Ducted wind turbine optimization and sensitivity to rotor position

Abstract

Abstract. The design of a ducted wind turbine modeled using an actuator disc was studied using Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) simulations. The design variables included the rotor thrust coefficient, the angle of attack of the duct cross section, the radial gap between the rotor and the duct, and the axial location of the rotor in the duct. Two different power coefficients, the rotor power coefficient (based on the rotor swept area) and the total power coefficient (based on the exit area of the duct), were used as optimization objectives. The optimal value of thrust coefficients for all designs was nearly constant, having a value between 0.9 and 1. The rotor power coefficient was sensitive to rotor gap but was insensitive to the rotor's axial location for positions ranging from upstream of the throat to nearly half the distance down the duct. Compared to the design that maximized rotor power coefficient, the design for maximal total power coefficient was characterized by a smaller angle of attack, a smaller rotor gap, and a downstream placement of the rotor. The insensitivity of power output to the rotor position implies that a rotor placed further downstream in the duct could produce the same power with a considerably smaller duct exit area and thus a greater total power coefficient. The design for that maximized total power coefficient exceeded Betz's limit with a total power coefficient of 0.67.

Experimental validation of a ducted wind turbine design strategy

“…The k −ω shear stress transport (SST) turbulence model was utilized, which, among the twoequation turbulence models, gives better prediction of flow separation. Further details of the methods employed can be found in Bagheri-Sadeghi et al (2018), and an example of the solution is shown in Fig. 5a.…”

“…The last curve on the plot, denoted by the heavy dashed line, is the numerical prediction by the actuator disk model in FLUENT, namely the solution used to generate the input velocity field profile for the mRotor design. The power predicted repre- Bagheri-Sadeghi et al (2018). The C p values, based on the rotor area, were also calculated for the data and are presented in Fig.…”

“…Unfortunately, such claims by inventors that they have "beaten Betz" have only served to give DWTs a bad reputation. Many studies have investigated the feasibility and associated augmentation factors seen in DWTs in an effort to further their development (Hu and Cheng, 2008;Igra, 1976Igra, , 1984Hansen et al, 2000;Werle and Presz Jr., 2008;van Bussel, 2007;Oman et al, 1977;Leoffler Jr. and Vanderbilt, 1978;Ohya et al, 2002Ohya et al, , 2008Politis and Koras, 1995;and Jamieson, 2009) with the largest prediction of 7 by Badawy and Aly (2000); however, conclusions have been quite varied. Werle and Presz Jr. (2008) used fundamental momentum principles and concluded that the possible augmentation factor could only approach 2 and that earlier studies had incorrect assumptions, leading to overly optimistic predictions.…”

Maximal power per device area of a ducted turbine

“…Achieving values of C P,total greater than the Betz's limit of 0.593 for a DWT is significant as it means a DWT can capture more power per unit area of the device than an open rotor turbine. Optimization studies of DWTs have shown that DWTs can achieve values of C P,total beyond Betz's limit (Aranake and Duraisamy, 2017;Bagheri-Sadeghi et al, 2018). C P,total not only is a useful metric to compare DWTs with open rotor wind turbines but could be an important design objective in certain problems like fully-integrated DWTs for sustainable 1 https://doi.org/10.5194/wes-2021-18 Preprint.…”

“…Since the experimental demonstration of the power augmentation provided by shrouding wind turbines (Sanuki, 1950), numerous studies on the design and optimization of the DWTs have been carried out (Lilley and Rainbird, 1956;Igra, 1981;Loeffler, 1981;Gilbert and Foreman, 1983;Georgalas et al, 1991;Politis and Koras, 1995;Hansen et al, 2000;Phillips et al, 2002;Ohya and Karasudani, 2010;Aranake and Duraisamy, 2017;Venters et al, 2018;Bagheri-Sadeghi et al, 2018). Only a few (Aranake and Duraisamy, 2017;Bagheri-Sadeghi et al, 2018;Venters et al, 2018) have used C P,total as a design metric while most other studies have focused on maximizing C P . The design variables of a DWT include the rotor blade design, its axial location, z rotor , and tip clearance or rotor gap, ∆n, and the angle of attack, α, length, l, and shape of the duct crosssection.…”