The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

References

References
1.
Speziale
,
C.
,
1997
, “
Computing Non-Equilibrium Turbulent Flows With Time-Dependent RANS and VLES
,” 15th International Conference on Numerical Methods in Fluid Dynamics (Lecture Notes in Physics, Vol.
490
),
P.
Kutler
, and
J. F. J.
Chattot
, eds., Springer, Berlin, pp.
123
129
.
2.
Spalart
,
P.
,
Jou
,
W.-H.
,
Strelets
,
M.
, and
Allmaras
,
S.
,
1997
, “
Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach
,”
First AFOSR International Conference on DNS/LES
, Reston, VA, Aug. 4–8, pp. 137–148.https://www.researchgate.net/publication/236888805_Comments_on_the_Feasibility_of_LES_for_Wings_and_on_a_Hybrid_RANSLES_Approach
3.
Spalart
,
P.
,
2000
, “
Strategies for Turbulence Modelling and Simulations
,”
Int. J. Heat Fluid Flow
,
21
(
3
), pp.
252
263
.
4.
Davidson
,
P.
,
2004
,
Turbulence: An Introduction for Scientists and Engineers
,
1st ed.
,
Oxford University Press
,
New York
.
5.
Hamba
,
F.
,
2011
, “
Analysis of Filtered Navier-Stokes Equation for Hybrid RANS/LES Simulation
,”
Phys. Fluids
,
23
(
1
), p.
015108
.
6.
Girimaji
,
S.
, and
Wallin
,
S.
,
2013
, “
Closure Modeling in Bridging Regions of Variable-Resolution (VR) Turbulence Computations
,”
J. Turbul.
,
14
(
1
), pp.
72
98
.
7.
Germano
,
M.
,
1992
, “
Turbulence: The Filtering Approach
,”
J. Fluid Mech.
,
238
(
1
), pp.
325
336
.
8.
Spalart
,
P.
,
Deck
,
S.
,
Shur
,
M.
,
Squires
,
K.
,
Strelets
,
M.
, and
Travin
,
A.
,
2006
, “
A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities
,”
Theoret. Comput. Fluid Dyn.
,
20
(
3
), pp.
181
195
.
9.
Girimaji
,
S.
,
2006
, “
Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method
,”
ASME J. Appl. Mech.
,
73
(
3
), pp.
413
421
.
10.
Girimaji
,
S.
,
Jeong
,
E.
, and
Srinivasan
,
R.
,
2006
, “
Partially Averaged Navier-Stokes Method for Turbulence: Fixed Point Analysis and Comparison With Unsteady Partially Averaged Navier-Stokes
,”
ASME J. Appl. Mech.
,
73
(
3
), pp.
422
429
.
11.
Srinivasan
,
R.
, and
Girimaji
,
S.
,
2014
, “
Partially-Averaged Navier-Stokes Simulations of High-Speed Mixing Environement
,”
ASME J. Fluids Eng.
,
136
(
6
), p.
060903
.
12.
Schiestel
,
R.
, and
Dejoan
,
A.
,
2005
, “
Towards a New Partially Integrated Transport Model for Coarse Grid and Unsteady Turbulent Flow Simulations
,”
Theoret. Comput. Fluid Dyn.
,
18
(
6
), pp.
443
468
.
13.
Pereira
,
F.
,
Eça
,
L.
,
Vaz
,
G.
, and
Girimaji
,
S.
,
2018
, “
Challenges in Scale-Resolving Simulations of Turbulent Wake Flows With Coherent Structures
,”
J. Comput. Phys.
,
363
, pp.
98
115
.
14.
Pereira
,
F.
,
Eça
,
L.
,
Vaz
,
G.
, and
Girimaji
,
S.
,
2019
, “
On the Simulation of the Flow Around a Circular Cylinder at Re = 140,000
,”
Int. J. Heat Fluid Flow
,
76
, pp.
40
56
.
15.
Hussain
,
A.
, and
Reynolds
,
W.
,
1970
, “
The Mechanics of an Organized Wave in Turbulent Shear Flow
,”
J. Fluid Mech.
,
41
(
2
), pp.
241
258
.
16.
Schiestel
,
R.
,
1987
, “
Multiple-Time-Scale Modeling of Turbulent Flows in One-Point Closures
,”
Phys. Fluids
,
30
(
3
), pp.
722
731
.
17.
Trucano
,
T.
,
Pilch
,
M.
, and
Oberkampf
,
W.
,
2002
, “
General Concepts for Experimental Validation of ASCI Code Applications
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2002-0341
.https://pdfs.semanticscholar.org/7867/f166a57143897964c79b2601adbc0917759e.pdf
18.
Oberkampf
,
W.
, and
Roy
,
C.
,
2010
,
Verification and Validation in Scientific Computing
,
1st ed.
,
Cambridge University Press
,
Cambridge, UK
.
19.
Breuer
,
M.
,
1998
, “
Numerical and Modeling Influences on Large Eddy Simulations for the Flow Past a Circular Cylinder
,”
Int. J. Heat Fluid Flow
,
19
(
5
), pp.
512
521
.
20.
de With
,
G.
, and
Holdo̸
,
A. E.
,
2005
, “
The Use of Solution Adaptive Grid for Modeling Small Scale Turbulent Structures
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
936
944
.
21.
Lakshmipathy
,
S.
, and
Girimaji
,
S.
,
2010
, “
Partially-Averaged Navier-Stokes (PANS) Method for Turbulence Simulations: Flow Past a Circular Cylinder
,”
ASME J. Fluids Eng.
,
132
(
12
), p.
121202
.
22.
Lysenko
,
D.
,
Ertesvåg
,
I.
, and
Rian
,
K.
,
2012
, “
Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 3900 Using the OpenFOAM Toolbox
,”
Flow Turbul. Combust.
,
89
(
4
), pp.
491
518
.
23.
Rosetti
,
G.
,
Vaz
,
G.
, and
Fujarra
,
A.
,
2012
, “
URANS Calculations for Smooth Circular Cylinder Flow in a Wide Range of Reynolds Numbers: Solution Verification and Validation
,”
ASME J. Fluids Eng.
,
34
(
12
), p.
121103
.
24.
Lehmkuhl
,
O.
,
Rodríguez
,
I.
,
Borrell
,
R.
, and
Oliva
,
A.
,
2013
, “
Low-Frequency Unsteadiness in the Vortex Formation Region of a Circular Cylinder
,”
Phys. Fluids
,
25
(
8
), p.
085109
.
25.
Sidebottom
,
W.
,
Ooi
,
A.
, and
Jones
,
D.
,
2015
, “
A Parametric Study of Turbulence Flow Past a Circular Cylinder Using Large Eddy Simulation
,”
ASME J. Fluids Eng.
,
137
(
9
), p.
091202
.
26.
Palkin
,
E.
,
Mullyadzhanov
,
R.
,
Hadz^iabdić
,
M.
, and
Hanjalić
,
K.
,
2015
, “
Scrutinizing URANS Models in Shedding Flows: The Case of Cylinder in Cross Flow
,”
Eighth International Symposium on Turbulence, Heat and Mass Transfer
(
THMT15
),
Sarajevo, Bosnia and Herzegovina
,
Sept. 15–18
, Paper No. E331.https://www.researchgate.net/publication/283538466_Scrutinizing_URANS_models_in_shedding_flows_the_case_of_cylinder_in_cross_flow
27.
D'Alessandro
,
V.
,
Montelpare
,
S.
, and
Ricci
,
R.
,
2016
, “
Detached-Eddy Simulations of the Flow Over a Cylinder at Re = 3900 Using OpenFOAM
,”
Comput. Fluids
,
136
, pp.
152
169
.
28.
Pereira
,
F.
,
Vaz
,
G.
,
Eça
,
L.
, and
Girimaji
,
S.
,
2018
, “
Simulation of the Flow Around a Circular Cylinder at Re = 3900 With Partially-Averaged Navier-Stokes Equations
,”
Int. J. Heat Fluid Flow
,
69
, pp.
234
246
.
29.
Wilcox
,
D.
,
1988
, “
Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,”
AIAA J.
,
26
(
11
), pp.
1299
1310
.
30.
Menter
,
F.
,
Kuntz
,
M.
, and
Langtry
,
R.
,
2003
, “
Ten Years of Industrial Experience With the SST Turbulence Model
,”
Fourth Turbulence, Heat and Mass Transfer
,
Antalya, Turkey
,
Oct. 12–17
, pp.
625
632
.
31.
Kok
,
J.
,
2000
, “
Resolving the Dependence on Freestream Values for the k–ω Turbulence Model
,”
AIAA J.
,
38
(
7
), pp.
1292
1295
.
32.
Lakshmipathy
,
S.
, and
Girimaji
,
S.
,
2006
, “
Partially-Averaged Navier-Stokes Method for Turbulent Flows: k–ω Model Implementation
,”
AIAA
Paper No. 2006-119.
33.
Menter
,
F.
,
1993
, “
Zonal Two Equation k–ω Turbulence Models for Aerodynamic Flows
,”
AIAA
Paper No. 93-2906.
34.
Menter
,
F.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.
35.
Pereira
,
F.
,
Vaz
,
G.
, and
Eça
,
L.
,
2015
, “
An Assessment of Scale-Resolving Simulation Models for the Flow Around a Circular Cylinder
,”
Eighth International Symposium on Turbulence, Heat and Mass Transfer (THMT15)
,
Sarajevo, Bosnia and Herzegovina
,
Sept. 15–18
, Paper No.
E158
.https://www.researchgate.net/publication/281684567_An_assessment_of_Scale-Resolving_Simulation_models_for_the_flow_around_a_circular_cylinder
36.
Gritskevich
,
M.
,
Garbaruk
,
A.
,
Schütze
,
J.
, and
Menter
,
F.
,
2012
, “
Development of DDES and IDDES Formulations for the k–ω Shear Stress Transport Model
,”
Flow Turbul. Combust.
,
88
(
3
), pp.
431
449
.
37.
Pereira
,
F.
,
2018
, “
Towards Predictive Scale-Resolving Simulations of Turbulent External Flows
,” Ph.D. thesis, Instituto Superior Técnico, Lisbon, Portugal.
38.
Zdravkovich
,
M.
,
1997
,
Flow Around Circular Cylinders. Volume 1: Fundamentals
,
1st ed.
,
Oxford Science Publications
,
Oxford, UK
.
39.
Prasad
,
A.
, and
Williamson
,
C.
,
1997
, “
The Instability of the Shear Layer Separating From a Bluff Body
,”
J. Fluid Mech.
,
333
, pp.
375
402
.
40.
Ong
,
L.
, and
Wallace
,
J.
,
1996
, “
The Velocity Field of the Turbulent Very Near Wake of a Circular Cylinder
,”
J. Exp. Fluids
,
20
(
6
), pp.
441
453
.
41.
Parnaudeau
,
P.
,
Carlier
,
J.
,
Heitz
,
D.
, and
Lamballais
,
E.
,
2008
, “
Experimental and Numerical Studies of the Flow Over a Circular Cylinder at Reynolds Number 3900
,”
Phys. Fluids
,
20
(
8
), p.
085101
.
42.
Norberg
,
C.
,
2002
, “
Pressure Distributions Around a Circular Cylinder in Cross-Flow
,”
Symposium on Bluff Body Wakes and Vortex-Induced Vibrations
(
BBVIV-3
),
Port Arthur, Australia
,
Dec. 17–20
, pp.
1
4
.https://www.researchgate.net/publication/271504619_Pressure_Distributions_around_a_Circular_Cylinder_in_Cross-Flow
43.
Norberg
,
C.
,
2003
, “
Fluctuating Lift on a Circular Cylinder: Review and New Measurements
,”
J. Fluids Struct.
,
17
(
1
), pp.
57
96
.
44.
ReFRESCO,
2018
, “ReFRESCO,” accessed Apr. 29, 2019, http://www.refresco.org
45.
Wilcox
,
D.
,
2006
,
Turbulence Modeling for CFD
,
3rd ed.
,
DCW Industries
,
La Cañada, CA
.
46.
Pereira
,
F.
,
Vaz
,
G.
, and
Eça
,
L.
,
2015
, “
Flow Past a Circular Cylinder: A Comparison Between RANS and Hybrid Turbulence Models for a Low Reynolds Number
,”
ASME
Paper No. OMAE2015-41235.
47.
Pereira
,
F.
,
Eça
,
L.
, and
Vaz
,
G.
,
2019
, “
Simulation of Wingtip Vortex Flows With Reynolds-Averaged NavierStokes and Scale-Resolving Simulation Methods
,”
AIAA J.
,
57
(
3
), pp.
932
948
.
48.
Breuer
,
M.
,
2018
, “
Effect of Inflow Turbulence on an Airfoil Flow With Laminar Separation Bubble: An LES Study
,”
Flow Turbul. Combust.
,
101
(
2
), pp.
433
456
.
49.
Norberg
,
C.
,
1987
, “
Effects of Reynolds Number and a Low-Intensity Freestream Turbulence on the Flow Around a Circular Cylinder
,” Chalmers University of Technology, Gothenburg, Sweden, Report No.
87/2
.https://www.researchgate.net/publication/272090433_Effects_of_Reynolds_Number_and_Low-Intensity_Freestream_Turbulence_on_the_Flow_Around_a_Circular_Cylinder
50.
Rajagopalan
,
S.
, and
Antonia
,
R. A.
,
2005
, “
Flow Around a Circular Cylinder—Structure of the Near Wake Shear Layer
,”
Exp. Fluids
,
38
(
4
), pp.
393
402
.
You do not currently have access to this content.