## 1 Introduction  
Currently, there has been growing interest in vertical axis wind turbines (VAWTs) because of their low costs of installation and maintenance and no need for a yawing system [1]. Nevertheless, wild applications of VAWTs are retarded by their low energy conversion efficiency compared with their horizontal counterparts [2]. Pitch regulation is a valid approach for enhancing the aerodynamic performance and acquiring power control of wind turbines [3]. Quite a few studies have been done on pitch-regulated VAWTs, and the effect of both static pitch and dynamic pitch on the aerodynamics of VAWTs has been analyzed by numerical simulations and experiments [4, 5]. [PERSON] et al. [6] evaluated the effect of the static pitch angle on the angles of attack (AoAs), aerodynamic force components, boundary layer events of the blades, and power coefficients of the wind turbine at length by the computational fluid dynamics (CFD) method and revealed that the power coefficient with a pitch angle of \(-2^{\circ}\) was 6.6% higher than that with a pitch angle of \(0^{\circ}\). [PERSON] and [PERSON] [7] pointed out that the self-starting ability of a VAWT changes with the pitch angle. [PERSON] et al. [8] proposed a new dynamic pitch strategy to broaden the azimuthal range of the high performance of a VAWT so as to obtain an 18.9% increase in the power coefficient at the optimal tip-speed ratio (TSR). [PERSON] et al. [9, 10] compared the performance of a VAWT with and without pitch control, and it was shown that pitch regulation could increase the power output with a reduction of the deformation of the blades at the same time. Furthermore, [PERSON] et al. [11] highlighted that lower blade-wake interactions of VAWTs could be obtained by pitch adaptation of the blades. On the contrary, [PERSON] and [PERSON] [12] investigated aerodynamic loads on the equator of the blades of a VAWT with three fixed pitch angles, using both a 2D panel model and a vorticity transport model. They demonstrated that changes in the fixed pitch angles--that is to say, changes of the bound circulation of the blades by constant values--could transfer instantaneous torque and thrust between the upwind and downwind region, but they did not notably change the average power of the wind turbine. The aerodynamic forces of the blades exert a significant influence on the performance and operational life of wind turbines. However, previous studies mainly focused on the tangential and normal forces of the blades [13; 14], lacking comprehensive discussion of the aerodynamic force components in the streamwise, lateral and vertical directions. [PERSON] et al. [15] measured the variations of the normal forces of a 12 kW VAWT prototype at an open site. [PERSON] et al. [16; 17] assessed the instantaneous tangential and normal forces of VAWTs, as well as blade surface pressure distributions with different numbers of blades and the solidity by multiport pressure devices in wind tunnel experiments. [PERSON] et al. [18] measured the aerodynamic forces of a high-solidity VAWT and proved its self-starting ability. [PERSON] et al. [19] used a free-wake vortex model to simulate the aerodynamic loads of two-, three- and four- bladed \(\Phi\)-shape VAWTs with the same solidity and found that the instantaneous torque, thrust and lateral force ripples of wind turbines were diminished with more blades, which was believed to prolong the service life of VAWTs. [PERSON] et al. [20; 21] conducted comparative analysis of VAWTs with a series of NACA airfoils and concluded that cambered airfoils could reduce structural vibration in wind turbines. Meanwhile, the aerodynamic force components of the blades are influenced mainly under the conditions of low TSRs by the airfoil thickness, whereas more are influenced at high TSRs by the airfoil camber. [PERSON] et al.