Adaptive Detached Eddy Simulation

Abstract: In simulations that resolve turbulent eddies, the requirement for fine grid resolution near walls is a major expense. Mitigating this expense has led to the idea of hybrid simulation, in which a layer near the wall is treated by a Reynolds averaged model (RANS), transitioning to eddy resolved simulation away from the surface. Detached Eddy Simulation (DES) is an attractive version of hybrid modeling. But, rather than thinking of it as a combination of RANS and LES regions, per se, it should be considered as a length scale prescription that is used in an eddy resolving simulation. As a hybrid method, DES invokes a length scale prescription that reverts to RANS or LES formulas, within regions of a turbulence simulation. In this approach the behavior of the simulation morphs from being similar to RANS, representing turbulent transport primarily with an eddy viscosity, to resolving the energetic scale, turbulent eddies, as the distance from the surface increases. The switch in behaviour is effected by placing a limit on the length scale. In previous two-equation DES models, an upper bound was placed on a dissipation length scale. The present two-equation approach, is based on the k-w model. The eddy viscosity is written nuT = l2w, so the upper bound on l directly reduces the eddy viscosity to a subgrid viscosity. From another perspective, production of k is decreased by the bound. k is the unresolved turbulent energy. The topic of this talk, Adaptive DES, has the virtue of seamlessly adapting to grid resolution and flow conditions, either permitting eddy resolving simulation, or invoking the RANS formulation. The length scale formula contains a coefficient CDES. The similarity between the l2-w model and the Smagorinsky LES model, suggests applying the dynamic procedure to determine this coefficient locally, via test filter stresses. However, the dynamic procedure fails if the grid is too coarse. This is prevented by introducing a lower bound that compares grid spacing to the Kolmogoroff scale, and restricts CDES if the grid is too coarse. The model constant adapts to the grid and flow. If the grid is fine enough CDES can become nearly zero. On a coarse grid it reverts to a default value of 0.12. Additionally, it turns out that when the grid is fine enough, the RANS region becomes thin and the eddy simulation region starts low in the boundary layer. Then a larger part of the flow is computed by eddy resolving simulation and predictions are more accurate than with a fixed constant. In channel flow, the RANS region can shrink below the log-layer. Adaptive DES will be illustrated by a variety of illustrative simulations, including separation in two and three dimensional geometries, rotating channel flow and a combustor swirler nozzle.