A new version of detached-eddy simulation, resistant to ambiguous grid densities

Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier-Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ _∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations ("LES content") have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation. For some research studies in small domains, Δ_∥ is made much smaller than δ, and LES content is generated intentionally. However for natural DES applications in useful domains, it is preferable to over-ride the DES limiter and maintain RANS behavior in boundary layers, independent of Δ_∥ relative to δ. For this purpose, a new version of the technique - referred to as DDES, for Delayed DES - is presented which is based on a simple modification to DES97, similar to one proposed by Menter and Kuntz for the shear-stress transport (SST) model, but applicable to other models. Tests in boundary layers, on a single and a multi-element airfoil, a cylinder, and a backward-facing step demonstrate that RANS function is indeed maintained in thick boundary layers, without preventing LES function after massive separation. The new formulation better fulfills the intent of DES. Two other issues are discussed: the use of DES as a wall model in LES of attached flows, in which the known log-layer mismatch is not resolved by DDES; and a correction that is helpful at low cell Reynolds numbers.