## 2 Materials and Methods
### Aerodynamic Methods  
The following section introduces the aerodynamic methods compared in this work. Some assumptions were made to limit the number of studies in this paper and to facilitate the understanding of the causes for potential differences among results. The limitations are listed below, and their potential impact is discussed in the Discussion section:  
* **No compressibility effects**: It is known from the literature that compressibility has a significant impact on whirl flutter stability through the change in the lift curve slope [28]. As most methods compared in this paper are based on potential flow aerodynamics, they neglect compressibility and can only account for it using correction techniques like Prandtl-Glauert correction factors. Despite being available in most codes, this correction is skipped for better comparability. * **Linear airfoil polars**: To keep the number of parameters small and to make the comparison among codes easier, linear airfoil polars for a symmetric NACA 0008 airfoil in potential flow are used. This results in a linear lift curve with slope \(C_{la}\). All other contributions, like drag or camber effects, are neglected in this study. * **Limited number of operating conditions**: The study is limited to a single operating range, a turboprop propeller in fast forward flight, since operating conditions with high advance ratios are the most relevant for whirl flutter. * **Only one geometry**: Only a generic five-bladed turboprop propeller is used for this study. No variations with respect to the blade aspect ratio, the number of blades or the blade geometry are conducted. * **Only blade aerodynamics**: In this work, only the unsteady aerodynamics attributed to the propeller blades are studied. Contributions from the spinner, nacelle or wing are neglected. * **Rigid propeller blades**: To perform a comparison with the classical Houbolt/Reed derivatives, the propeller blades are assumed to be rigid. For a study on the influence of elasticity, the reader is referred to the literature (e.g., [PERSON] and [PERSON] [15]). The different methods compared in this work with respect to unsteady propeller aerodynamics and their impact on whirl flutter stability predictions are listed in Table 1. The first column lists the methods and the name/abbreviation used throughout this paper. The following three columns contain a brief description of the relevant features distinguishing the methods from each other, split into the blade lift method, the wake method and the tip loss method. The order of magnitude for computational time is also given in the last column for comparison. The methods (or rows in Table 1, respectively) are split into three categories: The first four methods are categorized as mid-fidelity due to their explicit wake modeling and their ability to capture interference effects. The following three methods are categorized as low-fidelity due to the simplifications in modeling and their short run times. The last two rows represent the Houbolt/Reed method introduced earlier. In general, all aerodynamic methods used in this paper have to solve the equilibrium between local blade lift distribution and wake strength, as illustrated in Figure 3 for every given motion and time step. The specific implementation of the blade lift or wake formulation and their interaction depends on the method and solution of the coupled system in the tool used. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **Blade Lift Method** & **Wake Method** & **Tip Loss** & **Comp. Time** \\ \hline \multirow{3}{*}{UPM} & 2D vortex lattice on & & & \\  & camber surface & & & \\  & + 3D source/sink panels & Free panel wake & Included in & \\ \cline{1-1}  & on blade surface & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of aerodynamic methods used in this work.