Global carbon dioxide emissions have been increasing every year because of the extensive use of traditional fossil energy, which has triggered the greenhouse effect and brought huge environmental problems. Therefore, new types of clean, renewable, and sustainable energies are exploring and developing around the world [1
]. Among them, ocean energy, as a new type of renewable energy with great reserves, is focused and researched by scholars.
The marine energy turbines are usually employed to develop ocean energy and are mainly divided into horizontal axis hydrokinetic turbines and vertical axis hydrokinetic turbines (VAHT). Compared with the horizontal axis hydrokinetic turbine, the VAHT is more suitable for the development and utilization of ocean tidal energy under complex ocean conditions in the deep sea due to its low cost and simple structure [3
As an important type of VAHT, the Darrieus turbine has attracted attention because of its higher energy utilization rate. Kiho et al. [4
] did cross-strait experiments by installing a Darrieus turbine with a diameter of 1.6 m in the Kurushima Strait, the highest efficiency was 56% in the flow rate of 1.1 m/s. Then, Matsushita et al. [5
] studied the influence of blade tip clearance using a NACA0018 blade linear Darrieus rotor on power efficiency by experiments. After that, Dai et al. [6
] experimentally investigated the energy performance of four groups of NACA0025 blade hydrofoils with different chord lengths and radii, and the results revealed that the larger the rotor, the higher the power efficiency. Moreover, Furukawa et al. [7
] studied the turbine performance with or without a draft tube by changing the gap between the turbine and blade tip, and the maximum power efficiency was 57% with the NACA0018 hydrofoil. Results showed that the use of a draft tube can improve the efficiency. Meanwhile, they proposed that the draft tube and runner casing can be replaced by the water inlet, which can obtain more energy and increase the torque and self-starting ability of the water turbine. Additionally, a new Darrieus type was proposed by Shimokawa [9
], which is suitable for extremely low water head (2 m). Results showed that installing an inlet nozzle upstream can improve the performance of the hydraulic turbine. In addition, Benzerdjeb et al. [10
] discussed the influence of blade attack angle on its energy performance through experiments, and the results showed that when the blade angle was 1.75, the flow pattern was stable and the output power of turbine was the best. Roa et al. [11
] found that the structure with the shrouded configuration could improve the energy performance of the Darrieus turbine. Zhen et al. [12
] discovered the power coefficients of different startup modes for Darrieus turbines. Marsh et al. [13
] compared straight blades with spiral blades and found that Darrieus turbines with straight blades were more suitable for ocean current power. They also found that different connecting arms could affect the power output coefficients of turbines [15
]. Gruillaud et al. [3
] studied the optimal power coefficient of the Darrieus turbine by using the method of large eddy simulation and found that the maximum power coefficient could be obtained at optimal conditions. Khanjanpour et al. [16
] discussed the influence of turbine surface roughness on its power coefficient and found that reducing surface roughness could improve the energy conversion efficiency of the turbine.
Aside from studying the energy performance of the Darrieus turbine, researchers have also carried out a series of investigations on the vortex dynamics mechanism of the Darrieus turbine. In the vertical axis hydrokinetic turbine, when the blades move to the upstream of the rotor, stall shedding vortex generates, and the vortex will move to the tail along with the flow of water. Meanwhile, other blades and shafts influence the movement and development of the stall shedding vortex, and generate a flow-around shedding vortex, which act on the flow of the downstream rotor together with the stall shedding vortex and generate wake vortex and develop backward. Manganga et al. [17
] proved the dominant influence of turbulence intensity on the wake recovery length. Later, Mercier et al. [18
] used LDV (laser doppler velocimetry) to conduct experimental research on the wake shedding vortex of three-blade Darrieus turbine, which proved the accuracy of the computational fluid dynamics (CFD) method in predicting the Darrieus wake vortex. After that, Li Y et al. [19
] analyzed the three-dimensional effect of the Darrieus turbine by means of experimental measurements and numerical simulations. The authors found that the three-dimensional effect was significant when the turbine height was less than twice the radius. Then, Gorle et al. [20
] investigated the performance of a Darrieus turbine in limited flow area through numerical simulation and drag test and found that the numerical simulation had high consistency with the experimental results. Furthermore, Ouro et al. [21
] found that the stall characteristic was more obvious at low tip speed ratio. The wake vortex recovery was studied through experiments, and three wake regions were determined, a near-wake region (2D, D is rotor diamonds), a transition region (2D–5D), and a far-wake region (5D). Pellone [23
] and Marsh [25
] discovered that the two-dimensional model was difficult to capture depth vortex and the three-dimensional model significantly improved the performance prediction of the model through experiments and numerical calculation. The authors concluded that the horseshoe vortex generated at the trailing edge of the blade was the main reason affecting the calculation accuracy. Later, Mejia et al. [26
] found that the detached eddy simulation (DES) model improved the recognition of the vortex structure scale and could capture the flow phenomenon in the wake of the Darrieus turbine. Laín S et al. [27
] made a visual analysis of the change of vorticity at different rotational speeds and found that the omega vortex had a negative influence on turbine output power. Furthermore, in the stall regime, the length of the tip vortices increases with decreasing TSR.
The radial force of rotating hydraulic machinery will cause vibration, noise. and even fatigue failure of the turbine, which has great influence on the operation stability of the turbine [28
]. For a vertical axis Darrieus turbine, the radial force will affect the friction damage at the mechanical joint of the rotating shaft and the service life of the metal structure. Therefore, the research on radial force is significant and indispensable. From the above discussions, the energy performance and flow structure of Darrieus turbines have been investigated by many scholars, but there are a few relevant literatures studying the radial force, vortex structure characteristics, and their correlation mechanism.
The aim of this study was to investigate the energy performance, radial force, and the correlation mechanism between them by numerical simulation. First, the power coefficient curve of the numerical simulation was compared with that of the experimental results to validate the numerical method. Second, the radial force on the impeller was obtained, and the correlation mechanism between the radial force and the total power output was researched. Then, the vorticity transport equation was introduced, and the influence of vortex on the radial force of turbine investigated. Finally, the correlation mechanism between the radial force and vortex was studied.