Improved modeling of flow curvature effects and actuator line method with aerodynamic moment, with application to vertical-axis turbines

Abstract. We revisit the modeling, using actuator line methods (ALM), of flow-curvature effects on airfoils and their application to vertical-axis turbines (VAT); these effects being important when the ratio between the airfoil chord and the arm length is not small. The modeling can only use as input the aerodynamic coefficients of the airfoil in uniform flow and as function of the angle of attack (obtained here using wall-resolved CFD simulations). It then consists of analytical modifications of those coefficients. The models for the normal force and moment coefficients are based on the analogy with potential flow with curved streamlines past an airfoil; they are not new, although many authors have neglected the contribution of the aerodynamic moment. Moreover, their expression depends on both the airfoil pitch angle and the location of its attachment to the arm, and we develop and validate models that cover all possibilities, up to angles near stall. The model for the tangential force is new (the analogy with that of potential flow being flawed): its inviscid part correspond to thrust (i.e; negative drag) and is required to compensate for the aerodynamic moment.

The correction models are first validated against CFD data, obtained using wall-resolved simulations, of a steady flow: a rotating NACA0015 airfoil with ratio of airfoil chord to arm length of 2/7 and at various pitch angles, up to stall; also for two attachment points of the airfoil to the arm: at mid-chord and at quarter-chord.

The ALM with the improved models is then also implemented in the CFD framework, and is used to simulate the unsteady flow corresponding to a VAT configuration: the rotating NACA0015 airfoil without pitch placed in a free stream and operating at optimal tip speed ratio, and simulated for both attachment points. For that, a novel method is also developed to explicitly enforce the moment in the ALM. The various components of the ALM results are compared with those of the reference CFD data, and are found to be in good agreement throughout the rotation cycle.