an efficient adjoint-based UQ method is proposed and demonstrated using the three-dimensional transonic fan, NASA Rotor 67. The method proves to be not only hundreds of times faster than full-fidelity CFD but also yields results with satisfactory accuracy. The investigation into the underlying mechanism reveals that geometric uncertainties significantly influence shock waves, tip clearance vortices, corner vortices, and the radial distribution of three-dimensional flows, ultimately resulting in deviations in aerodynamic performance.

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.