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

We revisit the modeling, using actuator line methods (ALM), of flow curvature effects on airfoils and their application to vertical-axis turbines (VAT), which is important when the ratio of airfoil chord c to arm length R is not small. The models can only use the aerodynamic coefficients of the airfoil in uniform flow (here obtained using wall-resolved CFD of a NACA0015 airfoil at Rec=6.0×106); they then consist of analytical modifications of these coefficients. The models for the normal force and moment coefficients use the classic analogy of potential flow with curved streamlines past an airfoil; their expression depends on the airfoil pitch angle and its attachment point to the arm. They are known, yet many authors have neglected the contribution of the aerodynamic moment. We here extend the models so as to cover all possibilities of attachment point and pitch angle, and up to stall. Furthermore, we develop a new model for the tangential force (the analogy with that of potential flow being flawed): its inviscid part, which corresponds to negative drag, is required to compensate for the aerodynamic moment. The improved models are first validated in steady flow corresponding to the NACA0015 airfoil rotating with c/R=2/7. We cover the whole range of pitch angles, up to stall. The results are shown to compare well with those of the reference CFD data. This validation is carried out for two attachment points: at airfoil mid-chord and at quarter-chord. An ALM incorporating 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 of TSR=3.25. This is also simulated for both attachment points. Here, a novel method is also developed to explicitly enforce the moment in an 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.