## 3 Results and Discussion  
The concentration (Equation (13)) determines the average mass of particles residing per cell, from which it can be concluded that, given an abrupt increase in concentration in a cell, which also remains constant over time, it will represent a zone of particle accumulation. \[m_{DPM}=\frac{\overline{m_{p,cell}}\ t_{p}\ s_{p}}{v_{cell}}\left[\mathrm{kg/ m^{3}}\right] \tag{13}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Geometry** & **D** & \(L_{1}\)**[mm]** & \(L_{2}\)**[mm]** & \(\mathbf{R_{c}/R}\) [\(-\)] & \(\mathbf{\Theta}\) [\({}^{\circ}\)] \\ \hline C11 & 104 & 28D & 50D & 1 & 90 \\ C12 & 104 & 28D & 50D & 4 & 90 \\ C13 & 104 & 28D & 50D & 8 & 90 \\ C21 & 104 & 33D & 50D & 1 & 90 \\ C22 & 104 & 33D & 50D & 4 & 90 \\ C23 & 104 & 33D & 50D & 8 & 90 \\ \hline \end{tabular}
\end{table} 
Table 4: Geometric dimensions in the study cases. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**z** & **C11** & **C12** & **C13** & **C21** & **C22** & **C23** \\ \hline \(N_{x}\times N_{y}\times N_{z}\) & 56 \(\times\) 700 \(\times\) 1000 & 56 \(\times\) 700 \(\times\) 854 & 56 \(\times\) 700 \(\times\) 856 & 56 \(\times\) 700 \(\times\) 1000 & 56 \(\times\) 812 \(\times\) 906 & 56 \(\times\) 812 \(\times\) 938 \\ N\({}^{\circ}\) of elements & 700,533 & 597,800 & 620,200 & 700,533 & 735,672 & 761,656 \\ \(\Delta x\) [mm] & 5.8 & 5.8 & 5.8 & 5.8 & 5.8 & 5.8 \\ \(\Delta z\) [mm] & 10 & 10 & 10 & 10 & 10 & 10 \\ \(\Delta y_{min}\) [mm] & 1.35 & 1.35 & 1.35 & 1.35 & 0.54 & 0.54 \\ \(\Delta y_{max}\) [mm] & 4.13 & 4.13 & 4.13 & 4.13 & 3.37 & 3.37 \\ \(y+\) & 40 & 40 & 40 & 100 & 40 & 40 \\ Aspect Ratio & \textless{}12 & \textless{}7.5 & \textless{}7.5 & \textless{}12 & \textless{}19 & \textless{}19 \\ Orthogonality & \textless{}0.84 & \textless{}0.63 & \textless{}0.63 & \textgreater{}0.84 & \textgreater{}0.66 & \textgreater{}0.66 \\ Skewness & \textless{}0.45 & \textless{}0.62 & \textless{}0.62 & \textless{}0.45 & \textless{}0.61 & \textless{}0.61 \\ \hline \end{tabular}
\end{table} 
Table 5: \(\Delta x\) = azimuthal, \(\Delta y\) = radial and \(\Delta z\) = axial mesh grid size used and the number of elements in each direction \(N_{x}\), \(N_{y}\), \(N_{z}\), respectively. In the radial direction, a mesh refinement was made close to the wall, starting with \(\Delta y_{min}\) increasing towards the center until reaching \(\Delta y_{max}\) with a growth factor of 1.2. Figure 9: Example of mesh case C22. (**a**) Axial direction, middle plane; (**b**) radial direction, pipe entry. where \(\overline{m_{p,cell}}\) is the average particle mass in a cell, \(t_{p}\) is the particle residence time per cell, \(v_{cell}\) is the volume of each cell and \(s_{p}\) is the total particle flow rate per cell. Accumulation statistics studied by concentration and distribution of particles continuously injected from the pipe inlet, were collected between \(\mathrm{z^{\prime}}=-1\)D and \(\mathrm{z}=3\)D after a physical travel time \(t_{r}=1.5\) [s] and \(1\) [s] (for a flow velocity \(\mathrm{V_{1}}=8.7\) [m/s] and \(\mathrm{V_{2}}=24.6\) [m/s], respectively), where a constant flow of particles was achieved. Since the results were extensive due to the number of cases simulated and the variety of parameters studied (dp, Re and R/Rc), they are presented and discussed based on the concentration results of case C12d1. However, the analysis and conclusions made here are formulated always considering all the cases. Complementary information about the other cases is presented in Appendix A. Figure 10 shows the concentration distribution along the curve. A maximum concentration at \(\varphi=87^{\circ}\) can be identified for C12d1, which responds to a maximum concentration that remains constant over time \"C\({}_{\mathrm{max}}\)\", identifying a zone of particle accumulation. Figure 11 shows the concentration of the particles at \(\varphi=87^{\circ}\). Figure 11a,b presents the instantaneous positioning (for a statistically stationary flow) of the particles in 3D view, evidencing the accumulation zone inside the bend.