## 4 Simulation Results and Discussions
The velocity magnitude increases to a maximum level and then decreases rapidly along the flow direction for the OLDR of 1, presenting a parabola profile with no basin bottom. The velocity magnitudes only increase in the orifice zone along the flow direction for the OLDRs of 0.25 and 0.5. It has almost the same profile of the velocity magnitude along the line of \(n\)-\(c_{2}\) for various OLDRs. It can be concluded that the inverted basin effect of the fluid velocity magnitude is more obvious with increasing OLDRs in the orifice zone. In other words, there is a velocity magnitude hold effect in the orifice zone and it will be more remarkable with increasing OLDRs. In addition, the maximum oil velocity magnitude (\(v^{\prime}\)) in the orifice zone with respect to various OLDRs has the following relation:  
\[v^{\prime}{}_{1/d=0.25}<v^{\prime}{}_{1/d=0.5}<v^{\prime}{}_{1/d=5}<v^{\prime}{ }_{1/d=1}<v^{\prime}{}_{1/d=4}<v^{\prime}{}_{1/d=3}<v^{\prime}{}_{1/d=2} \tag{2}\]  
Turbulent intensity (\(I\)) is an important parameter to characterize turbulence of the flow field, which is defined as follows:  
\[I=\frac{u^{\prime}}{u_{arg}} \tag{3}\]  
where \(u^{\prime}\) depicts the root-mean-square of the velocity fluctuations, \(u_{arg}\) represents the mean flow velocity. Figure 4: Pressure patterns of various orifice length–diameter ratio (OLDRs) along the line of \(c_{1}\)–\(c_{2}\). (**a**) Node pressures of various OLDRs along the line of \(c_{1}\)–\(c_{2}\); (**b**) local enlarged view of I. The turbulent intensity patterns along the line of \(c_{1}\)-\(c_{2}\) for different OLDRs are depicted in Figure 6. It can be found from Figure 6 that the turbulent intensity is almost identical, about 0.07%, at the oil inlet and then it increases along the flow direction with almost the same growth rate for various OLDRs. The turbulent intensities of the fluid reach almost the same local peaks at different orifice inlets (\(m_{i}\), \(i=1\), \(2\)... 7) with various OLDRs. However, the turbulent intensity presents different profiles in the orifice zone along the line of \(m\)-\(n\) with respect to different OLDRs. Specifically, the turbulent intensity reaches a peak point at node \(m\) and then decreases slightly, and then increases slightly along the flow direction for the OLDRs of 3, 4, and 5, looking like a basin, and named a basin turbulent intensity profile in this paper. The turbulent intensities only decrease in the orifice zone along the flow direction for the OLDRs of 0.25, 0.5, 1, and 2. Furthermore, the turbulent intensity decreases to the valley point when the flow reaches the orifice outlet (node \(n\)) for the OLDR of 2. It has almost the same profile of the turbulent intensity along the line of \(n\)-\(c_{2}\) for various OLDRs. The turbulent intensity reaches its maximum (about 9.73%) at node \(O\) for various OLDRs. Based on the aforementioned analyses, it can be concluded that the turbulent intensity is very low  
Figure 5: Velocity magnitude patterns of various OLDRs along the line of \(c_{1}\)–\(c_{2}\). (**a**) Velocity magnitudes of various OLDRs along the line of \(c_{1}\)–\(c_{2}\); (**b**) local enlarged view of I.  
Figure 6: Turbulent intensity patterns of various OLDRs along the line of \(c_{1}\)–\(c_{2}\). (**a**) Turbulent intensities of various OLDRs along the line of \(c_{1}\)–\(c_{2}\); (**b**) local enlarged view of I.  
at the oil inlet, indicating that the fluid field is the laminar flow at the oil inlet. The basin effect of the fluid turbulent intensity is more obvious with increasing OLDRs in the orifice zone, presenting that there is a turbulent intensity hold effect in the orifice zone and it will be more remarkable with increasing OLDRs. The turbulent flow reaches its most intense at the transition point (node \(O\)) at which the fluid enters the oil film from the annular recess for various OLDRs.