# Influence of the Radial Gap on the External Gear Pump Performance
## 7 Conclusions  
The influence of radial gap on the performance characteristics of a certain specimen of an external gear pump was successfully studied using numerical and experimental results as well as the manufacturer's technical data. This numerical study was performed on the basis of a 2D CFD model developed and advanced in previous authors' works. The experimental study was carried out on a laboratory test bench. The presented numerical results were accurate in the entire pump operating range (500-3500 RPM), which was confirmed by validation both with our own experimental data and with data from the technical documentation. The analysis showed that the differences obtained during the verifications were in the range from \(-6.44\%\) to \(2.48\%\). This is the reason to use the presented CFD model to predict the pump's performance characteristics as it wears, which leads to increasing the radial gap between the housing and the gears tips.  
Based on the performance characteristics' fundamental theory, an original methodology was created. It allowed us to obtain the volumetric efficiency and overall efficiency of the pump as a function of the rotation frequency at any values of the radial gap, using the manufacturer's data for volumetric efficiency and power consumption at nominal radial gaps and CFD simulation results. This allowed us to evaluate the performance of the pump in the process of its wear and to predict the maximum allowable radial gap in different operating modes.  
The simulation results with a radial gap of 0.04 mm at an outlet pressure of 10.5 MPa showed a decrease in the overall efficiency by approximately 20% at the minimum rotation frequency (500-650 RPM). At a nominal rotational frequency (1450 RPM), there was a decrease in the overall efficiency by 5%, and at the maximum frequency of 3500 RPM, the decrease was less than 2%. The acceptable practice limit, at which the pump was considered unfit for normal operation as a result of wear, was when the flow rate was reduced to about 80% of its maximum value. Therefore, it can be concluded that a radial gap of 0.04 mm was close to the limit value for the studied pump if it was not operated at rotation frequencies above nominal.  
The presented original methodology can also be applied to other types of hydraulic displacement pumps in order to evaluate their performances in the wear process and to predict the maximum allowable value of a specific design parameter.  
Conceptualization, A.M., N.N. and I.K.; methodology, A.M. and N.N.; CFD model, N.N.; validation, A.M.; formal analysis, N.N. and A.M.; investigation, A.M. and N.N.; resources, A.M. and N.N.; data curation, N.N. and A.M.; writing--original draft preparation, A.M.  
Figure 13: Efficiency of the studied pump: (**a**) volumetric; (**b**) total.  
and N.N.; writing--review and editing, A.M., N.N. and I.K.; visualization, N.N.; supervision, A.M.; project administration, I.K.; funding acquisition, I.K. All authors have read and agreed to the published version of the manuscript.  
This work was accomplished with financial support by the European Regional Development Fund within the Operational Program \"Bulgarian national recovery and resilience plan\", the procedure for direct provision of grants \"Establishing of a network of research higher education institutions in Bulgaria\", under the project BG-RRP-2.004-0005 \"Improving the research capacity and quality to achieve international recognition and resilience of TU-Sofia (IDEAS)\".  
**Infrared Consent Statement:** Not applicable.  
**Data Availability Statement:** Dataset available on request from the authors.  
The authors declare no conflicts of interest.