Turbulence Input Parameters Correction Methodology in Water Lubricated Thrust Bearings

Abstract

Oil-lubricated bearings are widely used in high speed rotating machines such as those found in the aerospace and automotive industries. However, environmental issues and risk-averse operations are resulting in the removal of oil and the replacement of all sealed oil bearings with reliable water-lubricated bearings. Due to the different fluid properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. This requires finer meshes when compared to oil-lubricated bearings as the low-viscosity fluid produces a very thin lubricant film. Analyzing water-lubricated bearings can also produce convergence and accuracy issues in traditional oil-based analysis codes. Thermal deformation largely affects oil-lubricated bearings, while having limited effects on water lubrication; mechanical deformation largely affects water lubrication, while its effects are typically lower than thermal deformation with oil. One common turbulence model used in these analysis tools is the eddy-viscosity model. Eddy-viscosity depends on the wall shear stress, therefore effective wall shear stress modeling is necessary in determining an appropriate turbulence model. Improving the accuracy and efficiency of modeling approaches for eddy-viscosity in turbulence models is of great importance. Therefore, the purpose of this study is to perform mesh refinement for water-lubricated bearings based on methodologies of eddy-viscosity modeling to improve their accuracy. According to Szeri [1], εm/v for the Boussinesq hypothesis is given by Reichardt’s formula. Fitting the velocity profile with experiments having a y+ in the range of 0–1,000 results in Ng-optimized Reichardt’s constants k = 0.4 and δ+ = 10.7. He clearly states that for y+ > 1000 theoretical predictions and experiments have a greater variance. Armentrout and others [2] developed an equation for δ+ as a function of the pivot Reynolds number, which they validated with CFD simulations. The definition of y+ can be used to approximate the first layer thickness calculated for a uniform mesh. Together with Armentrout’s equation, the number of required elements across the film thickness can be obtained. For typical turbulence models, the y+ must be within a certain range to be accurate. On the condition that the y+ is fixed to that of a standard oil bearing for which an oil bearing code was validated, the number of elements across the film thickness and coefficients used in the eddy-viscosity equation can be adjusted to allow for convergence with other fluids other than that which the traditional oil bearing code was designed for. In this study, the number of required elements across the film for improved prediction quality was calculated based on the proposed eddy-viscosity model mesh correction from the known literature. A comparison between water lubrication using the parameter correction and oil lubrication was also made. The results of this study could aid in improving future designs and models of water-lubricated bearings.