1. Characteristics of Two-phase Flows in Vertical Pipe
W. G. Sim/Hannam University, N. W. Mureithi/ Ecole Polytechnique, Montreal,
B.M. Bae/KAERI, M.J. Pettigrew/ Ecole Polytechnique, Montreal,

2. Characteristics of Two-phase Flows in Vertical Pipe
Hannam University
Characteristics of Two-phase Flows in Vertical Pipe
W. G. Sim/Hannam University, N. W. Mureithi/ Ecole Polytechnique, Montreal,
B.M. Bae/KAERI, M.J. Pettigrew/ Ecole Polytechnique, Montreal,
ABSTRACT: The characteristics of two-phase flow in a vertical pipe are investigated to gain a better understanding of vibration excitation mechanisms. An analytical model for two-phase flow in a pipe was developed by Sim et al. (2005), based on a power law for the distributions of flow parameters across the pipe diameter, such as gas velocity, liquid velocity and void fraction. An experimental study was undertaken to verify the model. The unsteady momentum flux impinging on a ‘turning tee’ (or a ‘circular plate’) has been measured at the exit of the pipe, using a force sensor. From the measured data, especially for slug flow, the predominant frequency and the RMS value of the unsteady momentum flux have been evaluated. It is found that the analytical method, given by Sim et al. for slug flow, can be used to predict the momentum flux.

3. Hannam University , Ecole Polytechnique Montreal
Contents
Introduction
Drift Flux Model for Two-phase Flow in a Pipe
o Power Law for Distributions of Flow Parameters
o Average Values with Integral Analysis
o Reynolds Transport Theorem
Steady Momentum Flux, Unsteady Momentum Flux for Slug Flow
Experimental Investigations
o Test Loops
o Comparisons with Theory
Conclusions
Hannam University , Ecole Polytechnique Montreal

4. Hannam University , Ecole Polytechnique Montreal
Introduction
Initial Motivation
o Slender Structural Elements - Fretting Wear Damage
o Flow Mechanism of Two-phase Flow
Homogeneous Model - Only for Bubbly Flow
o Hydrodynamic Force – Momentum Flux
o Analytical Approach for Dynamic Response
Experimental Study, Reliable Prediction of Dynamic Response
Main Purpose
o To investigate characteristics of two-phase flow in vertical pipe
an analytical model proposed based on a power law, experimental study undertaken
o To verify the analytical model, with experimental results
o To obtain information on the reaction force
Hannam University , Ecole Polytechnique Montreal

5. Drift Flux Model for Two-phase Flow in a Pipe
Power Law for Distributions of Flow Parameters
Assumptions;
- neglecting adherence or reflection of bubble at the surface of the wall
Distributions of Flow Parameters
Void Fraction Velocity distribution
for bubbly flow for slug flow for gas and liquid
* Subscript “L” stands for local time average value
Hannam University , Ecole Polytechnique Montreal

6. Average Values with Integral Analysis
Void Fraction
Velocity
Volumetric Quality
Flow Quality
Slip Ratio
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7. Reynolds Transport Theorem
Momentum Equation
where
Hannam University , Ecole Polytechnique Montreal

8. Hannam University , Ecole Polytechnique Montreal
Steady Momentum Flux
o Momentum Flux by Liquid
o Momentum Flux by Gas
Momentum Multiplier
where mass flux
Hannam University , Ecole Polytechnique Montreal

9. Unsteady Momentum Flux for Slug Flow
Void Fraction;
Formulation;
- Frequency for Slug Flow by Heywood and Richardson(1979)
- Sequence of Momentum by liquid and Gas; Fourier series
C= for vertical flow C = for horizontal flow
Reduced Frequency;
Hannam University , Ecole Polytechnique Montreal

10. Unsteady Momentum Flux for Slug Flow
By Liquid
By Gas
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11. Hannam University , Ecole Polytechnique Montreal
RMS Value of Reaction Force by Slug Flow
Hannam University , Ecole Polytechnique Montreal

12. Experimental Investigations
Test Loops
EPM HNU
EPM
HNU
Test Cylinder
Length (m)
1.52
1.01
Inner Diameter (mm)
20.8 30
Mixture
Fine screen
Multiple inlet holes (equally distributed )
High contraction ratio
Control volume for the reaction force
Turning Tee
Circular Plate (Diameter=280 mm)
Hannam University , Ecole Polytechnique Montreal

13. Hannam University , Ecole Polytechnique Montreal
Flow patterns (Taitel et al., 1980) selected for bubbly and slug flow and dynamic time traces of the dynamic reaction force(HNU)
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14. Typical force spectra given by EPM for
Hannam University , Ecole Polytechnique Montreal

15. Typical force spectra given by HNU
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16. Steady parameters given by HNU ( )
Blue; Green; Red;
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17. Comparison of test results to analytical results ( __, o ; ) for
sec sec
EPM HNU
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18. Hannam University , Ecole Polytechnique Montreal
Comparison of test results to analytical results ( _ _ , ___ ; ) for (Blue) and (Red)
HNU EPM
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19. Reduced Frequency (Azzopardi and Baker, 2003)
EPM
HNU
Hannam University , Ecole Polytechnique Montreal

20. Hannam University , Ecole Polytechnique Montreal
Conclusions
An analytical model for two-phase flow in a pipe, based on a power law
The integral forms easily incorporated into models for momentum flux
Reaction force exerted by the momentum flux at the exit of the pipe.
– Two air-water loops were constructed.
– Momentum Flux (for bubbly flow; , slug flow; )
– Force spectra (for bubbly flow, slug flow)
– Reduced frequency (for slug flow)
Good agreement shown between the results
Hannam University , Ecole Polytechnique Montreal