Mean Kinetic Energy Replenishment Mechanisms in Vertical-Axis Wind Turbine Farms

Vertical-axis wind turbines (VAWTs) are the subject of renewed interest due to the potential for higher power generation per unit land used, as well as their lower center of mass (the generator is at the bottom of tower), which renders them favorable for offshore deployment. However, VAWT farms have hardly been studied. In this paper, using a previously tested actuator line model in a large eddy simulation code, we investigate the transport of the mean kinetic energy (MKE) that replenishes the power in the farm. The primary sources of MKE are (1) the initial advective streamwise influx through the frontal area and (2) the vertical planform influx through the top and bottom interfaces of the farm. The results show that, for realistic finite-size farms, the planform MKE transport is a loss term over the first six rows: in this initial zone the mean flow adjusts by slowing down, and an upward mean advection develops that results in an efflux loss of MKE from the farm volume. The power extracted from farms is thus mainly from the frontal advection over the first few rows. When the initial streamwise advective flux is exhausted, the planform regeneration of MKE from above the wind farm becomes the dominant source; it is primarily affected by turbulent-mean interaction. This regeneration continues to adjust until rows 8 to 10 in our setups, beyond which a fully developed flow (similar to an infinite wind farm) can be observed. In the fully developed region, actual mechanical power generation by the turbines is about one third of replenishment. A primary conclusion is that more irregular farms designs should be studied, while the current literature continues to focus on the very classic layouts.