Publications

Vertical-axis wind turbines’ simpler design and low center of gravity make them ideal for floating wind applications. However, efficient design optimization of floating systems requires fast and accurate models. Low-fidelity vertical-axis turbine aerodynamic models, including double multiple streamtube and actuator cylinder theory, were created during the 1980s. Commercial development of vertical-axis turbines all but ceased in the 1990s until around 2010 when interest resurged for floating applications. Despite the age of these models, the original assumptions (2-D, rigid, steady, straight bladed) have not been revisited in full. When the current low-fidelity formulations are applied to modern turbines in the unsteady domain, aerodynamic load errors nearing 50% are found, consistent with prior literature. However, a set of steady and unsteady modifications that remove the majority of error is identified, limiting it near 5%. This paper shows how to reformulate the steady models to allow for unsteady inputs including turbulence, deforming blades, and variable rotational speed. A new unsteady approximation that increases numerical speed by 5–10× is also presented. Combined, these modifications enable full-turbine unsteady simulations with accuracy comparable to higher-fidelity vortex methods, but over 5000× faster.

With interest resurging in vertical-axis wind turbines, there is a need for a fast and accurate vertical-axis turbine aerodynamics model. Although 3-D vortex methods are faster than 3-D computational fluid dynamics, they are orders of magnitude slower than required for design optimization. Lower fidelity models like actuator cylinder and double multiple streamtube are popular choices. However, both original formulations assume a steady-state infinite cylinder of unchanging radius, uncharacteristic of offshore turbines. Although stacks of cylinders can be used to approximate curved blades, this yields errors in excess of 50% and does not capture active deformation. Despite current consensus that these are errors inherent to the 2-D formulation, we show the error can nearly all be resolved by including considerations for curved blades. Unsteady effects have historically been captured using a first-order filter on the steady-state induced velocities. Although active deformation can be captured with proper discretization, the unsteady model requires a full revolution solution at each timestep. We found that with a rotating point iterative approach, only solutions at the blade positions are required, which gives a 5-10x speedup. These modifications together enable full-turbine unsteady simulations with accuracy comparable to vortex methods, but as much as 5000x faster.