## 3 Computational Model
### Aerodynamic Model of Double Multi Stream Tube (DMST) Model  
The DMST model makes use of the blade element momentum (BEM) theory, whereby the performance of the rotor is calculated by coupling the momentum equation in the mainstream direction of the wind and the aerodynamics analysis of the interactions between the airfoils in motion and the oncoming flow on the rotor [15; 26]. The first approach using a  
Figure 8: Configuration of an H-type vertical-axis wind turbine (VAWT). Figure 7: Illustration of new variable pitch. momentum model to analyze the flow field around a VAWT was developed by [PERSON] [27], who considered the rotor as an actuator disk enclosed in a simple stream tube, where the induced velocity through the swept volume of the turbine was assumed to be constant. An extension of this method to the multiple stream tubes model was developed by [PERSON] [28], who considered the swept volume of the turbine as a series of adjacent stream tubes. Additionally, [PERSON] [29] developed an analytical model, the DMST model, which considers a multiple-stream tube system divided into two parts, where the upwind and downwind components of the induced velocities at each level of the rotor are calculated by using the principle of two actuator disks in tandem. Subsequently, many predicted the performance of the [PERSON] turbine using the DMST model, and all of the results showed that the DMST model has a high prediction accuracy for predicting the aerodynamics of the lift-type VAWTs [24; 30; 31; 32; 33]. The Darrieus-type wind turbine at low TSRs normally experiences a large variation within its AoA, and the blades are dominated by dynamic stall. In such conditions, the prediction must consider the effect of the dynamic stall on the accuracy. However, in the paper, the detailed investigation is performed at a high TSR, which is higher than four. Meanwhile, the variation of the AoA is getting much smaller and no stall is occurring; thus it has little effect on the prediction accuracy [22]. Accordingly, the dynamic stall was neglected in the paper. The model relies on pre-existing lift and drag data to calculate the blade aerodynamics. In a cross-flow wind turbine, blade-vortex interactions may occur, but its effects are not clear. There is not a well-developed algorithm for the modification of the lift and drag data due to the impingement of the vortex on the blades [34]. Thus, the interaction was also neglected in our work. Since this investigation is focused on an H-type VAWT, a simplified version of the DMST model applicable to a straight-bladed rotor is briefly outlined below [35; 36; 37]. For an H-type VAWT, the resultant velocity, \(V_{\rm r}\), during the upwind half-cycle can be determined from the velocity vector triangle shown in Figure 2, which then gives:  
\[V_{\rm r}=V_{\rm w}\sqrt{\left(\lambda_{0}+a\cos\theta\right)^{2}+\left(a\sin \theta\right)^{2}} \tag{8}\]  
Applying the blade element theory and equating the change in momentum to the drag on the rotor for each stream tube, it is found that:  
\[fa=\pi\eta(1-a) \tag{9}\]  
where \(\eta=r/R\) is the dimensionless parameter of the radius, and \(f\) is the unwind function that characterizes the upstream half-cycle of the rotor on the blade element rotating in this zone. The upwind function is given by the following equation:  
\[f=\frac{Nc}{8\pi R}\int_{0}^{\pi}\biggl{(}C_{\rm N}\frac{\cos\theta}{\left| \cos\theta\right|}-C_{\rm T}\frac{\sin\theta}{\left|\cos\theta\right|}\biggr{)} \biggl{(}\frac{V_{\rm r}}{V_{\rm w}}\biggr{)}\mathrm{d}\theta \tag{10}\]  
where \(N\) is the number of the blades, and \(C_{\rm N}\) and \(C_{\rm T}\) can be calculated from Equations (2) and (3), respectively. The lift and drag coefficients, \(C_{\rm L}\) and \(C_{\rm D}\), respectively, are obtained by interpolating the known experimental data using both the local blade section Reynolds number \(Re_{\rm b}=V_{\rm r}c/V_{\rm w}\) and the local AoA. The local AoA can be calculated from Equation (1).