Design of Blood-Lubricated Bearings Using Fluent Presentation to the 2003 Fluent User Group Meeting Cambridge Technology Development, Inc. CTD Edward Bullister, Ph.D.

Overview  Physics of Thin-Film Lubrication  Governing Equations of the Lubrication Approximation  Numerical Implementation in Nekton Fluent  Example Problems  Steady  Unsteady

Physics of Lubrication Outflow < Inflow Couette Flow Becomes Unbalanced when Plates are not Paralllel UU

Approximation to N-S Equations  Assumptions:  Laminar Flow, Re Small (no inertia)  L/B - Large (reasonable; typically ~1000)  No Slip  Incompressible Case Presented Here

Lubrication Analogues Physical VariableComputational Analogue PressureTemperature Gap 3 /  Thermal Conductivity K RHSHeat Source Q Fluid FluxHeat Flux Note:  μ

Implementation in Fluent  UDFs for:  Material Properties  Heat Source  In Nonplanar Bearings, Integration of Pressure x- and y- Components

Computational Work Comparison Direct SolutionLubrication Approximation Dimensions:32 Equations:Full (Navier)-StokesEnergy

Force Predictions Comparison With Long–Bearing (L/D >> 1) Theory L/D Fluent Force Prediction (Newtons) Exact Solution(Newtons) Infinitely Long Difference76%10%0.6%  Conditions:  No cavitation (continuous film)  D = 40 mm; 3500 RPM; Gap = 2 mils; ε = 0.1; μ = 5 cp  Close Agreement where exact Solution is valid

Details of Journal Bearing at L/D = 1 Pressure (Pascal)

Cavitating Journal Bearing at L/D = 1 Pressure (Pascal)

Thrust Bearing  D = 40mm  ω = 3500 RPM  h = mils  4 Contoured Quadrants

Thrust Bearing – Steep Contours Pressure Footprint Beneath Rotating Thrust Bearing (Plotted via its Temperature Analogue) Computational Grid

Stiffened Thrust Bearing

Example: Unsteady Bearing

Bearing Stability Continuous vs. Cavitating  

Trajectories in Stable and Unstable Bearings

Stability Problem  Eigenvalue Analysis  Predicts continuous film bearing neutrally stable:  = 0 + i  /2  Simulations  Use unsteady time stepping procedure  Simulate with initial bearing eccentricity not at equilibrium with steady applied load  Track motion of piston in response to net forces

Unsteady Simulation Results  Bearing takes Circular Orbit around equilibrium position  Period of Orbit about ½ that of cylinder rotation consistent with: Eigenvalue Analysis Experimentally Observed “whirl” instability Trajectory of Simulated Bearing

Recommendations  Design for sufficient load capacity to maintain allowable gaps at operating speeds  For continuous film bearings, avoid symmetry  For unstable bearings, avoid symmetry

 Design of Fluidic Devices  Design Support and Analysis  CFD Analysis Brought to you by… attbi.com