Abstract

This paper aims to estimate the surface mesh size related discretization uncertainties using the γReθ transition model combined with the shear stress transport (SST) k–ω turbulence model. For comparison, this work employs an available experimental study performed with a 6:1 prolate spheroid. The grid convergence index (GCI) study is performed for axial force, surface skin friction, and pressure coefficients with three levels of meshes. The transition model estimates the axial force coefficients (CX), approximately half of which are obtained using fully turbulent calculations with higher GCI values. The GCI values around the axial force coefficients for the level-2 mesh are less than 1% based on fully turbulent calculations. However, with the transition model, these values for the same mesh level increase to 10%. While the GCI values of surface pressure coefficients are very small based on both fully turbulent and transition model calculations, these coefficients show differences at the trailing part of the spheroid. Significant differences are also observed in the surface friction coefficients. While the model captures drastic changes in terms of transition in the surface friction coefficients at the suction side of the spheroid, such drastic change is not observed in fully turbulent calculations. On the other hand, there is no sign of any transition phenomenon at the pressure side, contrary to the observations of experimental measurements. The transition model is not able to estimate the transition front geometry correctly. The GCI values of the surface friction coefficients increase dramatically, up to 765% around the transition regions.

References

1.
Schlichting
,
H.
, and
Gersten
,
K.
,
2000
,
Boundary-Layer Theory
, 8th ed.,
Springer-Verlag
,
Berlin/Heidelberg
.
2.
Sengupta
,
T. K.
,
2012
,
Instabilities of Flows and Transition to Turbulence
,
CRC Press
,
Boca Raton, FL
.
3.
Zheng
,
X.
,
Liu
,
C.
,
Liu
,
F.
, and
Yang
,
C.
,
1998
, “
Turbulent Transition Simulation Using the k − ω Model
,”
Int. J. Numer. Methods Eng.
,
42
(
5
), pp.
907
926
.10.1002/(SICI)1097-0207(19980715)42:5<907::AID-NME393>3.0.CO;2-T
4.
Wauters
,
J.
, and
Degroote
,
J.
,
2018
, “
On the Study of Transitional Low-Reynolds Number Flows Over Airfoils Operating at High Angles of Attack and Their Prediction Using Transitional Turbulence Models
,”
Prog. Aerosp. Sci.
,
103
, pp.
52
68
.10.1016/j.paerosci.2018.10.004
5.
Eca
,
L.
, and
Hoekstra
,
M.
,
2008
, “
The Numerical Friction Line
,”
J. Mar. Sci. Technol.
,
13
(
4
), pp.
328
345
.10.1007/s00773-008-0018-1
6.
Pasquale
,
D. D.
,
Rona
,
A.
, and
Garrett
,
S. J.
,
2009
, “
A Selective Review of CFD Transition Models
,”
AIAA
Paper 2009-3812.10.2514/6.2009-3812
7.
Boiko
,
A. V.
,
Kirilovskiy
,
S. V.
,
Maslov
,
A. A.
, and
Poplavskaya
,
T. V.
,
2015
, “
Engineering Modelling of the Laminar-Turbulent Transition: Achievements and Problems (Review)
,”
J. Appl. Mech. Tech. Phys.
,
56
(
5
), pp.
761
776
.10.1134/S002189441505003X
8.
Krumbein
,
A.
,
Krimmelbein
,
N.
,
Grabe
,
C.
, and
Shengyang
,
N.
,
2015
, “
Development and Application of Transition Prediction Techniques in an Unstructured CFD Code
,”
AIAA
Paper No. 2015-2476.10.2514/6.2015-2476
9.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Völker
,
S.
,
2006
, “
A Correlation-Based Transition Model Using Local Variables: Part I—Model Formulation
,”
ASME J. Turbomach.
,
128
(
3
), pp.
413
422
.10.1115/1.2184352
10.
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
11.
Grabe
,
C.
, and
Krumbein
,
A.
,
2013
, “
Correlation-Based Transition Transport Modeling for Three-Dimensional Aerodynamic Configuration
,”
J. Aircr.
,
50
(
5
), pp.
1533
1539
.10.2514/1.C032063
12.
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
13.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
14.
Vaz
,
G.
,
Jaouen
,
F.
, and
Hoekstra
,
M.
,
2009
, “
Free-Surface Viscous Flow Computations: Validation of URANS Code FreSCo
,”
28th International Conference on Ocean, Offshore and Arctic Engineering
, Vol.
43451
, Honolulu, HI, May 31–June 5, pp.
425
437
.
15.
Lopes
,
R.
,
Eca
,
L.
,
Vaz
,
G.
, and
Kerkvliet
,
M.
,
2021
, “
Assessing Numerical Aspects of Transitional Flow Simulations Using the RANS Equations
,”
Int. J. Comput. Fluid Dyn.
,
1
35
(
3
), pp.
157
178
.10.1080/10618562.2020.1870962
16.
Seyfert
,
C.
, and
Krumbein
,
A.
,
2013
, “
Comparison of a Local Correlation-Based Transition Model With a eN-Method for Transition Prediction
,”
New Results in Numerical and Experimental Fluid Mechanics VIII
, Vol.
121
,
Springer
,
Berlin/Heidelberg
, pp.
541
548
.
17.
Seyfert
,
C.
,
2011
, “
Application of a Transition Transport Model to Industrially Relevant Aerodynamic Configurations
,”
Conference Proceedings of ODAS 2011–11th ONERA-DLR Aerospace Symposium
, Toulouse, France, Feb. 8–10, pp.
1
8
.
18.
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
19.
Rumsey
,
C. L.
, and
Lee-Rausch
,
E. M.
,
2015
, “
NASA Trapezoidal Wing Computations Including Transition and Advanced Turbulence Modelling
,”
J. Aircr.
,
52
(
2
), pp.
496
509
.10.2514/1.C032754
20.
Vassberg
,
J. C.
, and
Lee-Rausch
,
E. M.
,
2018
, “
Introduction to DPW-VI Special Section
,”
J. Aircr.
,
55
(
4
), pp.
1317
1324
.10.2514/1.C035143
21.
Tinoco
,
E. N.
,
Brodersen
,
O. P.
,
Keye
,
S.
,
Laflin
,
K. R.
,
Feltrop
,
E.
,
Vassberg
,
J. C.
,
Mani
,
M.
,
Rider
,
B.
,
Wahls
,
R. A.
,
Morrison
,
J. H.
,
Hue
,
D.
,
Roy
,
C. J.
,
Mavriplis
,
D. J.
, and
Murayama
,
M.
,
2018
, “
Summary Data From the Sixth AIAA CFD Drag Prediction Workshop: CRM Cases
,”
J. Aircr.
,
55
(
4
), pp.
1352
1379
.10.2514/1.C034409
22.
Rumsey
,
C.
,
Long
,
M.
,
Stuever
,
R.
, and
Wayman
,
T.
,
2011
, “
Summary of the First AIAA CFD High Lift Prediction Workshop
,”
AIAA
Paper No. 2011–939.10.2514/1.C031447
23.
Rumsey
,
C. L.
,
Slotnick
,
J. P.
, and
Sclafani
,
A. J.
,
2019
, “
Overview and Summary of the Third AIAA High Lift Prediction Workshop
,”
J. Aircr.
,
56
(
2
), pp.
621
644
.10.2514/1.C034940
24.
Steed
,
R. G. F.
,
2011
, “
High Lift CFD Simulations With an SST-Based Predictive Laminar to Turbulent Transition Model
,”
AIAA
Paper No. 2011-864.10.2514/6.2011-864
25.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
,
Freitas
,
C. J.
,
Coleman
,
H.
, and
Raad
,
P. E.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainity Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.10.1115/1.2960953
26.
Kreplin
,
H. P.
,
Vollmers
,
H.
, and
Meier
,
H. U.
,
1985
, “
Wall Shear Stress Measurements on an Inclined Prolate Spheroid in the DFVLR 3m × 3m Low Speed Wind Tunnel, Gottingen
,” DFVLR-AVA, Göttingen, Germany, Report No. IB 222-84 A 33.
27.
Meier
,
H. U.
, and
Kreplin
,
H. P.
,
1980
, “
Influence on Free-Stream Turbulence on the Boundary Layer Development
,”
AIAA J.
,
18
(
1
), pp.
11
15
.10.2514/3.50724
28.
Charnay
,
G.
,
Comte-Bellot
,
G.
, and
Mathiew
,
J.
,
1971
, “
Development of a Turbulent Boundary Layer on a Flat Plate in an External Turbulent Flow
,” AGARD CP93, London, UK, Paper No. 27.
29.
Meier
,
H. U.
,
Michel
,
U.
, and
Kreplin
,
H. P.
,
1986
, “
The Influence of Wind Tunnel Turbulence on the Boundary Layer Transition
,” DFVLR-AVA, Göttingen, Germany, Report No. IB 222-86 A 39.
30.
Hancock
,
P. E.
, and
Bradshaw
,
P.
,
1983
, “
The Effect of Free Stream Turbulence Level in Turbulent Boundary Layers
,”
ASME J. Fluids Eng.
,
105
(
3
), pp.
284
289
.10.1115/1.3240989
31.
Phillips
,
T. S.
, and
Roy
,
C. J.
,
2014
, “
Richardson Extrapolation-Based Discretization Uncertainty Estimation for Computational Fluid Dynamics
,”
ASME J. Fluids Eng.
,
136
(
12
), p.
21401
.10.1115/1.4027353
You do not currently have access to this content.