This paper presents a study on the $k-ω$ turbulence model with regard to the numerical implementation of the ω boundary condition at a solid wall, where ω tends to infinity. Three different implementations are tested in the calculation of a simple two-dimensional turbulent flow over a flat plate. Grid refinement studies in grids with different near-wall grid line spacings are performed to assess the numerical uncertainty of the predicted drag coefficient $CD.$ The results are compared with the predictions of several alternative algebraic, one-equation, and two-equation eddy-viscosity turbulence models. For the same level of grid refinement, the estimated uncertainty of $CD$ obtained with the $k-ω$ model is one order of magnitude larger than for all the other models.

1.
Wilcox, D. C., 1998, Turbulence Modeling for CFD, 2nd ed., DWC Industries, La Canada, California.
2.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
, pp.
1598
1605
.
3.
Kok, J. C., 1999, “Resolving the Dependence on Free-stream values for the k-ω Turbulence Model,” NLR-TP-99295, http://www.nlr.nl/public/library/1999/99295-tp.pdf
4.
Thivet
,
F.
,
Daouk
,
M.
, and
Knight
,
D.
,
2002
, “
Influence of the Wall Condition on k-ω Turbulence Model Predictions
,”
AIAA J.
,
40
, pp.
179
181
.
5.
Hellsten, A., 1998, “On the Solid-Wall Boundary Condition of ω in the k-ω Type Turbulence Models,” Report B-50, Helsinki University of Technology, Laboratory of Aerodynamics, ISBN 951-22-4005-X; http://www.aero.hut.fi/Englanniksi/index.html
6.
Cebeci, T., and Smith, A. M. O., 1984, Analysis of Turbulent Boundary Layers, Academic Press, New York.
7.
Menter
,
F. R.
,
1997
, “
Eddy Viscosity Transport Equations and Their Relation to the k-ε Model
,”
J. Fluids Eng.
,
119
, pp.
876
884
.
8.
Spalart, P. R., and Allmaras, S. R., 1992, “A One-Equations Turbulence Model for Aerodynamic Flows,” AIAA 30th Aerospace Sciences Meeting, Reno, La Recherche Aerospatiale, 121, pp. 5–21.
9.
Chien
,
K. Y
,
1982
, “
Prediction of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model
,”
AIAA J.
,
20
(
1
), pp.
33
38
.
10.
Ec¸a, L., and Hoekstra, M., 2002, “An Evaluation of Verification Procedures for CFD Applications,” 24th Symposium on Naval Hydrodynamics, Fukuoka, Japan, Office of Naval Research, National Research Council, Washington.
11.
Roache, P. J., 1998, Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico.
12.
Ec¸a, L., and Hoekstra M., 2003, “An Example of Uncertainty Estimation in the Calculation of a 2-D Turbulent Flow,” 4th Marnet-CFD Workshop, Haslar, Qinetia, UK.
13.
Coles, D. E., and Hirst, E. A., eds., 1968, “Computation of Turbulent Boundary-Layers,” Proceedings of AFOSR-IFP-Stanford Conference, Vol. 2, Stanford University, California.
14.
Jose´, M. Q. B., Jacob, and Ec¸a, L., 2000, “2-D Incompressible Steady Flow Calculations with a Fully Coupled Method,” VI Congresso Nacional de Meca^nica Aplicada e Computacional, Aveiro, Jose´ M. Q. B. Jacob, Universidade de Aviero, Portugal.
15.
Hoekstra, M., and Ec¸a, L., 1998, “PARNASSOS: An Efficient Method for Ship Stern Flow Calculation,” Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan.
16.
Ec¸a, L., 2002, “Comparison of Eddy-Viscosity Turbulence Models in a 2-D Turbulent Flow on a Flat Plate,” IST Report D72-16, Instituto Superior Te´cnico, Lisbon, Universidade Tecnica de Lisboa, Portugal.
17.
Vinokur
,
M.
,
2002
, “
On One-Dimensional Stretching Functions for Finite-Difference Calculations
,”
J. Comput. Phys.
,
50
, pp.
215
234
.
18.
Di Mascio
,
A.
,
Paciorri
,
R.
, and
Favini
,
B.
,
2002
, “
Truncation Error Analysis in Turbulent Boundary Layers
,”
J. Fluids Eng.
,
124
, pp.
657
663
.