Abstract

A comparison of several Reynolds-averaged Navier–Stokes (RANS) based transition models is presented. Four of the most widespread models are selected: the γReθ, γ, amplification factor transport (AFT), and kTkLω models, representative of different modeling approaches. The calculations are performed on several geometries: a flat plate, the Eppler 387 and NACA 0012 two-dimensional (2D) airfoils at two angles of attack, and the SD7003 wing. Distinct features such as the influence of the inlet boundary conditions, discretization error, and modeling error are discussed. It is found that all models present a strong sensitivity to the turbulence quantities inlet boundary conditions, and with the exception of the AFT model, are severely influenced by the decay of turbulence predicted by the underlying turbulence model. This makes the estimation of modeling errors troublesome because these quantities are rarely reported in experiments. Despite not having specific terms in their formulation to deal with separation-induced transition, both the AFT and kTkLω models manage to predict it for the Eppler 387 foil, although presenting higher numerical uncertainty than the remaining models. However, both models show difficulties in the simulation of flows at Reynolds numbers under 105. The γReθ and γ models are the most robust alternatives in terms of iterative and discretization error. The use of RANS compatible transition models allows for laminar flow and features such as laminar separation bubbles to be reproduced and can lead to greatly improved numerical solutions when compared to simulations performed with standard turbulence models.

References

References
1.
Coder
,
J. G.
,
2018
, “
Standard Test Cases for Transition Model Verification and Validation in Computational Fluid Dynamics
,”
AIAA
Paper No. 2018-0029. 10.2514/6.2018-0029
2.
Baltazar
,
J.
,
Rijpkema
,
D.
, and
de Campos
,
J. F.
,
2018
, “
On the Use of the γ- R ̃ e θ t Transition Model for the Prediction of the Propeller Performance at Model-Scale
,”
Ocean Eng.
,
170
, pp.
6
19
.10.1016/j.oceaneng.2018.10.005
3.
Khayatzadeh
,
P.
, and
Nadarajah
,
S.
,
2014
, “
Laminar-Turbulent Flow Simulation for Wind Turbine Profiles Using the γ R e θ t–Transition Model
,”
Wind Energy
,
17
(
6
), pp.
901
918
.10.1002/we.1606
4.
Slotnick
,
J.
,
Khodadoust
,
A.
,
Alonso
,
J.
,
Darmofal
,
D.
,
Gropp
,
W.
,
Lurie
,
E.
, and
Mavriplis
,
D.
,
2014
, “
CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences
,” National Aeronautics and Space Administration, Hampton, VA, Report No.
NASA/CR-2014-218178
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140003093.pdf
5.
Pasquale
,
D.
,
Rona
,
A.
, and
Garrett
,
S. J.
,
2009
, “
A Selective Review of Transition Modelling for CFD
,”
AIAA
Paper No. 2009-3812. 10.2514/6.2009-3812
6.
Schlichting
,
H.
, and
Gersten
,
K.
,
2000
,
Boundary-Layer Theory
,
Springer
, Berlin.
7.
Morkovin
,
M. V.
,
1969
, “
On the Many Faces of Transition
,”
Viscous Drag Reduction
,
Springer
, Boston, MA, pp.
1
31
.
8.
van Ingen
,
J. L.
,
1956
, “
A Suggested Semi-Empirical Method for the Calculation of the Boundary Layer Transition Region
,” Delft University of Technology, Delft, The Netherlands, Report No. VTH-74.
9.
Smith
,
A. M. O.
, and
Gamberoni
,
N.
,
1956
, “
Transition, Pressure Gradient and Stability Theory
,” Douglas Aircraft Co., Long Beach, CA, Report No. ES 26388.
10.
Mack
,
L. M.
,
1977
, “
Transition and Laminar Instability
,” National Aeronautics and Space Administration, Pasadena, CA, Report No. NASA-CR-153203.
11.
Krumbein
,
A. M.
,
2007
, “
Automatic Transition Prediction and Application to Three-Dimensional Wing Configurations
,”
J. Aircr.
,
44
(
1
), pp.
119
133
.10.2514/1.22254
12.
Tanouti
,
N.
,
2017
, “
Coupling of eN Transition Prediction Method With Reynolds-Averaged Navier–Stokes Solver ENFLOW
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
13.
Stock
,
H. W.
, and
Haase
,
W.
,
2000
, “
Navier-Stokes Airfoil Computations With en Transition Prediction Including Transitional Flow Regions
,”
AIAA J.
,
38
(
11
), pp.
2059
2066
.10.2514/2.893
14.
Eça
,
L.
,
Lopes
,
R.
,
Vaz
,
G.
,
Baltazar
,
J.
, and
Rijpkema
,
D.
,
2016
, “
Validation Exercises of Mathematical Models for the Prediction of Transitional Flows
,”
Proceedings of the 31st Symposium on Naval Hydrodynamics
, Monterey, CA.
15.
Suzen
,
Y.
, and
Huang
,
P.
,
2000
, “
Modeling of Flow Transition Using an Intermittency Transport Equation
,”
ASME J. Fluids Eng.
,
122
(
2
), pp.
273
284
.10.1115/1.483255
16.
Dick
,
E.
, and
Kubacki
,
S.
,
2017
, “
Transition Models for Turbomachinery Boundary Layer Flows: A Review
,”
Int. J. Turbomach., Propul. Power
,
2
(
2
), p.
4
.10.3390/ijtpp2020004
17.
Langtry
,
R. B.
, and
Menter
,
F. R.
,
2009
, “
Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes
,”
AIAA J.
,
47
(
12
), pp.
2894
2906
.10.2514/1.42362
18.
Grabe
,
C.
, and
Krumbein
,
A.
,
2014
, “
Extension of the γ R e θ t Model for Prediction of Crossflow Transition
,”
AIAA
Paper No. 2014-1269. 10.2514/6.2014-1269
19.
Langtry
,
R. B.
,
Sengupta
,
K.
,
Yeh
,
D. T.
, and
Dorgan
,
A. J.
,
2015
, “
Extending the γ R e θ t Local Correlation Based Transition Model for Crossflow Effects
,”
AIAA
Paper No. 2015-2474. 10.2514/6.2015-2474
20.
Coder
,
J. G.
, and
Maughmer
,
M. D.
,
2014
, “
Comparisons of Theoretical Methods for Predicting Airfoil Aerodynamic Characteristics
,”
J. Aircr.
,
51
(
1
), pp.
183
191
.10.2514/1.C032232
21.
Seyfert
,
C.
, and
Krumbein
,
A.
,
2012
, “
Evaluation of a Correlation-Based Transition Model and Comparison With the eN Method
,”
J. Aircr.
,
49
(
6
), pp.
1765
1773
.10.2514/1.C031448
22.
Menter
,
F. R.
,
Smirnov
,
P. E.
,
Liu
,
T.
, and
Avancha
,
R.
,
2015
, “
A One-Equation Local Correlation-Based Transition Model
,”
Flow, Turbul. Combust.
,
95
(
4
), pp.
583
619
.10.1007/s10494-015-9622-4
23.
Walters
,
D. K.
, and
Cokljat
,
D.
,
2008
, “
A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier-Stokes Simulations of Transitional Flow
,”
ASME J. Fluids Eng.
,
130
(
12
), p.
121401
.10.1115/1.2979230
24.
Mayle
,
R. E.
, and
Schulz
,
A.
,
1997
, “
The Path to Predicting Bypass Transition
,”
ASME J. Turbomach.
,
119
(
3
), pp.
405
411
.10.1115/1.2841138
25.
Coder
,
J. G.
, and
Maughmer
,
M. D.
,
2014
, “
Computational Fluid Dynamics Compatible Transition Modeling Using an Amplification Factor Transport Equation
,”
Flow, Turbul. Combust.
,
52
(
11
), pp.
2506
2512
.10.2514/1.J052905
26.
Kim
,
D.
,
Kim
,
Y.
,
Li
,
J.
,
Wilson
,
R. V.
,
Martin
,
J. E.
, and
Carrica
,
P. M.
,
2018
, “
Boundary Layer Transition Models for Naval Applications: Capabilities and Limitations
,”
32nd Symposium on Naval Hydrodynamics, Hamburg, Germany, Aug. 5–10.
27.
Abdollahzadeh
,
M.
,
Esmaeilpour
,
M.
,
Vizinho
,
R.
,
Younesi
,
A.
, and
Pàscoa
,
J.
,
2017
, “
Assessment of RANS Turbulence Models for Numerical Study of Laminar-Turbulent Transition in Convection Heat Transfer
,”
Int. J. Heat Mass Transfer
,
115
, pp.
1288
1308
.10.1016/j.ijheatmasstransfer.2017.08.114
28.
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/OMAE2009-79398
29.
Menter
,
F. R.
,
Kuntz
,
M.
, and
Langtry
,
R.
,
2003
, “
Ten Years of Industrial Experience With the SST Turbulence Model
,” Proceedings of the Fourth International Symposium on
Turbulence, Heat and Mass Transfer
, Antalya, Turkey, pp.
625
632
.
30.
Coder
,
J. G.
,
2017
, “
Enhancement of the Amplification Factor Transport Transition Modeling Framework
,”
AIAA
Paper No. 2017-1709. 10.2514/6.2017-1709
31.
Coder
,
J. G.
, and
Maughmer
,
M. D.
,
2015
, “
Application of the Amplification Factor Transport Transition Model to the Shear Stress Transport Model
,”
AIAA
Paper No. 2015-0588. 10.2514/6.2015-0588
32.
Lopez
,
M.
, and
Walters
,
D. K.
,
2017
, “
A Recommended Correction to the k T k L ω Transition-Sensitive Eddy-Viscosity Model
,”
ASME J. Fluids Eng.
,
139
(
2
), p.
024501
.10.1115/1.4034875
33.
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.2014.01.006
34.
Roache
,
P.
,
1998
,
Verification and Validation in Computational Science and Engineering
,
Hermosa Publishers
,
Albuquerque, NM
.
35.
Wilcox
,
D. C.
,
2004
,
Turbulence Modeling for CFD
, 2nd ed.,
DCW Industries
, La Canada, CA.
36.
ERCOFTAC,
1990
, “ERCOFTAC Classic Collection Database,” accessed Dec. 10,
2019
, http://cfd.mace.manchester.ac.uk/ercoftac/
37.
Spalart
,
P. R.
, and
Rumsey
,
C. L.
,
2007
, “
Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations
,”
AIAA J.
,
45
(
10
), pp.
2544
2553
.10.2514/1.29373
38.
Lopes
,
R.
,
Eça
,
L.
, and
Vaz
,
G.
,
2017
, “
On the Decay of Free-Stream Turbulence Predicted by Two-Equation Eddy-Viscosity Models
,”
20th Numerical Towing Tank Symposium
, Wageningen, The Netherlands, pp.
133
138
.https://www.researchgate.net/publication/320235380_On_the_Decay_of_Free-stream_Turbulence_Predicted_by_Two-equation_Eddy-viscosity_Models
39.
Mcghee
,
R. J.
,
Walker
,
B. S.
, and
Millard
,
B. F.
,
1988
, “
Experimental Results for the Eppler 387 Airfoil at Low Reynolds Numbers in the Langley Low-Turbulence Pressure Tunnel
,” National Aeronautics and Space Administration, Hampton, VA, Memorandum No.
4062
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890001471.pdf
40.
Cole
,
G. M.
, and
Mueller
,
T. J.
,
1990
, “
Experimental Measurements of the Laminar Separation Bubble on an Eppler 387 Airfoil at Low Reynolds Numbers
,” University of Notre Dame, Notre Dame, IN, Report No. UNDAS-1419-FR.
41.
Selig
,
M. S.
,
Guglielmo
,
J. J.
,
Broeren
,
A. P.
, and
Giguère
,
P.
,
1995
,
Summary of Low Speed Airfoil Data
, Vol.
1
,
SoarTech Publications
, Virginia Beach, VA.
42.
Selig
,
M. S.
,
Lyon
,
C. A.
,
Broeren
,
A. P.
,
Giguère
,
P.
, and
Gopalarathnam
,
A.
,
1997
,
Summary of Low Speed Airfoil Data
, Vol.
3
,
SoarTech Publications
, Virginia Beach, VA.
43.
Williamson
,
G. A.
,
McGranahan
,
B. D.
,
Broughton
,
B. A.
,
Deters
,
R. W.
,
Brandt
,
J. B.
, and
Selig
,
M. S.
,
2012
,
Summary of Low Speed Airfoil Data
, Vol.
5
, Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Champaign, IL.
44.
Gregory
,
N.
, and
O'Reilly
,
C. L.
,
1970
, “
Low-Speed Aerodynamic Characteristics of NACA 0012 Aerofoil Section, Including the Effects of Upper-Surface Roughness Simulating Hoar Frost
,” NPL AERO, Middlesex, UK.
45.
Ol
,
M.
,
McCauliffe
,
B. R.
,
Hanff
,
E. S.
,
Scholz
,
U.
, and
Kähler
,
C.
,
2005
, “
Comparison of Laminar Separation Bubble Measurements on a Low Reynolds Number Airfoil in Three Facilities
,”
AIAA
Paper No.
2005
0029
.10.2514/6.2005-5149
46.
Swalwell
,
K. E.
,
Sheridan
,
J.
, and
Melbourne
,
W. H.
,
2004
, “
The Effect of Turbulence Intensity on Performance of a NACA4421 Airfoil Section
,”
AIAA
Paper No.
2004
0665
.10.2514/6.2004-665
47.
Fransson
,
J. H. M.
,
Matsubara
,
M.
, and
Alfredsson
,
P. H.
,
2005
, “
Transition Induced by Free-Stream Turbulence
,”
J. Fluid Mech.
,
527
, pp.
1
25
.10.1017/S0022112004002770
You do not currently have access to this content.