The objective of this study is to investigate the two-dimensional unsteady flow around art airfoil undergoing a Darrieus motion in dynamic stall conditions. Fbr 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 Petov-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.