# Numerical and Experimental Analysis of the Oil Flow in a Planetary Gearbox
## 3 Results and Discussion
### Comparison of Numerical and Experimental Results  
Exemplary simulation results with respect to the oil flow were compared with high-speed camera recordings to validate the oil distribution in the front part of the gearbox. The simulation results are shown after one rotation of the planet carrier, as no appreciable \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **GRAMC** & **General Approach** & **Net Gain \%** \\ \hline Simulation time for the analyzed gearbox & & & \\ (1 planet carrier rotation) & 20 h & 400 h & 95\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the computational effort between a standard and the newly implemented remeshing algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline Convergence criterion & \(1\times 10^{-5}\) \\ Maximum Courant number & 1 \\ Pressure solver & PCG (preconditioned conjugate gradient) \\ Velocity solver & PBiCG (stabilized preconditioned bi-conjugate gradient) \\ Time derivative discretization & First order implicit Euler scheme \\ Velocity discretization & Second order linear-upwind scheme \\ Convection of the volumetric fraction & Second order van Leer scheme \\ \hline \hline \end{tabular}
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Table 5: Numerical settings used in the simulations. For the SIM-id1v1 operating condition (Figure 6), the low rotational speed translates into a low amount of oil being dragged by the planet carrier rotation. This results in the formation of an oil track in the lower left region (red dashed rectangle) and only a small quantity is carried up by the planet carrier rotation. This behavior is well captured by the simulation. As the velocity increases (SIM-id1v2, Figure 7), more oil is dragged by the planet carrier. This reflects into higher splashing on the left area (red dashed rectangle), as well as into a pronounced oil ejection on the right side of the gearbox (blue dashed dot rectangle). Both phenomena are very well predicted by the CFD model. At the highest velocity (SIM-id1v3, Figure 8), the centrifugal forces promote a marked radial expansion of the oil towards the housing, also including the region above the planet carrier (red dashed arc). However, the simulation predicts a greater amount of oil in the upper region. A possible explanation for this difference could be related to the modeling of wall adhesion at the contact point between the wall surface and the interface, as explained in Section 2.4.4. These three operating conditions were investigated by [PERSON] et al. [2] as well. Moreover, in their model, the planet carrier rotation drags the oil from the sump and brings it to the upper part of the system. It was observed that the higher the rotational speed, the higher the amount of oil being splashed around. The fact that their model includes the bearings can introduce some differences in the small-scale flows in that region. Dedicated sub-models with a much finer mesh around the bearings and specific boundary conditions for the correct description of the rings' and rollers' kinematics would be necessary to accurately predict the oil flow and the velocity and pressure gradients in the bearings region [35]. Figures 9-11 show a side-by-side comparison for the high filling level operating conditions. For the SIM-id2v1 operating condition (Figure 9), from the high-speed camera recordings it can be observed that a peculiar shape of the oil originates: these are Taylor-Couette flows [36] that arise between the rotating planet carrier and the fixed internal surfaces of the housing, as demonstrated by [PERSON] et al. [7]. The wave that can be seen in front of the planet carrier is well predicted by the CFD model (red dashed rectangle). As the velocity increases (SIM-id2v2, Figure 10), the wave shape of the oil tends to cover a larger area in the gearbox (red dashed arc). A slight decrease in the oil sump level could be observed on the right side of the planet carrier (blue dashed dot rectangle).