Bubble formation at multiple orifices

BUBBLE FORMATION AT MULTIPLE ORIFICES

XIE SHUYI
(B. ENG, TJU)

A THESIS SUBMITTED
FOR THE DEGREE OF MASTER OF ENGINEERING
DEPARTMENT OF CHEMICAL AND ENVIRONMENTAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2003


ACKNOWLEDGEMENTS

I am greatly indebted to my supervisor, Assoc. Prof. Reginald B. H Tan, for his
invaluable guidance and constructive advice throughout this project. I am very fortunate
to have been his student during the years of this study. Without him, this work could not
have been possible.

Many people in the Department of Chemical and Environmental Engineering at National
University of Singapore also gave invaluable support to this project. Particular thanks go
to Dr. Wang Chi-Hwa for providing part of experimental facilities; Mr. Og Kim Poi and
other workshop staff for their help in constructing the experimental apparatus; colleagues
in the laboratory, particularly Dr. Zhang Wenxing, Dr. Deng Rensheng, Dr. Zhu Kewu
and Mr. Zhang Minping for their supportive comments and cheerful assistance.

Special thanks are also due my beloved family members, who always support me and
help me in so many ways. This thesis is dedicated to them.

Finally, I would also like to thank National University of Singapore, for awarding me
with scholarship and every possible practical help to facilitate my work.

i


TABLE OF CONTENTS

Acknowledgements

i

Table of contents

ii

Summary

vii

Nomenclature

ix

List of Figures

xii

List of Tables

xiv

Chapter 1 Introduction

1

1.1 Background

1

1.2 Objective of this work

2

1.3 Organization

3

Chapter 2 Literature Review
2.1 Bubble formation at single orifice

5
5

2.1.1 Bubbling dynamics

6

2.1.1.1 Static regime

6

2.1.1.2 Dynamic regime

7

2.1.1.3 Jetting regime

9

2.1.2 Physical factors affecting bubble formation

10

ii


2.1.2.1 Chamber volume

10

2.1.2.2 Orifice diameter

11

2.1.2.3 Liquid depth

13

2.1.2.4 Liquid properties

14

2.1.2.5 Gas properties

15

2.1.2.6 Liquid cross-flow

16

2.1.2.7 Static system pressure

17

2.1.3 Mathematical modeling

19

2.1.3.1 Spherical models

20

2.1.3.2 Non-spherical models

21

2.2 Bubble formation at multiple orifices

23

2.2.1 Experimental studies

23

2.2.2 Theoretical development

26

2.3 Summary

Chapter 3 Model Description

27

29

3.1 Assumptions

29

3.2 Bubble frequency f

31

3.3 Gas velocity through each orifice Vg

32

3.4 Gas chamber pressure Pc

33

Chapter 4 Experimental Work

35

4.1 Experimental apparatus

35

iii


4.1.1 Bubble column

36

4.1.2 Gas chamber

37

4.1.3 Orifice insert

38

4.1.4 Orifice plate

39

4.1.5 Gas supply system

39

4.2 Measurement techniques

40

4.2.1 Dynamic pressure transducer

40

4.2.2 High-speed video camera

41

4.3 Experimental conditions and procedures

Chapter 5 Results and Discussion
5.1 Bubbling modes at two orifices
5.1.1 Visualization

44

48
48
49

5.1.1.1 Synchronous bubbling

50

5.1.1.2 Alternate bubbling

50

5.1.1.3 Unsteady bubbling

51

5.1.2 Chamber pressure fluctuation

51

5.1.2.1 Synchronous bubbling

55

5.1.2.2 Alternate bubbling

55

5.1.2.3 Unsteady bubbling

56

5.1.3 Fast Fourier result

57

5.1.3.1 Synchronous bubbling

57

5.1.3.2 Alternate bubbling

58

iv


5.1.3.3 Unsteady bubbling
5.2 Effect of bubbling conditions on bubbling synchronicity and frequency

58
60

5.2.1 Orifice spacing

60

5.2.2 Liquid depth

65

5.3 Reproducibility of experimental data

67

5.4 Measurement of synchronicity

68

5.5 Comparison between model predictions and experimental results

70

5.5.1 Bubble frequency

70

5.5.1.1 Gas chamber volume

72

5.5.1.2 Orifice number

75

5.5.1.3 Comparison of experimental and calculated frequencies

75

5.5.2 Bubble radius

75

5.5.2.1 Gas chamber volume

77

5.5.2.2 Orifice number

78

5.5.3 Calculated gas chamber pressure fluctuations

Chapter 6 Conclusions and Recommendations
6.1 Conclusions

79

81
81

6.1.1 Conclusions from experimental investigations on
two-orifice bubbling behavior
6.1.2 Conclusions from mathematical modeling
6.2 Recommendations for future study

81
82
84

v


References

85

Appendix Sample Calculation

93

vi


SUMMARY

This work presents a systematic study of bubbling synchronicity and frequency for
bubble formation at multiple (two to six) orifices. In addition, a simple mathematical
model is proposed to predict bubble frequency and bubble size in synchronous multiorifice bubbling. Experimental results under various conditions are compared with the
model predictions.

High speed video images were applied to visualize bubble formation at the multiple
orifices. A highly sensitive dynamic pressure transducer was employed to record the
instantaneous pressure fluctuations in the gas chamber and time-pressure signals were
used to obtain bubble frequency via Fourier transform.

Regimes of synchronous, alternative and unsteady bubbling were clearly identified, and
the effects of orifice spacing and liquid depth on bubbling synchronicity and frequency
were studied. It is found that the degree of synchronicity generally decreases at high gas
flowrates due to the onset of unsteady bubbling. Both the orifice spacing and liquid depth
can affect the bubbling synchronicity via liquid pressure effects due to bubble-to-bubble
interaction, coalescence and the wake pressure of preceding bubbles.

vii


The modified theoretical model for predicting synchronous bubble frequency in multiorifice bubble formation works well. The predicted values of frequency under a variety of
operating conditions agreed within ±15% with experimental data in the highly

synchronous bubbling regime. These results should provide a sound basis for further
fundamental studies into bubble formation phenomena at multiple orifices.

viii


NOMENCLATURE

Symbol

Description

Unit

a

bubble radius

m

A

orifice area

m2

b

thickness of plate

m

Bo

Bond number, ( Bo = ρ l d 0 g / σ )

c

sound velocity in the gas

do

orifice diameter

CG

orifice coefficient for gas flow

D

diameter of gas chamber

m

f

bubble frequency

s-1

f'

fanning friction factor

Fr

Froude number, ( Fr = V g / d 0 g )
2

dimensionless

g

acceleration due to gravity

m.s-2

H

liquid height

Nc

capacitance number, N c =

Nc

2

'

dimensionless

m.s-1
m

dimensionless

dimensionless

m

capacitance number, N c =
'

g ( ρ l − ρ g )Vc
Aρ g c 2

ρ l gVc
A Ps

dimensionless

dimensionless

ix


N Re

Reynolds number, N Re = 4 ρ g Q / πd 0 µ g

dimensionless

Nw

gas flow rate number

dimensionless

N or

number of orifices

dimensionless

Pb

bubble pressure

Pa

Pc

chamber pressure

Pa

PcDET

chamber pressure at bubble detachment

Pa

Por

liquid pressure at orifice

Pa

Ps

static pressure at orifice

Pa

Pwo

wake pressure at orifice

Pa

Q

average gas injection rate to the chamber

m3.s-1

q

average gas flow rate through each orifice

m3.s-1

s

spacing

m

s or

the perpendicular distance between bubble center and orifice

m

ro

orifice radius

m

t

time

s

tf

bubble formation time

s

tw

waiting time

s

T

time during waiting

s

U

bubble vertical rising velocity

m.s-1

Ul

uniform liquid cross-flow velocity across orifices

m.s-1

VB

bubble volume

m3

x


Vc

chamber volume

Vg

average gas velocity through each orifice

m3
m.s-1

Greek symbols
Symbol

Description

Unit

γ

adiabatic exponent

µg

gas viscosity

σ

surface tension

ρg

gas density

kg.m-3

ρl

liquid density

kg.m-3

dimensionless

kg.m-1.s-1
N.m-1

xi


LIST OF FIGURES

Fig. 2.1

Bubbling state diagram of McCann and Prince (1971) from a 9.4
mm orifice in an air-water system

9

Fig. 2.2

The results of Park et al. (1977)

12

Fig. 2.3

Bubble volume vs. gas flowrate for five system pressures
(adapted from La Nauze and Harris, 1974)

18

Transition of bubbling regimes under different pressure systems
for orifice diameter 3.2 mm and 4.8 mm (adapted from La Nauze
and Harris, 1974)

19

Bubble volume vs. gas flowrate (left) and bubble volumes vs. the
radio between gas chamber volum and orifice number (adapted
from Titomanlio, Rizzo and Acierno (1974)

25

Fig. 3.1

Schematic diagram of physical system

30

Fig. 3.2

Typical gas chamber pressure vs. time for a bubble formation
period

32

Fig. 4.1

Experimental set-up

36

Fig. 4.2

Orifice insert configuration

38

Fig. 4.3

Pressure transducer system

41

Fig. 4.4

High-speed video camera system

42

Fig. 4.5

Typical high-speed frame for bubble formation at a two-orifice
plate

43

High-speed photographic images of bubble formation Vc = 480
cm3, d0 = 1.6 mm, H = 30 cm , s = 1 cm and (a) Q = 2.5 cm3/s; (b)
Q = 4.2 cm3/s; (c) Q = 8.3 cm3/s

52

Chamber pressure fluctuations: Vc = 480 cm3, d0 = 1.6 mm, H = 30
cm, s = 1 cm and (a) Q = 2.5 cm3/s; (b) Q = 4.2 cm3/s; (c) Q = 8.3
cm3/s. Total time = 20 s

56

Fig. 2.4

Fig. 2.5

Fig. 5.1

Fig. 5.2

xii


FFT analysis of chamber pressure fluctuations: Vc = 480 cm3, d0 =
1.6 mm, H = 30 cm, s = 1 cm and (a) Q = 2.5 cm3/s; (b) Q = 4.2
cm3/s; (c) Q = 8.3 cm3/s

58

Percentage of synchronous bubbling versus gas flowrate: Vc = 480
cm3, d0 = 1.6 mm, H = 30 cm. (a) s = 1 cm; (b) s = 4 cm

62

Bubbling frequency and synchronicity for different orifice spacing:
Vc = 480 cm3, d0 = 1.6 mm, H = 30 cm

64

Bubbling frequency and synchronicity for different liquid depths:
Vc = 560 cm3, d0 = 1.6 mm, s = 4 cm

66

Fig. 5.7

Reproducibility of bubble frequency

67

Fig. 5.8

Comparison of average gas velocity vs. frequency between model
predictions and experimental data with chamber volume as a
parameter. Nor = 3, d0 = 1.6 mm, H = 30 cm, s = 4 cm, b = 1 mm,
system: air-water

73

Comparison of frequency between model predictions and
experimental data with orifice number as a parameter. Vc = 480
cm3, d0 = 1.6 mm, H = 30 cm, s = 4 cm, b = 1 mm, system: airwater

74

Measure vs. calculated values of frequency. d0 = 1.6 mm, H = 30
cm, s = 4 cm, b = 1 mm, system: air-water

76

Comparisons of average bubble radius between model predictions
and experimental data with chamber volume as a parameter. Nor =
3, d0 = 1.6 mm, H = 30 cm, s = 4 cm, b = 1 mm, system: air-water

77

Comparison of average bubble radius between model predictions
and experimental data with orifice number as a parameter. Vc =
480 cm3, d0 = 1.6 mm, H = 30 cm, s = 4 cm, b = 1 mm, system: airwater

78

Calculated gas chamber pressure during a bubbling for chamber
volume 480 cm3 and 970 cm3

80

Fig. 5.3

Fig. 5.4
Fig. 5.5
Fig. 5.6

Fig. 5.9

Fig. 5.10
Fig. 5.11

Fig. 5.12

Fig. 5.13

xiii

LIST OF TABLES

Table 2.1

Bubbling state diagram of McCann and Prince (1971) for a 9.4 mm
orifice in an air-water system

8

Table 4.1

Physical properties of air and water at standard conditions

44

Table 4.2

Experimental conditions

45

Table 5.1

Percentage of synchronous signals with volume (Vc) as a
parameter. Nor = 3, d0 = 1.6 mm, H = 30 cm, s = 4 cm, b= 1 mm,
system:air-water

69

Percentage of synchronous signals with chamber volume ( Vc ) as a

parameter. Vc = 480 cm3, d0 = 1.6 mm, H = 30 cm, s = 4cm, b = 1
mm, system: air-water

71

Table 5.2

xiv


Introduction

CHAPTER 1

INTRODUCTION

1.1 Background

The dispersion of gas bubbles in liquids plays an important role in bringing about
efficient mass and heat transfer between the two phases. Important devices include
bubble columns and sieve plate columns, in which bubbles are generated by introducing a
stream of gas through orifices into the liquid phase. Investigations on bubble formation
mainly concern bubble frequency, size, shape, the influence of wake pressure of
preceding bubbles and liquid weeping accompanying bubble formation and detachment.

As a fundamental phenomenon, bubble formation at a single orifice has been widely
studied, although it is not in wide use practically. Numerous theoretical models have been
developed in order to predict bubble size, shape, frequency and rising velocity in single
orifice bubbling. On the other hand, some experimental studies of bubble formation from
industrial perforated plates have been undertaken.

However, few studies have addressed the case of multiple orifices as an extension of
single orifice bubble formation. There is a relative lack of fundamental understanding to
link a comprehensive body of knowledge on single orifices to industrial multi-orifice
distributors. For example, it is fairly obvious that even for two-orifice bubbling, bubble
sizes formed when both orifices are bubbling simultaneously would be different from the

1


Introduction

case when the orifices are “out of phase”. The degree of complexity would rise rapidly
for three and more orifices. Therefore, the prediction of bubbling frequency and bubble
sizes for multi-orifice bubbling becomes a more difficult task when compared with single
orifice bubbling.

1.2 Objective of this work

The motivation for this work is to systematically study bubbling synchronicity and
frequency for bubble formation at multiple orifices. Two main objectives are:

1. Experimentally study bubbling synchronicity and frequency for bubble formation
at two orifices. In particular, clarify the different modes with respect to
synchronous, alternate and unsteady bubbling regimes with operating parameters
of gas flowrate, orifice spacing and liquid height.

2. Propose a simple mathematical model to predict bubbling frequency in
synchronous multi-orifice bubbling. Compare the theoretical predictions of
bubble frequency and average radius with experimental data for various gas

chamber volume and number of orifices respectively.

It is hoped that the study would increase our understanding of the factors affecting
synchronicity and frequency in multi-orifice bubbling. The theoretical model is also

2


Introduction

expected to be able to predict bubbling frequency, bubble radius, and gas chamber
volume under various conditions.

1.3 Organization

This thesis is organized to address the study of bubble formation at multiple orifices both
experimentally and theoretically.

Chapter 2 reviews experimental and theoretical research into bubble formation at single
orifices, which represents the fundamental phenomenon in bubble formation. Important
physical factors affecting bubble formation will be also reviewed in this chapter. In
addition, previous work on multiple-orifice bubbling will be discussed.

Chapter 3 presents a mathematical model, which is a simple extension of a recently
developed single-orifice model. This new model should be able to predict bubble
frequency, bubble volume and gas chamber pressure under specified conditions for
multiple orifices.

Chapter 4 describes the experimental apparatus used in this work.

Measurement

techniques, experimental conditions and procedures will also be summarized in this
chapter.

3


Introduction

Results and discussion are presented in Chapter 5. Various bubbling modes at two-orifice
will be described. Factors influencing the bubbling synchronicity and frequency will be
addressed. In addition, the comparison between theoretical predictions and experimental
results will be also addressed.

Conclusions from the experimental study on bubbling synchronicity and theoretical
predictions of bubble frequency, bubble radius and gas chamber pressure are summarized
in chapter 6. Recommendations arising from this work include suggestions for further
study.

4


Literature Review

CHAPTER 2

LITERATURE REVIEW

The performance of any gas-liquid contacting system mainly depends on a

combination of the system geometrical configuration, operating procedures and
properties of the gas and liquid phases. It is very important that the effect of each
parameter is well understood so that such devices as sieve tray columns could be
reliably and efficiently designed and controlled. For the past several decades,
important research on bubble formation at a single orifice and on perforated plate
bubbling has been conducted, and results of primary practical importance have been
achieved with respect to the influence of each parameter. Studies on bubble formation
at multiple orifices (meaning two to, say, ten) have been relatively scarce, despite the
obvious need to relate the results from single-orifice investigations to industrial multiorifice trays.

The review is composed of there sections. Section 2.1 presents a general description
and discussion of bubble formation at single submerged orifice, which includes an
introduction of bubbling regimes, influence of various parameters on gas-liquid
interaction and theoretical development. Section 2.2 reviews the literature pertinent to
bubble formation at multiple orifices, both experimentally and theoretically. Finally, a
brief summary of this review is presented in section 2.3.

2.1 Bubble formation at single orifice

5


Literature Review

2.1.1 Bubbling dynamics

Volumetric gas flowrate into the gas chamber is a conveniently accessible control
parameter in industrial gas-liquid contacting systems. It is evident that low gas
flowrates lead to ineffective mass and heat transfer (Türkoğlu and Farouk, 1990),
while a highly elevated gas flow rate, resulting in an increased gas momentum, can

cause bubble formation to take on a very irregular behavior and affect mass and heat
transfer consequently (Rennie and Smith, 1965). Based on the gas flow rate, bubbling
regimes can be divided into static, dynamic and jetting regimes.

2.1.1.1 Static regime

The static bubbling regime occurs under the condition where only bubble buoyancy
and surface tension play significant roles and there is equality between these two
forces throughout the bubble formation. The gas flow rate in this regime is normally
very low (<1 cm3/s) (Van Krevelen and Hoftijzer, 1950) and bubble volume remains a
constant value at the detachment. The bubble volume can be calculated as follows:
VB =

πd 0σ
,
(ρl − ρ g )g

(2.1)

where ρ l and ρ g represent the liquid density and gas density respectively, g the
acceleration due to gravity, σ the surface tension and d0 the orifice diameter.
Conditions for constant bubbling volume normally occur when a dimensionless
Reynolds number N Re ( N Re = 4 ρ g Q / πd 0 µ g ) less than 100, where Q is the

volumetric gas flowrate into the gas chamber and µ g is the gas viscosity.

6


Literature Review

2.1.1.2 Dynamic regime

In the most realistic conditions, the gas flow rate is much higher and both bubble
volume and frequency change with an increase in gas flow ( N Re >100). This regime is
called Dynamic regime. Bubbling mode becomes much complicated and is further
divided into six bubbling patterns (McCann and Prince, 1971).

I.

Single bubbling: Bubbles grow successively and discretely and there is
no significant interaction between any two bubbles. This regime occurs
under the conditions of low gas flow rates and small chamber volumes.

II.

Pairing: The phenomenon occurs at large gas chamber volumes and
higher gas flow rates. The detachment of the bubble can cause an
intermediate formation of an elongated gas tube due to the remaining
pressure difference between chamber pressure and orifice pressure at
the moment of the detachment. The gas tube then quickly elongates
and joins with the bubble, connecting it momentarily with the orifice.
After this tube breaks rapidly at the orifice and move into the
preceding bubble, weeping of the liquid through the orifice may be
observed.

III.

Double bubbling: It occurs only at high gas flow rates or low chamber
volumes. The second bubble is sucked into the preceding one due to a

wake force caused by it and then two bubbles merge together and rise
as one. The phenomenon is similar with pairing except that the second

7


Literature Review

bubble cannot be regarded as a tube since its size is almost same with
the preceding bubble. Weeping may occur between two bubbles.

IV.

Double pairing: Similar with behavior of the double bubbling except
that each is a pair.

Single bubbling with delayed release: The bubbling pattern is very

V.

similar with pairing except that there is no clear separation between the
first bubble and the small gas tube.

VI.

Double bubbling with delayed release: The bubbling behavior is very
similar to single bubbling with delayed release except that there is also
double bubbling as a following sequence behind each single delayed
release behavior.

In particular, MaCann and Prince (1971) compared the phenomena of pairing and
double bubbling, as shown in Table 2.1.

Table 2.1 Comparison of “pairing” and “double bubbling” (adapted from McCann and
Prince (1971)).
Pairing

Double bubbling

Large chamber volumes

Small Chamber volumes

Bubbling with a “tail”

Two distinct bubbles

No weeping between the bubble
and the formation of its “tail”

Weeping may occur between the two
bubbles

8


Literature Review

Figure 2.1 shows the state diagram of McCann and Prince (1971) for a 9.4 mm orifice
in an air-water system. The conditions were summarized under which each of six

categories was observed to occur.

Figure 2.1 Bubbling state diagram of McCann and Prince (1971) for a 9.4 mm orifice
in an air-water system

2.1.1.3 Jetting regime

With increasing gas flow rates, bubbling regime loses its stability. Bubbling is
characterized by the onset of rapid sequential formation of bursts. This regime is
called “jetting regime”. The phenomenon of jetting normally occurs at higher
Reynolds numbers ( N Re >2000) (McNallan and King (1982)).

9


Literature Review

2.1.2 Physical factors affecting bubble formation

Many factors have been investigated to be expected to influence the bubble formation
at a single orifice (Jackson, 1964). The following subsections will review the
knowledge on components of the gas-liquid system and their effect on the bubble
formation.

2.1.2.1 Chamber volume

Gas chamber volume plays an important role in gas-liquid contacting system. Two
regimes are defined depending on the gas chamber volume: constant flow and
constant pressure.

Constant flow conditions occur in small gas chamber volume systems, corresponding
to large hole pressure drop due to either high gas flow rates or large hole resistance.
The changes in the gas chamber or bubble pressure have relatively a small effect on
the pressure drop. The gas flow rate tends toward a constant value.

The occurrence of constant pressure arises for a large chamber volume and fixed
chamber pressure (Kupferberg and Jameson, 1969; Park et al., 1977). Under such a
condition, the pressure fluctuation due to the bubble formation and detachment is
small. Therefore the chamber pressure remains virtually constant.

Hughes et al. (1955) developed a dimensionless capacitance number Nc from an
electrical equivalent to the injection system:

10