Go4hybrid
State of Art – FOI contribution to WP2.1
Stefan Wallin and Shia-Hui Peng
Aeronautics and Systems Integration, Swedish Defence Research Agency (FOI)
Variable resolution simulations
RANS
• Smooth variation of resolution:
RANS – LES – RANS
•
LES
Grey area problem:
•
•
Approaches
• Energy conservation principle
•
Transfer of energy:
resolved ↔ SGS
• Backscatter
•
RANS
delay of initial shear-layer growth
“double-counting” of turbulence
Mixed Gradient/Leonard model:
•
•
Forward scatter: resolved → SGS
Backscatter: SGS → resolved
Ref:
• Wallin & Girimaji, AIAA-2011-3105
• Wallin, Reyes & Girimaji, THMT-12
• Girimaji & Wallin, JoT, 2013
•
•
Peng, 2002
Peng & Davidson, 2009, 2012
•
Energy transfer between
scales
•
Energy balance
•
Commuting filter
resolved
cut-off
Fix cut-off: constant resolution
unresolved
•
Energy transfer between
scales
•
Extra energy transfer:
•
Dissipation of
resolved K
•
Production of SGS K
>0
•
Non-commuting filter
resolved
cut-off
Decreasing resolution (LES → RANS)
unresolved
•
Energy transfer between
scales
•
Extra energy transfer:
•
Production of
resolved K
•
Dissipation of SGS K
<0
•
Non-commuting filter
resolved
cut-off
Increasing resolution (RANS → LES)
unresolved
Modelling challenges
Quantification of
Resolved energy transfer:
•
•
Quantified by
•
Energy forcing (or
dissipation) of scales near
cut-off
•
Modelled as a viscous term
•
Negative viscosity no
“numerical” problem
Extended PANS analysis:
•
Analysis of model spectrum:
•
Additional term related to
dK / dt
•
Requires transport eq of
•
SGS energy
•
or related quantity (S-A DES)
•
•
growth limited by
Improvements…
•
DNS filtered with varying filter size
rapid variation of resolution –
commutation error
Commutation residue – the “additional
terms”
Resolved
•
•
Unresolved
• A-priori test by Hamba PoF
2011
D
Importance
Com. residue
Production
Production
Com. residue
Taken from Hamba PoF 2011
PANS DIT – decreasing resolution (LES → RANS)
PANS DIT – increasing resolution (RANS → LES)
Backscatter approach
• Smagorinsky SGS models are dissipative
•
•
Reducing/removing energy dissipation (NLR approach)
Introducing energy backscatter (FOI approach)
•
•
•
Backscatter → Resolved scales are forced
Forward scatter → Resolved scales are damped
Models accounting for energy backscatter:
•
•
•
Mixed model (e.g., Erlebacher et al., 1992; Zang et al., 1993) …
Dynamic model (Germano et al. 1991)
Stochastic models (e.g., Leith, 1990; Chasnov, 1991) …
Desirable with a simple SGS formulation in engineering LES
to represent underlying physics of energy backscatter or dissipation
HYB0 + backscatter → HYB0M
• The mixed SGS model takes the form
ui u j
2
 ij  C L f L D 
 2 sgs Sij with  sgs  Cs D  S
xk xk 


 Second Term
2
Leonard Term
• The Leonard term is directly related to the second term,
via an empirical function
• Incorporated into the HYB0 Model
ui u j
1
 ij  2h Sij  CL f L D  f d
with CL 
xk xk
12


2
Leonard Term
~
 h   sgs, if l  D
 h   t , otherwise
Example: Mixing layer (Vorticity)
HYB0
Plate T.E.
HYB0M
Plate T.E.
FOI contribution to WP2.1
Energy transfer method (Wallin & Girimaji)
• Generalization of variable fk PANS to DES (S-A
and SST)
• Generalization for complex geometries
• Validation and calibration
Backscatter formulation (Peng & Davidsson)
• Further exploration and refinement
Total effort: 6MM