The immersed boundary method is used to simulate the flow around a two-dimensional cross section of a rotating NACA 0018 airfoil in order to investigate the dynamic stall occurring on a vertical axis wind turbine. The influence of dynamic stall on the force is characterized as a function of tip-speed ratio and Rossby number. The influence of the Coriolis effect is isolated by comparing the rotating airfoil to one undergoing an equivalent planar motion that is composed of surging and pitching motions that produce an equivalent speed and angle-of-attack variation over the cycle. Planar motions consisting of sinusoidally varying pitch and surge are also examined. At lower tip-speed ratios, the Coriolis force leads to the capture of a vortex pair when the angle of attack of a rotating airfoil begins to decrease in the upwind half cycle. This wake-capturing phenomenon leads to a significant decrease in lift during the downstroke phase. The appearance of this feature depends subtly on the tip-speed ratio. On the one hand, it is strengthened due to the intensifying Coriolis force, but on the other hand, it is attenuated because of the comitant decrease in angle of attack. While the present results are restricted to two-dimensional flow at low Reynolds numbers, they compare favorably with experimental observations at much higher Reynolds numbers. Moreover, the wake-capturing is observed only when the combination of surging, pitching, and Coriolis force is present.

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The self-starting capability of a NACA 0018 multi-bladed vertical-axis wind turbine is numerically investigated. The immersed boundary method is used to simulate the flow around a two-dimensional cross section of the wind turbine and the predictor-corrector method is used to couple the equation of motion of the turbine. A simple load model, which is linearly proportional to turbine angular velocity, is used for the load of the turbine. The angular velocity is characterized as a function of Reynolds number, density ratio, and viscous coefficient of the proposed load model. The power outputs and moment coefficients of motor-driven and flow-driven vertical-axis wind turbine are compared. For a particular Reynolds number, as the load on the flow-driven turbine is increased, the tip speed is reduced until the turbine fails to coherently rotate. The flow-driven and motordriven moment coefficients in the computation have good agreement between each other and are qualitatively similar to the torque measured in experiments. 1 These computations suggest that the load of a flow-driven turbine can be well-represented by the proposed load model and a motor-driven turbine can reproduce the physics of a flow-driven turbine within the range of tip-speed ratio examined. A simple model is proposed in order to analyze the starting torque. By assuming that the inertia of the blade is much larger than the fluid, the turbine can be considered stationary in the flow. The starting torque distribution of a multi-bladed turbine indicates the important orientations corresponding to maximum torque generation, at which a self-starting turbine always starts, and a stable equilibrium, where a non-self-starting turbine oscillates. These features agree with observations from the full simulations of the starting process. We further model the starting torque distribution by considering a single blade at different orientations, and construct starting torque distributions for multi-bladed turbines by linearly combining the torques at the respective positions of the blades. We show that this approximation is valid for a sufficiently low turbine solidity of about 0.5. Using this model, we find optimal starting configuration for a multi-bladed low-solidity vertical-axis wind turbine. Nomenclaturec airfoil chord length C M moment coefficient C P power coefficient F friction coefficient of the load I O moment of inertia of the blade about the rotation center of the VAWT N b number of blades O turbine rotation center R radius of the turbine Re Reynolds Number t * convective time units U ∞ freestream velocity

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