# Improving the Design of a Multi-Gear Pump Switchgear Using CFD Analysis
## 3 Results
### Investigation of Manifold Geometry Variation in Fluid Velocity and Pressure Drop  
Since the prototype of a multi-gear pump is a multi-parameter task, another criterion was to obtain the lowest pressure drop when the liquid passes from the 'inlet' to 'outlet' zone. In this regard, a geometric optimization of the input space in the top cover manifold was performed. The radius was varied from 3 to 15 mm (Figure 11). The number of rotations was n = 1000 rpm. \begin{table}
\begin{tabular}{c c c c c} \hline
**No. of** & \multirow{2}{*}{**Speed, n, rpm**} & \multicolumn{2}{c}{**Coefficient of**} & \multirow{2}{*}{**Pressure Ps, kPa**} & **Pump Capacity** \\
**Experience** & & & **Dynamic Viscosity, \(\mu\), Pa-s** & & **Q, m\({}^{3}\)/s** \\ \hline \multicolumn{5}{c}{Series 1} \\ \hline  
\hline \end{tabular}
\end{table} 
Table 4: Variable parameters in the modeling of fluid flow in the pressure line of the distribution system. The fluid velocity and pressure distribution as a function of the radius are shown in Figures 12 and 13. The maximum velocity and pressure drop values are shown in Figure 14.  
Figure 11: Profile of the manifold inner cavity with a variable radius. Figure 12: Fluid velocity (**a**) and pressure (**b**) distribution diagrams with a transition radius of 3 mm in the manifold. Figure 13: Fluid velocity (**a**) and pressure (**b**) distribution diagrams with a transition radius of 15 mm in the manifold. As can be seen in Figure 14, the velocity of the fluid flow in the gear pump is almost unchanged depending on the change in radius in the manifold, and the pressure drop decreases from 42.384 kPa to 35.235 kPa when the radius increases from 3 mm to 15 mm. In the study, it was also hypothesized that the pressure drop across the manifold depends not only on the radius of the transition in the manifold but also on the number of revolutions. For this purpose, the DoE method was used. The input and output data for the DoE are presented in Table 5.  
Graphically, the dependence of the pressure drop on the transition radius on the inner surface of the collector and the speed is shown in Figure 15.  
Figure 14: Distribution of the pressure drop as a function of the radius of the transition in the manifold in the suction line of the distribution system. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(\boldsymbol{\mathsf{N}}\)} & **Collector Transition** & **Speed n, (\(\boldsymbol{\mathsf{X_{2}}}\)), rpm** & **Pressure Drop AP (Y), kPa** \\ \hline
1 & 15 & 800 & 342.328 \\ \hline
2 & 14 & 1000 & 351.135 \\ \hline
3 & 13 & 1200 & 362.234 \\ \hline
4 & 9 & 1200 & 351.432 \\ \hline
5 & 8 & 1000 & 361.753 \\ \hline
6 & 7 & 800 & 371.457 \\ \hline
7 & 5 & 800 & 412.532 \\ \hline
8 & 4 & 1000 & 421.384 \\ \hline
9 & 3 & 1200 & 431.224 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Input and output data for DoE. The dependence of the pressure drop \(\Delta\)P (Y) on the collector transition radius r (X\({}_{1}\)) and the speed n (X\({}_{2}\)) can be described using the multiple regression equation [33]. As a result of calculations, the multiple regression equation was obtained:  
\[\text{Y}=431.8137-6.6682\text{X}_{1}+0.00436\text{X}_{2} \tag{2}\]  
The constant estimates the aggregate effect of other factors (other than those accounted for in model Xi) on the result Y, and it means that Y, in the absence of Xi, would be 431.8137. The coefficient b\({}_{1}\) indicates that as X\({}_{1}\) increases by 1, Y decreases by 6.6682. The coefficient b\({}_{2}\) indicates that as X\({}_{2}\) increases by 1, Y increases by 0.00436. To assess the reliability of the multiple regression analysis, we calculated the criteria shown in Table 6.  
The statistical significance of the equation was checked using the coefficient of determination and [PERSON]'s criterion. In this situation, 76.99% of the total variability of Y