## 2 Methodology  
### Model Description  
The hydrodynamic and structural mechanics effects on critical configurations of a WSM were computationally studied in a sewage open-channel flow in the present study. The channel is located at the inlet of a WTP, and the screening mechanism is secured \begin{table}
\begin{tabular}{l c c} \hline \hline
**Aspect** & **[PERSON] et al. [7]** & **Present Study** \\ \hline Dimensionality (2D vs. 3D) & 2D & 3D \\ Sub-screen attachment to the floor & Pivot & Ascendable \\ Sub-screen angle relative to the floor & Adjustable & Fixed \\ Stress consideration & Plane stresses (2D) & 3D stresses \\ Flow impingement on the sub-screen & Single bar (2D) & Entire span of sub-screen (3D) \\ Rake pin consideration & Single rake pin (2D) & Entire span of the rake (3D) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of aspects of the present study with [PERSON] et al. [7]. with the channel bank near the water surface. Figure 1 shows a 3D representation of the screening mechanism that comprises a fixed main screen, a sub-screen that can slide over the main screen in the vertical direction, and a rake, along with the rake movement mechanism. Water flows in the channel through the aperture of the screening mechanism, where any insoluble solid waste of an appreciable size is filtered from flowing into the plant. This accumulation results in flow separation in the downstream region, not only hurting the flow entering the wastewater treatment plant but also risking damaging the screening mechanism. Any solid waste that floats on the water surface, such as twigs and plastic waste, accumulates in the upstream region of the screening system and tends to block the flow of water in the upper region of the channel. The model deals with this issue through a chain-driven rake system with gears. This system brings the rake downward along the posterior of the screen, comes to the front, and goes back up at the frontal region at certain times of the day, collecting and lifting the waste in the process. This waste can later be discarded once it is removed from the water surface. Similarly, any insoluble solid waste of an appreciable size that sinks to the channel floor, such as stones and heavy objects, accumulates in the upstream region of the screening system and tends to block the flow of water in the lower region of the channel. This issue is handled by a chain-driven gear system, which lifts the sub-screen after a certain bulk of solid waste is accumulated in this region. The mechanism can slide over the main screen due to the tilt of the screening. The sunken waste flows in bulk into the channel, where it can be discarded when the sub-screen is lifted. Figure 2 presents the geometric configuration of the main screen, sub-screen, and rake system, and the values of the parameters have been summarized in Table 2. The screening mechanism is placed at location A, 0.75 m away from the inlet and oriented at an angle of 15\({}^{\circ}\) with the vertical cross-sectional plane through the channel. The number of bars on the main screen is 37, and on the sub-screen, it is 39, including bars on the extremes, whose height is 0.74 m. The aperture size of the screening mechanism is \(\alpha\) = 0.075 m. Each finger of the rake has a breadth of 0.05 m and is spaced at 0.034 m to accommodate the bars. The total number of rake fingers is 36, and the width of each bar is 0.009 m. The flow channel under consideration has a width of \(w_{\text{ch,c}}\) = 3.40 m in the upstream region of the WSM and a width of \(w_{\text{ch,d}}\) = 3.10 m in the downstream region of the WSM. The physical dimensions and wastewater flow rates used in the present study were chosen based on the real flow conditions observed in a typical sewage channel in a WTP. Figure 1: A 3D representation of the WSM. The dimensions of wastewater screening channels can vary widely.