(by Tomer Avraham)
“The Grey Area” – Interfacing RANS and LES
While the ultimate goal is a model that may work in the RANS limit, LES limit and smoothly connect them at their interface (might it be zonal or monolithic formulation), it seems that in particular the interface termed “the grey area” stands problematic although in the focus of the CFD community for some time.
The main reason for that is in the fact that although seemingly the same form of formulation for the governing filtered equation is achieved the nature their derivation and their simulation objectives are fundamentally very different.
The RANS equations assume that a time average is much greater than the turbulent eddies time scale, hence turbulent stresses may be replaced by their averaged effect. usually this is done by defining an eddy viscosity (see Understanding The k-ω SST Model) proportional to the mean strain rate and resulting in a flow that is computationally very stable even at highly turbulent unsteady regions as the effective viscosity can be of orders of magnitude larger the molecular viscosity.
On the other hand, in an LES the formulation is derived by spatial filtering separating the scales that can be directly calculated from those that must be modeled (due to grid resolution – “filter width”). Generally the subgrid scales are also replaced with an effective viscosity that must be low enough as to not artificially damp the growth and transport of the resolved large-scale eddies that are supposed be captured.
In the Interface region the modelled turbulent stresses formerly derived by RANS may easily be too large to maintain those unsteady features desired to be captured by LES, and on the other hand not large enough to replace all the turbulent stresses for the upcoming RANS state.
The end result is seldom contamination of the LES region due to inconsistent treating of the turbulent stresses at the interface. The “grey area” is indeed one of the most important issues to be resolved as far as RANS-LES hybrid methods are concerned.
Subtleties such as “grid induced separation” formulation
Being so popular, I found some of the natural DES (P. Spalart 1997) inherent limitations are often overlooked in simulations as practitioners often apply the model in order to increase physics fidelity without dwelling on subtle issues. The following paragraphs address some of these subtleties.
In DES the hybrid formulation has a limiter switching from RANS to LES as the grid is reduced. The problem with natural DES is that an incorrect behavior may be encountered for flows with thick boundary layers or shallow separations. It was found that when the stream-wise grid spacing becomes less than the boundary layer thickness the grid may be fine enough for the DES length scale to switch the DES to its LES mode without proper “LES content”, i.e. resolved stresses are too weak (“Modeled Stress Depletion” or MSD”), which in turn shall reduce the skin friction and by that may cause early separation. The phenomenon is termed Grid Induced Separation (GIS).
mean velocity in different types of grids in a boundary layer –
top: natural DES, left: ambiguous grid spacing, right: LES
As a consequence of the original DES deficiencies an advancement to the model was devised, termed Delayed-DES (DDES). In the Fluent DES-SST formulation a DES limiter “shield” is added to maintain RANS behavior in the boundary layer without grid dependency.