Numerical investigation of cavitation flow in journal bearing geometry

The appearance of cavitation is still a problem in technical and industrial applications. Especially in automotive internal combustion engines, hydrodynamic journal bearings are used due to their favourable wearing quality and operating characteristics. Cavitation flows inside the bearings reduces the load capacity and leads to a risk of material damages. Therefore an understanding of the complex flow phenomena inside the bearing is necessary for the design development of hydrodynamic journal bearings. Experimental investigations in the fluid domain of the journal bearing are difficult to realize founded by the small dimensions of the bearing. In the recent years more and more the advantages of the computational fluid dynamics (CFD) are used to investigate the detail of the cavitation flows. The analysis in the paper is carried out in a two-step approach. At first an experimental investigation of journal bearing including cavitation is selected from the literature. The complex numerical model validated with the experimental measured data. In a second step, typically design parameters, such as a groove and feed hole, which are necessary to distribute the oil supply across the gap were added into the model. The paper reflects on the influence of the used design parameters and the variation of the additional supply flow rate through the feed hole regarding to cavitation effects in the bearing. Detailed pictures of the three-dimensional flow structures and the cavitation regions inside the flow film of the bearing are presented.


Introduction
The hydrodynamic journal bearing offer a wide range of application.This is due to the simple design and high sustainability.The life of a plain bearing depends on many factors.Among other cavitation can lead to a breakdown of the bearing.Investigation of cavitation in journal bearings was done for more than 50 years.
To detect the possible causes for the breakdown, it is necessary to understand the flow regime inside the bearing.Therefore experiments and numerical simulations were done.Cavitation is founded by three dimensional effects.That's why the investigations were done with the 3D-CFD Code OpenFOAM.The advantage of numerical simulations is that it is possible to see every detail of the flow field.In experiments it is almost impossible to see 3D effects like vortex.On the other hand an experiment is necessary to validate a numerical solution.Especially in the given case the numerical solver for cavitation need to be validated by an experiment.Therefore an experiment was selected from the literature.A numerical model was designed based on the experiment.In the first step the validation is done.Furthermore typical geometrical properties are added to the existing model to see what happen to the cavitation region and pressure curve.The geometrical changes are a groove in circumferentially direction and cross-flow of oil support by a feed hole in radial direction.

Experimental setup
The experiment was done by Jakobsson et.al.[1].The configuration is shown in fig. 1.The shaft rotates with the angular velocity ω and is eccentric to the outer cylinder with the eccentricity e.The gap between inner and outer cylinder is filled with oil.Pressure curve are measured along the line z = 0.1 B. This line is used to compare the computational results with the experimental results.Cavitation is reached downstream the smallest gap.The pressure in that region stays constant.In table 1 the geometrical properties of the experiment are given.
The flow regime inside the system is laminar with a Reynolds number Re = 23 based on equation 1.
(1)  Vapour pressure of the fluid 20 kPa

Numerical setup
The simulations are done with the CFD-Code OpenFOAM.The numerical code is based on the finite volume method and solves the three dimensional momentum and continuity equations.OpenFOAM includes a solver for cavitation.These solvers use the volume of fluid-method (VoF) to model the two phase flow.The volume fraction α is calculated by equation 4.
The phase change model base on a bubble dynamic approach according to Sauer [2].A description about the cavitation solver is given in Lu [3]. (2) (5) The basic model for validation of the numerical solution consists of the fixed outer cylinder and the rotating inner cylinder.Further design steps include a groove and a feed hole.The ends of the bearing are designed as open ends with ambient pressure boundary condition.The numerical grid is generated as a block structured mesh with hexagonal cells.The feed hole pipe is meshed with a typical O-grid.In radial direction the number of cells is 14, recommended by Schmidt et.al.[4].
The overall model is shown in fig. 2 and the boundary conditions are listed in table 2. To orientate in circumference direction the angle φ is introduced.The widest gap and the feed hole are at the position φ = 0°.The positive direction is defined by the convergent gap.
The incoming flow rate is equal to the inner volumetric flow rate calculated by equation 6.  3 Results and discussion

Validation of the experiment
In the first step the numerical simulation validated with the experimental measurement.In fig. 3 the comparison of experiment and simulation is illustrated.It should be observe that there is no groove and no additional flow.

Fig. 3. Pressure plot of experiment and simulation
The simulation is in good agreement to the experiment.In the divergent gap the pressure reaches the value of the fluid vapour pressure hence in fluid vaporization.In fig. 4 the isosurface of the volume fraction for vapour (α < 0.95) is shown.It is obvious that the vapour region reaches the largest degree in the symmetry plane of the bearing.Both, the divergent geometry of the gap and the ambient pressure at the ends influence the distribution of the vapour region.Therefore the vapour volume fraction decreases to the outlets.

Without groove and with cross-flow
In a second step some geometrical changes are done.First a feed hole is added to simulate fluid support by crossflow.The comparison of the pressure curves is illustrated in fig. 5. Caused by the volumetric flow the maximum pressure level is higher than in the experiment.The influence of the cross-flow to the pressure is obvious in the region φ = ±20°.The incoming fluid affects the pressure in that region (shown by the fluctuation there).The size of the cavitation region is also affected by the higher pressure level in general.The shape of the cavitation region is similar to the simulation without cross-flow.The size of the cavitation region is smaller than in the simulation of the experiment.The reason for that is the higher pressure level in general.

With groove and without cross-flow
In the next step the model extended with a groove.The groove improves the oil supply for the journal bearing.
The groove consider φ = ±90° around the widest gap.Fig. 6 shows the comparison of the pressure curve between the experiment and the simulation with groove.
It is obvious that the groove has an influence on the pressure curve and cavitation region.The maximum pressure is 13.2% less than without groove.Founded in the larger gap size caused by the groove the pressure generation is affected.In the groove the pressure is nearly on a constant level.The reason for that is the wider gap there.This is also a reason for a smaller cavitation region.The shape of the cavitation region is influenced by the groove fig. 7.In the middle of the cylinder it is a bit compressed, founded in the position of the groove.The whole cavitation region is smaller than without groove.

Fig. 5 .
Fig. 5. Pressure plot of experiment, simulation of experiment and simulation with cross-flow

Fig. 6 .
Fig. 6.Pressure plot of experiment, simulation of experiment, simulation with cross-flow and simulation with groove

Table 1 .
Properties of the experiment

Table 2 .
Boundary conditions for the simulation.