# Optimize Rotating Wind Energy Rotor Blades Using the Adjoint Approach
## 4 Results
### Additional Twist Computed by the Optimization  
The final additional twist of the blade for the various optimization cases is shown in Figure 7a-c. The dots represent the moving element nodes where the gradients of each element are projected on (see Figure 1). The lines represent the smoothed movement between the nodes, as the geometry movement is also smoothed by the optimization tool. This plotted twist is then added to the initial twist of the according blade. The shown twist are the final ones, summed up over all optimization steps.  
Figure 6: Development of the normalised thrust force over the optimization steps for the long blade part. The aimed force is \(900\pm 1.5\%\) N and the initial step sizes are \(10^{-2}\) (red dots, StSz1) and \(2\times 10^{-2}\) (blue squares, StSz2).  
All twist values increase from the first element node towards a maximal value close to a spanwise position of 4 m. Afterwards, the additional twist decreases and even reaches negative values for the last element. The positive values in this set-up lead to a reduced angle of attack.  
In general, those plots all show two trends: the shorter the movable section, the larger the additional twist. Furthermore, the more restrictive the aimed value, the more deformation is necessary to reach this value. This verifies the developed tool for optimizing rotating rotor blades.  
To investigate this behavior further, the spanwise production of thrust of the initial NREL Phase VI blade is plotted in Figure 8.  
Figure 8: Spanwise production of thrust of the original NREL Phase VI blade from 1 to 4.75 m in radial direction.  
Figure 7: Development of the normalized thrust force over the optimization steps for design parameters within varying deformable parts of the blade. Long: \(r_{1}\) = 2 m–4.5 m radial position, middle: \(r_{2}\) = 3 m–4.5 m radial position and short: \(r_{3}\) = 3.75 m–4.75 m radial position.  
It can be seen that the thrust production increases in the spanwise direction until a peak at a radial position of \(r=4\) m. Afterwards, the production of thrust decreases. Thus, the gradients follow the trend of production of thrust in size and direction, leading to a larger deformation around \(r=4\) m and decreased deformation towards the tip.  
Larger movements in the outer blade part, which are aerodynamically more efficient, also have a larger impact on the thrust. This is apparently also represented by the gradients leading to a larger deformation in the outer regions. Close to the tip of the blade, the vortices seem to destabilize the adjoint field and thus also the accuracy of the computed gradients. This is also underlined by the larger negative twist values, which where not expected beforehand, of the short deformable blade part \(r_{3}\) in comparison to the two longer ones. The deformable blade part \(r_{3}\) ends at 4.75 m, whereas the other two deformable blade parts \(r_{1}\) and \(r_{2}\) end at 4.5 m. Thus, the influence from the tip vortex seems to be stronger for \(r_{3}\), which reaches 0.25 m further towards the tip.  
The conducted optimizations are chosen to test the developed optimization tool. It is therefore important to reduce the occurring effects as far as possible and avoid converse effects that could arise when using cost functions based on various force components and constraints. For future applications of the developed tool, it is a challenge to extend this method to more important design constraints and more elaborate definitions of the cost function.