# An Experimentally Validated CFD Code to Design Coanda Effect Screen Structures
## 2 Materials and Methods
### Numerical Setup  
Two-dimensional fluid flow simulations were performed in Ansys(r) Workbench 2021 R2, ANSYS, Inc. (Canonsburg, PA, USA), with the software packages DesignModeler, Meshing, and Fluent. The 3D CAD model of the CES was loaded in STP file format and converted to a 2D cross-section by the \"Surfaces From Faces\" command. Two simplified geometries, see Figure 3a, were designed, one with the boundary conditions of the presented experimental setup and the second one as it was applied in [19], see Figure 3a, magenta. At the inlet, a Dirichlet boundary condition [22] defines the desired flow rates of 7 m\({}^{3}\)h\({}^{-1}\), 8 m\({}^{3}\)h\({}^{-1}\), and 9 m\({}^{3}\)h\({}^{-1}\), respectively. The inlet was elongated by 800 mm to provide a fully developed flow profile at the CES. This was created since it is not possible to insert the baffle plate in the 2D simulation in an appropriate way. The 800 mm elongation space was initialized with water to save computational time. All other boundary conditions are summarized in Figure 3a. All outlet boundary conditions were set to a constant pressure of 1013.25 mbar. Subsequently, an unstructured CFD mesh, consisting of quads with 4 nodes and triangles with 3 nodes (linear elements), was generated with 17 cells at the critical Coanda rake flow cross-section and five boundary cells, characterized by a smooth transition and a growth rate of 1.2 orthogonal to the wall boundary. The first cell of the boundary layer was set to 0.022 mm to model the viscous flow appropriately [22]. The resolution outside the boundary layer at the CES is set to 0.125 mm. Therefore, the functions \"face sizing\" and \"inflation\" within Ansys Meshing were used. In the \"face sizing\" function, the meshing behavior was set to soft to allow minor variation in the element size to improve the mesh quality. The final mesh had 589 272 nodes and 579,946 elements, with a maximum skewness of 0.86 and a maximum aspect ratio of 10.1. The mesh is shown in Figure 3b. To simulate the two-phase (water and air) flow, the Volume of Fluid (VoF) model was used with default parameters. The flow Reynolds number (Re) [23] at the inlet is around 34,000. Compared to the critical Re of pipe flow (2300 [23]), the flow is turbulent, and therefore the default Fluent turbulence model k-\(\omega\) SST was used, in the same way it was applied in [19]. Gravity, g = \(-\)9.81 ms\({}^{-2}\), was defined in the y-direction (see Figure 3a). The flow field was initialized at v = 0 ms\({}^{-1}\). The field was initialized with the standard initialization. With the numerical solution process, a stationary solution was found. Simulations were performed with second-order accuracy. Table 1 shows the numerical schemes and solution methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Adjustment** \\ \hline Turbulence model & k-\(\omega\) SST \\ Pressure velocity coupling & Coupled \\ Gradient & Least Squares Cell Based \\ Pressure & Presto! \\ Momentum & Second-order upwind \\ Volume fraction & Compressive \\ Turbulence Kinetic Energy & Second-order upwind \\ Turbulence Dissipation rate & Second-order upwind \\ Initialization & Standard \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical schemes and solution methods [24]. For the simulation, the scaled residuals for all conservation equations converged to the threshold < 1 \(\times\) 10\({}^{-4}\) (continuity < 1 \(\times\) 10\({}^{-4}\), x-velocity < 5 \(\times\) 10\({}^{-7}\), y-velocity < 5 \(\times\) 10\({}^{-7}\), k < 6 \(\times\) 10\({}^{-5}\), omega < 3 \(\times\) 10\({}^{-5}\), and vof < 4 \(\times\) 10\({}^{-6}\)). For comparison with the experiment, the relative water mass flow rate \(\Pi~{}=~{}\frac{\dot{m}_{bursts}}{\dot{m}_{inlet}}\) (see Figure 1) was evaluated. Furthermore, a mesh convergence study based on [25] with simplified boundary conditions (see Figure 3a, magenta lines) and 9 m\({}^{3}\)h\({}^{-1}\) was performed.