Streamtube expansion effects on the Darrieus wind turbine

The purpose of the work described in this paper was to determine the aerodynamic loads and performance of a Darrieus wind turbine by including the expansion effects of the streamtubes through the rotor. The doublemultiple streamtube model with variable interference factors was used to estimate the induced velocities with a modified CARDAAV computer code. Comparison with measured data and predictions shows that the streamtube expansion effects are relatively significant at high tip-speed ratios, allowing a more realistic modeling of the upwind/downwind flowfield asymmetries inherent in the Darrieus rotor. Two-Aetuator-Disk Models T HE Darrieus rotor is modeled by a pair of actuator disks arranged in tandem and capable of accounting for the difference in flowfield between the upwind and downwind half-cycles of the turbine. This concept, initially proposed by Lapin,1 gave rise to the development of a large number of aerodynamic models for studying the Darrieus wind turbine. The major differences between the various models are due to the assumptions used and the means of calculating the induced velocities through the rotor. However, several authors incorporated Holme's remark regarding the vortex theory2 in their momentum theories: that half the velocity retardation along a streamline occurs within the rotor. Thus, using linear aerodynamics and ignoring the effects of drag and stall, Sharpe and Read3 found a simple expression for the interference factors needed to calculate the induced velocities. The flowfield through the turbine was supposed to consist of straight but not parallel streamlines, yet the velocities everywhere were parallel to the V^ direction. A theoretical optimization technique was subsequently developed by Loth and McCoy4 for straight-bladed Darrieus wind turbines. They considered two semicylindrical actuator disks in series with separate cosine-type interference factors for the upwind and downwind half of the rotor; with this velocity distribution, the rotor blades become unloaded near the junction of the two rotor halves. In their inviscid analysis, the same authors used disks of equal area and found a Betz-type limit higher than the conventional value. An analysis for two uniformly loaded actuator-disks given by Newman 5 showed that the standard predictions (Cpmax = 16/27) are pessimistic and he calculated a new value of Cpmax = 16/25, which corresponds to those estimated by Ref. 4. A more practical analytical model was developed by Paraschivoiu6 using two constant interference factors over the front and back halves of the rotor for estimating the induced velocities. This double-multiple streamtube model is useful for predicting the overall aerodynamic performance and loads