## 6 Adaptive Wing CFD Model
There is a 1% error between the grid 4 and 5 results and a mesh size reduction of 1.266 million cells for grid 4, compared to the grid 5 density. Based on the Table 7 results, the grid 4 density will be used for all the adaptive wing simulations. Figure 21 shows only the mesh volumes of the adaptive wing model. The main motivation for determining these grid sensitivity results is to reduce the computational time while obtaining accurate results. The boundary conditions are required in CFD simulations to solve the differential equations for the fluid volume. An inlet surface allows the air mass to flow into the domain of the test velocity of 30.10 m/s, while a pressure outlet surface allows the air mass to flow out of this domain. Slip walls were imposed on the sides of the far field to improve the solution convergence, and a no-slip wall was enforced at the surface of the wing model to obtain a fluid velocity at its surface equal to zero. The simulation implicit solver had a time step size of 0.001 s, which was considered necessary for numerical stability, for which 400 total time steps were conducted to a converged solution at the residual target of \(1\times 10^{-5}\) for all the flow and turbulence variables. The CFD Fluent software was used to solve the adaptive wing model mesh, as described previously. The data obtained experimentally were compared with the \"steady state\" analysis results (simulations), but the errors and uncertainties were beyond the 10% validation metric limit, which will be explained in detail in Section 8. A rigid wind model, with no moving parts, in a laminar flow regime can be accurately predicted by the steady state Navier-Stokes equations by assuming, at simulation convergence, that the local speeds do not vary with time. In the case of an adaptable wing, the simulations have to be solved in a transient state analysis. A transient state allows for an accurate representation of flow behavior. The flow turbulence intensity was kept at 1% and therefore at the same turbulence levels as in the Price-Paidoussis wind tunnel tests. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid** & **Quantity of Cells** & \(C_{l}\) & \(C_{d}\) & \(C_{l}/C_{d}\) \\ \hline
1 & 900,542 & 0.02489 & 0.00920 & 2.70 \\
2 & 1,325,584 & 0.02435 & 0.008665 & 2.81 \\
3 & 1,854,000 & 0.02313 & 0.007896 & 2.92 \\
4 & 2,258,477 & 0.022869 & 0.007584 & 3.02 \\
5 & 3,524,648 & 0.022855 & 0.007545 & 3.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Grid sensitivity results. Figure 21: Mesh of the adaptive wing model. Selecting an accurate turbulence model for an accurate representation of wall-bounded flow, mild to important flow separation and recirculation, and flow transition is a challenging aspect in CFD simulations. The presence of a wing prototype with actuated/controlled leading edge and trailing edge surfaces generates additional turbulence characteristics to the flow regime in the test section. Four RANS models were tested with the CFD solver: Spalart-Allmaras (SA), K-epsilon (K-\(\epsilon\)), K-Omega (K-\(\omega\)), and the shear stress transport (SST). The Spalart-Allmaras model is a single-equation model involving wall-bounded flows and a low Reynolds number [36]. The SA model produced an absolute error of 20% compared to the experimental loads. The K-epsilon two-transport equation model solves for kinetic energy k and dissipation \(\varepsilon\), where dissipation is the rate at which the velocity fluctuations dissipate [37]. It uses coefficients that are found empirically, and it was found that the K-epsilon model is accurate for unsteady flow regimes. The absolute errors with the experimental loads were within the 10% validation limit. The K-Omega is a two-variables model, used to obtain the kinetic energy k and frequency \(\omega\). This model allows for a more accurate near-wall treatment and demonstrates superior performance for wall-bounded and low Reynolds number flows and for predicting transition [38].