# Development of a CFD-Based Wind Turbine Rotor Optimization Tool in Considering Wake Effects
## 3 Results and Discussion
### Rotor Optimizations
#### 3.4.2 Optimization Studies
As shown in Figure 13(a), a trade-off between thrust and power can be found in area \(B\). The final selected data is listed in Table 2 where the same ATP is maintained but the AEP is increased by \(1.14\%\). For the Case 2 design, the downwind rotor is optimized. After optimization, the rotor in the wake has an increased power production of \(1.78\%\), and there is also a small increase of thrust of \(0.34\%\). Using the optimized solutions from Case 1 and Case 2, further investigation is carried out in Case 3. The rotational speed of the upstream wind turbine is considered to be a new design variable that may affect the total energy product. In Table 3, by comparing the AEP of each wind turbine with its reference value, it is seen that the \(1\)st wind turbine has a negative change in AEP of \(-0.81\%\) and the second wind turbine has a positive change in AEP of \(1.2\%\). The overall gain of AEP is \(-0.04\%\) because of the contribution of higher wind resource from the \(1\)st wind turbine. The total thrust change of the two wind turbines is about \(1.69\%\). It is seen that loads can be decreased with a certain amount by decreasing the front rotor speed, but it is not possible to gain more power from Case 3 study. A study in Case 4 is therefore performed to seek more energy from the \(2\)nd rotor. The individual changes from each wind turbine and the overall changes are listed in Table 3. The reduction of the \(1\)st rotor speed leads to a change of its AEP with \(-3.46\%\). The \(2\)nd rotor is further optimized with a relatively large amount of AEP increase up to \(9.71\%\). The total amount of AEP in the two-wind-turbine system is increased with \(1.6\%\). The thrust is largely reduced for the \(1\)st wind turbine under the new design condition at a relatively low TSR. The final aerodynamic layouts of the optimized blades are gathered in Figure 14. The chord, twist and relative thickness distributions are given in Figure 14(a)-c, respectively. Based on the multi-objective optimizations, the chord length of the upstream wind turbine (Case 1) and downwind wind turbine (Case 2) deviates from the baseline chord distribution. The twist distribution of the two optimized blades is rather similar. The optimized rotor speed is shown in Figure 14(d). With limited lower and upper bounds, the Case 4 optimization suggests a much lower rotational speed as compared \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & **Case 1 (1 st Rotor)** & \multicolumn{2}{c}{**Case 2 (2 nd Rotor)**} \\ \hline Objective & AEP & ATP & AEP & ATP \\ Reference & 4.2665 & 0.8058 & 2.6559 & 0.6410 \\ Optimized & 4.3153 & 0.8058 & 2.7031 & 0.6432 \\ Relative & 1.14\% & 0 & 1.78\% & 0.34\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization results of Case 1 and Case 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Case 3 (1 st Rotor)** & \multicolumn{2}{c}{**Case 4 (Two Rotors)**} \\ \hline
**Objective** & **AEP** & **ATP** & **AEP** & **ATP** \\ \hline \multirow{3}{*}{Reference} & \(1\)st & 4.2653 & 0.8058 & 4.2653 & 0.8058 \\  & \(2\)rd & 2.6559 & 0.6410 & 2.6559 & 0.6410 \\  & Overall & 6.9212 & 1.4468 & 6.9212 & 1.4468 \\ \hline \multirow{3}{*}{Optimized} & \(1\)st & 4.2307 & 0.7919 & 4.1177 & 0.7522 \\  & \(2\)rd & 2.6875 & 0.6304 & 2.9139 & 0.6432 \\  & Overall & 6.9182 & 1.4224 & 7.0317 & 1.3955 \\ \hline \multirow{3}{*}{Relative} & \(1\)st & \(-0.81\%\) & \(-1.72\%\) & \(-3.46\%\) & \(-6.65\%\) \\  & \(2\)nd & \(1.2\%\) & \(-1.65\%\) & \(9.71\%\) & \(0.34\%\) \\ \cline{1-1}  & Overall & \(-0.04\%\) & \(-1.69\%\) & \(1.6\%\) & \(-3.55\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimization results of Case 3 and Case 4.  
with Case 3. As a result, the upwind rotor lost a certain amount of power which is gained by the downwind wind turbine. It is worth noting that the present study is only limited at aerodynamic optimization. Since the 1 st wind turbine also has a decrease of thrust of 6.65%, there is a big potential to further reduce the structure weight.