Quantification of model uncertainty in RANS simulations: A review

Abstract

In computational fluid dynamics simulations of industrial flows, models based on the Reynoldsaveraged Navier-Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.

Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

“…In [13], a nonlinear generalisation of the linear eddy viscosity concept was proposed. This concept has been used in several works on data-driven turbulence modelling [2,3]. The fundamental assumption is made that the anisotropy of the Reynolds-stress b ij not only depends on the strain rate tensor…”

“…Especially, PH serves as an important testbed for classical and data-driven approaches for turbulence modelling, e.g. [2,37], but also the other two have been introduced with the purpose of closure investigation.…”

“…especially for flows with separation, adverse pressure gradients or high streamline curvature. Data-driven methods for turbulence modelling based on supervised machine learning have been introduced to leverage RANS for improved predictions [2,3,4]. In [5], the source terms of the Spalart-Allmaras were learnt from data using a single hidden layer neural network, which served as a first feasibility study.…”

Flows over periodic hills of parameterized geometries: A dataset for data-driven turbulence modeling from direct simulations

“…On the other hand, attempts in combining models of different fidelity levels (e.g., hybrid LES/RANS models) have shown promises, but how to achieve consistencies in the hierarchical coupling of models is still a challenge and a topic of ongoing research. Consequently, Reynolds-Averaged Navier-Stokes (RANS) equations are still the workhorse tool in engineering computational fluid dynamics for simulating turbulent flows.It is well known that RANS turbulence models have large model-form uncertainties for a wide range of flows [2], which diminish the predictive capabilities of the RANS-based CFD models.Development of turbulence models has been stagnant for decades, which is evident from the fact that currently used turbulence models (e.g., k-ε, k-ω, and Spalart-Allmaras models [3-5]) were all developed decades ago despite unsatisfactory performance for many flows. In view of the importance and stagnation of turbulence modeling, NASA Technology Roadmap [6] called for sustained investment in improvements in the modeling of turbulent flows [7].…”

“…It is well known that RANS turbulence models have large model-form uncertainties for a wide range of flows [2], which diminish the predictive capabilities of the RANS-based CFD models.…”