# Influence of the Radial Gap on the External Gear Pump Performance
## 5 Radial Gap Size Influence on the Volumetric Flow Rate  
The values of the average volumetric flow rate \(q\) at a radial gap of 0.2 mm and at a radial gap of 0.04 mm (\(q_{0.04}\)) for different rotation frequencies \(n\) were obtained using the CFD model and presented in Table 2. In the same table, the differences \(\Delta q_{0.04}\) between \(q\) and \(q_{0.04}\) in L/min and percentages are shown.  
It can be seen that the absolute value of the flow rate losses \(\Delta q_{0.04}\) increased linearly with a decrease in the rotation frequency \(n\) when changing the radial gap from 0.02 mm to  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gap** & **0.02 mm** & & **0.04 mm** & \\ \hline \(n\) & \(q\) & \(q_{0.04}\) & \(\Delta q_{0.04}\) & \(\Delta q_{0.04}\) \\
**RPM** & **L/min** & **L/min** & **L/min** & **\%** \\ \hline
500 & 9.08 & 7.73 & 1.35 & 14.89\% \\
750 & 13.85 & 12.50 & 1.35 & 9.73\% \\
1000 & 18.63 & 17.31 & 1.32 & 7.08\% \\
1250 & 23.40 & 22.12 & 1.28 & 5.46\% \\
1450 & 27.22 & 25.95 & 1.27 & 4.67\% \\
2000 & 37.71 & 36.51 & 1.20 & 3.19\% \\
2500 & 47.25 & 46.09 & 1.16 & 2.46\% \\
3500 & 66.32 & 65.24 & 1.08 & 1.62\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: CFD results at gaps of 0.02 mm and 0.04 mm.  
Figure 9: Experimental data from the manufacturer’s technical documentation (Tech Data)—flow rate \(q_{Tech}(n)\), volumetric efficiency \(\eta_{v}(n)\), power consumption \(P_{m}(n)\), as well as other performance parameters in table form.  
0.04 mm--Figure 10. However, with the decrease in \(n\), the flow rate losses \(\Delta q_{0.04}\) increased in proportion to \(q_{0.04}\). As a result, the \(\Delta q_{0.04}(n)\) dependence, measured in percent, was a power-law function, also shown in Figure 10, with a smooth part at rotation frequencies above 1500 RPM and a steep part at rotation frequencies below 1500 RPM.  
The radial gap size influence on the flow rate was studied with four CFD simulations at 1000 RPM--with gap size values of 0.02, 0.03, 0.04, and 0.05 mm. The results are shown in Figure 11 where both the discrete values of the flow rate \(q_{i}\) and the average flow rate \(q\) are presented. It can be seen that the effect of increasing the radial gap was similar to the effect of decreasing the rotational frequency, illustrated in Figure 7. As the gap increased, the curve became more complex and different from the theoretical one, as well as noisier, in the other same conditions. Figure 11 shows that the average flow rate \(q\) decreases disproportionately with an increase in gap size [55]. To further evaluate this dependence, Table 3 and Figure 12 were created.  
Table 3 and Figure 12 show the average pump flow rate \(q\) as a function of the radial gap size in two measurement units--in L/min as well as in the percentage of the value 18.628 L/min, which was obtained at the nominal radial gap of 0.02 mm. It can be seen that the average flow rate decreased with an increased gap along a square parabola, i.e., the negative effect increased with the square of the radial gap.  
Figure 11: Effect of different radial gap sizes on the flow rate average and current values \(q\) and \(q_{i}\).  
Figure 10: Effect of increasing the gap from 0.02 mm to 0.04 mm at different rotation frequencies.