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Frequency characteristics of the noise of R600a refrigerantflowing in a pipe with intermittent flow pattern

Hyung Suk Han a, Weui Bong Jeong b,*, Min Seong Kim b

aNaval System Research Team, Busan Center, Defense Agency for Technology and Quality, 525-2, Gwangan 1 dong, Busan, Republic of KoreabDepartment of Mechanical Engineering, Pusan National University, Jangjeon-dong, Kumjung-ku, Busan 609-735, Republic of Korea

a r t i c l e i n f o

Article history:

Received 10 August 2010

Received in revised form

23 February 2011

Accepted 5 April 2011

Available online 13 April 2011

Keywords:

Refrigerant

Bubble

Noise

Resonance

Frequency

* Corresponding author. Tel.: þ82 51 510 233E-mail address: wbjeong@pusan.ac.kr (W

0140-7007/$ e see front matter ª 2011 Elsevdoi:10.1016/j.ijrefrig.2011.04.004

a b s t r a c t

The acoustic characteristics of a long-shaped cylindrical bubble for slug or churn flow in

a pipe are different from those of a freely rising spherical bubble in infinite liquid. In this

research, the theoretical estimation of the natural frequency of the long-shaped cylindrical

bubble was derived using the energy conservation law for a single bubble in a pipe. The

acoustic characteristics of bubbles in a pipe were also investigated with the R600a refrig-

erant, which is widely used in refrigerators when the flow pattern in a pipe is slug or churn

flow. In order to make slug and churn flow artificially, refrigerant-supplying equipment

was designed and developed. Using this test equipment, the frequency characteristics of

the long-shaped cylindrical bubble in 2-phase flow were investigated experimentally.

ª 2011 Elsevier Ltd and IIR. All rights reserved.

Caracteristiques de la frequence du bruit produit lors del’ecoulement du frigorigene R600a dans un tuyau avec unregime d’ecoulement intermittent

Mots cles : Frigorigene ; Bulle ; Bruit ; Resonance ; Frequence

1. Introduction

A refrigerant flowing in a pipe of a refrigerating system is in

a 2-phase state. In 2-phase flows, various types of bubbles of

different sizes and shapes are created, and when these

bubbles collapse or merge, acoustic noise can occur.

7; fax: þ82 51 517 3805..B. Jeong).ier Ltd and IIR. All rights

The acoustical characteristics of a rising bubble in infinite

liquid were first studied by Minnaert (1933) and Strasberg

(1956). Related to the subject of a bubble in a pipe, Devin

(1961) calculated the acoustical characteristics of a small air

bubble in a pipe immersed in unbounded water. By experi-

mental and theoretical approaches, he found that the

reserved.

Nomenclature

a amplitude of the oscillation of the bubble [m]

cp specific heat at the constant pressure [kJ K�1 kg�1]

cv specific heat at the constant volume [kJ K�1 kg]

ceq equivalent damping coefficient of N bubble

[Nsm�1]

f frequency [Hz]

fn natural frequency of the bubble [Hz]

Ff(t) friction force of a bubble [N]

Ff,max maximum friction force of a bubble [N]

k equivalent stiffness term of the bubble [N m�1]

keq equivalent stiffness of N bubbles [N m�1]

Kug Kutateladze parameter of the gas

l0 initial length of the bubble from center to the end

of the one side [m]

l length of the bubble from center to the end of the

one side [m]

L length from center of the bubble to the end of the

one side of liquid column [m]

M mass of the liquid surrounding on the bubble [kg]

meq equivalent mass of N bubbles [kg]

N numbers of the bubble in a pipe

p pressure of the liquid surrounding on the bubble

[Pa]

Ps sound pressure from the bubble [Pa]

p0 initial pressure of the gas inside of the bubble [Pa]

req equivalent radius of the sphere of the same

volume for the non-spherical bubble [m]

Rt radius of the tube [m]

t time [sec]

T period of the oscillation of the bubble [s�1]

v volume of the bubble [m3]

v0 initial volume of the bubble [m3]

V0 mean volume of the bubble [m3]

V(t) potential energy [N m]

T(t) kinetic energy [N m]

x vapor quality

X Martinelli parameter

x(t) variation of the radius or length of the bubble [m]

d dissipation constant

k polytrophic index

m coefficient of friction [kg m�1 s�1]

mf, mg viscosities of the gas and liquid [N s m�2]

rg, rf densities of the gas and liquid [kg m�3]

r density of the liquid surrounding on the bubble

[kg m�3]

4 phase angle [radian]

u angular frequency [radian]

un angular natural frequency [radian]

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 61498

resonance frequency of a pulsating air bubble at the geometric

center of a short open-ended pipe is lower than that of

a bubble of equal size in a free field. Oguz and Prosperetti

(1998) suggested the natural frequency of oscillation of gas

bubbles in tubes for several boundary conditions. Leighton

et al. (1998) measured the size of a bubble in a pipe using

acoustic detection technology with a hydrophone, ultrasonic

scanner and imaging signal transducer. He suggested the

formulation for the natural frequency of a bubble taking into

account of the reverberation field in a pipe. From the above

references, it is widely known that the acoustical character-

istics of a bubble in a pipe are different from those of a freely

rising bubble in an infinite liquid field.

Considering the acoustic characteristics of bubbles with

respect to their shape and size, the noise from the bubbles in

multiphase flow would vary according to the flow pattern in

a pipe. Diatschenco et al. (1994) suggested a passive acoustical

detectionmethodofflowregimes inamultiphaseflowbasedon

the acoustic characteristics, which changed according to the

shape and size of the bubbles. Wang et al. (1999) characterized

the sound generated by multiphase flow. From Wang’s results,

flow pattern can be identified according to its acoustic signal.

Han et al. (2010) suggested the shape design of evaporator-inlet

pipe for refrigerator not to be intermittent flow pattern at the

operating condition by monitoring and estimating the flow

pattern in a pipe with various flow pattern maps.

Flow pattern is considered to be strongly related to acous-

tical characteristics because the size and shape of bubbles are

different according to the flow pattern. Especially, when the

flow patterns in a pipe are slug or churn flows, which have

long-shaped bubbles, the noise from the bubbles should be

more serious than those of other flow patterns such as annular

and stratified flows. Refrigerant-induced noise from the inter-

mittent flow of the refrigerant has not been studied exten-

sively, but only as a subject of interest for troubling shooting of

refrigerators and air-conditioners (Han and Aoyama, 2006;

Umeda, 1994; Hirakuni et al., 1998; Han et al., 2009).

In this research, theoretical estimation of the natural

frequency of the long-shaped cylindrical bubble was derived

by energy conservation law for a single bubble in a pipe. In

addition, experimental studies for the bubbles in intermittent

flow were performed using the refrigerant-supplying equip-

ment, which can transition the flow pattern in a pipe,

artificially.

Through these experimental studies, the variations of the

natural frequencies of the bubbles rising freely in infinite

liquid and those in a pipe were investigated. The variations of

the noise when the flow pattern transitioned from slug flow to

churn flow were also investigated by experiment.

2. Theoretical background for bubbleacoustics in a pipe

When the equivalent radius of a bubble is larger than the tube

diameter, the bubble will deform in the axial direction and

become a long-shaped cylindrical bubble. The long-shaped

cylindrical bubble is widely known as the Taylor bubble,

which is bullet-shaped. The difference of bubbles between

cylindrically-shaped and bullet-shaped is just their shapes at

the ends. If the bullet-shaped parts at the end of bubbles do

not affect dynamic behavior as much as long cylindrically-

shaped parts do, it can be assumed that the bullet-shaped

bubble can be simplified to the cylindrical-shaped bubble

Liquid

Bubble

l

L

l

L

l

L

l

L

aa

aa

Liquid

Bubble

Rt

x

Fig. 1 e Circular-cylinder shaped bubble (Taylor bubble).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 6 1499

with same volume. Therefore, in this research, the shape of

the Taylor bubble in slug flow is assumed to be simply cylin-

drical-shaped, as shown in Fig. 1.

In Fig. 1, the cylindrical bubble is assumed to oscillate only

in its axial direction as given in Eq. (1) because themovement in

the radial direction is constrained by the rigid wall of the pipe.

l ¼ l0 þ xðtÞ; where; xðtÞ ¼ a sin 2pft (1)

Here, l0 is the initial length of the bubble from the center to

the end of one side [m], l is the length of the bubble from

center to the end of the one side [m], a is the amplitude of the

oscillation of the bubble [m], x(t) is the axial displacement of

the bubble [m], t is time [sec] and f is frequency [Hz].

Assuming adiabatic expansion of the bubble, the gas

pressure ratio in a bubble can be written as Eq. (2).

p0

p¼�vk

vk0

�¼�1þ xðtÞ

l

�k

(2)

Here, p is the pressure of the gas inside the bubble [Pa], p0 is

the initial pressure of the gas inside the bubble [Pa], v is the

volume of the bubble [m3], v0 is the initial volume of the bubble

[m3] and k is the polytrophic index (¼cp/cv). In Eq. (2), the

pressure inside the bubble is equal to the pressure of the liquid

surrounding the bubble if the surface tension of the bubble is

ignored.

For small oscillations x << l, Eq. (2) can be rewritten as Eq.

(3) by ignoring the higher order terms of the Taylor series.

p� p0 ¼ kpxðtÞl

(3)

The velocity of the bubble surface contacting the liquid and

the liquid particles at distance “L” from the center of the

bubble in a pipe is described by Eq. (4).

dLdt

¼ dldt

¼ x$ ðtÞ ¼ 2pfa cos 2pft (4)

Assuming that there are “N” bubbles in a pipe, the potential

energy of the bubbles and kinetic energy of the liquid can be

represented as Eq. (5) and Eq. (6), respectively.

VðtÞ ¼ �N�Zn

n0

�p� p0

�dn ¼ 2N�

ZxðtÞ0

kpxðtÞl

$pR2t dxðtÞ

¼ N� kppR2t xðtÞ2l

¼ 12keqxðtÞ2 (5)

TðtÞ ¼ 2N� 12

Z �dLdt

�2

dM ¼ 2N� r

2

ZLl

_xðtÞ2 $p R2t dl

¼ N� p r R2t_xðtÞ2ðL� lÞ ¼ 1

2meq _xðtÞ2 (6)

Here, V(t) is the potential energy [J], T(t) is the kinetic energy

[J], N is the number of bubbles in a pipe, v is the volume of the

bubble [m3], Rt is the radius of the tube [m], M is the mass of

the liquid surrounding the bubble [kg], r is the density of the

liquid surrounding the bubble [kg m�3], keq is the equivalent

stiffness of N bubbles [Nm�1]andmeq is the equivalentmass of

N bubbles [kg].

Since the normal force on the wall of the pipe is the same

as the force by the pressure in a pipe, the friction force of

bubbles including the liquid column in the pipe can be written

as given in Eq. (7).

Ff ðtÞ ¼ mNp� 2pRtL ¼ mN

�p0 þ kpxðtÞ

l

�2pRtLyN� Ff ;max; (7)

where,

Ff ;max ¼ m p0 2p Rt L

Here, Ff(t) is the friction force [N], Ff,max is the maximum

friction force of bubbles [N] and m is the coefficient of friction

[kg m�1 s�1]. Therefore, the work-done by the friction force

can be given in Eq. (8).

DE¼ 4Za0

Ff ðtÞdx¼ 4Za0

N�Ff ;maxdx¼ 4N�Ff ;max$a¼ pu ceqa2 (8)

Here, DE is the work-done from the friction [J], ceq is the

equivalent viscous damping coefficient of N bubbles [Nsm�1]

and u is the angular frequency [radian].

Through the equivalent stiffness, mass and damping

coefficient from Eqs. (5), (6) and (8), the equation of motion of

N bubbles can be written as shown in Eq. (9).

meq€xðtÞ þ ceq _xðtÞ þ keqxðtÞ ¼ F0ej2pft (9)

where,

meq ¼ 2prNR2t ðL� lÞ; keq ¼ 2N

kppR2t

l; ceq ¼ 8mNRtLp0

ua

Here, F0 is the external force acting on N bubbles. The

steady-state amplitude of displacement of Eq. (9) is given in

Eq. (10).

a ¼ F0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihkeq � ð2pfÞ2meq

i2þ�2pfceqðaÞ�2

r (10)

Considering equivalent viscous damping coefficient is

function of amplitude a, solution of Eq. (10) gives the ampli-

tude of displacement of oscillating bubble as shown in

Eq. (11).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 61500

F

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4N� Ff ;max

vuuu

a ¼ 0

keq

pF0

1��u

un

�2uut (11)

fn ¼ 12p

ffiffiffiffiffiffiffiffikeq

meq

s¼ 1

2pl

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikp

rðL=l� 1Þr

(12)

From Eqs. (11)e(12), it can be seen that the friction does not

affect the resonance frequency of the bubble, but make the

amplitude of the oscillating bubble less.

When Eq. (12) is applied to define the natural frequency of

the long-shaped bubble, below assumption should be

considered.

1. The small amount of liquid streaming downward is

ignored.

2. The energy losses from the non-linear effects such as

viscosity and thermal conduction are ignored.

Based on the assumptions and calculations as above, the

natural frequency of the long-shaped cylindrical bubble such

as a slug and churn bubble can vary according to their length

as well as the cyclic condition of the inner and the outer fluid.

The natural frequency of a spherical bubble rising freely in

infinite liquid is given in Eq. (13) (Minnaert, 1933).

fn ¼ 1T¼ 1

2preq

ffiffiffiffiffiffiffiffi3kpr

s(13)

Here, req is the equivalent radius of the sphere of the same

volume for a non-spherical bubble [m].

Minnaert formula given in Eq. (13) assumed a bubble

vibrates in a radial direction maintaining its spherical shape.

However, in the case of long cylindrical bubble in a pipe,

bubble cannot move in a radial direction due to the

constraints of the pipe. Because of these different boundary

conditions, the potential and kinetic energy of the bubbles in

an infinite liquid are different from those in a pipe filled with

liquid.

EEV(5)

Condenser(2)

P

P

Sub-cooler(4)

R600aCompresor(1

Bypass EE

Eva

PHeater(6)

Compresor

EEVEEV

Condenser

R12

Fan

H

Flow meter

Fig. 2 e Tes

Therefore, Eq. (12) was derived assuming a bubble in a pipe

has only a longitudinal vibration maintaining its cylindrical

shape different from that of the spherical bubble in an infinite

liquid given in Eq. (13).

Strasberg (1956) estimated the sound pressure of the

bubble by Eqs. (14)e(16).

Ps ¼ pse�rfndt cos

�2pfnt� f

�(14)

ps ¼ r fn2e

h_v0 þ 4p2f 2n ðv0 � V0Þ2

i1=2(15)

f ¼ tan�1

� _v0

2pfnðv0 � V0Þ

(16)

Here, Ps is the sound pressure from the bubble [Pa], fn is the

natural frequency of the bubble [Hz], d is the dissipation

constant, 4 is the phase angle [radian], v0 is the initial volume

of the bubble [m3] and V0 is the mean volume of the bubble

[m3]. From Eqs. (14)e(16), the sound pressure depends on the

bubble size (v0) and the volume variation of the bubble ( _v0).

Therefore, with respect to the bubble size, slug and churn

flowsmay produce a larger sound than the other flow patterns

such as annular and wavy. Especially, the sound pressure of

churn flow should be larger than that of slug flow because the

volume variation of churn flow ismuch larger than that of slug

flow.

3. Experiment

3.1. Experimental setup and conditions

Fig. 2 shows the test setup for determining the acoustical

characteristics of the long-shaped bubble according to the

flow pattern in a pipe. The refrigerant to be tested is R600a

and the linear compressor (1) supplies it to the test equip-

ment. The refrigerant goes through the condenser (2), and

the high pressure of refrigerant is controlled by the amount

of heat exchanging given in the 2nd cyclic line (3) of R12

)

V

Anechoic chamber

porator(8)

Power Meter

2nd Cycle Line(R12)(3)Main Cycle Line(R600a)

Fan

ThermocoupleP Pressure Sensor

Camcoder

Microphone

eater

Orifice(9)

Test Section(7)

2nd capillary(10)

t setup.

x=0.39 x=0.24

x=0.12

x=0.02 1.E-01

1.E+00

1.E+01

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

X

Ku

g

Slug & Churn

Annular

Annular-slug/churn transition

x=0.39 x=0.24

x=0.12

x=0.02

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000 10000

j/ (gD)

β

Slug

Churn

Slug-churn transition

a

b

Fig. 3 e Flow pattern estimation by Taitel and Dukler flow

pattern map.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 6 1501

refrigerant. The sub-cooler (4) is linked to the condenser and

controls the degree of sub-cooling of the refrigerant. The

sub-cooled refrigerant is expanded by an electric expansion

valve (5) and enters the heater (6), which controls the vapor

quality of the expanded refrigerant. Test section (7) is

installed between the heater (6) and evaporator (8). Test

section is made as a glass tube to monitor the flow pattern

in the pipe according to cyclic conditions. An orifice (9) is

installed at the end of the glass tube to change the volume

of the bubble in a pipe, forcibly. The refrigerant from the

orifice is additionally expanded by a 2nd capillary (10) and

enters the evaporator (8). In order to visualize the flow

pattern in a test section, the digital camcorders were

installed near by the section. A microphone (B&K 4189) and

accelerometer (B&K Type 4393) were also installed to

measure the acoustic noise as well as the acceleration of the

pipe when the bubble went through the test section. The

microphone was installed 30 cm apart from the test section

and the accelerometer was installed on the orifice. The

sampling rates of the acoustic noise as well as the acceler-

ation were 32,768/sec and measured at 1 Hz narrowband as

well as 1/12 octave band spectra. The acoustic noise and

acceleration were collected for 60 s after the cyclic condition

became steady.

The test condition in this research is given in Table 1. The

flow patterns at each condition of vapor quality are estimated

by the TaiteleDuklermap (1977). The vapor quality of R600a at

the initial condition is set 0.02 and increased to 0.39.

Fig. 3 shows the estimation of the flow pattern by the

TaiteleDukler map. The flow pattern is closely related to the

mass quality of the refrigerant, which represents the flow rate

of the gas in a pipe. Therefore, in Fig. 3(a), Taitel and Dukler

used the Martinelli parameter, representing the mass quality,

as well as other properties such as the density and viscosity of

the gas and liquid, which affect the flow pattern in a pipe, as

given in Eq. (17), to classify the flow pattern.

X ¼ ðdp=dzÞfðdp=dzÞg

¼�1� xx

�0:875 rg

rf

!0:5 mf

mg

!0:125

(17)

Here, X is the Martinelli parameter, x is the vapor quality,

rg, rf are the densities of the gas and liquid, mf, mg are the

viscosities of the gas and liquid, (dp/dz)f is the pressure drop

when only liquid flows in a pipe, and (dp/dz)g is the pressure

drop when only gas flows in a pipe.

At a typical value of the Martinelli parameter, the flow

pattern transitions from slug (or churn) to annular flow when

the value of the Kutateladze parameter of the gas, as given in

Eq. (18), increases.

Table 1 e Test conditions.

Item Value

High pressure 0.375 Mpa � 5%

Low pressure 0.125 Mpa � 5%

Vapor quality 0.02, 0.12, 0.24, 0.39

Mass flow rate 2.7 kg hr�1 � 10%

Kug ¼ jgr1=2g

.hg�rf � rg

�si1=4 (18)

Here, Kug is the Kutateladze parameter of the gas, which

represents the superficial velocity of the gas including the

other properties of the gas and liquid. jg is the superficial

velocity of the gas, g is the acceleration due to gravity and s is

the surface tension.

When the gas velocity increases due to the increase of the

gas flow rate, the liquid is swept up to the surface of the pipe

and becomes annular flow. Based on this theory, the condition

of transition from slug or churn to annular flow is given in Eqs.

(19) (Taitel and Dukler, 1977).

Kug ¼ 3:09

�1þ 20Xþ X2

�1=2�X�1þ 20Xþ X2

�1=2 (19)

When the flow pattern is estimated to be intermittent flow

from Fig. 3(a), the detailed classification of the flow pattern,

whether it is slug or churn flow, can be found from Fig. 3(b). In

Fig. 3(b), the horizontal axis represents jg/( gD)1/2and the

vertical axis represents the volumetric quality denoted by b.

D denotes the diameter of the tube. From the estimation of the

flow pattern from TaiteleDukler flow pattern map, as given in

Fig. 3, it can be estimated that the flow pattern was initially

slug flow but transitioned to churn flow when the vapor

quality reached 0.24.

When the flow patterns are slug and churn flow, the

bubbles have long cylindrical shape. Therefore, in the next

Fig. 4 e Pictures of the flow pattern in accordance with its vapor quality.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 61502

section, the acoustic characteristics of bubbles when the flow

patterns are slug and churn flows in a pipe are measured, and

the frequency characteristics of the noise and vibration of

bubbles from the experiment are compared with those from

the theoretical approach presented in this paper.

3.2. Experiment results

Fig. 4 shows the pictures of the flow pattern photographed by

the digital camcorder for 4 different conditions of vapor

quality. The other conditions are given in Table 1. In Fig. 4(a),

Fig. 6 e Sound pressure of the bubble in a pipe.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 6 1503

slug bubbles are produced when the vapor quality is very low

(x ¼ 0.02). As the vapor quality increases, the slug bubbles

become fully developed and the number of the slug bubbles

increases, as shown in Fig. 4(b) (x¼ 0.12) and Fig. 4(c) (x¼ 0.24).

When the amount of heat increases by the heater, the vapor

quality of the refrigerant increases and the flow pattern

transitions to churn flow, as shown in Fig. 4(d) (x ¼ 0.39). From

inspection by the camcorder, the lengths of the bubbles are

distributed from 20mm to 80mm, and the ratio of the bubbles

and the liquid column (L/l ) is distributed from 2.0 to 5.5 as

shown in Fig. 5 when the flow pattern is slug flow (x ¼ 0.24).

Fig. 5 was obtained by monitoring the pictures of bubbles in

the sight glass by the camcorder. When bubbles in a pipe were

pictured by camcorder, a rulerwas installed beside of the sight

glass to check the length of bubbles. Because the minimum

gradation on the ruler was 1 mm, the error bound of the

measured length of bubbles should be �1 mm. Pictures were

collected for 60 s and the numbers of all bubbles according to

their sizes (2l and L/l ) were examined one by one. However,

when the flow pattern is churn flow (x ¼ 0.39), the sizes of

bubbles could not be examined due to their complicated

properties. Because the churn flow is developed from the slug

flow having highly oscillation, the size of the churn bubble

may have almost the same size with the slug bubble. There-

fore, it is assumed that the frequency characteristics of the

churn bubbles are same as that of the slug flow. Figs. 6 and 7

show the time signal of the sound pressure and acceleration

on the pipe when the flow pattern in a pipe is either slug

(x¼ 0.12) or churn (x¼ 0.39). From Figs. 6 and 7, it can be found

that the sound from bubbles increases as the numbers of the

Fig. 5 e Numbers of bubbles versus size of slug bubbles at

x [ 0.24 measured for 60 s. Fig. 7 e Acceleration of the bubble in a pipe.

x=0.12

x=0.24

x=0.39

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

00001000100101

Frequency[Hz]

So

un

d P

ressu

re[P

a]

Sound from collapsing bubbles passing through the orifice

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

00001000100101

Frequency[Hz]

So

un

d P

ressu

re[P

a]

Sound from collapsing bubbles passing through the orifice

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

00001000100101

Frequency[Hz]

So

un

d P

ressu

re[P

a]

1X of compressor rotating frequency

2X of compressor rotating frequency

Sound from collapsing bubblespassing through the orifice

a

b

c

Fig. 8 e 1/12 octave spectra of the acoustic noise on the

orifice.

x=0.12

x=0.24

x=0.39

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

00001000100101

Frequency[Hz]

Acceleratio

n[m

s

-2

]

Acc. from the long shaped bubble

Acc. from collapsing bubbles passing through the orifice

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

00001000100101

Frequency[Hz]

Acceleratio

n[m

s

-2

] 1X, 2X and 3X of compressor rotating frequency

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

00001000100101

Frequency[Hz]

Acceleratio

n[m

s

-2

] Acc. from the long shaped bubble

Acc. from collapsing bubbles passing through the orifice

a

c

b

Fig. 9 e 1/12 octave spectra of the acceleration on the

orifice.

Fig. 10 e Natural frequencies of the slug bubbles calculated

by Minnaert equation given in Eq. (13).

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 61504

bubble increases and the flow pattern transitions from slug to

churn flow.

Even though slug flow is widely known to have much

irregular noise, it has little noise at the initial state (L >> l ),

where frequency and velocity are both low. Therefore, it can

be estimated that the noise from slug flow is strongly depen-

dent on the velocity of the flow and the frequency of the

creation of the slug bubbles.

Fig. 8 shows the 1/12 octave spectra of the sound pressure.

The most dominant frequency affected by the increase of

bubbles in slug and churn flows is 3e4 kHz, as shown in Fig. 8.

The slug bubbles will collapse when they pass through the

orifice.Assuming thecollapsedbubbleshave the same radiusas

the orifice radius (r ¼ 2 mm), the natural frequency of the

Fig. 11 e Natural frequencies of the slug bubbles calculated

by Eq. (12) suggested in this research.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 6 1505

collapsed bubbles can be calculated to be 3.43 kHz fromEq. (13).

Therefore, the noise at 3e4 kHz is the natural frequency of the

collapsed bubbles when they are passing through the orifice.

However, the noise at the low frequency range from the long-

shaped cylindrical bubbles discussed in the previous section

didnot appeardominantlyon thespectraof thesoundpressure.

Therefore, the 1/12 octave spectra of acceleration on the

pipe are acquired additionally, as shown in Fig. 9. The accel-

eration at the low frequency range from the long-shaped

cylindrical bubbles discussed in the previous section appears

to range from 100 to 400 Hz, as shown in Fig. 9. The acceler-

ation at the range of frequency from 100 to 400 Hz increases as

the vapor quality increases. The frequency ranges,

100e400 Hz, are similar to those calculated from themeasured

sizes of bubbles as shown in Fig. 4.

Referring to Fig. 3(b), Fig. 9(a) (x¼ 0.12) and Fig. 9(b) (x¼ 0.24)

represent slug flow, while Fig. 9(c) (x ¼ 0.39) represents churn

flow. The frequencies at which bubble noise occurs are almost

the same, regardless of the vapor quality. However, experi-

ments showed that the magnitudes of the bubble noise of the

churn flow are greater than that of slug flow.

The distribution of the natural frequencies of bubbles can

be predicted from those of bubble size given in Fig. 5. Fig. 10

shows the distribution of the natural frequency of bubbles

obtained from Minnaert formula given in Eq. (13) by using all

possible equivalent radiuses of sphere which has the same

volume as the cylindrical bubble. When the range of the

frequency for the acceleration of the long-shaped bubbles by

Fig. 12 e Natural frequencies of the slug bubbles calculated

by Devin’s theory given in Eq. (20).

measurement is depicted together in Fig. 10, it can be found

that the natural frequency calculated by Eq. (13) is much

higher than those by measurement.

Substituting all possible cases of l and L/l given in Fig. 5 into

Eq. (12), the distribution of natural frequencies of bubbles

were obtained as shown in Fig. 11. The frequency range

calculated by Eq. (12) is from 133.9 to 501 Hz, which is in good

agreement with the frequency range given by the test results

(100e400 Hz).

Comparing Figs. 10 and 11, it can be found that the natural

frequencies of the long-shaped bubbles in a pipe are lower

than those of the spherical ones in an infinite liquid.

Fig. 12 shows the distribution of the natural frequencies for

those bubbles calculated by Devin’s theory (1961), as given in

Eq. (20).

f ¼ f0

" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 2req

Rt

s �L=2þ DL

Rt� 1:109

�#(20)

Here, DLy1:22Rt.

The range of the natural frequency is estimated from 170 to

775.5 Hz. Fig. 12 shows that Devin’s theory estimated a little

higher than the experimental results. In Devin’s research, it is

assumed that bubbles are created from the nozzle, therefore

diameter of bubble is less than that of tube. Therefore, Devin’s

theory may not be proper to evaluate the natural frequencies

of the slug bubbles in a pipe.

Finally, it can be verified that the natural frequencies of

slug and churn bubbles derived in this paper showed good

agreement with the test results.

4. Conclusion

Considering energy conservation for long-cylindrical shaped

bubbles in a pipe such as the bubbles in slug and churn flows,

the theoretical formula of their natural frequencies was

derived. This formula was validated by experiments.

In addition, the refrigerant-supplying equipment was

designed and developed to make intermittent flow pattern

artificially. The characteristics of refrigerant-induced noise

related to the flow pattern in a pipe were found by experi-

ments as below.

(1) Two kinds of bubble noisewere found by experiments: one

is the noise that occurs when larger bubbles collapse

passing through the orifice, and the other is the noise due

to the long-cylindrical shaped bubble oscillating in the

axial direction in a pipe.

(2) When large bubbles passed through the orifice and con-

verted to small bubbles, they produced noise and vibration

at the frequency of the bubble whose radius is the same as

the orifice radius.

(3) The theoretical formula of the natural frequencies pre-

sented in this paper for the long-cylindrical shaped bubble

oscillating in the axial direction in a pipe showed good

agreement with experimental results.

(4) The natural frequencies of the long-cylindrical shaped

bubble inapipeweremuch lower thanthoseof the spherical

bubbles rising freely in infinite liquid of the same volume.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 4 9 7e1 5 0 61506

(5) The bubbles in the initial slug flow surrounded with a long

liquid columnhad little noise and vibration. But, when slug

flow was developed by increasing the vapor quality, the

bubbles produced larger noise and vibration.

(6) Comparing the spectra of slug flow to that of churn flow,

the frequencies at which high amplitude noise and vibra-

tion occur were almost the same, regardless of the vapor

quality.

(7) Estimated from bubble acoustics theories and experi-

ments, the sound pressure and acceleration were found to

increase when slug flow transitioned to churn flow.

r e f e r e n c e s

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Oguz, H.N., Prosperetti, A., 1998. The natural frequency ofoscillation of gas bubbles in tubes. J. Acoust. Soc. Am. 103,3301e3308.

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Wang, J., Van der Spek, A., Georgi, D.T., Chance, D., 1999.Characterizing Sound Generated by Multiphase Flow. SPEAnnual Technical Conference and Exhibition. Society ofPetroleum Engineers, pp. 747e756.