Conservation of Mass Effects on Flow Through VAWT Actuator Disks Rotating at High Tip Speed Ratios

Inviscid flows through VAWTs is modeled at high tip speed ratios using actuator disk theory with the constraint of conserving mass as well as momentum and energy in the flow. Cylindrical and spherical disks are considered. Conservation of mass flow in a stream tube requires that the magnitude of the normal force exerted on this flow be the same through the upwind and down wind segments of theactuator disk. Since this force sequentially shows and deflects the flow away from and then back towards the undisturbed wind direction in the wake of the disk, it plays a primary role in determining the onset of choked flow (i.e., no flow) through outboard segments of the disk. The effect is to reduce the capture area of inflow wind from which energy can be extracted to produce power. Thiseffect appears to be more pronounced with the cylindrical then the spherical actuator disk. Predicted power coefficients differ little from those obtained with the DMST CODIF code (no conservation of mass constraint) for disks having low solidity and hence low induction effects at high tip speed ration. With increasing solidity or tip speed ration, choking constrains power coefficients tomaximum values approaching 0.5, after which they decrease substantially with the spread of choked flow. This effect occurs earlier and is more pronounced with the cylindrical actuator disk. In contrast, the DMST code generally predicts increasing power coefficients with increasing solidity or tip speed ration, with maximum values in the neighborhood of 0.6. It is concluded that the constraint ofconservation of mass can more severely influence the performance of cylindrical than spherical actuator disks. These disks simulate VAWTs with height-to-diameter ratios (H/D) of infinity and 1, respectively. A model of flow through the equatorial region of actuator disks with intermediate values of H/D indicates that performance approaches that of cylindrical disk for values of H/D much inexcess of 2.