# Novel Numerical Analysis of a Self-Circulating Bearing
## 3 Results and Discussion
The relaxation factors for the pressure iteration could be employed to achieve convergence, but the simulation would no longer be time accurate. The similar load capacity behavior of the two larger permeabilities demonstrates one of the more helpful aspects of a numerical model--finding design plateaus. Designers will know there is no significant increase in load capacity for permeability changes above \(10^{-12}\) for the current bearing dimensions and environment. Readers are reminded that the injection velocity, which drives the bearing load and stability, is directly affected by the passive reservoir pressure. The pressure within this reservoir, while currently set to a constant value, would be affected in application by the initial charge of fluid into the system and the amount of side leakage. An important advancement in the modeling effort will be to realistically model the side leakage and, in practice, demonstrate the need for good seals on the axial ends of the bearing. The sub-figure demonstrates that there is also an increase in bearing stability to accompany the increase in load capacity, as the attitude angle is larger at each eccentricity. The approach towards the semi-circle shape characteristic of a solid journal bearing becomes apparent as the permeability decreases [25,26]. The increased load capacity for increased permeability has been demonstrated experimentally for porous journal bearings, along with a higher attitude angle [27]. These experimental results show  
Figure 6: Effect of changing bushing thickness (**a**) and permeability (**b**) on injection velocity. that, with the correct reservoir dimensions, the behavior of the self-circulating bearing mimics that of a porous journal bearing. A thicker bushing is shown to promote a larger bearing load capacity in Figure 8; this is expected from the lower injection velocity shown in Figure 6a. The passive reservoir pressure was lower than the pressure developed in the bearing clearance, so a larger restriction on the fluid leaving the clearance provided a larger load capacity. Due to the low change in feeding parameters, the difference in load capacity, as well as the stability, was minimal. This information highlights that self-circulating bearing characteristics can be altered significantly without requiring more real estate (larger bushing radius), which is beneficial for many applications. Increasing the bushing thickness will limit the fluid leaving the bearing clearance, which increases the load capacity. This would be relevant for applications with low speed and cool temperatures that are not at severe risk for vaporous cavitation. Applications at high vaporous cavitation risk would aim to promote fluid motion to lower the overall fluid temperature. While the results demonstrated here are valuable, the limitations of the current model require discussion. The constant property assumption may prove to be unrealistic for high-speed applications or those with large temperature differentials. The model also assumes constant supply pressure which, in application, would vary. The foundation created with this numerical model will allow for future versions to account for temperature-dependent fluid properties, multigrade fluids, and cavitation. The next proposed step in developing the model is to include gaseous cavitation to vary the fluid properties throughout bearing operation. Future applications could also include adaptations for textured porous bushings. Once the energy equation is incorporated, vaporous cavitation and heat transfer studies within the bearing will be of value for designers to recognize functioning limits based on cavitation and heat transfer. Figure 7: Effect of changing permeability on bearing load capacity and stability.