Abstract
Reynolds-averaged Navier-Stokes (RANS) models are widely used for the simulation of engineering problems. The turbulent-viscosity hypothesis is a central assumption to achieve closures in this class of models. This assumption introduces structural or so-called epistemic uncertainty. Estimating that epistemic uncertainty is a promising approach towards improving the reliability of RANS simulations. In this study, we adopt a methodology to estimate the epistemic uncertainty by perturbing the Reynolds stress tensor. We focus on the perturbation of the turbulent kinetic energy and the eigenvalues separately. We first implement this methodology in the open source package OpenFOAM. Then, we apply this framework to the backward-facing step benchmark case and compare the results with the unperturbed RANS model, available direct numerical simulation data and available experimental data. It is shown that the perturbation of both parameters successfully estimate the region bounding the most accurate results.
Highlights
The motion of a fluid in the turbulent regime is fully described by the Navier-Stokes equations.A numerical solution encompassing all spatial and temporal scales is referred to as direct numerical simulation (DNS)
We focus on the perturbation of the turbulent kinetic energy and the eigenvalues separately
We apply this framework to the backward-facing step benchmark case and compare the results with the unperturbed Reynolds-averaged Navier-Stokes (RANS) model, available direct numerical simulation data and available experimental data
Summary
The motion of a fluid in the turbulent regime is fully described by the Navier-Stokes equations.A numerical solution encompassing all spatial and temporal scales is referred to as direct numerical simulation (DNS). A systematic approach of the epistemic uncertainty quantification (EUQ) in RANS models, focusing on the Reynolds stress tensor, was first proposed by Emory et al [1]. The same method was used later in a simulation by Gorle et al [3] comparing RANS with LES results for an under-expanded jet in a supersonic cross flow. Another contribution, proposed by Gorle et al [3] and further developed by Gorle and Iaccarino [4], was to introduce the perturbation in the momentum equations and in the turbulent scalar fluxes in the scalar transport equation
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