Efficient Quantification of Structural Uncertainty in RANS Simulations of a Transonic Axial Compressor using Anisotropic Perturbations

Abstract This study proposes an efficient strategy for quantifying the structural uncertainty of Reynolds-averaged Navier–Stokes models in transonic axial compressors, designed to reduce the computational cost associated with existing eigenspace perturbation frameworks. The approach builds upon the non-uniform eigenvalue perturbation method, which directly perturbs the eigenvalues of the Reynolds stress anisotropy tensor. The approach is demonstrated on NASA Rotor 37, where perturbations are shown to modify shock structures and affect aerodynamic performance, confirming the approach's applicability under transonic conditions. In this method, a relaxation factor ωr is introduced to adjust the perturbation strength. A systematic sensitivity analysis reveals that ωr strongly influences the predicted uncertainty bounds, while the performance response gradually saturates as ωr increases, exhibiting diminishing marginal returns. Based on these findings, a preliminary reference range of ωr = 2.0–2.5 is suggested for the one-component perturbation mode, balancing coverage, convergence, and computational efficiency. By integrating the present results with previous work, a practical uncertainty quantification strategy is established: reliable predictions can be achieved by considering only the non-uniform eigenvalue perturbation with the one-component and three-component limiting states of turbulence anisotropy, combined with an appropriate choice of ωr. This strategy significantly reduces computational requirements while maintaining predictive robustness, providing an efficient and implementable tool for uncertainty quantification in turbomachinery applications.