Theory for the Detached Eddy Simulation Interfaces
Detached Eddy Simulation combines Large Eddy Simulation and RANS, resolving the large turbulent eddies in the bulk and modeling the unresolved eddies, in the bulk using a LES approach, and in the near-wall region using a RANS approach. As for LES, the simulations must be three-dimensional and time dependent. The current implementation of the DES interfaces is suitable for incompressible flow only. Turbulent stresses, modeled by a Boussinesq closure, are added to the existing LES models using the Spalart-Allmaras model (see The Turbulent Flow, Spalart–Allmaras Interface), and the wall distance in the transport equation for is limited by the size of the mesh cell. The implementation, based on the IDDES method (see Ref. 1), has been adjusted to comply with residual-based LES models. , in the Spalart-Allmaras equation (Equation 3-153), is modified as
(3-225)
and
(3-226)
where Dw is the distance to the closest wall and h is the length of the longest edge of the mesh element. The function fd is defined as
(3-227)
The first argument is non-zero inside attached turbulent boundary layers. The function fstep depends on the distance to the closest wall, and h as
(3-228)
fstep is 1 for Dw<0.5275CDESh and sharply approaches 0 away from the wall. At Dw=CDESh, fstep=0.01266. The function frestore is only non-zero in the region 0<Dw<0.5275CDESh, and is added to amplify the RANS length scale, and thereby the turbulent viscosity, outside the viscous sublayer and the log layer. It is defined as
(3-229)
where
(3-230)
The amplification factor Ψ is purely empirical and is expressed in terms of the Spalart-Allmaras parameters
(3-231)
and
(3-232)
where
(3-233)
with the parameters
(3-234)
Inspecting Equation 3-226 and Equation 3-227, it can be seen that for Dw<0.5275CDESh, the DES model operates in RANS mode with an amplified turbulent viscosity within regions outside the viscous sublayer and the log layer (determined by the function famp). For Dw>0.5275CDESh, the DES model operates in DDES (Delayed Detached Eddy Simulation) mode inside attached turbulent boundary layers (determined by the first argument in Equation 3-227), or smoothly approaches the LES mode of operation away from the wall. The extent of the inner, “protected” RANS region can be controlled by changing the value of the CDES parameter.