# Computational Fluid Dynamics Applied to
## 1 Introduction  
The lubrication of mechanical components plays a key role in ensuring their reliable functioning in terms of wear reduction, efficiency improvement, and in maintaining an appropriate operating temperature both by reducing the heat generation and by promoting its dissipation [1]. However, even if the lubrication allows the reduction of power losses due to friction, the interaction between the lubricant and the moving structures implies additional power losses due to viscous and inertial effects [2]. The prediction of these power losses has been studied in the past through experimental tests. Based on these measurements, several empirical/analytical models have been proposed [3]. However, those models are unreliable for predicting power losses when the geometries, the speeds or the lubricant properties differ from those observed/selected during the experimental tests [3]. In other words, their ranges of applicability are only those on which they have been calibrated. Moreover, the analytical models do not provide any indications on the lubricant distribution, a fundamental aspect to ensure/confirm the proper lubrication for all the critical components [3]. Therefore, nowadays, with the aim of studying lubricant behavior in machine components and predicting the related power losses, CFD analyses can be exploited. Indeed, in addition to the possibility to simulate different lubricant properties, CFD simulations can be applied to any geometricalconfiguration and operating condition [4]. This allows overcoming the limitations of the empirical and analytical models even if it requires higher computational efforts. Moreover, the possibility to get information in each point of the computational domain (i.e., the studied volume in which fluids can be present) helps to understand the physical phenomena behind the lubrication and its effectiveness. In order to carry out CFD analysis simulating the lubricant behavior in machine components, it is necessary to deal with many challenges that affect both the effectiveness and the efficiency of the simulations. Indeed, since the main lubricated components are gearboxes, pumps and bearings, it is easy to understand how different systems require the study of different physical phenomena, e.g., windage (single-phase), churning (multi-phase), cavitation, etc., by handling topological changes of the computational domain and/or defining specific boundary conditions. The CFD approaches can be classified into mesh-based or meshless (mesh-free) approaches [5]. Some hybrid methods can be found in the literature, e.g., fast fluid dynamics [6] and the particle in cell method [7]. However, these hybrid methods are not used in the study of lubrication of mechanical systems. Mesh-based approaches can accurately describe the phenomena at any physical scale. However, any topological modification of the computational domain and/or the motion of the boundaries affect their applicability [3; 5]. On the other hand, the meshless approaches discretizes the fluid instead of the spatial domain [8]. Indeed, these approaches divide the fluid (i.e., the lubricant) into a set of discrete elements also called particles [8; 9]. The evaluation of a field variable that can be the viscosity, the density etc. can be calculated by summing the relevant properties of all the particles. Although the meshless approaches can be easily applied to simulate the lubricant behavior in complex systems (since the mesh-handling issues are not present), the accuracy of the results in terms of power losses have been proved to be inadequate for most of the mechanical engineering applications [3]. Therefore, on one hand, mesh-based CFD approaches can simulate multiple physical phenomena accurately but their applicability is limited by challenge of discretizing the computational domain at each time step.