Numerical method for steady ideal 2-D flows of finite vorticity with applications to vertical-axis wind turbine aerodynamics

This paper presents a new method for approximately modeling 2-D ideal steady fluid flows with finite vorticity induced by actuator curves of arbitrary shape. An actuator curve is an infinitesimally thin region containing a body force density acting on the flow, while the rest of the flow is force-free. The approach can be used for any flow satisfying this description, but, like other actuator methods, it is naturally suited for modeling turbines or propellers. We derive a weak formulation of the governing equations in the Lagrange streamfunction psi$$ \psi $$ and solve it using finite elements. Compared to related methods such as the actuator cylinder (AC) approach, our formulation is uniquely suited for computations involving wake-wake or wake-turbine interactions. We validate the method by computing the flow through a single Darrieus vertical-axis wind turbine (VAWT) and comparing with previous work. To demonstrate the ability to simulate interacting actuators of arbitrary configuration, we simulate a three-VAWT array. The turbines are modeled in a freestream, and the loading is chosen to represent ideal airfoils. The standard VAWT results are consistent with previous work, validating the method. The three-VAWT array demonstrates a higher efficiency than the single VAWT (0.56 vs. 0.52), with differing optmal tip speed ratios for the upwind and downwind turbines (upwind: 3.9, downwind: 3.1. The optimum for a single turbine is 3.6). The flow field of the three-VAWT array shows expected features such as an acceleration of flow between the two counter-rotating upwind turbines.

Automated summary

This paper presents a new method for approximately modeling 2-D ideal steady fluid flows with finite vorticity induced by actuator curves of arbitrary shape. The method is validated by computing the flow through a single Darrieus vertical-axis wind turbine (VAWT) and simulating a three-VAWT array. The results show a higher efficiency for the three-VAWT array compared to the single VAWT, demonstrating the effectiveness of the method.