# A Virtual Prototype for Fast Design and Visualization of Gerotor Pumps
## 4 Results  
We present the results of a design case while using the presented virtual prototype tool to design and simulate a gerotor pump. We also compare the obtained results with the data imported from an external CFD simulation for the same geometry, fluid properties, and operating conditions. Figures 15 and 16 present the volumetric data that were calculated by our tool for the pump design used in this test run. Figure 14: Example of the pressure data collected from the experimental setup sensors. Figure 13: Geometry visualization: (a) inner and outer gear of the pump, (b) fluid chambers with transparent ports. Figure 15a shows the selected analysis chamber. In this case, we have selected the maximum volume chamber when the pump is at initial position \(t=0\), even though our tool can perform the geometric analysis of all chambers simultaneously. Figure 15b shows the area evolution for the analysis chamber. Notice that it starts with the maximum value and diminishes until it reaches the minimum value for chamber area around halfway through a revolution. The minimum value for the area is not exactly zero because of the gaps in the meshing between the internal and external rotors described in the previous section. The area then rises until it reaches the maximum value once the revolution of the pump is completed. Figure 16a shows the intersection area between the analysis chamber and the input port (area through which the working fluid enters the pump). Notice that the intersection area increases at first, because, at initial position, the port and the chamber are only partially overlapped (as seen in Figure 15a). When the chamber is no longer overlapping with the input port and has started discharging fluid (overlapping with the output port), the intersection area with the input port becomes zero. The same analysis corresponds to the intersection area between the chamber and output port shown in Figure 16b. Figure 17 shows the history of areas for all chambers in the pump; the periodicity is explained by the cyclic design of the pump. Figure 16: Volumetric data results from the virtual prototype: (**a**) history of intersection area between chamber \(CV_{1}\) and input port and (**b**) history of intersection area between chamber \(CV_{1}\) and output port. Figure 15: Volumetric data results from the virtual prototype: (**a**) profile of geometry with highlighted chamber (\(CV_{1}\)) and (**b**) history of area in a z-cut for selected chamber. We now discuss the results of a fluid dynamics simulation with our virtual prototype tool. The fluid properties, operating conditions and initial pressure conditions that are used for the simulation presented, are described in Table 1:  
Figure 18 shows the history of calculated pressure inside an analysis chamber. Notice that the analysis chamber \(CV_{1}\) (Figure 18a) is initially near the maximum volume position and, therefore, the initial pressure \(P_{t=0}\) will be low (near input port pressure). As the pump rotates, the volume of the chamber reduces and increases the pressure inside the chamber. The maximum value of the pressure in chamber is reached in the minimum volume position and, once the analysis chamber enters the discharge cycle, the pressure starts to reduce as a result of the discharge of fluid and increase in volume of the chamber itself. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Value** & **Units** \\ \hline Pressure at input port (\(p_{in}\)) & 1 & bar \\ \hline Pressure at output port (\(p_{out}\)) & 4.5 & bar \\ \hline Density of fluid at 1 atm (\(\rho_{oil}\)) & 1005 & kg/m\({}^{3}\) \\ \hline Bulk modulus of fluid at 1 atm (\(\beta_{oil}\)) & 1.4 & GPa \\ \hline Angular speed of inner rotor (\(\omega\)) & 100 & rad/s \\ \hline Dynamic viscosity (\(\mu\)) & 0.01 & Pa*s \\ \hline Pressure in chambers at \(t=0\) & 1 & bar \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation conditions for test operating point. Figure 17: History of area for all 9 chambers in the pump.