# Optimize Rotating Wind Energy Rotor Blades Using the Adjoint Approach
## 5 Conclusions  
An optimization tool for rotating wind energy rotor blades at realistic Reynolds numbers was developed and implemented based on the adjoint approach in OpenFOAM. In this work, it was tested for the NREL Phase VI blade. The rotation is represented using the MRF method, both for the flow and adjoint field. A projection for gradients to nodes similar to beam nodes in FSI tools was developed and implemented. This optimization tool is very flexible with respect to the cost function and other optimization settings, using the same dictionary-based input as OpenFOAM.  
In this work, the cost function is a least square of the thrust and various aimed values and allowed ranges for the cost function were defined. The different test cases were used to test the stability and convergence behavior of the developed optimization tool. Defining a rather easy cost function allows for interpreting the optimization results based on rotor blade theory.  
The 12 test cases all converged within a reasonable amount of CFD iterations. It was found that pre-convergence of both the flow and adjoint field is absolutely necessary in order to achieve usable gradient information. Still, a large influence of the chosen step size for the evaluation of the gradients was observed. This effect got more evident with aimed values further away from the initial value and tighter ranges around this aimed value. An initial study for a range of step sizes, which leads to good convergence behavior, might help to avoid zig-zagging. In the future, gradients can be used in more efficient optimization algorithms like SQP or Quasi-Newton. These algorithms also avoid zig-zagging that can appear when purely following the gradient direction. In addition, known implementations of these algorithms already have an automatized adjustment of the step sizes in run time.  
In addition, an adjoint turbulence model is a promising approach to increase the quality of the gradients in future work and thereby the optimization convergence and stability. Using this tool for a blade of a turbine that is not stall regulated could perform better with respect to convergence of the flow and adjoint field.  
The applicability of the developed tool, even for a challenging test case based on a rotating, stall regulated turbine at high Reynolds numbers, was shown in this work. When the suggested improvements of the gradient estimation are applied, the optimization tool is expected to perform in a more stable manner. This will allow the usage within the design process--for example, using more elaborate cost functions and being under consideration of constraints.  
**Author Contributions:** Conceptualization, L.V.; Methodology, L.V. and B.S.; Software, L.V.; Writing--Original Draft Preparation, L.V.; Writing--Review and Editing, J.P.; Supervision, J.P.; Project Administration, B.S.  
**Funding:** This research received no external funding.  
**Acknowledgments:** For the simulations, we use the high performance computing cluster Eddy of the University of Oldenburg [28].  
**Conflicts of Interest:** The authors declare no conflict of interest.