# Optimize Rotating Wind Energy Rotor Blades Using the Adjoint Approach
## 3 Simulation and Optimization Set-Ups  
This is a conceptual work in which we want to show a new optimization approach for wind energy applications. Therefore, the optimizations are conducted for the NREL Phase VI turbine. This turbine is a stall-regulated, two-bladed turbine with a rated power of 19.8 kW. It was used for experiments in the NASA/Ames 24.4 m \(\times\) 36.6 m wind tunnel [23] and is often used for validation of CFD. The S809 airfoil with 21% thickness was used for the construction of the blade [24]. In this work, the cone angle of the rotor is 0\({}^{\circ}\) and the pitch angle of the blade is 3\({}^{\circ}\). To include rotational effects in steady-state simulations, the Multiple Reference Frame (MRF) is used. The rotation is modelled via a source force, that adds a rotational component to each cell. This way, the rotor does not have to move within the mesh reducing the computational effort, as no mesh update is necessary to include the rotation. The MRF method is also adopted to the adjoint field, so that the used schemes and solution methods for both fields stay similar. The mesh used in this work was created by the bladeBlockMesher (BBM) developed by [PERSON] et al. [25] for the automatic mesh generation for wind turbine rotor blades. The grid quality and validation based on the NREL Phase VI turbine is also shown in their publication. In this work, a grid with 5.2 million cells is used with a \(y^{+}\)-value below 1. A symmetry plane is used to exploit the symmetry of the two bladder rotor. In Figure 2 the domain and the mesh around a cut along the chord of the blade is shown. A rounded tip is created and meshed via the BBM. The k-\(\omega\)-SST turbulence model is chosen for the flow field, whereas for the adjoint field the frozen turbulence approach is applied. This approach was used in various publications and it was shown that the gradient quality is adequate [7; 18]. Standard boundary conditions are applied, similar to those in Rahimi [25]. The inflow velocity is 10 m/s and the rotational speed is 7.54 rad/s, i.e., 72 rpm and the density equals 1.225 kg/m\({}^{3}\). This velocity leads the stall regulated turbineto already partially separate flow at large parts of the blade. Steady state CFD computations of this turbine at separated flow are known to differ from the experimental data at those separated areas [25]. As it was shown above, the adjoint field is driven by the flow field and therefore it is expected that the adjoint field converges even less as good as the flow field. Still, this velocity was chosen in this work, as even small changes in AoA have a large impact on the forces, when separation is reduced. As the adjoint field moves upstream, the boundary conditions are switched compared to the flow field. The adjoint velocity has a Neumann boundary condition at the inlet, and a Dirichlet boundary condition at the outlet and at the blade. The adjoint pressure has a Dirichlet boundary condition at the inlet and Neumann boundary condition at the outlet and blade. For a higher stability, the adjoint velocity at the hub is put to zero. This was necessary, as the transition between hub and blade root led to large instabilities in the adjoint field. It was shown in Section 2.1 that the adjoint field is driven by the primal field. Therefore, preconverged solutions of the flow field are used in order to stabilize the adjoint equations. A convergence of the velocity up to a residual in the range of \(10^{-7}\) is aimed before the adjoint field equations are switched on. An initial study using the same numerical grid based on the initial geometry was conducted to find adequate amounts of CFD iterations to reach good convergence of both fields. As a result, 25,000 iterations are used solving the flow field based on the SIMPLE algorithm [19]. An additional 15,000 iterations are used for solving the adjoint and flow field before the optimization tool is started. These pre-converged fields are used for all optimizations, as the initial blade geometry and flow boundary conditions are identical.