## 7 IRMI Method
### Analysis Results  
(1) Effect of mutual interference on hydrodynamic characteristics  
Figure 14 shows the analysis results with the effect of the mutual interference ignored by setting \(b=0\). Under this condition, the equilibrium point is simply determined by the torque characteristics of each individual rotor in Figure 9.  
Figure 14: IRMI results with mutual induction ignored.  
This analysis does not consider the deceleration caused by the thrust of the neighboring rotor, so the rotor speed (or TSR) is high. Therefore, under conditions where the TSR of the FR is approximately 2 or less, the torque and thrust coefficients are generally higher than those of the MP model CFD due to the higher TSR.  
The analysis results considering the mutual induction factor, which is the original IRMI, are shown in Figure 15 together with the CFD results from Section 4. This condition considers the inherent mutual induction between the rotors, and the thrust of the FR reduces the speed of the RR by 4% to 12%, while the RR reduces the speed of the FR by 12% to 39%. When considering the mutual induction factor, the rotational speed (or TSR) of the RR decreases compared to when it is ignored. As a result, each aerodynamic coefficient is reduced, and the results are almost consistent with those of the MP model CFD.  
Figure 15: IRMI results when considering mutual induction.  
As shown in Figure 8, the TSR at which the maximum power coefficient of each individual rotor is obtained is approximately 6 for the FR. Even in the CCRR, the power coefficient of the FR tends to increase as the TSR increases, but the power coefficient of the RR tends to decrease from around 1.5, and the power coefficient of the CCRR saturates around 1.7. This is because, as the TSR increases, the thrust coefficient also increases (Figure 7), which increases the mutual induction factor. Therefore, overall, the TSR is significantly lower than in the case of a single rotor.  
(2) Control  
Another important finding in this research is the control of generators. When a single rotor is operated at a rotor speed (or TSR) that maximizes the power coefficient under a constant wind speed, if the rotor speed increases/decreases due to some disturbance, the torque decreases/increases as shown in Figure 9. The rotor speed returns to the equilibrium point in both cases. Therefore, the generator can be controlled by the torque relative to the rotational speed, and the fluctuations in the torque are small. However, in the case of the CCRR, when operating at a TSR of approximately 2, where the power coefficient is maximized, the torque will also increase/decrease as the rotational speed increases/decrease, so the above control is not possible. In this case, it is necessary to control the rotation speed at a constant value or to a set value using other parameters such as the flow velocity, instead of controlling the rotation speed with the torque. In this case, the instability in the rotational direction of the CCRR is suppressed by controlling the generator's torque, resulting in large fluctuations in the torque or output power. This is undesirable from the viewpoint of the variation of the power and loads.  
(3) Analysis time  
As mentioned in Section 4, three to five different conditions are required to calculated for one specific equilibrium condition to balance the torques of the two rotors in CFD with the MP model. On the other hands, the present IRMI method needs CFD with the MP model for the individual rotor and CFD with the ADM for the mutual induction in advance, and the calculation time to find the balanced point is as short as negligible. Therefore, the total amount of time for the IRMI is not dependent on the number of cases, but almost constant, almost the same as one case by the CFD with the MP model for the CCRR. It means, the simulation time of the IRMI would be almost counter-proportional to the numbers of TSR conditions to solve as compared with the CFD with the MP model.