Taylor Vortices Induced Instability and Turbulence in Journal Bearing Microscale Flow

Abstract

This paper elaborates on the relationship between the onset and the development of the Taylor instability and their relationship to the phenomenon of what is accepted to be “turbulence” in the narrow gaps of concentric and eccentric cylinders. When do bearings function in the Taylor instability regime and when in the actual turbulent regime? To start answering this question, the viscous flow in the gap (0.01 in.) between two cylinders with eccentricities varying from 0.0 to 0.8 is investigated by using commercial software. The inner cylinder is rotating while the outer one is at rest. The fluid between the two cylinders is a silicone oil (ρ = 1048 kg/m ³ and μ = 0.099 kg/m-s). This research has found that Taylor vortices (cells) begin to form at certain but different “critical” speeds as a function of eccentricity. As the speed grows, the vortices become fully developed and evolve further into wavy patterns. Calculations show that critical speed itself increases monotonically with the increase in eccentricity. The onset of instability is clearly characterized by a discontinuity in the Torque-√Ta curve slope. For the cases with eccentricities ≤0.4, the change in slope of the Torque-√Ta graph is clearly visible, while for the cases with eccentricities > 0.4, the slope change is less noticeable. These torque slope changes are considered indicative of increases in the apparent fluid viscosity. To be noted, historically, changes in the fluid viscosity have also been associated with the changes from the laminar to the turbulent regime flow in a bearing. It will be shown here that, in fact, for a large range of operational conditions that cover the Taylor flow instability regime, it is the velocity gradient at the wall, rather than the viscosity, that changes considerably and is responsible for the discontinuity in the Torque-√Ta curve slope. The positions of the maximum vortex intensity vary from θ = 0° to θ = 120° downstream of the maximum clearance as the speeds and eccentricities vary. To validate the results presented herein, a comparison is made between present calculations and the data of DiPrima ( 1 ), DiPrima and Stuart ( 2 ), Vohr ( 3 ), and Cole ( 4 )–( 6 ). The two sets of results are in good agreement with each other.

KEY WORDS:

• Taylor Vortices
• Instability
• Turbulence
• Narrow Gap
• Taylor Number
• Flow Pattern
• Velocity Profile
• Velocity Gradient

Acknowledgments

Presented at the STLE 60th Annual Meeting and Exhibition in Las Vegas, Nevada May 15-19, 2005, Review led by Josiah Knight