Bayesian estimates of parameter variability in the k–ε turbulence model

Abstract

In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k − ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coefficients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which reproduces these flows accurately, we perform 13 separate Bayesian calibrations-each at a different pressure gradient-using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the total solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncertainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.

Pedestrian level wind environment assessment around group of high-rise cross-shaped buildings: Effect of building shape, separation and orientation

“…From the set recommended by Guillas et al [38], two test ranges were evaluated, as shown in Table 3. Guilles et al [38] and Edeling et al [39] have indicated that the lower values of s k (0.53 and 0.462) and s ε (0.5 and 0.42) significantly improve the performance of the SKE turbulence model. In this study, C m and C ε2 Table 2 Wind speed regions based on normalized wind speed (NWS).…”

“…A universal set of closure coefficients is unavailable. Various studies have reported that the closure coefficient may require fine-tuning for accurate results [38,39]. In this study, the fine-tuning of closure coefficients was performed.…”

Comparison of Turbulence Models for Flow Past NACA0015 Airfoil Using OpenFOAM

“…The two transport equations comprised of the model, model and algebraic stress model were used to estimate Reynolds stresses. The model focused on effects of the turbulent kinetic energy [6,7]. In the model, the turbulent kinetic energy was the product of a velocity scale and a length scale which happened into the rotational flow structure [8].…”

Implementation and Validation of OpenFOAM for Thermal Convection of Airflow

“…The turbulence model was necessary to be developed for predicting and obtaining results which were close to the mean flow equation [5]. The model was the two additional transport equations and the most widely used turbulence models to predict Reynolds stresses which focused on the turbulent kinetic energy effects [6][7][8]. Particularly, the CFD of flow simulation inside the ovens preferred to use the model to other turbulence models.…”