An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

Abstract

Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

“…There is, however, a reason to believe that in swirling flow like the present one, the results from URANS might not be accurate due to a bad estimation of the mean flow swirl profile. A mathematically and physically fully consistent approach would be to linearize an algebraic Reynolds stress model (Wallin & Johansson 2000), which is very complicated even in 1D (Gupta 2014), and was therefore considered to be out of the scope of the present study.…”

“…However, an accurate representation of the physics requires a model which can reproduce both the mean flow and the perturbation field accurately. For swirling flows, URANS models generally struggle to predict the mean flow swirl profile accurately (Wallin & Johansson 2000;Dunham et al 2008), whereas the mean swirl profile is crucial for vortex breakdown instabilities as seen above. Hence, we need to adopt an approach which ensures correct mean flow scales.…”

“…Hence, we need to adopt an approach which ensures correct mean flow scales. Algebraic Reynolds stress models might be appropriate (Wallin & Johansson 2000), but are very complicated to linearize even in one dimension (Gupta 2014), while our mean flow is two-dimensional.…”

Modelling of subcritical free-surface flow over an inclined backward-facing step in a water channel

“…The EARSM model represents a simplification of the Reynolds stress models and it is based on a nonlinear relation between the Reynolds stresses and the mean strain rate and vorticity tensors. The used version corresponds to the models proposed by Wallin and Johansson [7] and Hellsten [8]. The constitutive relation for the turbulent viscosity is replaced by the introduction of the anisotropy tensor a ij by the relation …”

Numerical solution of turbulent jet flows

“…The used turbulence models are eddy viscosity ones (SST [4], k- [7]) and EARSM model by Wallin and Hellsten [1,6]. The system of governing equations is solved using artificial compressibility method where the continuity equation is modified by adding pressure time derivative.…”