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This paper investigates the capabilities of two subgrid-scale (SGS) models suitable for unstructured grids for predicting the complex flow in transitional separated bubbles. The flow over a NACA 0012 airfoil at Reynolds number Re = 5 × 10 4 and angles of attack (AOA) AOA = 5° and 8° is here considered. The SGS models investigated are: the wall-adapting eddy viscosity model within a variational multiscale method (VMS-WALE) and the QR eddy-viscosity model. Both are well suited for large-eddy simulations (LES) in complex geometries with unstructured grids. The models are assessed and compared to the results of direct numerical simulations (DNS) on the basis of first and second order statistics. Based on the good results obtained, specially with the VMS-WALE model, challenging simulations at high Reynolds numbers and various AOA are also performed. It has been found that predictions of the lift and drag coefficients agree reasonably well with experimental data.

The incompressible Navier–Stokes equations constitute an excellent mathematical model of turbulence. Unfortunately, direct simulations with the available computational resources are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, we consider regularizations of the convective term that preserve the symmetry and conservation properties exactly. This yields to a class of regularizations [Verstappen R. On restraining the production of small scales of motion in a turbulent channel flow. Comput Fluids 2008:37;887–97] that restrain the production of small scales of motion in an unconditionally stable manner. In this way, the new set of equations is dynamically less complex than the original Navier–Stokes equations, and therefore more amenable to be numerically solved. It relies on a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must be stopped at the scale set by the grid [Trias FX, Verstappen RWCP, Gorobets A, Soria M, Oliva A. Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity. Comput Fluids 2010:39;1815–31]. To do so, a new criterion based on the invariants of the local strain tensor is proposed and tested here.

Traditionally, turbulence modelling of industrial flows in complex geometries have been solved using RANS models and unstructured meshes based solvers. The lack of precision of RANS models in these situations and the increase of computational power, together with the emergence of new high-efficiency sparse parallel algorithms, have made possible the use of more accurate turbulent models such as Large Eddy Simulation (LES). Recently, relevant improvements on turbulence modelling based on regularization techniques for the convective (non-linear) terms have been developed. They basically alter the convective terms to reduce the production of small scales of motion by means of vortex-stretching and preserving exactly all inviscid invariants. If symmetry and conservation properties of the convective terms are preserved, this yields a novel class of regularizations (i.e. symmetry-preserving regularization models). These models restrain the convective production of small scales in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (enstrophy norm in 2D). Thus, the numerical algorithm used to solve the governing equations must preserve the symmetry and conservation properties too. At this stage, results using symmetry-preserving regularization models at relatively complex geometries and configurations are of extreme importance for further progress. The main objective of the present paper is the assessment of symmetry-preserving regularization models on unstructured meshes. Three different test cases have been studied: the impinging jet flow, the flow past a circular cylinder and a simplified Ahmed car. The properties of the filters and their performance on general unstructured meshes have also been considered. A detailed analysis considering the Gaussian and the Helmholtz differential filters is presented.