Oil-lubricated bearings are widely used in high-speed rotating machines such as those found in automotive industries and aerospace. 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. The low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. This requires finer meshes for finite element modeling 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. Fitting the velocity profile with experiments having a nondimensional wall distance y+ in a certain range results in Ng-optimized Reichardt's constants k and δ+. The definition of y+ can be used to approximate the first layer thickness calculated for a uniform mesh. 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. This study proposed a new methodology to preserve the y+ value to make water-lubricated thrust bearing models valid. A method for determining the required number of cross-film elements in water-lubricated bearings was found. The results of this study could aid in improving future designs and models of water-lubricated bearings.

Oil-lubricated bearings are widely used in high-speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water-lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy viscosity, while eddy viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high-speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy viscosity for turbulence modeling. Eddy viscosity together with flow viscosity forms the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model's ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt's formula were used to model eddy viscosity in the fluid film. These methods are for determining where one wall's effects begin and the other wall's effects end. Trying to find a suitable model to capture the wall's effects of these bearings, with an aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil- and water-lubricated bearings.

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.

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries. However, with some applications including underwater machinery and environmentally friendly applications, water lubricated bearings have become increasingly used. Due to the different fluid properties between oil and water — namely viscosity — the use of water increases the Reynolds numbers drastically and, therefore, makes water-lubricated bearings prone to turbulence and fluid inertia effects. In other words, the linear approximation of the fluid film reaction forces due to the stiffness and damping parameters — as suggested in the traditional Reynolds equation — is not adequate and should be amended to include lubricant added mass. This is because water-lubricated bearings exhibit large lubricant inertia forces on the order of viscous forces. Additionally, stiffness and damping coefficients should be calculated with the turbulence effects included. The aim of this study was to investigate the methodology of modifying the traditional Reynolds equation to include lubricant inertia effects. This paper reviews the current status of research in the lubricant inertia of bearings and explores the development of methodologies to modify the Reynolds equation to include lubricant inertia in bearings. The Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films in lubrication theory. The thin film hypothesis is used to directly relate the bearing film thickness to the lubricant film pressure. Adding lubricant inertia to the Reynolds equation is vital to improving the accuracy of the bearing model and more specifically its film pressure which is essential to predicting load carrying capabilities. The film pressure relates the gradient of the velocity tensor through the Reynolds equation, and resulting shear stresses then allow the turbulent momentum equations to be written in terms of an eddy-viscosity value. An extended Reynolds equation should be developed which takes into account turbulence and both convective and temporal inertia. The most complete form of the temporal inertia effect model should be developed and applied to the turbulent regime, consisting of both primary and secondary temporal inertia terms. The convective inertia model follows Constantinescu’s approach. This analysis develops a lubricant inertia model applicable to water-lubricated bearings. The results of this study could aid in improving future designs and models of water-lubricated bearings.

Oil-lubricated bearings are widely used in high speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy-viscosity, while eddy-viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy-viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy-viscosity for turbulence modeling. Eddy-viscosity together with flow viscosity form the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model’s ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt’s formula were used to model eddy-viscosity in the fluid film. These methods are for determining where one wall’s effects begin and the other wall’s effects end. Trying to find a suitable model to capture the wall’s effects of these bearings, with aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil and water lubricated bearings.