Abstract:This paper presents a new analytic approach for estimating the local power coefficient of a turbine experiencing anisotropic local blockage effects. Data-driven methods are employed first to approximately obtain a known analytic expression for isotropic local blockage effects, and then deployed to find candidate expressions for anisotropic local blockage effects. The dataset for the analysis of anisotropic local blockage is collected from 3D Reynolds-averaged Navier-Stokes (RANS) simulations of an infinitely w… Show more
“…One possible cause of the discrepancies observed in figure 16 is the geometric differences between the quasi-1-D and the full 3-D flow domain. As the RANS simulations utilise a square (not circular) cross-section, the variation in radial blockage (or ‘anisotropy’ of the blockage) may have an impact especially for these high blockage ratios (Juniper & Nishino 2022). Figure 16.Theoretical vs for uniform and varied thrust across the actuator disc surface compared with 3-D RANS, for .…”
Predicting the performance of large turbine arrays requires the understanding of many physical factors, such as array geometry, turbine operation, inflow conditions and turbulent wake mixing. Due to the large parameter space that an array may be optimised over, low-order models with low computational cost are often employed. This paper extends one of these models, the inviscid–viscous coupled model, for multi-row turbine modelling. Firstly, an extension to the inviscid actuator disc theory is presented by removing the limit on the number of discrete streamtubes computed. The extended model allows for the quantification of the impact of shear in the bypass and core flows separately. In particular, it is shown that averaging a sheared bypass flow profile can result in a substantial over-prediction of the power of a turbine in a laterally bounded flow as the effective blockage of the flow increases. The model is also used to confirm that an approximation using a limited number of streamtubes in some previous applications of the inviscid–viscous approach has a negligible impact on the results. Secondly, we explore the performance of a multi-row array with either uniform or varying turbine resistance across different rows. Results suggest that by varying resistance across rows, the array may outperform the uniform resistance case. The performance gain is dependent, however, on the arrangement and inter-turbine spacing both in the spanwise and streamwise directions.
“…One possible cause of the discrepancies observed in figure 16 is the geometric differences between the quasi-1-D and the full 3-D flow domain. As the RANS simulations utilise a square (not circular) cross-section, the variation in radial blockage (or ‘anisotropy’ of the blockage) may have an impact especially for these high blockage ratios (Juniper & Nishino 2022). Figure 16.Theoretical vs for uniform and varied thrust across the actuator disc surface compared with 3-D RANS, for .…”
Predicting the performance of large turbine arrays requires the understanding of many physical factors, such as array geometry, turbine operation, inflow conditions and turbulent wake mixing. Due to the large parameter space that an array may be optimised over, low-order models with low computational cost are often employed. This paper extends one of these models, the inviscid–viscous coupled model, for multi-row turbine modelling. Firstly, an extension to the inviscid actuator disc theory is presented by removing the limit on the number of discrete streamtubes computed. The extended model allows for the quantification of the impact of shear in the bypass and core flows separately. In particular, it is shown that averaging a sheared bypass flow profile can result in a substantial over-prediction of the power of a turbine in a laterally bounded flow as the effective blockage of the flow increases. The model is also used to confirm that an approximation using a limited number of streamtubes in some previous applications of the inviscid–viscous approach has a negligible impact on the results. Secondly, we explore the performance of a multi-row array with either uniform or varying turbine resistance across different rows. Results suggest that by varying resistance across rows, the array may outperform the uniform resistance case. The performance gain is dependent, however, on the arrangement and inter-turbine spacing both in the spanwise and streamwise directions.
“…This term, isotropic blockage, is used in literature to describe the blockage that occurs uniformly in all directions. However, studies on anisotropic blockage, which occurs in specific directions, are limited [9].…”
Blockage effects are a consequence of the interaction between a body and the surrounding boundaries in a constrained flow. For the case of tidal rotors, global blockage (β) is usually defined bythe ratio between the swept area of the rotor and the cross-sectional area of a channel. Increasingblockage tends to increase the limits of power extraction (Garrett and Cummins, 2007), as well asthrust on a rotor through an attendant increase of through-rotor mass flow. While these observations have been studied and demonstrated for isotropic blockage effects (e.g., Zilic de Arcos et al.2020, Bahaj 2007 , Mikkelsen 2002), questions remain regarding the validity of such assumptionsfor non-isotropic blockage in channels with, e.g., rectangular cross-sections with varying aspectratios.
In this work, we will use CFD simulations to analyze the effect of non-isotropic blockage on atidal rotor. The study aims to explore these effects using an Actuator-Line representation of anaxial-flow rotor, simulated under different blockage ratios (1 %, 5 %, 10%, and 19.7 %), aspectratios (0.25, 0.5, 0.75, and 1), and tip speed ratios (4, 5, 6, and 7). A total of 64 cases will beconsidered. For each simulated case, the power, thrust, and spanwise force distributions will beextracted as functions of time, and used to understand the effect of blockage on the performanceof tidal rotors.
Our preliminary results, in agreement with existing literature, indicate that blockage affectswake development, as seen in Figure , along with power and thrust. These results, for a constantaspect ratio, show power increases up to 26 % for a blockage of 20 %. The bulk of the simulationmatrix, including the different aspect ratios, is currently under production and is expected to beready before the paper submission deadline.
ReferencesGarrett, C., Cummins, P. (2007). The efficiency of a turbine in a tidal channel. Journal of fluidmechanics, 588, 243-251.Zilic de Arcos, F., Tampier, G., Vogel, C. R. (2020). Numerical analysis of blockage correctionmethods for tidal turbines. Journal of Ocean Engineering and Marine Energy, 6, 183-197Bahaj, A. S., Molland, A. F., Chaplin, J. R., Batten, W. M. J. (2007). Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitationtunnel and a towing tank. Renewable energy, 32(3), 407-426.Mikkelsen, R., Sørensen, J. N. (2002). Modelling of wind turbine blockage. In 15th IEAsymposium on the aerodynamics of wind turbines, FOI Swedish Defence Research Agency.
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