Wall models for large-eddy simulation (LES) are a necessity to remove the prohibitive resolution requirements of near-wall turbulence in high Reynolds turbulent flows. Traditional wall models often rely on assumptions about the local state of the boundary layer (e.g., logarithmic velocity profiles) and require a priori prescription of tunable model coefficients. In the present study, a slip velocity boundary condition for the filtered velocity field is obtained from the derivation of the LES equations using a differential filter. A dynamic procedure for the local slip length is additionally formulated making the slip velocity wall model free of any a priori specified coefficients. The accuracy of the dynamic slip velocity wall model is tested in a series of turbulent channel flows at varying Reynolds numbers and in the LES of a National Advisory Committee for Aeronautics (NACA) 4412 airfoil at near-stall conditions. The wall-modeled simulations are able to accurately predict mean flow characteristics, including the formation of a trailing-edge separation bubble in NACA 4412 configuration. The validation cases demonstrate the effectiveness of this wall-modeling approach in both attached and separated flow regimes.

1.
H.
Choi
and
P.
Moin
, “
Grid-point requirements for large eddy simulation: Chapman's estimates revisited
,”
Phys. Fluids
24
,
011702
(
2012
).
2.
D. K.
Chapman
, “
Computational aerodynamics development and outlook
,”
AIAA J.
17
,
1293
(
1979
).
3.
U.
Schumann
, “
Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli
,”
J. Comput. Phys.
18
,
376
404
(
1975
).
4.
F.
Jaegle
,
O.
Cabrit
,
S.
Mendez
, and
T.
Poinsot
, “
Implementation methods of wall functions in cell-vertex numerical solvers
,”
Flow, Turbul. Combust.
85
,
245
272
(
2010
).
5.
E.
Balaras
and
C.
Benocci
, “
Subgrid-scale models in finite-difference simulations of complex wall-bounded flows
,”
AGARD Conf. Proc.
551
,
2
1
2
5
(
1994
).
6.
E.
Balaras
,
C.
Benocci
, and
U.
Piomelli
, “
Two-layer approximate boundary conditions for large-eddy simulation
,”
AIAA J.
34
,
1111
1119
(
1996
).
7.
W.
Cabot
and
P.
Moin
, “
Approximate wall boundary conditions in large-eddy simulation of high Reynolds number flow
,”
Flow, Turbul. Combust.
63
,
269
291
(
2000
).
8.
M.
Wang
and
P.
Moin
, “
Dynamic wall modeling for large-eddy simulation of complex turbulent flows
,”
Phys. Fluids
14
,
2043
2051
(
2002
).
9.
S.
Kawai
and
J.
Larsson
, “
Wall-modeling in large eddy simulation: Length scales, grid resolution, and accuracy
,”
Phys. Fluids
24
,
015105
(
2012
).
10.
M.
Shur
,
P.
Spalart
,
M.
Strelets
, and
A.
Travin
, “
A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities
,”
Int. J. Heat Fluid Flow
29
,
1638
1649
(
2008
).
11.
P.
Spalart
, “
Detached-eddy simulation
,”
Annu. Rev. Fluid Mech.
41
,
181
202
(
2009
).
12.
F.
Nicoud
,
J.
Baggett
,
P.
Moin
, and
W.
Cabot
, “
Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation
,”
Phys. Fluids
13
,
2968
2985
(
2001
).
13.
J. A.
Templeton
,
M.
Wang
, and
P.
Moin
, “
A predictive wall model for large-eddy simulation based on optimal control techniques
,”
Phys. Fluids
20
,
065104
(
2008
).
14.
U.
Piomelli
and
E.
Balaras
, “
Wall-layer models for large-eddy simulations
,”
Annu. Rev. Fluid Mech.
34
,
349
374
(
2002
).
15.
S.
Hickel
,
E.
Touber
,
J.
Larsson
, and
J.
Bodart
, “
A parameterized non-equilibrium wall-model for large-eddy simulations
,” in
Proceedings of the 2012 Center for Turbulence Research Summer Program
(
Stanford University
,
2012
), pp.
127
136
.
16.
C.
Pantano
,
D.
Pullin
,
P.
Dimotakis
, and
G.
Matheou
, “
LES approach for high Reynolds number wall-bounded flows with application to turbulent channel flow
,”
J. Comput. Phys.
227
,
9271
9291
(
2008
).
17.
D.
Chung
and
D.
Pullin
, “
Large-eddy simulation and wall modelling of turbulent channel flow
,”
J. Fluid Mech.
631
,
281
309
(
2009
).
18.
S.
Ghosal
and
P.
Moin
, “
The basic equations for the large eddy simulation of turbulent flows in complex geometries
,”
J. Comput. Phys.
118
,
24
37
(
1995
).
19.
O.
Vasilyev
,
T.
Lund
, and
P.
Moin
, “
A general class of commutative filters for LES in complex geometries
,”
J. Comput. Phys.
146
,
82
104
(
1998
).
20.
M.
Germano
, “
Differential filters of elliptic type
,”
Phys. Fluids
29
,
1757
1758
(
1986
).
21.
M.
Germano
, “
Differential filters for the large eddy simulation of turbulent flows
,”
Phys. Fluids
29
,
1755
1766
(
1986
).
22.
W.
Layton
and
R.
Lewandowski
, “
On a well posed turbulence model
,”
Discrete Contin. Dyn. Syst., Ser. B
6
,
111
128
(
2006
).
23.
S. T.
Bose
, “
Explicitly filtered LES: With application to grid adaptation and wall modeling
,” Ph.D. thesis,
Stanford University
,
2012
.
24.
D.
You
,
S. T.
Bose
, and
P.
Moin
, “
Grid-independent large-eddy simulation of compressible turbulent flows using explicit filtering
,” in
Proceedings of the 2010 Center for Turbulence Research Summer Program
(
Stanford University
,
2010
), pp.
203
210
.
25.
T.
Min
and
J.
Kim
, “
Effects of hydrophobic surface on skin-friction drag
,”
Phys. Fluids
16
,
L55
(
2004
).
26.
M.
Germano
,
U.
Piomelli
,
P.
Moin
, and
W.
Cabot
, “
A dynamic subgrid-scale eddy viscosity model
,”
Phys. Fluids
3
,
1760
1765
(
1991
).
27.
J.
Jiménez
, “
On why dynamic subgrid-scale models work
,” in
Center for Turbulence Research Annual Research Briefs
(
1995
), pp.
25
34
.
28.
A.
Scotti
,
C.
Meneveau
, and
M.
Fatica
, “
Dynamic smagorinsky model on anisotropic grids
,”
Phys. Fluids
9
,
1856
1858
(
1997
).
29.
S.
Hoyas
and
J.
Jiménez
, “
Scaling of the velocity fluctuations in turbulent channel flows up to Reτ = 2003
,”
Phys. Fluids
18
,
011702
(
2006
).
30.
F.
Ham
and
G.
Iaccarino
, “
Energy conservation in collocated discretization schemes on unstructured meshes
,” in
Center for Turbulence Research Annual Research Briefs
(
2004
), pp.
3
14
.
31.
F.
Ham
,
K.
Mattsson
, and
G.
Iaccarino
, “
Accurate and stable finite volume operators for unstructured flow solvers
,” in
Center for Turbulence Research Annual Research Briefs
(
2006
), pp.
243
261
.
32.
N.
Hutchins
and
I.
Marusic
, “
Large-scale influences in near-wall turbulence
,”
Philos. Trans. R. Soc. London, Ser. A
365
,
647
664
(
2007
).
33.
R.
Moser
,
J.
Kim
, and
N.
Mansour
, “
Direct numerical simulation of turbulent channel flow
,”
Phys. Fluids
11
,
943
945
(
1999
).
34.
N. V.
Nikitin
,
F.
Nicoud
,
B.
Wasistho
,
K. D.
Squires
, and
P. R.
Spalart
, “
An approach to wall modeling in large-eddy simulations
,”
Phys. Fluids
12
,
1629
1632
(
2000
).
35.
A.
Wadcock
, “
Flying hot wire study of two-dimensional turbulent separation on an NACA 4412 airfoil at maximum lift
,” Ph.D. thesis,
California Institute of Technology
,
1978
.
36.
D.
Coles
and
A.
Wadcock
, “
Flying hot wire study of flow past an NACA 4412 airfoil at maximum lift
,”
AIAA J.
17
,
321
329
(
1979
).
37.
NASA Langley Research Center Turbulence Modeling Group
, “
NACA 4412 trailing edge separation
,” see http://turbmodels.larc.nasa.gov/naca4412sep_val.html (
2012
), online; accessed 9/2012.
38.
P.
Durbin
,
N.
Mansour
, and
Z.
Yang
, “
Eddy viscosity transport model for turbulent flow
,”
Phys. Fluids
6
,
1007
(
1994
).
39.
K.
Jansen
, “
Preliminary large-eddy simulation of flow around a NACA 4412 airfoil using unstructured grids
,” in
Center for Turbulence Research Annual Research Briefs
(
1995
), pp.
61
72
.
40.
S.
Kawai
and
J.
Larsson
, “
Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers
,”
Phys. Fluids
25
,
015105
(
2013
).
You do not currently have access to this content.