Epistemic uncertainty quantification for RANS modeling of the flow over a wavy wall

While Reynolds-averaged Navier-Stokes (RANS) simulations remain the most affordable technique for simulating complex turbulent flows, the inability of linear eddy viscosity models to correctly predict flow separation and reattachment limits the reliability of the simulation outcome. A methodology to quantify the uncertainty in the simulation outcome related to the form of the turbulence model used, i.e., the epistemic uncertainty, would facilitate using the models for supporting engineering design decisions. In the present work we address epistemic uncertainty quantification (EUQ) for RANS simulations of the flow over a wavy wall. The goal of the study is to establish a method which can capture the uncertainty in the prediction of the separation region. The methodology used is that proposed in Emory et al. (2011) and consists of directly introducing perturbations in the Reynolds stress tensor computed by the model and used in the momentum equations. The perturbations are defined in terms of a decomposition of the Reynolds stress tensor, i.e., its magnitude and the eigenvalue decomposition of the normalized anisotropy tensor. In Gorlé et al. (2011), this approach was extended to include EUQ of the mixing model. The perturbation functions used were based on the available LES data set and the method was shown to effectively capture the uncertainty in the mixing of a jet in supersonic cross flow configuration. The goal of the present study, focusing on a more simple flow configuration, is to investigate a more general methodology for defining the perturbation functions. A direct numerical simulation (DNS) database for the configuration from Rossi (2011) will be used for analyzing the turbulence model errors and validating the approach. The remainder of this research brief is organized as follows. Section 2 introduces the test case considered and summarizes the EUQ methodology used. Section 3 presents the definition of the perturbation functions, mainly focusing on the DNS/RANS comparison for the turbulence kinetic energy. Section 4 presents the results of the resulting EUQ study and the conclusions and future research are presented in Section 5.