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 !