Efficient Quantification of Aerodynamic Performance Uncertainty due to Geometric Variability Using an Adjoint Method

Abstract 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 escalating manufacturing costs, accurate and efficient evaluation of aerodynamic uncertainty, known as uncertainty quantification (UQ), is crucial. The computational 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 geometric deviation space with a large number of dimensions. 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.