# Stability Evaluation of a Simplified Reclaimer Using Fluid-Structure Interaction
## 2 Materials and Methods
### Mathematical Model
#### 2.1.2 Numerical Model
The physical model is an ore reclaimer installed at the port of Sao Luis in Maranhao, Brazil. It had a width of 34 m and a height of 77 m (Figure 2). Its primary purpose was to extract material from stockpiles and load ships for iron ore exportation for Vale, shown in Figure 2. Due to the high computational effort required to simulate the real structure, a simplified model was used in this paper, represented in Figure 3. The simplified model has the same mass, frontal area, and superior and bottom parts as the real reclaimer. The parts are overlapped with contact steel-steel properties, fixed to the ground, and able to move in the other degrees of freedom. The principal data used for modeling the reclaimer were the project drawings with all the structure information. Figure 3 shows all parts from the reclaimer and an example ore pile beside it. This 3D CAD (computer-aided design) was developed in SolidWorks software as a base for discretization and simplification to a numerical model. The first developed model (left in Figure 4) used the full CAD 3D model trying a tetrahedral mesh in all solids of the CAD 3D model with all details. This model had a complexity to mesh that increased the number of elements (about 50-60 million) and decreased the quality, making it impossible to run in the solvers proposed to be used in this work. Then, the most simplified model was developed (right in Figure 4) by removing the more complex parts and keeping the principal dimensions (height, width, and frontal area). This simplified model enabled the use of some hexahedral elements and decreased the number of elements (about 1-2 million), making it possible to run mainly because of the quality increase. Figure 3: CAD 3D model. Figure 2: Real ore reclaimer. In computational fluid dynamics, the selection and optimization of mesh configurations play a pivotal role in the accuracy and efficiency of simulations conducted within platforms such as OpenFOAM. This study presents a comparative analysis between two mesh configurations: a simplified model significantly reducing the element count by approximately fifty times, and a complex model incorporating elements of comparatively lower quality. The simplified model showcased a maximum aspect ratio of 15.5351354, skewness not exceeding 1.01987345, and a non-orthogonality peak at 74.4576614\({}^{\circ}\), with a mere dozen faces presenting severe non-orthogonality issues (beyond 70 \({}^{\circ}\)). In contrast, the complex model exhibited escalated values in these parameters with a maximum aspect ratio reaching 38.3411, skewness peaking at 1.95792, and an utmost non-orthogonality of 81.1284\({}^{\circ}\), alongside a substantial increase in the count of severely non-orthogonal faces to 418. This juxtaposition elucidates the inherent trade-offs between mesh complexity and element quality, emphasizing the crucial impact of mesh characteristics such as skewness, aspect ratio, and non-orthogonality on the fidelity and computational demands of fluid dynamics simulations. The main properties applied to solid and fluid models are presented in \[\frac{\partial}{\partial t}(\rho u)+\frac{\partial}{\partial x}(\rho uu)+ \frac{\partial}{\partial y}(\rho uv)+\frac{\partial}{\partial z}(\rho uv)=- \frac{\partial P}{\partial x}+\mu\left(\frac{\partial^{2}u}{\partial x^{2}} +\frac{\partial^{2}u}{\partial y^{2}}+\frac{\partial^{2}u}{\partial z^{2}} \right)+\frac{\partial}{\partial x}\left(\rho k\frac{\partial k}{\partial x }\right)-\rho\varepsilon+S_{Mx} \tag{4}\]0 The air was assumed as an ideal gas, with properties evaluated at 20 \({}^{\circ}\)C and ambient pressure of 1 atm. The simplification used simple geometrical forms to represent the main model. Figure 3 shows a comparison between the more complex and simplified models.