# Development of a CFD-Based Wind Turbine Rotor Optimization Tool in Considering Wake Effects
## 4 Conclusions  
This paper presented detailed numerical methodologies and convincing results for wind turbine rotor aerodynamic optimizations. To simulate the aerodynamic forces on the wind turbine rotor, a 2D actuator disc method is implemented in the incompressible flow solver favored by the axisymmetric boundary condition defined at the center line. The combined flow solver is more accurate and powerful than existing engineering models such as blade element momentum theory. On the other hand, it is order of magnitude faster than the 3D flow solver. However, the 2D and 3D solver implemented with same AD method should give same results. In addition to the AD flow simulations, two turbulent flow cases were investigated to proof the advantage of the modified \(k\)-\(\omega\) turbulence model. With the fast CFD solver, the rotor optimization was carried out for single wind turbine with uniform flow and two wind turbines combined with wake interaction. The multi-objective optimization method NSGA-II is applied in the design loop and the two design objectives of high AEP and low ATP are required. The four optimization cases aimed at single rotor optimization without wake effect, single rotor optimization with wake effect, multi-wind turbine optimization with constant rotor speed and multi-wind turbine optimization with variable rotor speed. In general, single rotor optimizations are faster and they provide clear optimization trend. For the multi-wind turbine optimization cases, it was found that high aerodynamic performance is achieved when the upstream and downstream  
Figure 15: The comparisons of optimization results of wind turbine ((**a–c**) belong to Case 1, Case 2, Case 4; (**d**) belongs to Case 3 and Case 4). (**a**) Chord; (**b**) Twist angle; (**c**) Relative thickness; (**d**) Rotational speed.  
wind turbine both change their blade shape and rotational speed. These results indicate that traditional rotor optimization methods might not be sufficient due to the complex wake effect.  
On a single PC with a developed parallel computation tool, the estimated time is 30 h for optimizing a single rotor, and for the coupled two-rotor optimizations, the simulation time is almost doubled. Future work will be carried out for more complicated design cases which may include the whole column of wind turbines such as the Horns Rev wind farm case. In such an optimization, the wind turbine spacing will be included as an important design parameter, to this end, the method can be applied for simple layout optimization.  
[PERSON] conceived the rotor optimization method and wrote most part of the paper; [PERSON] carried out most of the programming part and the simulations; [PERSON], [PERSON] and [PERSON] put a lot of effort on guidance the overall structure of the paper as well as results and discussions.  
This work was funded by the Jiangsu Province Natural Science Foundation (BK20160476), the National Science Foundation (11672261), and the National Basic Research Program of China (973 Program) (No. 2014 CB046200), and the National Science Foundation (51761165022), and the Yangzhou University Science and Technology Innovation Training Foundation (2016 CXJ039) and (2017 CXJ041).  
The corresponding author wish to express special acknowledgement to the National Nature Science Foundation under grant number 11672261, the Jiangsu Province Natural Science Foundation (BK20160476).  
The authors declare no conflict of interest.