## 4 Conclusions  
In the current research work, the aerodynamic performance of a double Nautilus-type vertical-axis wind turbine was studied in detail through numerical simulation using the Reynolds-averaged Navier-Stokes equations and dynamic sliding mesh technology, as well as a 3D unsteady incompressible turbulent model. The results showed that the average power coefficient of the entire wind turbine group can be significantly improved by reasonably optimizing the wind turbine array configuration. The following conclusions can be drawn from this study:  
1. When the distance between two wind turbines is 2D and the wind direction is 90\({}^{\circ}\), the average power coefficient of the entire group is the highest, and the lateral layout of the wind turbines can significantly improve the performance of the entire wind turbine, which is a performance advantage that HAWTs do not have.
2. When the wind turbines are laterally arranged and the distance between them is 1.2D, the maximum C\({}_{\text{P}}\) (average) of the double wind turbine group compared to a single wind turbine has a _TPGF_ of 10.2%. The closer the distance, the stronger the performance improvement, mainly due to a promoting and enhancing effect among wind turbines. Each wind turbine can obtain energy from the adjacent wake field and wind field, thereby improving power output. This effect, which is not present in HAWTs, provides novelty to this study and explains the essence of the enhancement phenomenon. In actual production, the material performance of the wind turbine should also be taken into consideration, and the distance between wind turbines should not be too small to avoid damage to the wind turbine.
3. Compared with a single wind turbine, the double-turbine system can improve the power coefficient for all three different rotation directions, especially for the counter down rotating, where the gain factor _TPGF_ reaches 11.1%. Overall, the average maximum power coefficients for the three rotation modes are not significantly different.
4. Several array layouts are proposed based on the above research, and compared to the conventional rectangular symmetrical layout, the array layouts proposed in this study can significantly improve performance in wind energy capture.
5. A prototype experimental platform was built for experimental comparison analysis, and the speed error was 8.1%, indicating that the CFD simulation results were reliable.  
In the future, we will conduct double-rotor experiments to ensure the accuracy of the CFD simulations. The VAWTs array is affected by two important factors, wind direction and spacing. By utilizing these parameters reasonably, the array cluster of VAWTs can significantly improve the average power coefficient relative to a single VAWT, indicating that the array configuration of VAWTs has enormous potential to increase the power density of the wind field. In the future, the construction of VAWT arrays should fully consider local weather and meteorological conditions, as well as the material performance of the parrot-type wind turbines themselves, to better serve humanity.  
Conceptualization, G.X. and Y.C.; methodology, G.X.; software, Y.C.; validation, G.X.; formal analysis, G.X. and Z.Q.; investigation, Z.Q. and G.W.; resources, G.X., Y.C. and J.W.; data curation, J.W., T.G. and W.Z.; writing--original draft preparation, G.X.; Visualization, Y.C. and Y.Y.; Supervision, Y.C. and Y.Z.; Project administration, Y.C., Z.Q., Y.Z., T.G. and Y.W.; Funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.  
This work was completed with the support of the National Natural Science Foundation of China (grant number 51376096), \"Thirteenth Five-Year Plan\" Provincial Key Construction Discipline Project of Jiangsu Province (2016-0802 Mechanical Engineering) and Jiangsu Engineering Research Center for Wind Energy Application.  
Not applicable.