## 3 Method
### Problem Setup for CFD Model
#### 3.5.2 Convergence on the Drag Coefficient of Multiple Twines in Tandem at Various Angles of Attack  
In this section, we quantified the effect of multiple twines in tandem on the drag coefficient at a low angle of attack. As a matter of fact, the shielding effects are only observed at low angles of attack. An example of the illustration of this effect is depicted in Figures 14 and 15 for \(\mathcal{R}e_{t}^{*}=1000\). It can be seen that only the leading twine conserves the vortex-shedding pattern, which is responsible for the unsteady separation of the flow, whereas the following twines exhibit broken patterns due to the wake of their respective preceding twine. Therefore, the goal of this section was to show the number of twines \(\mathrm{N}_{t}^{*}\) for which the average drag coefficient is no longer changing.  
Figure 12: Illustration of a complex boundary layer separation at \(\mathcal{R}e_{t}^{*}=1000\) as seen in the research of [PERSON] and [PERSON] [47], [PERSON] and [PERSON] [48], [PERSON] and [PERSON] [49] captured by [PERSON] [33]. Vorticity field (**top**) and the quadtree structure (**bottom**).  
Figure 13: Illustration of the drag coefficient and the numerical parameters related to its computation. (**a**) Instantaneous drag coefficient at \(\mathcal{R}e_{t}^{*}=1000\) for various smallest grid sizes. (**b**) Instantaneous drag coefficient at \(\mathcal{R}e_{t}^{*}=1600\) for various smallest grid sizes. (**c**) Instantaneous number of cells for \(\delta^{s-1}=128\) as a function of \(c\) at \(\mathcal{R}e_{t}^{*}=1000\). (**d**) Instantaneous number of cells for \(\delta^{s-1}=128\) as a function of \(c\) at \(\mathcal{R}e_{t}^{*}=1600\). (**e**) Instantaneous drag coefficient for \(\delta^{s-1}=128\) as a function of \(c^{*}\) at \(\mathcal{R}e_{t}^{*}=1000\). (**f**) Instantaneous drag coefficient for \(\delta^{s-1}=128\) as a function of \(c^{*}\) at \(\mathcal{R}e_{t}^{*}=1600\).  
In Figure 16, we compare the time history of the instantaneous averaged drag coefficient computed as in Equation (18), but relative to the \(x\)-axis. It shows a very clear dependence on the number of twines \(N_{t}^{*}\). For small \(N_{t}^{*}\), the drag coefficient is underestimated by more than 50%. For our following analysis, it is obvious that we considered only \(N_{t}^{*}\geq 32\). Since the difference between \(N_{t}^{*}=32\) and \(N_{t}^{*}=64\) is acceptable and for a relatively modest computational effort, we chose \(N_{t}^{*}=32\).  
Figure 14: Close-up illustration of the shielding effect mechanism for \(\theta=8^{\circ}\) at \(\mathcal{R}e_{t}^{*}=1000\). Blue and red, respectively, indicate negative and positive values of the vorticity fields.  
Figure 15: Illustration of the flow structure using the velocity field \(u_{x}\) as a function of \(\theta\) at \(\mathcal{R}e_{t}^{*}=1000\) and \(t^{*}=90\). Blue and red, respectively, indicate low and high values of \(u_{x}^{*}\).  
In order to improve our DT, we extracted the drag and lift correlations as seen in Figures 17 and 18. By analyzing these correlations, we can gain a better understanding of the behavior of an object in a fluid medium and how factors such as the angle of attack and velocity affect the drag and lift. It is worth noting that the drag coefficient is almost three-times higher for high angles of attack compared to very low angles of attack. This underscores the importance of considering a wide range of angles of attack when modeling the behavior of a net in a fluid medium and highlights the need for accurate drag and lift correlations in order to create more-precise predictions.  
Figure 16: Influence of the number of twines \(N_{t}^{*}\) on the instantaneous total drag coefficient for various low angles of attack \(\theta\) at \(\mathcal{R}e_{t}^{*}=800\).  
Figure 17: Dependence of the drag coefficient on the angle of attack. The median of the fluctuations is shown with the standard deviation.