Framework for systematic flow manipulation by wind and hydrokinetic energy turbine arrays

Wind and hydrokinetic energy turbines are often constrained to locations where the available energy is limited by the operation of the turbines themselves. In two-dimensions, we describe how an array can manipulate the steady flow, redirecting more fluid kinetic energy to itself. Two computational examples of turbine arrays present solutions of the Navier-Stokes equations to illustrate the feasibility of flow manipulation, and motivate an idealized model. Using inviscid fluid dynamics, we underscore the relation between bound vorticity and flow deflection, and between free vorticity and energy extraction. To understand and design flow manipulations that increase the kinetic energy incident on the turbines, we consider an idealized deflector-turbine array constrained to a line segment, acting as an internal flow-boundary. We impose profiles of bound and shed vorticity on this segment by parameterizing the flow deflection and the wake deficit, respectively, and analyze the resulting flow using inviscid fluid dynamics. We find that the power extracted by the array is the product of two components: (i) the deflected kinetic energy incident on the array, and (ii) the array efficiency, both of which vary with deflection strength. The array efficiency, or its ability to extract a fraction of the incident energy, decreases slightly with increasing deflection from about 57\% at weak deflection to 39\% at high deflection. This decrease is outweighed by increasing incident kinetic energy with deflection, resulting in monotonically improved power extraction, thus highlighting the benefits from flow deflection.