# Advanced 2D Computational Fluid Dynamics Model of an External Gear Pump Considering Relief Grooves
## 5 Experimental Study for Validation  
A laboratory experimental setup has been developed and used for testing an external gear pump at different operating modes. Figure 12 presents the hydraulic circuit diagram of the experimental system and its realization. A detailed description of the shown system is given in [3]. The developed experimental setup makes it possible for a real-time measurement of the gear pump basic working parameters: flow rate, output pressure and rotation frequency. The system consists of the studied pump, driven by an electric motor with a power of 7.5 kW and a nominal rotation frequency of 1450 min\({}^{-1}\). The electric motor is equipped with a frequency inverter enabling the pump rotation frequency to be changed, and hence the flow rate. The pump outlet pressure is varied by a loading system consisting of a direct-operated pressure relief valve and a parallel-connected hydraulic throttle check valve. The maximum pressure value is set with the pressure-relief valve and the pressure load value is set with the precision throttle valve for a certain mode of operation. Figure 11: Simulated flow rate: (**a**) \(\Delta p\) = 150 bar and \(n\) = 950–1450 min\({}^{-1}\); (**b**) \(n\) = 1450 min\({}^{-1}\) and \(\Delta p\) = 5–150 bar. Flow rate and pressure are measured using a gear flow meter equipped with a pressure sensor. The signals from the two sensors are processed by a developed data acquisition (DAQ) system which is based on NI USB 6211. For signals recording and processing, a user interface has been developed in LABView(r) ver. 2010 environment. The recorded in a table form experimental data are processed automatically via a specially developed program procedure in MATLAB(r) ver. 2009. Experimental studies were carried out with the described setup in order to validate the results of the numerical studies based on the advanced 2D CFD model. Experimental and numerical studies were performed in two groups of operation modes. In the first group, a maximum output pressure load of 150 bar is maintained (\(\Delta p=\text{const}\)), and the rotation frequency is a variable parameter in the range of 950-1450 min\({}^{-1}\). The experiment design and results are shown in Table 1. A results comparison via the characteristic of the average pump flow rate \(q_{AVG}\) as a function of the rotation frequency \(n\) is shown in Figure 13a. In order to distinguish the designation of the flow rate obtained by the experiment from that obtained numerically, the indices \(EXP\) and \(CFD\) have been added to the \(q_{AVG}\) in Tables 1 and 2. In the second group of operation modes, a constant nominal value of the rotation frequency is maintained (\(n=\text{const}\)), and the pressure load is a variable parameter in the range of 5-150 bar. The experiment design and results for this configuration are shown in Table 2. A results comparison via the characteristic of the average pump flow rate \(q_{AVG}\) as a function of the pressure \(\Delta p\) is shown in Figure 13b. Estimation of the percentage match between the model and experiment results is performed by calculating the quantitative index \(FIT\). It is defined as  
\[FIT=\left(1-\frac{|q_{AVG,EXP}-q_{AVG,CFD}|}{q_{AVG,EXP}}\right)100,\ \%, \tag{12}\]  
where \(q_{AVG,EXP}\) is the experimentally obtained average flow rate of the pump, and \(q_{AVG,CFD}\) is the simulation average flow rate obtained by the advanced 2D CFD model. The graphical comparison between the numerical and real experiment results (Figure 13) shows an excellent match for all operating modes. This is once again confirmed by the calculated quantitative indicator FIT, of which the value varies in the range of 97.93-99.82% (Tables 1 and 2). It is possible to achieve an even better match by fine adjustment to the imaginary meshing gap value described in Section 2, but the currently achieved match proves that the developed advanced 2D CFD model successfully considers the design features of this pump type, and especially the influence of the relief grooves on the flow process.