A Study into the effect of underlining RANS model on a Delayed DetachedEddy Simulation
Researcher:
Neil Ashton
Supervisor(s): Dr A Revell, Dr R Prosser
Sponsor: EPSRC (DTA award)
Start Date: July 2008 End Date: July 2012
Keywords: DDES, Hybrid RANSLES
Overall Research Aim
The principle aim of this research is to undertake a comprehensive review of DDES formulations based on novel RANS models for industrial test cases.
Research Progress
Introduction  Why Delayed DetachedEddy Simulation (DDES)?
Hybrid RANSLES models have become a viable alternative to RANS and LES methods for solving massively separated turbulent flows. The shortcomings of RANS models and the excessive computational expense of a fully resolved LES has provided a void for these hybrid approaches to fill. One such hybrid RANSLES approach is DetachedEddy Simulation (DES), or its successor, Delayed DetachedEddy Simulation (DDES).
DDES
This approach is based upon a seamless switch between a RANS and LES turbulent length scale depending on the local grid size, velocity gradient and eddy viscosity.
Several DDES formulations have been implemented into Code_Saturne to establish the effect of the underlining RANS model on a DDES. The Decaying Isotropic Turbulence (DIT) test case has been used to partly validate and illustrate the importance of the correct numerical scheme and to calibrate each DDES formulation.

%BEGINLATEX{label="eq:fddes"}% \begin{equation*} L_{DDES} = \frac{L_{RANS}}{L_{RANS}  f_{d} \ max \left(0,L_{RANS}  L_{LES}\right)} \end{equation*}%ENDLATEX%
%BEGINLATEX{label="eq:functions"}% \begin{align*}
f_{d} \ &= 1  tanh\left(\left[8r_{d}\right]^{3}\right) \r_{d} \ & = \ \frac{\nu_{t} + \nu}{\sqrt{U_{i,j}U_{i,j}}\kappa^{2}d_{w}^{2}} \\end{align*}%ENDLATEX%
%BEGINLATEX{label="eq:length"}% \begin{align*}
L_{RANS} \ &= \ \frac{k^{3/2}}{\varepsilon} & L_{LES} \ & = \ C_{DDES}\Delta \\end{align*}%ENDLATEX%
Calibration of the %$C_{DDES}$% constant

Numerics  A Hybrid Numerical Scheme
Just as DDES seamlessly switches from a RANS branch to a LESlike branch depending on the local flow and grid conditions, the numerical scheme should also switch according to the requirement of each mode. A new hybrid numerical scheme has been developed consistent with the concept of DDES.
Code_Saturne_ Implementation
In order for DDES to be optimum in the LESlike mode, a convective scheme exhibiting low numerical dissipation should be used.
In the case of
Code_Saturne, this is the 2nd order Central differencing scheme (CDS). It is known however that RANS models may suffer from excessive oscillations for high cell Péclet numbers and coarse grids when a central differencing scheme is employed. It is therefore optimum to utilize the 2nd order linear upwind scheme (SOLU) in these regions.
In order to comply with both of these requirements, a new hybrid numerical scheme has also been developed to ensure that each branch of this approach is paired with the correct convective scheme. The hybrid numerical scheme uses localized flux blending for the convective fluxes, %$\phi_{f}$%,that is based on Equation 2. Its formulation is:
%BEGINLATEX{label="eq:numerics"}% \begin{align*}
\phi_{f} \ &= \ \phi_{f,SOLU} & \ if \ L_{RANS} < L_{LES} \\phi_{f} \ & = \ (1f_{d}) \phi_{f,SOLU} \ + \ f_{d} \ \phi_{f,CDS} & \ if \ L_{RANS} > L_{LES}
\end{align*}%ENDLATEX%
IsoSurfaces of the Q criteria for the 2D wallmounted hump
Last Modification:
r29  20120622  16:15:58 
DongHoSeo
Topic revision: r29  20120622  16:15:58 
DongHoSeo