## 6 Validation of CFD-Evaluated Force Coefficients and Flutter Derivatives
### Flutter Derivatives  
The same three samples were tested in the wind tunnel to obtain their flutter derivates for the 0\({}^{\circ}\) AoA, and the experimental values are compared with the CFD-based forced-oscillation simulations. For the numerical evaluation of the flutter derivatives, the forced-oscillation simulations were conducted separately for the heave and pitch degrees of freedom, following the procedure in [31]. The amplitude of the forced oscillations in the pitch degree of freedom was 3\({}^{\circ}\), while, in the heave degree of freedom, an amplitude of \(h_{0}/D_{\text{ref}}=0.7\) was adopted. The velocity of the incoming flow was adjusted within the range (3.7 m/s, 21.3 m/s) and the frequency of oscillation within the range (3.2 rad/s, 36 rad/s), aiming at covering a range of reduced velocities up to \(Ur=U/(fB)=20\). In Figure 8, the experimental and CFD values for the flutter derivatives \(H_{i}^{*}\) and \(A_{i}^{*}\), \(i=1\), 2 and 3, are reported for sample g01. It can be noted that the experimental values were obtained with the adoption of two different initial pitch angles at release. Figure 8: Experimental and CFD-evaluated flutter derivatives at 0\({}^{\circ}\) AoA for sample g01. Figure 7: Experimental and CFD force coefficients vs. AoA for samples (**a**) g01, (**b**) g04 and (**c**) g07. the set of 15 samples considered in the definition of the surrogate model are reported. The application of the RBF surrogate enables the approximation of the drag, lift and moment coefficients for any angle of attack in the range (\(-2^{\circ}\), \(2^{\circ}\)) and for any geometry within the considered deck shape design domain; therefore, a quantitative linkage is established between the twin-box deck geometry and angle of attack with the force coefficients. In the RBF model, the maximum number of neurons is set to 15, similar to the number of initial designs, and the number of display neurons is set to 25. In Figure 11, the graphical representation of the surrogate model for the drag coefficient is depicted as a matrix of charts over the range of \(C/C_{\text{ref}}\) and \(D/D_{\text{ref}}\) considered in this study, while constant values are adopted for the angle of attack and \(G/D_{\text{ref}}\) inputs, defining the rows and columns of the matrix representation. It is to note that this criterium is adopted to aim to efficiently represent this surrogate model comprising four input variables. It can also be noted that larger gap-to-depth ratios provide higher drag coefficient, as a longer slot facilitates the flow through the gap, increasing the drag contribution of the downwind box panel facing the gap. Furthermore, narrower boxes (smaller \(C/C_{\text{ref}}\)) are linked to larger drag coefficients, although this is mainly related to the smaller value adopted as the reference dimension in Equation (1) for the calculation of the drag coefficient, while the overall drag action is roughly unchanged. It is noted that, in [23], a similar trend was identified for short gap twin-box decks. As expected, smaller box depths produce lower drag coefficients, as the exposed deck area facing the incoming flow is decreased. The impact of the angle of attack in the drag coefficient is minor for the studied narrow range of AoA around \(0^{\circ}\). Similarly to the drag coefficient, the graphical representation of the lift coefficient provided by the RBF surrogate model over the considered design domain is depicted in Figure 12. In this case, for \(G/D_{\text{ref}}\) values between 2.5 and 4.5, a minimum in the lift coefficient can be identified for values of \(C/C_{\text{ref}}\cong-0.015\) and \(D/D_{\text{ref}}\cong-0.05\). In general, shorter gaps show stronger changes in the lift coefficient, depending on the geometry of the boxes.