A framework for epistemic uncertainty quantification of turbulent scalar flux models for Reynolds-averaged Navier-Stokes simulations

Abstract

Reynolds-averaged Navier-Stokes (RANS) simulations are a practical approach for solving complex multi-physics turbulent flows, but the underlying assumptions of the turbulence models introduce errors and uncertainties in the simulation outcome. The flow in scramjet combustors is an example of such a complex flow and the accurate characterization of safety and operability limits of these engines using RANS simulations requires an assessment of the model uncertainty. The objective of this paper is to present a framework for the epistemic uncertainty quantification of turbulence and mixing models in RANS simulations. The capabilities of the methodology will be demonstrated by performing simulations of the mixing of an underexpanded jet in a supersonic cross flow, which involves many flow features observed in scramjet engines. The fundamental sources of uncertainty in the RANS simulations are the models used for the Reynolds stresses in the momentum equations and the turbulent scalar fluxes in the scalar transport equations. The methodology consists in directly perturbing the modeled quantities in the equations, thereby establishing a method that is completely independent of the initial model form to overcome the limitations of traditional sensitivity studies. The perturbations are defined in terms of the decomposed Reynolds stress tensor, i.e., the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. The turbulent scalar fluxes are perturbed by using the perturbed Reynolds stresses in a generalized gradient diffusion model formulation and by changing the model constant. The perturbations were parameterized based on a comparison between the Reynolds stresses obtained from a baseline RANS simulation and those obtained from a large-eddy simulation database. Subsequently an optimization problem was solved, varying the parameters in the perturbation functions to maximize a quantity of interest that quantifies the downstream mixing. The result encompasses the value for the quantity of interest obtained from the LES database. It is shown that a traditional sensitivity study, in which the turbulent Schmidt number is varied, cannot capture this uncertainty, which further demonstrates the effectiveness of the proposed approach.