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Elliptic blending Reynolds stress model for use in hybrid RANS-LES methods
Rajib Roy, Michael StöllingerDepartment of Mechanical Engineering
AIAA-RM: 3rd Annual Technical SymposiumOctober 24th, 2014
Overview1. Motivation2. RSM-RANS model3. Periodic Hill Case4. Naca 4412 Case5. Conclusions/Outlook
Motivation RANS turbulence models are known to be inaccurate in
separated and other non-equilibrium flows!
LES provides better accuracy for separated flows but it is computationally too expensive for high Re flows!
Hybrid LES-RANS combine the advantage of RANS and LES:
RANS used only very close to the wall (cheap) LES used away from the wall in recirculation region
(accurate)
So far hybrid models are based on eddy-viscosity RANS models:
Question: Is it beneficial to use a Reynolds Stress Model (RSM) in a hybrid RANS-LES context?
Possible benefits:
More accurate description of the RANS near wall region
Better representation of modeled stresses in the energy containing scales
Smoother transition from RANS to LES
Approach: use a RANS Reynolds stress model that does not rely on Re to describe closeness to wall
doesn't involve wall distance or geometric wall information
is not too complex to implement
Wall treatment Candidates: Elliptic relaxation model (Durbin)
Six additional elliptic equations Elliptic blending model (Hanjalić & Manceau, Thielen et al.)
One additional elliptic equation, slightly less accurate
2. RSM-RANS modelLet with over-line indicating Reynolds average
Redistribution model:
blending function
homogeneous model: e.g. LRR, SGG
near wall model
“Wall” normal vector
Near wall model:
3. Case: Periodic Hill
Image Source: Jakirlic et. al (2011)
Image Source: Jakirlic et. Al (2011)
Re = 37000
2d grid 196x130 cells
y+ < 1
Unsteady simulation: second order backward Euler
Solution remains “steady” x/h =2 x/h =4
x/h = 2
x/h = 4
[ LES performed in MGLET code with 4.1e6 cells; source: Jakirlic et. al. (2012) ]
NACA 4412 at
Unsteady solver based on PISO (Pressure Implicit with Splitting of Operators)
Courant number limited to 0.2 ~0.3 for stability
Mixed central difference schemes
Second order backward Euler
Experiment Reference: Wadcock et. Al (1987) and NASA Langley Turbulence Modeling Resource
Grid: Wind Tunnel structured grid
3D-1 cell in Z; 99,696 hexahedral cells)
471 points on airfoil
y+ < 1
CD CL
Experiment 0.0423 1.4500SST 0.0196 1.6585RSMeb 0.0273 1.5534
x/c = 0.529
x/c = 0.952
5. Conclusions/Outlook
The RSMeb model performs better than SST in these two cases where
flow separation and reattachment exist (as it should!)
Elliptic equation to describe near wall distance works well!
Computational cost increased by 70%
More tests: other methods, higher Re, more complex flows will give a
clearer picture about the relative benefits of the RSMeb model
We will use RSMeb model in a hybrid LES-RANS method to better
capture the separation/reattachment !
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