# Parametric Analysis Towards the Design of Micro-Scale Wind Turbines: A Machine Learning Approach
## 2 Methodology
### Wind Turbine Simulation  
The turbine has been simulated using the QBlade wind turbine simulation tool. QBlade employs deterministic models for blade aerodynamics and structural dynamics, and couples between them for an aeroelastic analysis. For the aerodynamic model, blade element momentum (BEM) and Double-Multiple Stream tube Model (DMS) are used to calculate the aerodynamic loads and power performance of both the blades and the turbine rotor. For the structural model, QBlade employs the Euler-Bernoulli beam theory to formulate a co-rotational multibody dynamics model [14].  
The main constraint that has been followed is that the rotor should be of a 45 cm diameter to be used in domestic applications like charging batteries for vehicles or sailboats. A blade of 20 cm length has been designed based on several design parameters for the purpose of conducting a parametric analysis. The blade is divided into 5 sections equally spaced along the 20 cm span. For each section, the chord length, twist angle, and airfoil type are set to different values. Then the blade pitch angle is changed for each simulation. These design parameters were changed one at a time while fixing the other parameters at a fixed value. Figure 1 shows the blade with different design parameters shown.  
The design parameters were changed such that the blade taper differs through the chord length at different sections while fixing the chord length near the hub at the value of 5 cm. The twist angle changes linearly through the blade span while fixing the twist angle near the hub at the value of 0\({}^{\circ}\). And the blade pitch angle was to be in both negative and positive directions. Four different airfoils were used for each blade design. NACA 4-digit series were used, where the first digit represents the maximum camber in % of the chord, the second digit represents the location of the maximum camber in terms of the chord, and the last two digits represent the airfoil thickness in % of the chord length. In Table 1, the values for each design parameter are shown, as well as the wind velocity range which has been used as an input parameter to the simulations. Figure 2 shows the airfoils used for the simulations, as shown in the Airfoil Design Module on QBlade.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value(s)/Type(s)** \\ \hline Chord Length Near Hub (cm) & 5 \\ Chord Length at the Tip (cm) & 1.5, 2.2, 2.9, 3.0, 3.2, 3.5, 4.0 \\ Chord Length Change Through Span (–) & Linear \\ Twist Angle Near Hub (\({}^{\circ}\)) & 0 \\ Twist Angle at the Tip (\({}^{\circ}\)) & 0, 5, 10, 15 \\ Twist Angle Change Through Span (–) & Linear \\ Airfoil (–) & NACA 2413, NACA 4412, NACA 5015, NACA \\  & 6409 \\ Blade Pitch Angle (\({}^{\circ}\)) & \(-\)3 to 3, step size: 1 \\ Wind Velocity (m/s) & 1 to 12, step size: 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design and operating parameters used for the simulations.  
Figure 1: Blade design and parameters: (**a**) the full blade in isometric view, (**b**) side view of the blade showing the twist angle between the chord line and the reference rotor plane, and (**c**) plane view of the blade showing the blade span and chord lengths at each section.  
The simulation is run for each case, at different wind speeds, and the main outputs of concern are the coefficient of power (\(C_{P}\)) to measure the power performance and efficiency, normal force -flapwise- (\(F_{N}\)), and tangential force -edgewise- (\(F_{T}\)) midspan of the blade to measure the structural loads, and the rotor torque (\(T\)) as a measure of the power production capability. The simulations have been cross-validated among the authors to ensure the correctness of simulation results and the reliability of the data.  
The data are then collected into a dataset where all the input parameters and output measures are tabulated. This dataset is the core input for further analyses and machine learning models' training.