Abstract:The performance and economics of turbines in a tidal array are largely dependent on the power per turbine, and so approaches that can increase this power are crucial for the development of tidal energy. In this paper, we combine a two-scale partial array model and a one-dimensional channel model to investigate the effects of blockage, turbine arrangement, and channel dynamics on tidal turbines. The power per arXiv:1711.00364v3 [physics.flu-dyn]
“…Otherwise, even in steady flow, the reference velocity u 1 that is used to calculate C P,Betz is influenced by the array operation and design, as shown in section IV. Thus maximising C P,Betz does not necessarily led to P T,max , when the assumption of unaltered flow is changed to head-driven flow for a further investigation, as shown in [21], [22]. This was avoided in model (IV) and (V) by using the unaltered (flow without the array) flow velocity u 0 instead of u 1 as energy reference to calculate the Betz coefficient of performance and P avail .…”
Section: B Discussionmentioning
confidence: 99%
“…Therefore optimal coefficient of performance does not necessarily lead to optimal operation in terms of maximized power output. This was shown by [21], [22] and is highly misleading for developers.…”
Section: B Reference Energy Scale In Tidal Channelsmentioning
A turbine array is an adjustable flow resistanceR placed in a tidal channel. Ideally, it is designedand operated to maximise energy yield. Garrett & Cummins(2005), using optimal control theory applied to the RCelementchannel (R) and basin (C), showed: the energyextraction from the flow PT + PD is maximised when theflow rate is slowed down by a factor of 1/√3. This resultis independent of the ratio of the extracted mechanicalpower PT to the total power extraction including the powerloss PD due to the mixing of the bypass flows within theturbine field. The optimisation task for turbine arrays ismaximising PT. This objective raises two questions: ”Whatis the maximum power PT that can be extracted, and what isthe optimal design (size, topology) and operation to achievethis output?” When addressing them, the literature stilluses the Betz ‘limit’ as a reference. The work presentedhighlights two major problems. First, the Betz ’limit’ isnot a constant upper bound for open channel flow. Thisproblem has been discussed and solved by the first author(2011, 2020). Second and more importantly, the presentedpaper points out the misconception under which severalresearch studies referred to array topologies as ‘optimal’with regard to design and operation. Hereby, the presentedpaper contributes to the advancement of tidal power on anaxiomatic basis. The misleading by Betz and overvaluingof transient effects is made transparent in a scientificdiscourse.
“…Otherwise, even in steady flow, the reference velocity u 1 that is used to calculate C P,Betz is influenced by the array operation and design, as shown in section IV. Thus maximising C P,Betz does not necessarily led to P T,max , when the assumption of unaltered flow is changed to head-driven flow for a further investigation, as shown in [21], [22]. This was avoided in model (IV) and (V) by using the unaltered (flow without the array) flow velocity u 0 instead of u 1 as energy reference to calculate the Betz coefficient of performance and P avail .…”
Section: B Discussionmentioning
confidence: 99%
“…Therefore optimal coefficient of performance does not necessarily lead to optimal operation in terms of maximized power output. This was shown by [21], [22] and is highly misleading for developers.…”
Section: B Reference Energy Scale In Tidal Channelsmentioning
A turbine array is an adjustable flow resistanceR placed in a tidal channel. Ideally, it is designedand operated to maximise energy yield. Garrett & Cummins(2005), using optimal control theory applied to the RCelementchannel (R) and basin (C), showed: the energyextraction from the flow PT + PD is maximised when theflow rate is slowed down by a factor of 1/√3. This resultis independent of the ratio of the extracted mechanicalpower PT to the total power extraction including the powerloss PD due to the mixing of the bypass flows within theturbine field. The optimisation task for turbine arrays ismaximising PT. This objective raises two questions: ”Whatis the maximum power PT that can be extracted, and what isthe optimal design (size, topology) and operation to achievethis output?” When addressing them, the literature stilluses the Betz ‘limit’ as a reference. The work presentedhighlights two major problems. First, the Betz ’limit’ isnot a constant upper bound for open channel flow. Thisproblem has been discussed and solved by the first author(2011, 2020). Second and more importantly, the presentedpaper points out the misconception under which severalresearch studies referred to array topologies as ‘optimal’with regard to design and operation. Hereby, the presentedpaper contributes to the advancement of tidal power on anaxiomatic basis. The misleading by Betz and overvaluingof transient effects is made transparent in a scientificdiscourse.
“…On the other hand, water surface waves, combined with the turbulent wake flow from the upstream turbines and the local unsteadiness of the stream current, may produce a series of negative impacts, such as the inflow turbulence, dynamic structural loading and the variations in the hydrodynamics of flow–structure interaction and the performance of the turbine output. These influences have been investigated by theoretical [6–9], experimental [10–15] and physical oceanography studies [16,17]. Figure 1Schematic of the blockage effect of a tidal turbine in an open channel flow.…”
Tidal current is a promising renewable energy source. Previous studies have investigated the influence of surface waves on tidal turbines in many aspects. However, the turbine wake development in a surface wave environment, which is crucial for power extraction in a turbine array, remains elusive. In this study, we focus on the wake evolution behind a single turbine and its interaction with surface waves. A numerical solver is developed to study the effects of surface waves on an industrial-size turbine. A case without surface wave and two cases with waves and different rotor depths are investigated. We obtain three-dimensional flow field descriptions near the free surface, around the rotor, and in the near- and far-wake. In a comparative analysis, the time-averaged and instantaneous flow fields are examined for various flow characteristics, including momentum restoration, power output, free surface elevation and vorticity dynamics. A model reduction technique is employed to identify the coherent flow structures and investigate the spatial and temporal characteristics of the wave–wake interactions. The results indicate the effect of surface waves in augmenting wake restoration and reveal the interactions between the surface waves and the wake structure, through a series of dynamic processes and the Kelvin–Helmholtz instability.
“…The global blockage ratio is then defined as B G = B A B L (= nπd 2 /4hw), where w is the channel width and B A is the array blockage, which represents the ratio between the cross-sectional areas of the array, hn(d +s), and the channel, hw. Willden et al [29] and Gong et al [30] have also sought to combine two-scale theory with the simple channel model of Garrett and Cummins [7] in order to analyse the performance of partial-width arrays in channels. More recently, however, Bonar et al [8] have shown that these coupled one-dimensional models may, under certain oscillatory flow conditions, neglect leading-order physics.…”
Numerical simulations are used to explore the potential for local blockage effects and dynamic tuning strategies to enhance the performance of turbines in tidal channels. Full- and partial-width arrays of turbines, modeled using the volume-flux-constrained actuator disc and blade element momentum theories, are embedded within a two-dimensional channel with a naturally low ratio of drag to inertial forces. For steady flow, the local blockage effect observed by varying the cross-stream spacing between the turbines is found to agree very well with the predictions of the two-scale actuator disc theory of Nishino and Willden (2012, “The Efficiency of an Array of Tidal Turbines Partially Blocking a Wide Channel,” J. Fluid Mech., 708, pp. 596–606). For oscillatory flow, however, results show that, consistent with the findings of Bonar et al. (2019, “On the Arrangement of Tidal Turbines in Rough and Oscillatory Channel Flow,” J. Fluid Mech., 865, pp. 790–810), the shorter and more highly blocked arrays produce considerably more power than predicted by two-scale theory. Results also show that, consistent with the findings of Vennell (2016, “An Optimal Tuning Strategy for Tidal Turbines,” Proc. R. Soc. A, 472(2195), p. 20160047), the “dynamic” tuning strategy, in which the tuning of the turbines is varied over the tidal cycle, can only produce significantly more power than a temporally fixed turbine tuning if the array has a large number of turbine rows or a large local blockage ratio. For all cases considered, trends are consistent between the two turbine representations but the effects of local blockage and dynamic tuning are found to be much less significant for the more realistic tidal rotor than for the idealized actuator disc.
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