The objective of this study is to investigate the two-dimensional unsteady flow around an airfoil undergoing a Darrieus motion in dynamic stall conditions. For this purpose, a numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunction-vorticity formulation in a non-inertial frame of reference was developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by an eddy viscosity model. Our investigation centers on an evaluation of the algebraic Cebeci-Smith model (CSM) and the nonequilibrium Johnson-King model (JKM). In an effort to predict dynamic stall features on rotating airfoils, first we present some testing results concerning the performance of both turbulence models for the flat plate case. Then, computed flow structure together with aerodynamic coefficients for a NACA 0015 airfoil in Darrieus motion under dynamic stall conditions are presented.

1.
Allet
A.
, and
Paraschivoiu
I.
,
1988
, “
Aerodynamic Analysis of the Darrieus Wind Turbines Including Dynamic-Stall Effects
,”
Journal of Propulsion and Power
, Vol.
4
, No.
5
, pp.
472
477
.
2.
Cebeci, T., and Smith, A. M . O., 1974, Analysis of Turbulent Boundary Layers, Academic Press, New York.
3.
Gunzburger
M. D.
, and
Peterson
J . S.
,
1988
, “
On Finite Element Approximations of the Streamfunction-Vorticity and Velocity-Vorticity Equations
,”
International Journal for Numerical Methods in Fluids
, Vol .
8
, pp .
1229
1240
.
4.
Johnson
D. A.
, and
Coakley
T. J.
,
1990
, “
Improvements to a Nonequilibrium Algebraic Turbulence Model
,”
AIAA Journal
, Vol.
28
, No.
11
, pp.
2000
2003
.
5.
Johnson
D. A.
,
1987
, “
Transonic Separated Flow Predictions with an Eddy Viscosity/Reynolds-Stress Closure Model
,”
AIAA Journal
, Vol.
25
, No.
2
, pp.
252
259
.
6.
Johnson
D. A.
, and
King
L. S.
,
1985
, “
A Mathematically Simple Turbulence Closure Model for Attached and Separated Turbulent Flows
,”
AIAA Journal
, Vol.
23
, No.
11
, pp.
1684
1692
.
7.
Klebanoff, P. S., 1955, “Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient,” Report 1247, National Advisory Committee for Aeronautics.
8.
McCroskey
W. J.
,
1977
, “
Some Current Research in Unsteady Fluid Dynamics— The 1976 Freeman Scholar Lecture
,”
Journal of Fluids Engineering
, Vol.
99
, pp.
8
39
.
9.
Oler, J. W., Strickland, J. H., Im, B. J., and Graham, G. H., 1983, “Dynamic Stall Regulation of the Darrieus Turbine,” Sandia Report SAND83-7029, Albuquerque, NM.
10.
Peeters
M. F.
,
Habashi
W. G.
, and
Dueck
E. G.
,
1987
, “
Finite Element Streamfunction-Vorticity Solutions of the Incompressible Navier-Stokes Equations
,”
International Journal for Numerical Methods in Fluids
, Vol.
7
, pp.
17
27
.
11.
Rostand
P.
,
1989
, “
Algebraic Turbulence Models for the Computation of Two-Dimensional High-Speed Flows Using Unstructured Grids
,”
International Journal for Numerical Methods in Fluids
, Vol.
9
, pp.
1121
1143
.
12.
Saad, Y., and Schultz, M., 1983, “GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems,” Research Report YALEU/DCS/RR-254.
13.
Shida
Y.
,
Kuwahara
K.
,
Ono
K.
, and
Takami
H.
,
1987
, “
Computation of Dynamic Stall of a NACA-0012 Airfoil
,”
AIAA Journal
, Vol.
25
, No.
3
, pp.
408
413
.
14.
Tchon, K.-F., 1993, “Simulation Nume´rique du Dee´crochage Dynamique surun Profil d’aile en Mouvement de Rotation,” Ph.D. thesis, E´cole Polytechnique de Montre´al, Montre´al, Que´bec, Canada.
15.
Tezduyar
T. E.
,
Glowinsky
R.
, and
Liou
J.
,
1988
, “
Petrov-Galerkin Methods on Multiply Connected Domains for the Vorticity-Streamfunction Formulation of the Incompressible Navier-Stokes Equations
,”
International Journal for Numerical Methods in Fluids
, Vol.
8
, pp.
1269
1290
.
16.
Van Dam
C. P.
, and
Hafez
M.
,
1989
, “
Comparison of Iterative and Direct Solution Methods for Viscous Flow Problems
,”
AIAA Journal
, Vol.
27
, No.
10
, pp.
1459
1461
.
17.
Visbal
M. R.
,
1990
, “
Dynamic Stall of a Constant-Rate Pitching Airfoil
,”
Journal of Aircraft
, Vol.
27
, No.
5
, pp.
400
407
.
18.
Wilcox, D. C, 1993, “Turbulence Modeling for CFD,” DCW Industries, Inc., La Can˜ada, California.
19.
Zienkiewicz
O. C.
,
Emson
C.
, and
Bettess
P.
,
1983
, “
A Novel Boundary Infinite Element
,”
International Journal for Numerical Methods in Engineering
, Vol.
19
, pp.
393ndash;404
393ndash;404
.
This content is only available via PDF.
You do not currently have access to this content.