# Computational Fluid Dynamics Applied to
## 5 Results
### Categorization of Relevant Papers Exploiting the Rigid Mesh Motion and Sliding Meshes Approaches  
The paper exploiting RMM/MSL approaches are summarized in Table 4. The literature search has highlighted 29 pertinent papers (the highest number of relevant papers using a specific CFD approach). In particular, 11 papers studying gears, 11 papers simulating pumps, and seven papers considering bearings. Figure 3: Number of studies exploiting the rotating/multi reference frame approaches shown based on the accuracy achieved and the complexity of the modelling. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Paper** & **Year** & **Software** & **System** & **Target** & **Validation** & **Accuracy** & **Complexity** \\ \hline
[23] & 2007 & Comm. & Gears & Forces & Yes & 90\%–95\% & 2 \\
[82] & 2007 & Comm. & Pump & Fluxes & Yes & Qualitat. & 2 \\
[26] & 2010 & Comm. & Gears & Forces & Yes & \textgreater{}95\% & 2 \\
[24] & 2011 & Comm. & Gears & Forces & Yes & \textgreater{}95\% & 2 \\
[72] & 2012 & Comm. & Gears & Forces & No & N.A. & 2 \\
[25] & 2012 & Comm. & Gears & Forces & No & N.A. & 2 \\
[77] & 2012 & Comm. & Pump & Forces & Yes & 80\%–90\% & 2 \\
[73] & 2013 & Comm. & Gears & Forces & Yes & 90\%–95\% & 2 \\
[29] & 2013 & Comm. & Bearing & Fluxes & No & N.A. & 2 \\
[30] & 2015 & Comm. & Bearing & Fluxes & No & N.A. & 2 \\
[78] & 2016 & Comm. & Pump & Fluxes & No & N.A. & 2 \\
[84] & 2016 & Open & Pump & Both & Yes & \textgreater{}95\% & 2 \\
[28] & 2017 & Comm. & Gears & Both & No & N.A. & 2 \\
[85] & 2017 & Open & Bearing & Both & Yes & 80\%–90\% & 2 \\
[27] & 2018 & Comm. & Gears & Both & Yes & 90\%–95\% & 2 \\
[83] & 2018 & Comm. & Pump & Both & Yes & \textgreater{}95\% & 2 \\
[74] & 2019 & Comm. & Gears & Forces & Yes & 90\%–95\% & 2 \\
[84] & 2019 & Comm. & Gears & Forces & No & N.A. & 2 \\
[79] & 2019 & Open & Pump & Both & Yes & 80\%–90\% & 2 \\
[80] & 2019 & Comm. & Pump & Both & No & N.A. & 2 \\
[81] & 2019 & Comm. & Pump & Both & Yes & 90\%–95\% & 2 \\
[76] & 2020 & Comm. & Gears & Both & Yes & \textgreater{}95\% & 2 \\ \hline \end{tabular}
\end{table} 
Table 3: Classification of the pertinent papers exploiting the rotating/multi reference frame approaches. With respect to the papers studying the lubrication of gears through RMM/MSL approaches, it is possible to find works aimed at stimulating the oil flow in spur gears [86; 87] and calculating the power losses in ordinary gears [32; 88]. The lubrication of vehicle drive axles was studied in [89; 90; 91] and a tractor transmission was simulated in [92]. The power losses in planetary gearboxes were investigated in [35; 93] and the oil jet lubrication for an high speed gear was studied in [94]. The oil jet lubrication was simulated through RMM/MSL approaches also in ball bearings, e.g., [95; 96; 97]. The hydraulic power losses in tapered roller bearings were investigated in [98; 99], in cylindrical roller bearings were studied in [31], and in ball bearing were simulated in [100]. Through RMM/MSL approaches several kind of pumps were simulated. In particular, an oil pump was modelled in [101], a gerotor pump in [102], a trochoidal-gear pump in [103], a gear pump in [104], an electrical submersible pump in [105], a pump for hemodynamic application in [106], centrifugal pumps in [33; 34; 107], a pump mixer in [108], and a pump as a turbine in [109]. In addition, in Table 4 it is possible to notice that 22 papers out of 31 present an experimental validation. It is interesting that more than a third (12 out of 29) of the works implementing the RMM/MSL approaches exploit open-source software. In particular, OpenFOAM(r) was used in [31; 32; 33; 34; 87; 88; 93; 102; 103; 104; 107; 108]. With respect to commercial software, ANSYS FLUENT was used in [35; 36; 90; 94; 95; 96; 105], and ANSYS CFX was exploited in [98]. In [101] was used the commercial software PumpLix(r) by Sincerics Inc.(r) (Bellevue, WA, USA).