Design of

Blood-Lubricated Bearings Using Fluent

Presentation to the 2003 Fluent User Group Meeting

Cambridge Technology Development, Inc.CTDCTD

Edward Bullister, Ph.D.

eb@alum.mit.edu

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 < InflowCouette Flow Becomes Unbalanced when Plates are not Paralllel

U U

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 Variable Computational Analogue

Pressure Temperature

Gap3/ Thermal Conductivity K

RHS Heat Source Q

Fluid Flux Heat 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 Solution Lubrication Approximation

Dimensions: 3 2

Equations: Full (Navier)-Stokes Energy

Force Predictions Comparison With Long–Bearing (L/D >> 1) Theory

L/D 1 10 100

Fluent Force Prediction (Newtons)

103 3860 42550

Exact Solution(Newtons)

Infinitely Long

428 4284 42840

Difference 76% 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 = 1- 10 mils 4 Contoured Quadrants

Thrust Bearing – Steep Contours

Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, lam)

Apr 09, 2003

1.63e+06

1.55e+06

1.47e+06

1.39e+06

1.31e+06

1.22e+06

1.14e+06

1.06e+06

9.80e+05

8.98e+05

8.16e+05

7.35e+05

6.53e+05

5.71e+05

4.90e+05

4.08e+05

3.27e+05

2.45e+05

1.63e+05

8.16e+04

0.00e+00

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

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