Adjoint Design Optimization Under the Uncertainty Quantification of Reynolds-Averaged Navier-Stokes Turbulence Model

Considering the structural uncertainties of Reynolds-averaged Navier-Stokes (RANS) models, a design optimization method under eigenspace perturbations of the RANS model has been proposed for aerodynamic applications. Optimized geometries with confidence intervals with improved performance have been obtained for U-pipe, Busemann airfoil, and supersonic separator. The perturbations are injected into the eigenvalues and eigenvectors of turbulence anisotropic tensors nonuniformly and adaptively; thus, the uncertainty interval of the RANS model is obtained by six simulations. The adjoint method is employed to perform single-objective optimization on three physical models based on uncertainty quantification. The geometric profiles before and after optimization are presented, and the area surrounded by different profiles reflects the differences in geometric optimization caused by the uncertainty of the model form. Shape optimization within the confidence interval achieves enhanced performance with robust improvements, reducing the sensitivity to manufacturing tolerances. Design optimization under the framework of uncertainty quantification may have great practicability as an engineering application tool.