Abstract
A new partially averaged Navier–Stokes (PANS) closure is derived based on the (KSKL) model. The aim of this new model is to incorporate the desirable features of the KSKL model, compared to the shear stress transport model, into the PANS framework. These features include reduced eddy-viscosity levels, a lower dependency on the cell height at the wall, well-defined boundary conditions, and improved iterative convergence. As well as the new model derivation, the paper demonstrates that these desirable features are indeed maintained, for a range of modeled-to-total turbulence kinetic energy ratios (fk), and even for multiphase flow.
Issue Section:
Techniques and Procedures
References
1.
Nallasamy
,
M.
, 1987
, “
Turbulence Models and Their Applications to the Prediction of Internal Flows: A Review
,” Comput. Fluids
,
15
(2
), pp. 151
–194
.10.1016/S0045-7930(87)80003-82.
Pope
,
S.
, 2000
, Turbulent Flows
,
Cambridge University Press
, London.3.
Argyropoulos
,
C.
, and
Markatos
,
N.
, 2015
, “
Recent Advances on the Numerical Modelling of Turbulent Flows
,” Appl. Math. Modell.
,
39
(2
), pp. 693
–732
.10.1016/j.apm.2014.07.0014.
Pereira
,
F.
,
Eça
,
L.
,
Vaz
,
G.
, and
Girimaji
,
S.
, 2021
, “
Toward Predictive RANS and SRS Computations of Turbulent External Flows of Practical Interest
,” Arch. Comput. Methods Eng.
,
28
(5
), pp. 3953
–4029
.10.1007/s11831-021-09563-05.
Smagorinsky
,
J.
, 1963
, “
General Circulation Experiments With the Primitive Equations: I. The Basic Experiment
,” Mon. Weather Rev.
,
91
(3
), pp. 99
–164
.10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;26.
Spalart
,
P.
, 1997
, “
Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach
,” Proceedings of 1st AFOSR International Conference on DNS/LES
, Ruston, LO, Aug. 4–8,
Greyden Press
, pp. 1
–11
.https://www.researchgate.net/publication/236888805_Comments_on_the_Feasibility_of_LES_for_Wings_and_on_a_Hybrid_RANSLES_Approach7.
Girimaji
,
S.
, and
Abdol-Hamid
,
K.
, 2005
, “
Partially Averaged Navier-Stokes Model for Turbulence: Implementation and Validation
,” AIAA
Paper No. 2005-502.10.2514/6.2005-5028.
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
.10.1115/1.21512079.
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
.10.1016/j.ijheatfluidflow.2017.11.00110.
Klapwijk
,
M.
,
Lloyd
,
T.
, and
Vaz
,
G.
, 2019
, “
On the Accuracy of Partially Averaged Navier-Stokes Resolution Estimates
,” Int. J. Heat Fluid Flow
,
80
, p. 108484
.10.1016/j.ijheatfluidflow.2019.10848411.
Klapwijk
,
M.
,
Lloyd
,
T.
,
Vaz
,
G.
, and
Van Terwisga
,
T.
, 2020
, “
Evaluation of Scale-Resolving Simulations for a Turbulent Channel Flow
,” Comput. Fluids
,
209
, p. 104636
.10.1016/j.compfluid.2020.10463612.
Abdol-Hamid
,
K.
, and
Girimaji
,
S.
, 2004
, “
A Two-Stage Procedure Toward the Efficient Implementation of PANS and Other Hybrid Turbulence Models
,” NASA Langley Research Center, Hampton, VA, Technical Memorandum.13.
Basu
,
D.
,
Hamed
,
A.
, and
Das
,
K.
, 2007
, “
Assessment of Partially Averaged Navier Stokes (PANS) Multiscale Model in Transonic Turbulent Separated Flows
,” ASME
Paper No. FEDSM2007-37630.10.1115/FEDSM2007-3763014.
Basara
,
B.
,
Krajnovic
,
S.
, and
Girimaji
,
S.
, 2008
, “
PANS vs. LES for Computations of the Flow Around a 3D Bluff Body
,” Proceedings of 7th International Symposium on Engineering, Turbulence, Modelling and Measurements
, Vol.
2
, Limassol, Cyprus, June 4–6, p. 3
.15.
Jeong
,
E.
, and
Girimaji
,
S.
, 2010
, “
Partially Averaged Navier-Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder
,” ASME J. Fluids Eng.
,
132
(12
), p. 121203
.10.1115/1.400315316.
Davidson
,
L.
, and
Friess
,
C.
, 2019
, “
A New Formulation of fk for the PANS Model
,” J. Turbul.
,
20
(5
), pp. 322
–336
.10.1080/14685248.2019.164160517.
Friess
,
C.
, and
Davidson
,
L.
, 2020
, “
A Formulation of PANS Capable of Mimicking IDDES
,” Int. J. Heat Fluid Flow
,
86
, p. 108666
.10.1016/j.ijheatfluidflow.2020.10866618.
Luo
,
D.
,
Yan
,
C.
,
Liu
,
H.
, and
Zhao
,
R.
, 2014
, “
Comparative Assessment of PANS and DES for Simulation of Flow Past a Circular Cylinder
,” J. Wind Eng. Ind. Aerodyn.
,
134
, pp. 65
–77
.10.1016/j.jweia.2014.08.01419.
Bensow
,
R.
, and
van den Boogaard
,
M.
, 2019
, “
Using a PANS Simulation Approach for the Transient Flow Around the Japan Bulk Carrier
,” J. Ship Res.
,
63
(2
), pp. 123
–129
.10.5957/JOSR.0918006420.
Kamble
,
C.
, and
Girimaji
,
S.
, 2020
, “
Characterization of Coherent Structures in Turbulent Wake of a Sphere Using Partially Averaged Navier-Stokes (PANS) Simulations
,” Phys. Fluids
,
32
(10
), p. 105110
.10.1063/5.002485421.
Saroha
,
S.
,
Sinha
,
S.
, and
Lakshmipathy
,
S.
, 2019
, “
Evaluation of PANS Method in Conjunction With Non-Linear Eddy Viscosity Closure Using OpenFOAM
,” Int. J. Numer. Methods Heat Fluid Flow
,
29
(3
), pp. 949
–980
.10.1108/HFF-09-2018-052922.
Saroha
,
S.
,
Chakraborty
,
K.
,
Sinha
,
S.
, and
Lakshmipathy
,
S.
, 2020
, “
An OpenFOAM-Based Evaluation of PANS Methodology in Conjunction With Non-Linear Eddy Viscosity: Flow Past a Heated Cylinder
,” J. Appl. Fluid Mech.
,
13
(5
), pp. 1453
–1469
.10.1115/1.404520923.
Basara
,
B.
,
Pavlovic
,
Z.
, and
Girimaji
,
S.
, 2018
, “
A New Approach for the Calculation of the Cut-Off Resolution Parameter in Bridging Methods for Turbulent Flow Simulation
,” Int. J. Heat Fluid Flow
,
74
, pp. 76
–88
.10.1016/j.ijheatfluidflow.2018.09.01124.
Zhang
,
J.
,
Minelli
,
G.
,
Rao
,
A.
,
Basara
,
B.
,
Bensow
,
R.
, and
Krajnović
,
S.
, 2018
, “
Comparison of PANS and LES of the Flow Past a Generic Ship
,” Ocean Eng.
,
165
, pp. 221
–236
.10.1016/j.oceaneng.2018.07.02325.
Pereira
,
F.
,
Grinstein
,
F.
,
Israel
,
D.
,
Rauenzahn
,
R.
, and
Girimaji
,
S.
, 2021
, “
Modeling and Simulation of Transitional Taylor-Green Vortex Flow With Partially Averaged Navier-Stokes Equations
,” Phys. Rev. Fluids
,
6
(5
), p. 054611
.10.1103/PhysRevFluids.6.05461126.
Menter
,
F.
,
Egorov
,
Y.
, and
Rusch
,
D.
, 2006
, “
Steady and Unsteady Flow Modelling Using the
Model
,” ICHMT Digital Library Online
,
Begell House Inc
., Danbury, CT, pp. 1
–20
.27.
Larsson
,
L.
,
Raven
,
H.
, and
Paulling
,
J.
, 2010
, Ship Resistance and Flow. Principles of Naval Architecture
,
Society of Naval Architects and Marine Engineers
, Jersey City, NJ.28.
Menter
,
F.
, and
Egorov
,
Y.
, 2004
, “
Revisiting the Turbulent Scale Equation
,” IUTAM Symposium on One Hundred Years of Boundary Layer Research
, Göttingen, Germany, Aug. 12–14,
Springer
, pp. 279
–290
.29.
Liebrand
,
R.
,
Klapwijk
,
M.
,
Lloyd
,
T.
, and
Vaz
,
G.
, 2021
, “
Transition and Turbulence Modeling for the Prediction of Cavitating Tip Vortices
,” ASME J. Fluids Eng.
,
143
(1
), p. 011202
.10.1115/1.404813330.
Eça
,
L.
,
Pereira
,
F.
, and
Vaz
,
G.
, 2018
, “
Viscous Flow Simulations at High Reynolds Numbers Without Wall Functions: Is
Enough for the Near-Wall Cells?
,” Comput. Fluids
,
170
, pp. 157
–175
.10.1016/j.compfluid.2018.04.03531.
Menter
,
F. R.
, 1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,” AIAA J.
,
32
(8
), pp. 1598
–1605
.10.2514/3.1214932.
Hoekstra
,
M.
, and
Vaz
,
G.
, 2009
, “
The Partial Cavity on a 2D Foil Revisited
,” Proceedings of 7th International Symposium on Cavitation
, MI, Aug. 16–20, pp. 1
–12
.33.
Rijpkema
,
D.
,
Baltazar
,
J.
, and
de Campos
,
J.
, 2015
, “
Viscous Flow Simulations of Propellers in Different Reynolds Number Regimes
,” Proceedings of 4th International Symposium on Marine Propulsors
, Austin, TX, May 31-June 4, pp. 1
–12
.https://www.marinepropulsors.com/proceedings/2015/T B4-1.pdf34.
Vaz
,
G.
,
Hally
,
D.
,
Huuva
,
T.
,
Bulten
,
N.
,
Muller
,
P.
,
Becchi
,
P.
,
Herrer
,
J.
,
Whitworth
,
S.
,
Macé
,
R.
, and
Korsström
,
A.
, 2015
, “
Cavitating Flow Calculations for the E779A Propeller in Open Water and Behind Conditions: Code Comparison and Solution Validation
,” Proceedings of 4th International Symposium on Marine Propulsors
, Austin, TX, May 31–June 4, pp. 1
–16
.https://www.researchgate.net/publication/275622126_Cavitating_Flow_Calculations_for_the_E779A_Propeller_in_Open_Water_and_Behind_Conditions_Code_C35.
Vaz
,
G.
,
Lloyd
,
T.
, and
Gnanasundaram
,
A.
, 2017
, “
Improved Modelling of Sheet Cavitation Dynamics on Delft Twist 11 Hydrofoil
,” Proceedings of VII International Conference on Computational Methods in Marine Engineering
, Nantes, Frances, June 15–17, pp. 1
–14
.36.
Klaij
,
C.
,
Hoekstra
,
M.
, and
Vaz
,
G.
, 2018
, “
Design, Analysis and Verification of a Volume-of-Fluid Model With Interface-Capturing Scheme
,” Comput. Fluids
,
170
, pp. 324
–340
.10.1016/j.compfluid.2018.05.01637.
Eça
,
L.
, and
Hoekstra
,
M.
, 2014
, “
A Procedure for the Estimation of the Numerical Uncertainty of CFD Calculations Based on Grid Refinement Studies
,” J. Comput. Phys.
,
262
, pp. 104
–130
.10.1016/j.jcp.2014.01.00638.
Lopes
,
R.
,
Fernandes
,
E.
,
Eça
,
L.
,
Vaz
,
G.
, and
Kerkvliet
,
M.
, 2020
, “
Coupling Two Correlation-Based Transition Models to the
Eddy Viscosity Turbulence Model
,” AIAA J.
,
59
(5
), pp. 1735
–1748
.10.2514/1.J05952339.
Pereira
,
F.
,
Eça
,
L.
, and
Vaz
,
G.
, 2017
, “
Verification and Validation Exercises for the Flow Around the KVLCC2 Tanker at Model and Full-Scale Reynolds Numbers
,” Ocean Eng.
,
129
, pp. 133
–148
.10.1016/j.oceaneng.2016.11.00540.
Vaz
,
G.
,
Jaouen
,
F.
, and
Hoekstra
,
M.
, 2009
, “
Free-Surface Viscous Flow Computations: Validation of URANS Code FRESCO
,” ASME
Paper No. OMAE2009-79398.10.1115/OMAE2009-7939841.
Germano
,
M.
, 1992
, “
Turbulence: The Filtering Approach
,” J. Fluid Mech.
,
238
, pp. 325
–336
.10.1017/S002211209200173342.
Hirt
,
C.
, and
Nichols
,
B.
, 1981
, “
Volume of Fluid (VoF) Method for the Dynamics of Free Boundaries
,” J. Comput. Phys.
,
39
(1
), pp. 201
–225
.10.1016/0021-9991(81)90145-543.
Schnerr
,
G.
, and
Sauer
,
J.
, 2001
, “
Physical and Numerical Modeling of Unsteady Cavitation Dynamics
,” Proceedings of ICMF, 4th International Conference on Multiphase Flow
, New Orleans, May 27–June 1, pp. 10
–12
.https://www.researchgate.net/publication/296196752_Physical_and_Numerical_Modeling_of_Unsteady_Cavitation_Dynamics44.
Reyes
,
D.
,
Cooper
,
J.
, and
Girimaji
,
S.
, 2014
, “
Characterizing Velocity Fluctuations in Partially Resolved Turbulence Simulations
,” Phys. Fluids
,
26
(8
), p. 085106
.10.1063/1.489208045.
Spalart
,
P.
, and
Rumsey
,
C.
, 2007
, “
Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations
,” AIAA J.
,
45
(10
), pp. 2544
–2553
.10.2514/1.2937346.
Lopes
,
R.
,
Eça
,
L.
,
Vaz
,
G.
, and
Kerkvliet
,
M.
, 2021
, “
Assessing Numerical Aspects of Transitional Flow Simulations Using the RANS Equations
,” Int. J. Comput. Fluid Dyn.
,
35
(3
), pp. 1
–22
.10.1080/10618562.2020.1870962 47.
Klapwijk
,
M.
,
Lloyd
,
T.
,
Vaz
,
G.
, and
Van Terwisga
,
T.
, 2021
, “
On the Use of Synthetic Inflow Turbulence for Scale-Resolving Simulations of Wetted and Cavitating Flows
,” Ocean Eng.
,
228
, p. 108860
.10.1016/j.oceaneng.2021.10886048.
Lopes
,
R.
, 2021
, “
Simulation of Transition From Laminar to Turbulent Regime in Practical Applications of Incompressible Flow
,” Ph.D. thesis,
Universidade de Lisboa, Instituto Superior Técnico
,
Portugal
.49.
Xu
,
C.-Y.
,
Zhang
,
T.
,
Yu
,
Y.-Y.
, and
Sun
,
J.-H.
, 2019
, “
Effect of Von Karman Length Scale in Scale Adaptive Simulation Approach on the Prediction of Supersonic Turbulent Flow
,” Aerosp. Sci. Technol.
,
86
, pp. 630
–639
.10.1016/j.ast.2019.01.03050.
Klapwijk
,
M.
,
Lloyd
,
T.
,
Vaz
,
G.
, and
Van Terwisga
,
T.
, 2019
, “
PANS Simulations: Low Versus High Reynolds Number Approach
,” Proceedings of VIII International Conference on Computational Methods in Marine Engineering
, Göthenburg, Sweden, May 13–15, pp. 48
–59
.https://www.researchgate.net/publication/333395278_PANS_SIMULAT IONS_LOW_VERSUS_HIGH_REYNOLDS_NUMBER_APPROACH51.
Moser
,
R.
,
Kim
,
J.
, and
Mansour
,
N.
, 1999
, “
Direct Numerical Simulation of Turbulent Channel Flow Up to
,” Phys. Fluids
,
11
(4
), pp. 943
–945
.10.1063/1.86996652.
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
.10.1016/j.jcp.2018.02.03853.
Zhang
,
Y.
, 2017
, “
Critical Transition Reynolds Number for Plane Channel Flow
,” Appl. Math. Mech.
,
38
(10
), pp. 1415
–1424
.10.1007/s10483-017-2245-654.
Pennings
,
P.
,
Westerweel
,
J.
, and
Van Terwisga
,
T.
, 2015
, “
Flow Field Measurement Around Vortex Cavitation
,” Exp. Fluids
,
56
(11
), p. 206
.10.1007/s00348-015-2073-955.
Xie
,
Z.-T.
, and
Castro
,
I.
, 2008
, “
Efficient Generation of Inflow Conditions for Large Eddy Simulation of Street-Scale Flows
,” Flow Turbul. Combust.
,
81
(3
), pp. 449
–470
.10.1007/s10494-008-9151-556.
Lloyd
,
T.
,
Vaz
,
G.
,
Rijpkema
,
D.
, and
Reverberi
,
A.
, 2017
, “
Computational Fluid Dynamics Prediction of Marine Propeller Cavitation Including Solution Verification
,” Proceedings of 5th Symposium on Marine Propulsion
, Espoo, Finland, June 12–15, pp. 58
–70
.https://www.researchgate.net/publication/316240685_Computational_fluid_dynamics_prediComputationalFluidDynamicsPredictionofMarinePropellerCavitationIncludingSolutionVerificationction_of_marine_propeller_cavitation_including_solution_verification57.
Asnaghi
,
A.
,
Svennberg
,
U.
, and
Bensow
,
R.
, 2020
, “
Large Eddy Simulations of Cavitating Tip Vortex Flows
,” Ocean Eng.
,
195
, p. 106703
.10.1016/j.oceaneng.2019.10670358.
Reverberi
,
A.
, 2016
, “
Cavitation Modelling of E779A Propeller Accounting for Transition Effects
,” MARIN, Wageningen, the Netherlands, Technical Report.59.
Bosschers
,
J.
, 2018
, “
Propeller tip-vortex cavitation and its broadband noise
,” Ph.D. thesis,
University of Twente
,
the Netherlands
.Copyright © 2022 by ASME
You do not currently have access to this content.