Ducted wind turbines for urban microgeneration

The paper presents an extension to ducted rotors of the nonlinear actuator disk theory of Conway (J. Fluid Mech., vol. 365, 1998, pp. 235–267) and it is exact for incompressible, axisymmetric and inviscid flows. The solution for the velocities and the Stokes stream function results from the superposition of ring vortices properly arranged along the duct surface and the wake region. Using a general analytical procedure the flow fields are given as a combination of one-dimensional integrals of expressions involving complete as well as incomplete elliptic integrals. The solution being exact, the proper shape of the slipstream whether converging or diverging is naturally accounted for, even for heavy loads. A semi-analytical method has been developed that enables the flow induced by an actuator disk housed in a contoured duct to be solved duly accounting for the nonlinear mutual interaction between the duct and the rotor. Non-uniform load distributions, rotor wake rotation and ducts of general shapes and thickness distribution can be dealt with. Thanks to its reduced numerical cost, the method is well suited for the design and/or analysis of ducted rotors for marine, wind and aeronautical applications.

This work investigates the performance of ducted wind turbines (DWTs) through the axial momentum theory (AMT) as well as through a semi-analytical approach. Although the AMT points out that the duct thrust plays a key role in the enhancement of the power extraction, it does not allow for the evaluation of the flow field around the duct. For this reason, a semi-analytical model is also used to investigate the local and global features of the flow through a DWT. In comparison to the AMT, the proposed semi-analytical method can properly evaluate the performance of the device for each prescribed rotor load distribution and duct geometry. Moreover, in comparison to other linearised methods, this approach fully takes into account the wake rotation and divergence, and the mutual interaction between the turbine and the shroud. The analysis shows the opportunity to significantly increase the power output by enclosing the turbine in a duct and that the growth in the duct thrust has a beneficial effect onto the device performance. Finally, some insights on the changes occurring to the performance coefficients with the rotor thrust and the duct camber are obtained through a close inspection of the local features of the flow field.

The paper presents the validation of a generalised semi-analytical actuator disk model as applied to the study of the flow around ducted propellers. The method, which returns the exact solution as a superposition of ring vortex, duly accounts for the rotation of the wake, the convergence of the slipstream, and the nonlinear mutual interaction between the duct and the propeller. Furthermore, it can deal with an arbitrary radial distribution of the load and ducts of general shape. In order to validate the previously mentioned actuator disk model, results obtained through it are compared with those provided by the so-called " CFD actuator disk method ". The latter is a widely diffused tool for the analysis of the flow around open and ducted propellers which models the rotor by means of radial profiles of blade forces distributed over a disk surface. In this paper, evidence has been given of the excellent agreement between the results of the two methods. Thanks to its extremely reduced computational cost the semi-analytical method is well suited to be integrated into design systems based on the repeated analysis scheme of hierarchical type.

Diffuser-augmented wind-turbines are drawing increasing attention since they can beat the Betz-limit referred to the rotor-area. However, their diffusion is still prevented by some issues including: 1) the attainable power has not yet been shown to be larger than that of an open-turbine with the same frontal-area, 2) the classical analysis methods rely on the one-dimensional-flow and no-tip-gap assumptions whose impact has never been quantified. The paper addresses these two items investigating the potential of ideal diffuser-augmented wind-turbines using a newly-developed Axial-Momentum-Theory approach, and an extended version of a free-wake ring-vortex actuator-disk model. In comparison with similar methods, the novelty of the first approach is that it accounts for the two-dimensional effects and the tip-gap presence. Since this approach cannot evaluate the performance of a turbine for a given duct-geometry, a ring-vortex method is also developed. This is the first low-computational-cost method relying on the exact solution of the inviscid-flow through a uniformly-loaded ducted-turbine with a finite-size tip-gap. It strongly couples the flow induced by the duct and the wake which are modelled as the superposition of ring-vortices. The combined use of axial-momentum and ring-vortex methods leads to the following results. Firstly, it is clearly shown that an ideal diffuser-augmented turbine can extract more power than a Betz disk with the same frontal-area. To strengthen this statement, a new duct geometry with a remarkable value of the exit-area power-coefficient equal to 0.6098 is presented. This value is significantly higher than that of a base-line NACA5415 duct profile, i.e. 0.4800. Secondly, the impact of the one-dimensional-flow and no-tip-gap assumptions is evaluated. It is also shown that the tip-gap has negligible effects. Moreover, the one-dimensional-flow hypothesis has a low impact for high values of the rotor load, while the errors grow up decreasing the rotor thrust.