Diffuser augmented wind turbines: review and assessment of theoretical models R. Bontempo ∗ and M. Manna Dipartimento di Ingegneria Industriale, Università degli Studi di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy Abstract Due to their potential to beat the Betz-Joukowsky limit for power extraction, diffuser-augmented wind-turbines have experienced a great research interest, especially in the last two decades. This paper presents a thorough critical-analysis and review of the most important theoretical models conceived for the performance analysis and design of this wind-concentrator system. The models are classified and compared between each other, and their main analogies and differences are highlighted and explained. New bridging relations between several models are also laid down. All methods are verified and validated using new and/or existing numerical and experimental data. For the first time, the impact of the simplifying assumptions, typically used in these models, is evaluated and discussed on a quantitative basis. Attention is also paid to the optimization procedures aimed at evaluating the maximum power- coefficient attainable by a diffuser-augmented wind-turbine. It is revealed that none of these procedures is valid for a given duct geometry, whereas they still offer some usefulness from a design point of view. Finally, the review points out the main limitations, shortcomings and open-issues associated with theoretical models, paving the way for future research lines and improvements of this kind of models. Keywords: diffuser augmented wind turbine; ducted wind turbine; actuator disk 1 Introduction Due to the more and more urgent need to reduce greenhouse- gas emissions and the dependence upon fossil fuels, a signif- icant increase in the energy demand from renewable sources took place in the last decades, so much so that, in 2018, the renewable power-capacity reached 33% of the total one [1]. Among others, technologies for the exploitation of the wind- resource are one of the most reliable and with a long history of commercial success. In fact, wind energy contributes 25% to the global renewable power-capacity, and it is the first re- newable source after the hydropower [1]. However, due to the low power density of wind-energy conversion-systems, new methods for extracting more power from the wind have always sparked great interest. In this context, several types of wind concentrators [2–4] have been developed, albeit the so-called Diffuser-Augmented Wind- Turbine (DAWT) (also named ducted or shrouded wind- turbine) is the most diffused and studied. In this kind of de- vice, the turbine is installed inside an annular wing which, thanks to its sectional circulation, induces an increase in the mass flow swallowed by the rotor. By doing so, the power extracted by the turbine raises, and the Betz-limit can be ex- ceeded both in terms of the rotor and duct-exit area [5]. Other collateral advantages of DAWTs are the reduced cut-in speed, the lessened tip losses [6] and noise [7], the low sensitivity to variations of the yaw-angle [8, 9], and the opportunity to be naturally used in airborne applications for the harnessing of the stable and strong high-altitude wind-streams [10–13], as well as for the installation in urban environment [14, 15]. The first work published on DAWT was probably due to Betz [16], who developed a theoretical model (TM) based on the mechanical-energy balances (MEBs). Assuming a zero * Corresponding author: e-mail address rodolfo.bontempo@unina.it, tel. +39-081-7683281 gauge-pressure at the diffuser exit, Betz concluded that a DAWT can extract at maximum 65% of the power of an open wind turbine (OWT) with the same frontal-area. Due to this unfair conclusion, DAWTs disappeared from the global research agenda till the ’50s when Vezzani [17] pro- posed to integrate a DAWT in a pumped-storage facility. In the same period, Sanuki [18, 19] and Iwasaki [20] experimen- tally obtained a gain in the extracted power equal to 88% and 30%, respectively. In 1953, Lilley and Rainbird [21] presented a landmark report mainly dealing with a MEB-TM includ- ing duct-incidence effects and diffuser losses. They obtained an increment in the power output by increasing the diffuser exit-to-rotor area-ratio and, consequently, promoting a nega- tive gauge-pressure at the duct exit. By doing so, however, a boundary-layer separation can occur, leading to an abrupt performance decrease. The research activity on DAWTs slowly continued in the ’60s, when the sole work carried out at the Technion by Kogan and Seginer [22] appeared. They experimentally observed a power coefficient 3 times greater than the Betz limit in the no- yaw case. However, to avoid boundary-layer separation with- out decreasing the exit-to-rotor area-ratio, they used a very long and unpractical diffuser with a small apex-angle (8.5 ◦ ). The 1973 oil crisis significantly boosted the interest in DAWTs [23], and a long series of theoretical and experimen- tal works due to Igra [24] and to the Grumman Aerospace [25–27] appeared over ten years. Using as a guide the results of MEB-TMs [24, 28, 29], compact and cost-effective ducts characterised by high exit-to-rotor area-ratios were developed. To prevent boundary-layer separation, they introduced numer- ous innovations, including multi-slotted diffusers, boundary- layer blowing [30], and annular flaps. By doing so, Igra [24] and the Grumman Aerospace [31, 32] were capable of obtain- ing a power coefficient of 2.8 and 3.4 times the Betz limit, re- spectively. Other relevant aspects investigated in these works 1 Bontempo R., Manna M., "Diffuser augmented wind turbines: review and assessment of theoretical models", Applied Energy, Vol 280, pp 115867, 2020 DOI: 10.1016/j.apenergy.2020.115867