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. 2

3 Context of Study – Bearing:

Context of Study: Condition Effective Realistic based analysis of the models monitoring available data  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. 4

5 Mineral Oil Polymer additives Solvent: The Issue: Multi-Grade Oil

Fluid Models: Viscoelastic Formulation Viscous Formulation   Fluid motion is modelled by the Cauchy Fluid behaviour modelled by a equation of motion (neglecting body generalized Navier-Stokes Formulation: forces): � ��̅ �� � �̅ ∙ � �̅ � ��̅ �� � �̅ ∙ � �̅ � ��� � � ∙ �̿ � ��� � � ∙ � ��̅ � � � � �̅ � - Density of the fluid. �̅ - Velocity field. � - Density of the fluid. � - Pressure field. �̅ - Velocity field. � � - Extra-stress tensor. � - Pressure field. 6

Heat Transfer:  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 7

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. 8

Coupling of Fluid Formulations: Viscoelastic Formulation Viscous Formulation Velocity Field Velocity Field Viscosity Temperature Dependencies Field Viscosity Temperature Polymer Dependencies Field Stress Field 9

Solvers Developed: Viscoelastic Viscous Formulation Formulation Viscous Giesekus Fluid Fluid Stokes Oldroyd-B Fluid Flow 10

Driving Forces for the Flow: Rotating Journal Shearing of Oil Simulation of a full scale journal bearing would require 5 � 10 � control volumes! 11

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 12 Converging section

Weak Coupling - Viscous Formulation: Difference between formulations Velocity Profiles 0.12 1 0.1 0.8 0.08 0.6 R/C ∆ 0.06 0.4 0.04 0.2 0.02 0 0 0 20 40 60 80 0 0.2 0.4 0.6 0.8 1 V [m/s] R/c Coupled Stokes Formulation Coupled Stokes Formulation Coupled Viscous Formulation Coupled Viscous Formulation Uncoupled Viscous Formulation Classical Formulation Uncoupled Viscous Formulation 13

Weak Coupling – Viscoelastic Formulation: Difference between Velocity Profiles formulations 1 0.06 0.05 0.8 0.04 0.6 R/c ∆ 0.03 0.4 0.02 0.2 0.01 0 0 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 1.2 V [m/s] R/c Coupled Giesekus Coupled Oldroyd-B Classic Formulation Coupled Oldroyd-B Coupled Giesekus 14

Strong Coupling – Viscous Formulation: Difference between Velocity Profiles formulations 1.2 1.6 1.4 1 1.2 0.8 1 ∆ 0.8 R/c 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 50 100 150 200 R/c V [m/s] Coupled Stokes Formulation Coupled Stokes Formulation Coupled Viscous Formulation Coupled Viscous Formulation Uncoupled Viscous 15 Uncoupled viscous formulation Classical Formulation formulation

Strong Coupling – Viscoelastic Formulation: Difference between Velocity Profiles formulations 1.2 0.7 0.6 1 0.5 0.8 0.4 0.6 0.3 0.4 0.2 0.2 0.1 0 0 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 1.2 Strong Coupled Formulation (Giesekus) Strong Coupled Formulation (Giesekus) Weaker Coupled Formulations (Oldroyd-B) Weaker Coupled Formulation (Oldroyd-B) 16

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! 17

Questions? 18