7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The Effect of Bubbles on a Heat Transfer in a Turbulent Downward
GasLiquid Flow in a Pipe: Experimental and Numerical Study
Oleg Kashinskyl, Pavel Lobanovl, Maksim Pakhomov2 and Victor TerekhoV2
1Lab. of Plwsical and Chemical Hydrodynamics, Kutateladze Institute of Thermoplwsics, Siberian Branch of Russian
Acadenw of Sciences, Novosibirsk, 630090, Ac. Larrent'ev Ave. 1, Russia
Email: kashinsky~,itp.nsc.ru
2Lab. of Thermal and Gas Dynamics, Kutateladze Institute of Thermoplwsics, Siberian Branch of Russian Acadenw of
Sciences, Novosibirsk, 630090, Ac. Larrent'ev Ave. 1, Russia
Email: terekhov~itp.nsc.ru
Keywords: Turbulent heat transfer, void fraction, bubbly flow, twofluid model
Abstract
The work presents results of predictions and experimental studies of the local structure and heat transfer in the downward
gasliquid flow in vertical pipe. The mathematical model is based on the Euler description for both phases taking into account
fragmentation and coalescence of bubbles. Influence of the variation initial diameter of the gas phase at the inlet, gas volumetric
flow rate ratio, initial temperature of liquid and its velocity on the flow dynamics, friction and heat transfer in the twophase
flows has been studied. Flow structure and wall friction are qualitatively similar to the ones for the flow without heat transfer.
Addition of the gas phase causes heat transfer growth, at that, this effect becomes more evident along with the gas content
increased.
Introduction
Downward bubbly flows with and without of heat transfer
between the wall and twophase medium are widespread in
chemical technology, heat and nuclear power engineering,
and etc. As experimental and numerical investigations of
such flows show downward bubbly flow is characterized by a
number of specific features compared to the upward one (see
for example Ganchev & Peresad'ko 1986: Wang et al. 1987:
Usui & Sato 1989: Kashinsky & Randin 1999; Hibiki et al.
2004; Sun et al. 2004; Zaichik et al. 2004; Kashinsky et al.
2006; Liu & Tryvgasson 2006).
Profile of the local void fraction in the downward flow is
characterized by the present area free from the bubbles near
the wall; in the turbulent core of the flow it has practically
constant value of gas bubbles concentration; whereas in the
upward flow local void fraction maximum is observed in the
nearwall part of the pipe. Presence of the area practically
free of bubbles is explained by the transverse forces such as
Saffman and turbophoresis turbulentt migration). Liquid
velocity in the downward flow can have local maximum at
some distance from the channel wall. Intensity of
longitudinal fluctuations of liquid velocity in the wall region
of the pipe is less than the respective value for the
singlephase flow, and in the turbulent core of the flow it is
the other way round. Suppression of pulsation intensity in the
wall area of the pipe is explained by the fact that the bubbles
leaving the nearwall part of the pipe increase thickness of
viscous sublayer, and turbulent vortexes are destroyed.
Generation of liquid turbulence in the axial zone of the pipe
takes place because of vortex formation at the streamline of
bubbles by shear flow of liquid.
Note that the bubbly vertical flows at present heat transfer
between the pipe wall and the twophase system have been
studied less than the isothermal flows. Mention the
theoretical works by Sato et al. 1981; Marie 1987:
Mikielewicz 2003 and experimental ones by Bobkov et al.
1973; Sekoguchi et al. 1980: Ganchev & Peresad'ko 1986:
Cui et al. 2006.
At that, Bobkov et al. 1973 is devoted to the description of
both upward and descending flows, and only in the work by
Ganchev & Peresad'ko 1985 there are results of investigation
of downward flows' hydrodynamics and heat transfer. In all
other abovementioned works studies were carried out only in
the upward regime of the twophase mixture flow.
In the work by Ganchev & Peresad'ko 1986 the flow
structure, wall friction, local void fraction and heat transfer in
the downward gasliquid flow were investigated in the modes
of cocurrent flow and gas phase handing. Hydrodynamic
measurements were carried out in the steel pipes with the
diameter of 27, 40 and 52 mm, and heat transfer was
measured only in the copper cylindrical channel with 27 mm
diameter. Liquid velocity was U=0.081.6 m/s and P=031
%. Bubble dimensions were not measured in the work, but
according to the estimates their size ranged d=3.55.5 mm,
and increased with gas volumetric flow rate ratio growth.
All works demonstrate substantial increase of heat transfer
and change of the liquid flow turbulent structure at the
addition of gas bubbles. Unfortunately, use of measurement
data is rather complicated because of the incompleteness of
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
the liquid flow and open for the gas flow. The gas was
supplied to the mixer from highpressure pipeline. The gas
pressure, dropped down with the help of a pressure regulator
installed at the inlet to the setup, was 1 atm. The gasliquid
flow was produced in an upward section to enter, through a
Ubend, a downward section, presenting a vertical
stainlesssteel pipe with 2R=20 mm I.D. At this section,
visualization unit and measuring unit were mounted. The
hydrodynamic characteristics of the flow were measured
using the electrochemical technique. To determine the
profiles of liquid velocity and the local void fraction profiles,
a "bluntnose" type flow velocity probe was used. To
measure the wall friction, an electrochemical wall shear
stress probe was used. More detailed description of the
measuring setup without heat transfer area is given in
Kashinsky et al. 2006.
The heat transfer measuring unit is a thin wall stainless steel
pipe 20 mm I.D. and 580 mm long. The platinum sensors
were utilized to measure the temperature of liquid in the test
pipe entrance, measuring unit and the test pipe exit. Electric
current from the high current system heated the pipe. The
knowledge of these temperatures allows us to determine the
heat transfer coefficients of the flow. To perform
measurements around the bubble 12 temperature probes
were used spaced 10 mm apart. The first one was placed
225 mm downstream the beginning of the heated section.
The initial liquid temperature was measured immediately
after the rotameters, the final liquid temperature was
measured in the outlet section of the pipe. At low liquid
Reynolds numbers a deviation of experimental data from the
onephase heat transfer regularities of about 5 % was
detected. With increasing the Reynolds number the
difference of experimental and calculated data in a single
phase flow decreases and becomes about 1 % for Re=6000.
The estimated error of measurements by the heat loss was
about one percent.
The resistance of the heated pipe was 0.0272 Ohm. The
electric current through the pipe was 112.5 A. Therefore, the
pOwer emitted at the heating section was 345 W.
Numerical Model
Numerical model is based on the use of Euler description
for both phases. The system of nonsteady state
axisymmetric RANS equations is used to describe transfer
processes in both phases in the pipe. Initially Euler model
was developed to describe heat and mass transfer in
separated axisymmetric gasdroplets flow downstream of
the sudden pipe expansion, Terekhov & Pakhomov 2009. To
close the system of mean motion equations LRN k i
turbulence model in modification of Hwang and Lin 1998
was used.
Numerical model of Terekhov & Pakhomov 2009 was
upgraded by the authors to describe dynamics and heat
transfer in gasliquid flow taking into account the force of
aerodynamic drag, effect of the added mass (Bass force),
gravity and Archimedean forces, Saffman forces, turbulent
homogenous diffusion of bubbles and nearwall force. The
model of Reynolds stress (aubt b3trnsfer in disperse
phase by Zaichik et al. 2004 is used. Equation of
temperature fluctuationss 90 and turbulent heat fluxi
information necessary for numerical computation. This
proves the necessity of test experimental studies of heat
transfer in the downward gasliquid flows.
The objective of this investigation is to carry out numerical
and experimental simulation of hydrodynamic and heat
transfer processes occurring in the downward turbulent
bubbly flow in the pipe.
Nomenclature
Cr wall friction coefficient
d bubble diameter (m)
g gravitational constant (ms')
h heat transfer coefficient (Wm2K')
k turbulent kinetic energy (m2S2)
P pressure (Nm2)
R pipe radius (m)
T temperature (K)
U, velocity components in axial and radial
directions (ms ')
U. friction velocity (ms')
u2') ,? V2m.S. velocity fluctuations of the gas phase
in axial and radial directions (m2S2)
(uLuI Reynolds stresses (m2S2)
V ~averaged bubble volume (m3)
x1 axial and radial coordinates (m)
y coordinate normal to the wall (m)
Re Reynolds number
Nu Nusselt number
Greek letters
8 dimensionless temperature
oc void fraction
P volumetric gas flow rate ratio
dissipation of the turbulent kinetic energy
(m2S3)
gRt temperature fluctuations in the dispersed
phase, K2
9 us turbulent heat flux in the dispersed phase,
b3 Kms
zw wall shear stress (Pa)
Subsripts
0 onephase water flow
1 parameter under inlet conditions
b bubbles
c ~pipe centerline
W wall
+ denotes the dimensionless variables in
dynamic universal units
Acronym
CVs control volumes
LRN low Reynolds number
I.D. inner diameter
Experimental Facility
In the experiment, the electrodiffusion technique was used in
combination with electrical conductivity measurements. The
experimental setup was a twophase flow loop, closed for
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
distribution of liquid velocity over the pipe section. The
largest deformation of velocity profiles is observed at small
distance from the wall and agrees with the data of Wang et
al. 1987: Kashinsky & Randin 1999; Sun et al. 2004;
Kashinsky et al. 2006 for the bubbly flow without heat
transfer. In the axial region liquid velocity profiles in the
twophase flow have lesser value that at singlephase flow
of water.
Distribution of liquid phase temperature
8= (Tn T)/(Tn,T, ) along the channel radius is presented
in the Fig. lb, where Try is wall temperature and To is
temperature of liquid on the pipe axis. Increase of initial
bubble diameter results in the growth of temperature profile
fullness in the wall area that proves increased heat transfer
between the wall and the twophase flow. Liquid
temperature profiles in the turbulent core of the twophase
flow are qualitatively similar to the ones in the singlephase
flow of pure liquid. For Ganchev & Peresad'ko, 1986
measurements is also specific the increase of temperature
profile fullness in the vicinity of the wall in the gasliquid
Results of numerical simulations prove that in the
downward nonisothermal bubbly flow gas bubbles group in
the vicinity of the pipe axis (see Fig. Ic). In the main zone
of the channel distribution of local void fraction is
practically even over the pipe section. For the profiles of
void fraction zero value of oc is specific in the nearwall area
of the pipe. The value of the nearwall layer of "pure" liquid
depends on P and bubble diameter in Kashinsky et al. 2006.
Smaller bubbles approach closer to the pipe wall that can be
explained by lower values of radial forces, such as lifting
power, turbulent migration and nearwall force. Analogous
results is observed also for the gasliquid flow without heat
transfer in Kashinsky & Randin 1999; Kashinsky et al.
2006).
In the Fig. 2 are presented results of wall friction coefficient
Oba) ob3 O bbbles also take the fonrm according to Zaichik
et al. 1997. It should be noted that initially equations of
temperature pulsations and turbulent heat flux in the
disperse phase were developed for gas flows with solid
particles, but as predictions of this work has shown these
models can be successfully used for the description of heat
transfer in gasliquid flows. The work considers bubbles
breakup and coalescence according to the balance equation
for the bubble transfer with the averaged volume v
analogously to Lehr and Mewes 2001. Initially the model of
Lehr and Mewes 2001 was developed for the bubble
columns, but according to our calculations it can be applied
to describe bubbly flows at small value of gas volumetric
flow rate ratio p<:10 % as well.
Calculations were performed on the grid containing 200x 100
control volumes (CVs). Nodes were thickened in the vicinity
of the wall and at the pipe inlet. In addition numerical
simulations were performed on the grid containing 300x200
CVs. Difference in the predictions of Nusselt number for
gasliquid turbulent flow and liquid and bubble velocities did
not exceed 12 %.
The first calculation CV was located at the distance v =0.4
from the wall. In viscous sublaver there were not less than 10
CVs
In the inflow crosssection liquid parameters are taken from
preliminary calculation of the singlephase flow of water in
the 1.5 m long pipe (L/(2R) = 75). Further monodisperse
bubbles were introduced in the water flow evenly over the
section. Temperature of the twophase system at the inlet to
the computing domain was tl=tb=20 ''C, further its
temperature changed for the account of heat exchange with
the wall. On the pipe axis symmetry conditions are set for the
gas and disperse phases. On the wall impermeability and
adhesion conditions are set for the gas phase as well as the
value of its constant temperature varying in the range
txy=2540 ''C. In the outflow crosssection boundary
conditions are set as zero derivative parameters in axial
direction.
Results and Discussion
Diameter of disperse phase in the inflow crosssection
varied in the range d=02 mm and remained constant only
in the inflow of the pipe. Further down the flow the bubble
dimensions in this work changed for the account of
coalescence and breakup. Gas volumetric flow rate ratio at
the inlet was P=010 %. Liquid flow velocity was
U1=0.33.5 m/s, that agreed with the Reynolds number of
the flow Re=U12R/v=(0.57)x104. Profiles of parameters
distribution over the channel section were calculated at the
distance L/(2R)=100, that conforms to hydrodynamically
stabilized area.
Flow Structure
Predicted velocity and temperatures profiles of liquid and
local void fraction over the pipe radius are shown in the Fig.
1. Influence of gas bubbles diameter on the velocity of
liquid phase is presented in the Fig. la, where Uo is velocity
of singlephase flow of liquid on the pipe axis. Points are
powerlaw profile in the singlephase flow, Schlichting 1960.
Note that change of bubble size in this research (d=0.52
mm) does not result in significant difference in the
r
predictions
2
By
~Yin the twophase flow depending
pU:
on Reynolds number at various values of P (Fig. 2a) and
bubble diameter (Fig. 2b). Lines 1 in the Figs. 2 show
results of friction coefficient calculations for singlephase
liquid flow at other identical conditions. The law of
resistance for turbulent singlephase flow modes takes the
form
C, 0.0396
'= q(1)
2 Re"
At the calculation of Reynolds number the channel diameter
was assumed fixed parameter.
The wall friction at singlephase liquid flow regime (P=0)
well agree with the formula (1). At the growth of Reynolds
number of the flow decrease of friction drag is observed in
the turbulent flow mode that agrees with the data of
Terekhov & Pakhomov 2008 for the downward bubbly flow
at the absence oh heat transfer between the wall and the
twophase medium. At further increase of Reynolds number
friction in twophase mode decreases practically to the value
of the singlephase mode. Increase of the gas volumetric
flow rate ratio and size of disperse phase results in the
increase of resistance coefficient. Note, that at p increase
specific is change of the slope of curves Cr with appropriate
change of the constant in the drag law.
0 0,2 0,4 0.6 0,8
y/R
0 0.1 0.2 0.3 0.4 0.5
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
1,0
S0.8
0.2
1i
Re7x104
5 4
i
_7
7x10
Figure 2: Friction as a function of Reynolds number. (a):
d=1.5 mm, 1 Blasius formula (1), 2 P=0 % (onephase
water flow), 3 1, 4 5, 5 10. (b): 1 Blasius formula (1),
2 d=0 mm (onephase water flow), 3 0.5, 4 1.5, 5 2.
et al. 1973; Ganchev & Peresad'ko 1986 and calculations of
Mikielewicz 2003, stating that effect of bubbles on heat
transfer becomes less noticeable compared to the "proper
turbulence of the liquid flow.
In the Fig. 3b are shown the data of initial bubble size
influence on heat transfer enhancement St/Stein the bubbly
flow. It is apparent that bubble size has significant impact
on heat transfer in gasliquid flows. Increase of bubble
diameter results in the increase of heat transfer
intensification parameter in the downward flow, whereas the
opposite trend is observed in the upward flow mode in the
boundary laver, Mikielewicz 2003.
The increase of the wall temperature tw (see Fig. 4) results
in the growth of the parameter St/Sto that agrees with the
experimental data of the work by Ganchev & Peresad'ko
1986. Effect of the wall temperature on heat transfer is more
prominent in the area of its small values. Further along with
the growth of tw this effect decreases.
Influence of gas volumetric flow rate ratio on the change of
thermalhydraulic parameter St/Sto/(Cf/Cfo) is shown in the
Fig. 5, where Cs, is friction in the singlephase liquid flow.
Value of thermalhydraulic parameter increases with the
increase of the bubbles size and volume consumption gas
content. This is proved by the data of the Figs. 2 and 3
stating that heat transfer and friction increase along with the
growth of gas volumetric flow rate ratio. Note that friction
in the twophase flow increases more intensely than heat
transfer intensification and, respectively, parameter of
0,15
0,e0
on
3 0
Figure 1: Velocity (a), temperature (b) profiles of the liquid
phase and local void fraction distribution (c) across the pipe
radius. 2R=20 mm, x/(2R)=100, tl=20 "C, 1 = 0, DC, P=5 %.
(a) and (b): 1 onephase water flow (d = 0 mm), 2 d=0.5
mm, 3 1, 4 1.5, 5 2. (c): 1 d= 0.5 mm, 2 d=1, 3
 1.5, 4 2.
Heat Transfer
Change of heat transfer intensification ratio St/Sto depending
on the gas volumetric flow rate ratio and size of dispersed
phase is given in the Fig. 3, where Stois Nusselt number for
singlephase liquid flow. Increase of P causes significant
increase of heat transfer between the wall and the twophase
flow in the whole area of bubbles gas volumetric flow rate
ratio. With the growth of Reynolds number intensification
decrease of heat transfer from the wall to the bubbly flow is
observed. This agrees with the experimental data of Bobkov
.I I
2 4 6 8 10
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
S1.6
12
0.8 C
0.6 C
0246810
Figure 5: Effect of bubbles on the thermolwdraulic
parameter. Re= 10 1 P= 1 %, 2 5, 3 10.
is x/(2R)=70. Predicted results fairly correlate with
measurement data of Kamp et al. 1995 and numerical
calculations of Zaichik et al. 2004. In the downward flow
bubble velocity is less than liquid velocity that can be
explained by the lifting effect of Archimedean force.
Distribution of phases velocities profiles are monotonous
character. Velocity profile for gas bubbles has a flatter form
due to the presence of liquid velocity gradients in the wall
zone for the account of friction with the channel wall.
Data on local void fraction oc in the downward gasliquid
flOw in the pipe without heat transfer between the wall and
the twophase flow were compared with measurement and
numerical results of Kashinsky et al. 2006 (see. Fig. 7).
Numerical study of Kashinsky et al. 2006 was performed for
the boundary layer approach with using of Euler/Euler
method.
Simulations were made for the parameters that agree with
the experimental ones in the work by Kashinsky et al. 2006
for lwdrodynamically developed gasliquid flow. In the
distribution of local gas content in the wall area of the pipe
we observe the zone practically free of the bubbles.
Whereas in the turbulent core of the flow a has practically
constant value that agrees with the measurement data. Note
that smaller bubbles can approach closer to the pipe wall for
the account of small values of transverse forces, such as
Saffman force and turbulent migration.
For the case of descending gasliquid flow in the heated
cylindrical channel experiments by Ganchev & Peresad'ko
1986 (see fig. 8) were used, where he and Cro are heat
transfer coefficients and friction in the singlephase liquid
flow at other identical conditions. It should be noted that
from the data of Ganchev & Peresad'ko 1986 it is known
that measurements were carried out at conditions q,= const,
but the value of the heat flux on the wall was not indicated.
In the Fig. 8 there are results of our predictions that are the
closest to the measurement data. Initial bubble size were not
clearly indicated as well, but according to the estimates of
Ganchev & Peresad'ko 1986 for the conditions given in the
Fig. 8, bubble size was d=3.5 mm. Increase of the density of
the heat flux results in heat transfer increase that agrees with
the data of our calculations.
Conclusions
Euler twoliquid model has been developed for the
4 6 810
S2,0
~1 6
1,2
Figure 3: Heat transfer enhancement ratio for various
Reynolds number (a) and bubbles diameter (b). (a): d=1.5
mm, 1 Re=5000, 2 10 3 1.5x104 4 2x10 (b):
Re=10 1 d=0.5 mm, 2 1, 3 1.5, 4 2.
1,6 
1,4 
1,2 I
35 c
t,, O
Figure 4: The effect of wall temperature on the heat transfer
augmentation in bubbly flow. Re= 10 1 P= 1 %, 2 5, 3 
10
thermallwdraulic efficiency in all flow regimes is less than
one.
Comparison with Experimental Results for Downward
Bubbly Flows with and without Heat Transfer between
Wall Surface and TwoPhase Systems
Distributions of the averaged axial velocities of liquid (lmne
1) and gas (line 2) phases along the pipe diameter for
lwdrodynamically developed gasliquid flow are shown in
the Fig. 6. Coordinate where measurements were provided
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
description of the processes of impulse, heat and mass
transfer in the downward gasliquid flows in the pipes
COnsidering breakup and coalescence of bubbles within the
frameworks of the model by Lehr & Mewes 2001. To model
turbulence in the carrying agent modified turbulence model
kE is used. For the dispersed phase correlations from the
work by Zaichik et al. 1997; 2004 were used. In addition to
verify reliability of the developed model experimental
investigation has been carried out.
Numerical predictions of the downward bubbly flow in the
pipe has been performed. Flow structure and friction on the
wall at the addition of the bubbles behave analogously to the
gasliquid flow without heat transfer. Addition of the gas
phase causes increase of heat transfer, at that, this effect
becomes more noticeable along with gas content growth.
Growth of bubble diameter results in the increase of heat
transfer rate in the twophase downward flow compared to
the singlephase one. Flow velocity increase leads to the
decrease of heat transfer intensification parameter.
Comparison with our experimental results has been carried
out. It is shown that this model correctly describes local
void fraction along the channel section. Fair agreement
between the calculation results and measurements of local
void fraction profiles along the pipe section and heat
transfer is observed. Thus, the Euler model developed by
the authors and taking into account breakup and coalescence
of bubbles can adequately describe complex regularities of
gasliquid flow parameters distribution.
Acknowledgements
This work was partially supported by the Russian
Foundation for Basic Research (Project No. 080800543).
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ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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