Investigating the Influence of a Coupled Formulation on Journal - - PowerPoint PPT Presentation

Investigating the Influence of a Coupled Formulation on Journal Bearing Models

Student: Jacq Crous Supervisor: Stephan Heyns Co-Supervisor: Jaco Dirker

Context of Study – Rotor-Bearing-Seal System:

This study was concerned with the bearing models.

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Context of Study – Bearing:

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Context of Study:

Condition based monitoring Effective analysis of the available data Realistic models

• In order to monitor the condition of steam turbines in real time we need to use

the available information more effectively.

• This requires the development of a complete, realistic model of the rotor-bearing

system.

• Armand Kruger is working on the rotor model and my study was concerned with

the bearing models.

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The Issue:

Multi-Grade Oil

Polymer additives Solvent: Mineral Oil

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Fluid Models:

Viscoelastic Formulation Viscous Formulation

• Fluid motion is modelled by the Cauchy

equation of motion (neglecting body forces):

̅ ̅ ∙ ̅ ∙ ̿

• Density of the fluid.

̅ - Velocity field.

• Pressure field.
• Extra-stress tensor.
• Fluid behaviour modelled by a

generalized Navier-Stokes Formulation:

̅ ̅ ∙ ̅ ∙ ̅ ̅

• Density of the fluid.

̅ - Velocity field.

• Pressure field.

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 The first law of thermodynamics in differential form, for

incompressible fluids, is used to model the heat transfer:

• ̅ ∙

: ̅ ∙

• heat capacity of fluid.

k - Thermal conductivity of the fluid.

• Cauchy stress tensor

Heat Transfer:

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Numerical Solvers:

 OpenFOAM was used to develop the numerical solvers.  OpenFOAM is a C++ library that provides various

interpolation schemes as well as algebraic solvers.

 OpenFOAM solves PDEs and can give tensor, vector

and scalar fields as outputs.

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Coupling of Fluid Formulations:

Viscoelastic Formulation Viscous Formulation

Velocity Field Temperature Field Viscosity Dependencies

Velocity Field Temperature Field Polymer Stress Field Viscosity Dependencies

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Solvers Developed:

Viscoelastic Formulation

Giesekus Fluid

Oldroyd-B Fluid

Viscous Formulation

Viscous Fluid Stokes Flow

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Driving Forces for the Flow:

Shearing of Oil

Rotating Journal

Simulation of a full scale journal bearing would require 5 10 control volumes!

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Alternative Approach

 A section of the bearing is extracted form the converging

section of the bearing.

 The extracted section has the same driving forces in the

same measure as the corresponding point in the bearing.

Oil Journal

Converging section

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Weak Coupling - Viscous Formulation:

0.2 0.4 0.6 0.8 1 20 40 60 80

R/C V [m/s]

Velocity Profiles

Coupled Stokes Formulation Coupled Viscous Formulation Uncoupled Viscous Formulation Classical Formulation 0.02 0.04 0.06 0.08 0.1 0.12 0.2 0.4 0.6 0.8 1

∆ R/c

Difference between formulations

Coupled Stokes Formulation Coupled Viscous Formulation Uncoupled Viscous Formulation

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Weak Coupling – Viscoelastic Formulation:

0.2 0.4 0.6 0.8 1 20 40 60 80 100

R/c V [m/s]

Velocity Profiles

Coupled Giesekus Coupled Oldroyd-B Classic Formulation 0.01 0.02 0.03 0.04 0.05 0.06 0.2 0.4 0.6 0.8 1 1.2

∆ R/c

Difference between formulations

Coupled Oldroyd-B Coupled Giesekus

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Strong Coupling – Viscous Formulation:

0.2 0.4 0.6 0.8 1 1.2 50 100 150 200

R/c V [m/s]

Velocity Profiles

Coupled Stokes Formulation Coupled Viscous Formulation Uncoupled viscous formulation Classical Formulation 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.2 0.4 0.6 0.8 1 1.2

∆ R/c

Difference between formulations

Coupled Stokes Formulation Coupled Viscous Formulation Uncoupled Viscous formulation

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Strong Coupling – Viscoelastic Formulation:

0.2 0.4 0.6 0.8 1 1.2 20 40 60 80 100 120

Velocity Profiles

Strong Coupled Formulation (Giesekus) Weaker Coupled Formulations (Oldroyd-B) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2 0.4 0.6 0.8 1 1.2

Difference between formulations

Strong Coupled Formulation (Giesekus) Weaker Coupled Formulation (Oldroyd-B)

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Conclusion:

 The coupling, whether weak or strong, was seen to

significantly affect the fluid behaviour.

 The Strong coupling was seen, in particular, to change

the nature of the flow behaviour by departing form the classical formulation in a non-homogeneous way.

 A coupled formulation is vitally important to accurately

model large scale journal bearings!

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Questions?

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