## 5 Conclusions  
A computational fluid dynamics (CFD) simulation method is developed and validated to study the influence of rotor overlapping azimuth on compound coaxial helicopter performance. The following conclusions can be drawn:  
1. By comparing the numerical results with the wind tunnel experiment data of the hovering and forward flight of the NASA coaxial rotor, it is found that the numerical simulation results are in good agreement with the experiment data. It is proved that the simulation method proposed in this paper is appropriate for the performance calculation of coaxial helicopters and can achieve high calculation accuracy. 2. In the hovering flight of isolated rotors, the amplitude and peak values of the total thrust coefficients, and total torque coefficients and total power loads of the upper and lower rotors are essentially identical in the two states, and the phase difference of the coefficients in the two states is \(90^{\circ}\). It demonstrates that the aerodynamic performance of isolated rotors is not affected by the rotor overlapping azimuths. 3. In the forward flight of isolated rotors, the peak of the upper and lower rotor's thrust coefficients in state 1 has the identical phase, and the phase difference of the peak of the upper and lower rotor's thrust coefficients in state 2 is \(90^{\circ}\). Compared with state 1, the minimum value of the total thrust coefficients is \(61.3\%\) larger, the maximum value of the thrust coefficients is \(24.9\%\) smaller, and the amplitude of the total thrust coefficients is \(76.3\%\) smaller in state 2. After SMA processing, the total thrust coefficients of state 2 are reduced by \(0.87\%\) compared to state 1. It can be seen that the aerodynamic performance of isolated rotors in state 2 is superior to that of isolated rotors in state 1 in forward flight. 4. In the hovering flight of compound coaxial helicopter, the variations of the total thrust coefficients of the rotors in the two states are consistent with the hovering flight of isolated rotors. After SMA processing, due to the interference between the rotor and wing and flat tail, the thrusts of the upper rotor and the lower rotor are \(1\%\) and \(5\%\) larger than that of isolated rotors in hover, respectively, and the total thrust is \(3\%\) larger than that of isolated rotors in hover. Compared with state 1, the minimum value of the wing lift is \(0.3\%\) larger, the maximum value is \(8.1\%\) smaller, and the amplitude of fluctuation is \(42.7\%\) smaller in state 2. Compared with state 1, the minimum value of the flat tail lift is \(2.4\%\) larger, the maximum value is \(11.3\%\) smaller, and the amplitude of fluctuation is \(52.4\%\) smaller in state 2. After SMA processing, compared with that of state 1, the lift of the wing and flat tail in state 2 is reduced by \(1\%\) and \(1.7\%\), respectively. It can be found that the aerodynamic performance of the compound coaxial helicopter in hover is more favorable in state 2. 5. In the forward flight of compound coaxial helicopter, the phase difference between the peak of the thrust in state 2 is \(90^{\circ}\) between the two rotors. The variations of the total thrust coefficients of the upper and lower rotors in the two states are consistent with the forward flight of isolated rotors. Compared with state 1, the minimum value of total thrust is \(92.8\%\) larger, the maximum value is \(28.7\%\) smaller, and the amplitude of fluctuation is \(83.5\%\) smaller in state 2. After SMA processing, the total thrust coefficients of state 2 were reduced by \(0.87\%\) compared with state 1, the upper rotor's thrust, lower rotor's thrust, and total thrust are \(1.2\%\), \(2\%\), and \(1.65\%\) smaller than isolated rotors in forward flight, respectively. Due to the aerodynamic interference between the rotor and the wing and the flat tail, compared to state 1, the minimum value of wing lift is \(1.4\%\) larger, the maximum value is \(2.1\%\) smaller, and the amplitude of fluctuation is \(61.2\%\) smaller in state 2.