Download BREAKUP CHARACTERIZATION OF TWO

Breakup Mechanisms, Fluid Velocity
and Dimension Characteristics
in
Impinging Liquid Jets
Sunny Ri Li, Nasser Ashgriz
Department of Mechanical and Industrial Engineering
University of Toronto
Introduction
When two cylindrical jets of equal diameters collide they
form an expanding sheet in the plane at a right angle to the
plane containing the axes of the two jets.
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Multiphase Flows and Spray Systems Laboratory
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Experimental Method and Apparatus
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Breakup Regimes
Pre-sheet formation
Regime I:
Capillary Instability
(Closed-rim sheet)
Smooth sheet
Ruffled sheet
Open-rim sheet
Regime II:
Kelvin-Helmholtz
instability
Turbulent sheet
1. High-frequency circumferential waves
2. Very high Reynolds number
3. High impinging angle
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Multiphase Flows and Spray Systems Laboratory
Regime III:
Impact-wave
4
Breakup Regimes
- Critical Single-Jet & Impingement Reynolds Numbers
3500
Turbulent sheet
Reynolds number
3000
Re  Ud 
2500
Open-rim sheet
Ruffled sheet
2000
Smooth sheet
1500
1000
Pre-sheet formation
500
0
Impinging angle: 60 deg.
90 deg.
120 deg.
3500
Reynolds number
Ud  sin 
Re i 

3000
Turbulent sheet
2500
2000
1500
Open-rim sheet
Ruffled sheet
Smooth sheet
1000
500
Pre-sheet formation
0
Impinging angle: 60 deg.
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90 deg.
Multiphase Flows and Spray Systems Laboratory
120 deg.
5
Breakup Regimes - Critical Sheet Reynolds Numbers



hi  R sin  e   1 e  1  
hA 
…..Thickness of the impact region



he   /  U 2 sin 2 [ / 2eln2 /  1 /   ]
Re s 
700
Reynolds number of the sheet
600
  U  hA

 sin  2e

U 2
….Edge thickness of the sheet
R  sin 


h

h
d


0 e i
2

1
2
2
ln  2  1  
0


1
d
90 deg.
120 deg.
Turbulent sheet
500
Impinging angle: 60 deg.
400
Open-rim sheet
300
Ruffled sheet
Smooth sheet
200
Pre-sheet formation
100
0
0
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500
1000
1500
2000
2500
Reynolds number of the jet
3000
Multiphase Flows and Spray Systems Laboratory
3500
4000
6
Surface Velocity - Experimental Method
The surface velocity, which is defined here as the stream velocity
on the sheet, was determined by measuring the wave motion on the
surface.
Measurement was made on two angular positions on the sheet: 0
and 25 degree.
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Multiphase Flows and Spray Systems Laboratory
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Surface Velocity - Distribution of Surface velocity
1.4
Mean jet velocity
1.3
Surface velocity
at 0 deg.
Surface velocity
at 25 deg.
Deviation
Velocity (V/U)
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
2
3
4
5
6
Mean jet velocity (m/s)
7
8
(Impinging angle 90 deg.)
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Dimensional Characteristics - Equations
The following equations are based on the work of Taylor [1959] and
Ibrahim [1991], which assumed the fluid velocity throughout the
sheet is equal to the mean jet velocity.

 

L  R 2 U 2 e  sin 2   1 / 2 e   1
….Maximum length
  cot max   1  cos  eln2  1    
eln2  1   ln 2  sin   eln2  1   
max
max
max
W  2  re max   sin  max 
….Maximum width
 e  1
1

Where β can be obtained by solving cos    
2
 e  1  1    
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Dimensional Characteristics - Total Length
35
30
90 deg.
120 deg.
60 deg.
60 deg.
90 deg.
exp. (120)
Theoretical:
Length (mm)
25
Experiemntal:
20
15
10
5
0
0
1
2
3
4
5
6
7
8
Mean jet velocity (m/s)
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Dimensional Characteristics - Maximum Width
25
60 deg.
90 deg.
120 deg.
60 deg.
90 deg.
120 deg.
Experiemtal:
20
Width (mm)
Theoretical:
15
10
5
0
0
1
2
3
4
5
6
7
8
Mean jet velocity (m/s)
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Dimensional Characteristics - Review of Early Theory

sin 2   2 /  U 2 he

Taylor [1959] assuming the fluid velocity
on the sheet equal to jet velocity
To retain its validity for non-uniform fluid velocity on the sheet,
    sin 1 2 V 2 he   sin 1 2 U 2 he 
V : Fluid velocity on the sheet
he : Edge thickness of the sheet with non-uniform velocity distribution
0.5
0.5
he : Edge thickness of the sheet with uniform velocity distribution

e
V h  U he
2
2
U 
he  he  
V 
When V  U ,
When
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V  U,
2
he h e
he h e
Multiphase Flows and Spray Systems Laboratory
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Dimensional Characteristics – Edge Thickness
Ibrahim [1991]:


he  2 /  U 2 sin 2 [ / 2eln2 /  1 /   ]
0.02
0.018
Thickness (mm)
2   2
0.016
U  3.98m / s
0.014
0.837 mm
0.012
0.084 mm
0.01
0.008
-4
-3
-2
-1
0
1
2
3
4
Angular position on the sheet (radian)
1) The edge thickness of the sheet thickness cannot be predicted by assuming
uniform velocity on the sheet.
2) The real edge thickness is has higher order of magnitude than the ideal thickness.
3) he hi  R sin   r e eliminates the drawback, hereby making the subsequently
derived equations still valid.
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Conclusions
1. Three major breakup regimes of the liquid sheet
were identified in this work, namely capillary
instability regime, Kelvin-Helmholtz instability regime
and impact wave regime.
2. The distribution of fluid velocity on the sheet was
examined and found not uniform throughout the
sheet.
3. The dimensional characteristics of the spray sheet
were investigated by reviewing early theories. It was
found that the theories can predict the shape of the
sheet but not the sheet thickness.
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Multiphase Flows and Spray Systems Laboratory
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