Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 16.7.2 - CHF in a Non-Uniform Circumferential Heating Tube under Low-Pressure and Low-Mass-Flux Condition – Influence of the Heated Length
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00410
 Material Information
Title: 16.7.2 - CHF in a Non-Uniform Circumferential Heating Tube under Low-Pressure and Low-Mass-Flux Condition – Influence of the Heated Length Boiling
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Umekawa, H.
Hotta, K.
Ami, T.
Ozawa, M.
Mishima, K.
Saito, Y.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: CHF
non-uniform heating tube
liquid film re-distribution
entrainment
deposition
 Notes
Abstract: CHF is one of the limitation factor of designing the boiling system, thus so many investigations have been conducted so far. Although most of those investigations have been conducted under uniformly heated condition, actual boiling systems have the heat flux distribution. In this paper, the CHF under non-uniform heat flux along the circumferential direction was experimentally investigated under low-mass-flux and low-pressure condition. The test section was SUS304 tube with dimensions 20mm in inner diameter, 24mm in outer diameter, and the eccentricity was 1.5mm. This test section was heated by Joule heating of A.C./D.C. power, and the heat flux distribution could be achieved by the distribution of the electrical resistance caused by the distribution of the wall thickness. The heating length was 450mm, 900mm and 1800mm, and the tube orientation was vertical. These results expressed the importance of the liquid film re-distribution to the characteristics of CHF, and several factors influenced on the film re-distribution were estimated. These characteristics have been also confirmed by using the calculation model on the basis of the Butterworth model. The shorter test-section, 450mm in the heated length, showed the quite different tendency by comparison with longer test-sections. This characteristic could be considered as the influence of the increasing of the entrainment that caused by the high heat flux. Moreover, another mechanism, DNB, was also observed under higher heat flux condition.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00410
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1672-Umekawa-ICMF2010.pdf

Full Text

Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


CHF in a Non-Uniform Circumferential Heating Tube
under Low-Pressure and Low-Mass-Flux Condition
Influence of the Heated Length -


H. Umekawa, K. Hotta, T.Ami, M.Ozawa, K.Mishima and Y.Saito

Kansai University, Faculty of Engineering Science, Department of Mechanical Engineering
Yamate-cho 3-3-35, Suita, Osaka 564-8680, Japan
niilcki\\ i a ki l iii-I 1 ip


Keywords: CHF, non-uniform heating tube, liquid film re-distribution, entrainment, deposition




Abstract

CHF is one of the limitation factor of designing the boiling system, thus so many investigations have been conducted so far.
Although most of those investigations have been conducted under uniformly heated condition, actual boiling systems have the
heat flux distribution. In this paper, the CHF under non-uniform heat flux along the circumferential direction was
experimentally investigated under low-mass-flux and low-pressure condition. The test section was SUS1'-4 tube with
dimensions 20mm in inner diameter, 24mm in outer diameter, and the eccentricity was 1.5mm. This test section was heated by
Joule heating of A.C./D.C. power, and the heat flux distribution could be achieved by the distribution of the electrical
resistance caused by the distribution of the wall thickness. The heating length was 450mm, 900mm and 1800mm, and the tube
orientation was vertical. These results expressed the importance of the liquid film re-distribution to the characteristics of CHF,
and several factors influenced on the film re-distribution were estimated. These characteristics have been also confirmed by
using the calculation model on the basis of the Butterworth model. The shorter test-section, 450mm in the heated length,
showed the quite different tendency by comparison with longer test-sections. This characteristic could be considered as the
influence of the increasing of the entrainment that caused by the high heat flux. Moreover, another mechanism, DNB, was also
observed under higher heat flux condition.


Introduction

Critical heat flux (CHF) is one of the important designing
factors of boiling systems, thus many investigations have
been conducted so far (e.g. Ahmed(2010)). Although most
of those investigations have been done by using the
uniformly heated tube, actual industrial utilities have the
non-uniform heat flux distribution along the
circumferential/axial direction.
Of course several investigations concerned with the
non-uniformly heat flux condition have been done until
now(e.g. Butterworth(1971), Celata(1994), Inasaka(1998),
Schipkov(2000), Mishima(2002), Boyd Sr(2002),
Olekhnovitch (2008)). These investigations were roughly
divided into two categories. One of them was the
investigation concerned with the conventional boiler, and
other was the investigation interested in the quite high heat
flux equipment such as diverter. In the case of former
investigation, the experimental condition was normally high
mass flux and high system pressure conditions. In the case
of the latter investigation, most of the investigations were
done by using the small diameter tubes. These
investigations presented meaningful results, but
non-uniform heating in another condition has become more
important in the development of high performance compact


boiler (Nishikawa(1999)).
In the designing of the small boiler, the specific furnace heat
release rate and the residence time of combustion gas had
been more important factor than the heat flux owing to the
scaling law. But even in the case of the small boiler, new
concept, such as the jaggy fireball (JAFI) boiler, requires
the more detailed understanding of the CHF. Normally the
operating condition of small boiler is low-pressure and
low-mass-flux condition, but the information of the
non-uniform heating under these conditions was quite few.
In the series of this investigation, CHF of the
circumferentially non-uniform heating under low mass flux
and low pressure condition has been widely investigated. In
the investigations, several results were reported, i.e. the
treatment of the pressure drop, the estimation of the heat
transfer coefficient. The role of the liquid film redistribution
in the estimation of the CHF was also reported, and also the
calculation by using the finite different scheme with the
concept of Butterworth model was confirmed, so on (eg.
Umekawa (2006), Ami(2009)).
In this pqper, similar investigation with the former
investigations was done by using the short heated length
tube. By using the short tube, the magnitude of the heat flux
increased. In this paper, the influence of the magnitude of
the heat flux on CHF was reported by comparing with the






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


former investigations

Nomenclature

Bo Boiling number (=qG-1HLG-1)
Bo* modified Boiling number(=(qm,-q,,n)G1'HLG-1)
G mass flux (kgm2s 1)
h heat transfer coefficient (WmK K1)
HLG latent heat (Jkg-')
L, heated length (m)
Mf mass flux of liquid film (kgm 2s1)
md mass flux of deposition (kgm 2s1)
me mass flux of entrainment (kgm 2s1)
mb mass flux of entrainment(boiling) (kgm 2s1)
mes mass flux of entrainment(shearing) (kgm 2s1)
ms, mass flux of liquid film spreading (kgm 2s1)
mv mass flux of evaporation (kgm 2s1)
pex system pressure (Pa)
q heat flux (Wm2)
qcHF critical heat flux (Wm-2)
R inner radius of tube (m)
t tube wall thickness (mm)
T,n inlet temperature (deg.C)
Two outer wall temperature (deg.C)
xeq thermal equilibrium quality
z axial distance from the inlet (m)


Greek letters
Ap pressure difference
e Eccentricity in Fig.2
3 spreading coefficient
Xtt Lockhart-Maritnelli parameter


(Pa)
(mm)
(mm)


Figure 1: Experimental apparatus.


2
ceanvic Itube
Cross SCCL ion


Subsripts
AVE averaged value
cal calculation result
exp experimental result
TP two-phase flow
0 local location along the circumferential direction


Experiment

The experimental apparatus was a forced convective boiling
channel system of ion-exchanged water. As shown in Fig.1,
the experimental apparatus is mainly composed of a reserve
tank, a pump, a flow meter, an orifice, a test section and a
separator.
Test sections were SUS' '4 tubes, heated by Joule heating of
A.C. power. The heated length of test section is 450mm with
the outer diameter of 24mm and the inner diameter of 20mm
as shown in Fig.2. Experimental results of previous paper by
using the 900mm and 1800mm tubes were also used for
comparison. In Fig.2 the eccentricity e is defined as
center-to-center distances of the inner and the outer tube
surfaces. One of the test sections was a normal tube
(e=0mm), and another was an eccentric tube (e=1.5mm).
The circumferential distribution of the heat flux was caused
by the distribution of the electric resistance depending on
the wall thickness distribution. The local heat flux qe is
approximated by using wall thickness ratio within 7% error
relative to the accurate local heat flux estimated by using
FEM(Umciii\ li.-'"'iin. This error is negligible small in


I
Normal lube
Cross Sec ion


Figure 2: Test Section (LT=450mm)


measuring heat transfer characteristics. Thus, in this
investigation the local heat flux qe was approximated by the
next equation,


to AVE
t
lAVE


where te is the wall thickness at the angle 0, and the origin
of angle was set at the center of the inner surface of tube,
and tAVE is the average wall thickness, which is 2mm in this
experiments. qAVE is the average heat flux at the inner
surface. By using Eq.(1), maximum/minimum heat flux
ration becomes 1.0 for e=0mm-tube, and 7.0 for
e=1.5mm-tube, respectively.
On the surface of the test section, 0.5mm type-K
thermocouples were welded, and the critical heat flux
condition was defined as the heat flux when the wall


Paper No





Paper No


temperature exceed a predetermined threshold temperature
which was set at 400deg.C (In the case of the e=1.5mm-tube
with 450 mm heated length, slightly higher temperature,
500deg.C, was used. as the threshold to protect the
miss-detection of DNB.)
The experimental condition was as follows; the mass flux
G=20-140kgm2/s, the system pressure defined at the
separator was pex=0.3, 0.4MPa, and the inlet temperature Tm
was 80deg.C.


Results and Discussion

Pressure Drop
Figure 3 shows the correlation of the experimental results
with calculation results of pressure drop. In the calculation,
the void fraction was estimated by using drift-flux model of
Ishii with the flow pattern map by Mishima-Ishii, and the
friction term was calculated by using Lockhart-Martinelli
model. To calculate these values, the average heat flux was
used(UmickmLili2 -'i I,. Even in the case of the short tube,
this estimation method shows a good agreement with the
experimental results. These facts show that the flow
characteristic is not influenced by the distribution of the heat
flux, and is just only influenced by the total amount of the
vapour generation.


Heat Transfer coefficient
Figure 4 shows the correlation


Apexp kPa


Figure 3: Pressure Difference.
107, ,


104

103

10,


of the heat transfer


hTexp W/m2K


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

coefficient between the experimental results and calculation
results. Number in the legend express the location of the
thermocouples and correspond to the number in Fig.2. The
calculation of the heat transfer coefficient was used by the
modified correlation of Schrock-Grossman(1962)
(Ami(2009)).


hT = 0.739hLo Bo X 104 +1.5


1
Xtt, A


:ji


In Eq.(2), Boiling number expresses the magnitude of the
nucleate boiling, thus it should be considered as the function
of the local heat flux qe. On the other hand, the term of the
Lockhart-Martinelli parameter expresses the influence of the
forced convection, thus this term must be estimated by the
average heat flux qAVE, as shown in the results of the
pressure difference.
As the results, in Fig.4, calculation results of Eq.(2) show
good agreements with experimental results. It expresses that
the heat transfer of this system is mainly decided by the
nucleate boiling, but is slightly influenced by the forced
convection.

Critical Heat Flux in Uniformly Heated Tube
Figure 5 presents the critical heat flux of the uniformly
heated tube with several correlations and the condition of
Xeq=0.5 1.0 at exit.
In the case of the long tube (LT=900 mm Fig.5(b), LT=1800
mm Fig.5(c)), Katto's correlation shows a good agreement
with the experimental result. But, Katto's correlation
slightly takes the higher value in the case of the short
tube(LT450 mm Fig.5(a)). These tendencies are also
confirmed by the decreasing of the exit quality, and it can be
considered as the difference of the amount of the
entrainment.
The estimation of this effect is also important in the latter
discussion of the non-uniformly heated tube. Thus in this
section the estimation method of the entrainment will be
confirmed by using the calculation of the liquid film model.
Figure 6 shows the calculation results of liquid film model,
and Fig.7 also shows the amount of the entrainment and
deposition.
In liquid film model, the dryout of liquid film is estimated
by using the next equation. In this paper liquid film
thickness was treated as unity for calculation of mass
balance.


dMf
--+m, +md -m =0
dz


Deposition ratio is in proportion to the concentration of
droplet Cd as follows,


md = kdCd


In the case of steam-water annular flow under low pressure
and high vapour quality condition, the deposition mass
transfer coefficient kd was derived by Okawa(2003),


Figure 4: Heat Transfer Coefficient.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


G kg/m2s
(a) LT=450mm


G kg/m s
(b) LT=900mm
800 , - - , ,


600


400


200


20 40 60
G kg/m2
(c) LT=1800mn


80 100 120


Figure 5: Critical Heat Flux (e=0.0mm)
-_ 05
kd= 0.009C Re 3Sc2/3 (5)



Entrainment rate caused by the breakup of roll wave due to
interfacial shear force can be expressed as follows,


mes= kePL ) (6)

f rj2
where ",e = / (7)


In this equation, interfacial friction factor is evaluated by


G k/m2s
(b) LT=900mm


"0 20 40 60 80 100
G kg/m2s
(c) LT=1800mm
Figure 6: Critical Heat Flux
(e=0.0mm Liquid film model)


the correlation of Wallis, and film thickness 6 is calculated
by the force balance between the interfacial shear and wall
friction forces. The entrainment mass transfer coefficient ke
and n in Eq.(4) were selected as follows,

k, =3.1x102,n = 2.3;re <0.0675

k,=1.6x10 3,n=1.2

k, = 6.8 x 104,n = 0.5;0.295 < e

These calculation results are shown in Fig.6 as "me=m;',
and show good agreement with experimental results except
the case of Ly450mm.
This is the same tendency with that of the Katto's


Paper No


S-0.4'MPa, T,, =80de.C, '
L =1800mm, e=0.0mm q 1. .
T eq.--5.....
Bownng -
WeberJohannsen
KLowdemik Katto(L)
Olekhnovitch
lacbeth(1963) 5 Shah

--. -

S Groeneveld(1986) ,Groenevjid(1996)






Paper No


G kg/m2s
(a) Mass flow Rate of Entrainment.


G kg/m2s
(b) Mass flow Rate of Deposition


G kg/m2s
(c) Mass flow Rate of Entrainment Droplet.


Figure 7: Magnitude of Entrainment
(Liquid Film Model).
correlation, and it can be considered as the influence of
another mechanism of entrainment caused by the high heat
flux.
Okawa evaluated the entrainment caused by the boiling in
liquid film, on the basis on the experimental results of
falling film by Ueda(1981).


( 125 075

HLc QJg


where HLG is a latent heat, ym is a mean film thickness
when von Karman's universal velocity profile is assumed
in the liquid film.
Ueda expresses the proportionality factor Ceb depends on
the fluid and 477 is recommended for water. In Fig.6(a),
the value calculated by this amount is shown as


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

"me=mes+meb(Ceb=477)". In the calculation mes and meb is
treated as the linear relation for tentative.
(c lim,2i l'"1) who used the similar method, and expressed
this treatment showed good agreement with experimental
data. But for the presented data, this method overestimated.
This difference may be caused by the difference of the
magnitude of the heat flux. But anyway one tenth value, i.e.
Ceb=47.7, show good agreement with present results.
Similar tendency was also pointed out by Okawa, and this
effect will be considered as the suppression effect of forced
convection of annular flow. The detail mechanism is not
clear, but in this experiment this treatment is adopted to the
data of 450mm tubes.
In Fig.6(b) and (c), same calculation results are also
plotted as "me=mes+meb". In the case of the LT=900mm,
weekly influence of meb can be observed in data, but it's
not so clear under this condition.
The magnitude of the entrainment caused by boiling is
clearly observed in Fig.7. In Fig.7, the deposition and the
entrainment are converted to the mass flow rate. As shown
in Fig.7, influence of the entrainment caused by boiling
increases with the decreasing in the heated length, which is
related to the heat flux. In the case of the 450mm tube, the
entrainment caused by the boiling becomes dominant.
On the contrary, the deposition rate does not increase in
short heated length, even under high droplet concentration.
It can be considered as the lack of the actual length of
annular flow regime, and this effect finally appeared as the
difference of the final amount of droplet. Then, in this
condition, the dryout occurred under low quality condition.

Critical Heat Flux in Non-uniformly Heated Tube
The critical heat flux value of non-uniformly heated
condition in LT=450mm is plotted in Fig.8. In this figure,
3000 I '-I- i iI- "- I -.
pe = 0.4 MPa, T,,= 80 OC /, X 1-0
2500 Kutateladze (pool boiling CHEf .

2000u- Katto-Ohno IA

S1500 -Macbeth 3 -, / 0.5_-

1000- AA
'- E Expenment '
500 - O Normal tube
f - = 0.3 Eccentric tube
o I I I I E ? ave
0 20 40 60 80 100 120 140
G kg/m2s
Figure 8: Critical Heat Flux(e=1.5mm LT=450mm).


d.4 MPa, T,,= '80 deg'C, L4 450mm
450 Z

SA A
300- turflow A A A


150 Slug flow mm
0 1.5
Location of CHF A
Trans tion to gnnular flow -'--
0 20 40 60 80 100 120 140
G k/m s
Figure 9: Axial Location of CHF.






Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


50 04='O4MP T 7 798degC, G=: *I 3000 . .. -
qAVE= E m L, p,=0.4MPa, T,,n 80deg.C,
U 400 L7 =450mm ,-' =0.9
S300 CHF at Pool boiling -
2000 ,-"

100 ,-
O-et 100' 0.36exp(-75.91JL
Outlet 0^ 0.100
(z450mm)
me
----- mes+meb(ceb-47.7)
niet 0 5 10 15 20 0 20 40 60 80 100 120 140
(z0 Omm) Time sec G kg/m2s

(a) LT=450mm
(a) G=36kg/m2s
,, 9 7 ldegC, G 947kg/m2s '0 4 I e I I -
2o 79 deg C, G 94 =0.4Pa, T,7 =80deg.C,
500 2 i ,,, =-l 5nmn, L,=450mm
oo 400 1500 -
" 3_______o_________/ 00

300
200 1000 -
100 me=mes
S=0.1+0.36exp(-75.91JL)
Outlet 0 500
(z-450mm) ,


jnlet 0 5 10 15 20 25 30 35 40 0 20 40 60 80 100 120
(z0 0mm) Time sec G k/m2s
(b) LT=900mm
(b) G=95kg/m2s
Figure 10:Wall Temperature at CHF Condition.. 1000
S-0.4MPa, T, =80deg.C,'
L =1800mm
maximum heat flux is expressed by the triangle plots, and 800 _1
circle plots present the average heat flux. The results of
uniformly heated tube are also plotted by square plots. 600
The location where CHF was detected, and the location of
the annular flow transition calculated by Wallis's 400 me=m
correlation (1969) are also plotted in Fig.9. Wall =0.1+0.36exp(-75.91JL)
temperature movements at the maximum heat flux point
under CHF condition are also plotted in Fig. 10. As shown 2 200
in Fig.8, CHF in this condition show the upper limit when
the mass flux becomes larger than 60kg/m2s. On the basis 0 20 40 60 80 100 120
of the location of the CHF (Fig.9) and temperature profile G kg/m2s
(Fig. 10), CHF in this condition cannot be considered as the (c) L=1 mm
liquid film dryout at the exit part. In Fig.8, the pool boiling Figure 11: CHF of Non-unifoly Heated Tube...
condition(Collier (1994)) is also drawn and it shows a
good agreement with that of the upper limit of CHF. Thus, 2 i
two mechanism of CHF, i.e. the dryout of liquid film and Pex= 0.4 MPa, Tn, = 80deg.C L 4mm
0 450
DNB under high mass flux condition, can be expected in 15 900
this result. 1800
In Fig. 11, the maximum heat flux at CHF of non-uniformly
heated tubes is plotted with the calculation results. In o0
calculation the liquid film redistribution is expressed by s -------Q ~.._------- .m m_.
the next equation on the basis of the Butterworth
model(1971) 0.5 O 0
0, 0)
dMf
N (7) 0 20 40 60 80 100
n t1 /Be*
Figure 12: Spreading Coefficient.
In this case, liquid film model is modified as next equation,






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


S10x10
pe, 0.4MPa, T,, =80deg.C,
8 s=1.5mm

6- L,=-450mm -' -

4
SLr 900mm
-, Z,
LT 1800
j


1
m
-0
S.0.5
5


coefficient in next equation,


1m-


10 20 40 60 80 100 120 140
G kg/m2s
(a)Mass Flow Rate of Entrainment.
X 103
p,, 0'4MPa,' T,, =8deg.C, '
1 -=1.5mm
Film flow model
casel-: 0.9
--case-II; i -
L,=1800mm -
.5- L =900
L, =450mmn -/i


0 20 40 60 80 100 120 140
G kg/m2s
(b)Mass Flow Rate of Deposition.


0 20 40 60 80 100 120 140
G kg/m2s
(c)Mass Flow Rate of Liquid Film Spreading.


G kg/m2s
(d)Component of Liquid Film Re-distribution.
Figure 13: Magnitude of Liquid Film Re-distribution.

dMs dN
+ + m +me md = 0 (8)
dz RdO

Calculation results of previous paper is expressed by solid
line, and this value is calculated by using the spreading


= 0.1+0.36exp(-75.91JL)


m


As shown in Fig. 11(b)(c), i.e. the case of the longer tubes,
calculation results by this method expresses well the
experimental results, but this value is slightly lower than
that of the experimental results in short case (Fig. 1(a)).
In Fig.12, the spreading coefficient calculated by the
experimental result is plotted against the inverse of the
modified Boiling number. In the calculation of Boiling
number, the difference of the heat flux between the
maximum value and the minimum value was used. This
non-dimensional number expresses the non-uniformity of
the liquid film.
As shown in Fig.12, magnitude of spreading coefficient
may be correlated with the Bo 1. The detail estimation will
be appeared in the next step, but in this stage =0.9 mm is
used to the LT=450mm tube.
The calculation results with =0.9mm are plotted in
Fig.11(a), and it expresses the experimental results
approximately, but it slightly over estimated the calculation
results. This difference will be considered as weak
influence of the entrainment caused by the boiling meb.
The results included the estimation of meb are expressed by
broken lines, and it expresses the experimental results well.
In Fig. 13, each parameter also plotted against the mass flux
as mass flow rate.
In these figures, bold line expresses the calculation model
which finally used in this paper. As shown in Fig.13(a),
owing to the evaluation of the entrainment caused by the
boiling, 450mm tube takes the high entrainment rate, but
the deposition rate does not show the drastic increasing in
Fig.13(b).
On the other side, the spreading flow rate of 450mm
drastically increases by estimating of the entrainment
caused by the boiling in Fig.13(c). Figure 13(d) expresses
the ratio of the liquid film spreading against the total
amount of the liquid film redistribution. These results
express even under high concentration of droplet case, the
flow redistribution caused by the deposition is less than
1%, and most of the liquid film redistribution is considered
as the results of the spreading of the liquid film itself. Also
the Fig.13(c) means that the high spreading amount of
liquid film is generated by the strong non-uniformity
caused by the large entrainment amount.
Finally, calculation results of all tubes are plotted as


0 .5 I 1- I I I I -
20 40 60 80 100 120 140
G kg/m2s
Figure 14: CHF of Non-Uniform Heat Flux Condition.


Paper No


pex =0.4MPa,'T,, =86deg.C,
=1.5mm _
Film flow model
--se- L,=1800mm
L~ L
LT =900nmm ii ,,n"'
LT =450mm -


----- ----------
-------
------------ --






Paper No


qCHF(MAX)qxeq-1 0, in Fig.14. In this figure, bold lines also
correspond to the calculation results which finally used in
this paper. In this figure, the pool boiling condition
calculated by Kutatelade (Colier 1994) is also drawn. As
shown in the figure, present method expresses the critical
heat flux characteristics of this investigation very well.


Conclusions

In this paper, heat transfer and flow characteristics of
non-uniformly heated tube, especially short tube case, were
experimentally investigated, and following results were
obtained.
1) The pressure drop can be estimated by using the averaged
heat flux. This means that the main flow characteristic is
decided by the total amount of the vapour generation
2) The heat Transfer coefficient can be estimated by using
the modified Schrock-Grossman correlation. This result
means that the nucleate boiling is dominant mechanism, but
weakly influence of forced convection cannot be neglected.
3) Critical heat flux of uniform tubes especially in short tube,
the entrainment value caused by the boiling cannot be
negligible. These effects are well expressed by using the
liquid film mode.
4) Critical heat flux in non-uniformly heated tube can be
expressed well by using the liquid film model. By using the
liquid film model and the pool boiling condition, the
calculation results show a good agreement with the
experimental data.

Acknowledgements
This is a product of research which was financially
supported in part by the Kansai University Research Grants;
Grant-in-Aid for Joint Research, 2009-2010.

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7th International Conference on Multiphase Flow
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