Impulsively started planar actuator surfaces in high-Reynolds-number steady flow

Abstract

AbstractThe characteristics of unbounded flow past an impulsively started planar energy extracting device, such as a wind or tidal turbine, are studied theoretically, numerically and experimentally. The initial thrust on an impulsively started device, which can be more than double the steady thrust, is an important consideration for design and safe operation. The energy sink is modelled here as an ‘actuator surface’ which imposes a uniform pressure discontinuity in the fluid proportional to the square of the fluid speed normal to the surface, the fluid density, and a dimensionless resistance coefficient. The flow past the actuator is studied theoretically for the case of weak resistance using an unsteady model which recovers steady linear momentum theory in the limit of long time. For the case of strong resistance the flow is studied numerically using the point vortex method. Experimental measurements of thrust on a mesh towed through static water are compared to the numerical results and show good agreement. The thrust on an impulsively started device is estimated, for a typical installation, to fall to within 10 % of the steady value within ∼1 min. The numerical model is also used to simulate the gradual startup of a device, yielding estimates of the time constant necessary in a control system in order to reduce peak thrusts in practice.