Uncertainty Quantification of Spalart–Allmaras Turbulence Model Coefficients for Simplified Compressor Flow Features

Abstract

Abstract Turbulence model in Reynolds-averaged Navier–Stokes (RANS) simulations has a crucial effect on predicting the compressor flows. In this paper, the parametric uncertainty of the Spalart–Allmaras (SA) turbulence model is studied in simplified two-dimensional (2D) flows, which includes some of the compressor tip flow features. The uncertainty is quantified by a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the velocity profile, the Reynolds stress profile, the shock front, and the separation size. An artificial neural network (ANN) is applied as the metamodel, which is tuned, trained, and tested using databases from the flow solver. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of the model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the high-fidelity data of the quantities of interest cannot be fully enveloped by the uncertainty band in regions with separation and shock. Crucial model coefficients on the quantities of interest are identified. However, recalibration of these coefficients results in contradictory prediction of different quantities of interest across flow regimes, which indicates the need for a modified Spalart–Allmaras turbulence model form to improve the accuracy in predicting complex flow features.