Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.64 - Numerical Investigation of Bubble Growth in Subcooled Flow Boiling
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00460
 Material Information
Title: P1.64 - Numerical Investigation of Bubble Growth in Subcooled Flow Boiling Cavitation
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Yuan, D.-W.
Pan, L.-M.
Chen, D.-Q.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: bubble growth
subcooled flow boiling
VOF model
UDF subroutine
numerical simulation
 Notes
Abstract: Bubble growth in subcooled flow boiling is a quite complicated process. It includes not only micro-layer evaporation on heating wall, but also involves top condensation when the bubble emerges to subcooled bulk. In present paper, a bubble growth model for subcooled flow boiling is proposed to simulate bubble dynamics with CFD method. A micro-layer evaporation model at the bubble bottom and a heat and mass transfer model on bubble interface are used. User Defined Function (UDF) interface in Fluent platform is applied to realize this model. The volume of fluid (VOF) multiphase flow model combined with phase change model is used to simulate bubble growing. The effects of bulk velocity, liquid subcooling, wall superheating and vapor-liquid contact angle are considered in present model. The results reveal that bubble growth process in subcooled flow boiling is a dynamic result of evaporation and condensation. With increasing wall superheating, the bubble growth rate will be accelerated; however, with higher liquid subcooling, the bubble growth rate will decrease. The simulation also reveals that the evolution of bubble shape is a complex process. During bubble growing, the pressure inside the bubble decreases and distributes uniform inside the vapor bubble; and there will be a flow liquid region of having minimum pressure in the vicinity of a growing bubble. The eddy can be seen on both side of a growing bubble and accelerates contraction of the vapor-liquid interface at bottom of bubble. With the distance from the heating wall increasing, the flow liquid temperature decreases. In superheated liquid region, the temperature gradient which does not change with bubble growth time is very great, while the temperature of subcooled liquid region which is far from the heating wall increases with bubble growing.
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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Bibliographic ID: UF00102023
Volume ID: VID00460
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P164-Yuan-ICMF2010.pdf

Full Text


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


Numerical Investigation of Bubble Growth in Subcooled Flow Boiling


De-wen Yuan, Liang-ming Pan*, De-qi Chen
School of Power Engineering, Chongqing University, Chongqing 400044, China
E-mail: cneng~cqu.edu.cn

Keywords: bubble growth; subcooled flow boiling: VOF model: UDF subroutine: Numerical simulation

Abstract: Bubble growth in subcooled flow boiling is a quite complicated process. It includes not only micro-layer
evaporation on heating wall, but also involves top condensation when the bubble emerges to subcooled bulk. In present paper,
a bubble growth model for subcooled flow boiling is proposed to simulate bubble dynamics with CFD method. A micro-layer
evaporation model at the bubble bottom and a heat and mass transfer model on bubble interface are used. User Defined
Function (UDF) interface in Fluent platform is applied to realize this model. The volume of fluid (VOF) multiphase flow
model combined with phase change model is used to simulate bubble growing. The effects of bulk velocity, liquid subcooling,
wall superheating and vapor-liquid contact angle are considered in present model. The results reveal that bubble growth
process in subcooled flow boiling is a dynamic result of evaporation and condensation. With increasing wall superheating, the
bubble growth rate will be accelerated; however, with higher liquid subcooling, the bubble growth rate will decrease. The
simulation also reveals that the evolution of bubble shape is a complex process. During bubble growing, the pressure inside
the bubble decreases and distributes uniform inside the vapor bubble; and there will be a flow liquid region of having
minimum pressure in the vicinity of a growing bubble. The eddy can be seen on both side of a growing bubble and
accelerates contraction of the vapor-liquid interface at bottom of bubble. With the distance from the heating wall increasing,
the flow liquid temperature decreases. In superheated liquid region, the temperature gradient which does not change with
bubble growth time is very great, while the temperature of subcooled liquid region which is far from the heating wall
increases with bubble growing.


Introduction
In order to understand and optimize the process of boiling
heat transfer, it is vital to understand the mechanism of
bubble nucleation, growth and departure. As a complex
process, the investigation of model for bubble formation and
disappearance has gotten only limited success. In recent
years, some investigations about single bubble growth
model for nucleate boiling have been performed.
Mei and Chen et al. (1995) performed a numerical analysis
about bubble growth in saturated heterogeneous boiling.
They considered the bubble growth is determined by
simultaneous energy transfer between vapor bubble and
liquid micro-layer or heating wall. Finite different solutions
for temperature fields of micro-layer and heating wall were
obtained on expanding coordinates as the bubble growing.
Samuel (1998) presented a numerical analysis about
axis-symmetric vapor bubble growth. An interface tracking
method in conjunction with a finite volume method on a
moving unstructured mesh was used. The control volume
continuity, momentum and energy equations were modified
at the presence of a phase interface to include surface
tension and discontinuous pressure and velocity.
Heo and Koshizuka et al (2002) showed a numerical study
about the growth of bubble in transient pool boiling through
moving particle semi-implicit with mesh less advection by
flow-directional local grid (MPS-MAFL) method. The
growth process of a bubble with different initial radii was
calculated with high heat flux and high subcooling
condition.
Li and Yan et al (2003) provided a new understanding about
the interfacial transport characteristics of inviscid spherical
bubble with different geometric parameters, rising in a
stagnant hot or bi-solution liquid. The flow and temperature
fields around bubbles and similarly sized rigid spheroids
were computed. The interfacial transport characteristics of
spherical bubbles were studied numerically.


Liao and Mei et al (21***-0 developed a physical model for
vapor bubble growth in saturated nucleate boiling that
includes heat transfer through the micro-layer and the bulk
superheated liquid surrounding the bubble as well. Both
asymptotic and numerical solutions for the liquid temperature
field surrounding a hemispherical bubble indicated that there
is a thin unsteady thermal boundary layer existed adjacent to
the bubble dome. During the early stages of bubble growth,
heat transfer to the bubble dome through the unsteady
thermal boundary layer constitutes a substantial contribution
to vapor bubble growth,
Genske and Stephan (2006) considered that the region around
a single growing bubble can be subdivided into three
sub-regions: micro-region, bubble area, and surrounding
liquid. Their results showed that the flow pattern in the liquid
around a growing vapor bubble is not only determined by the
movement of the bubble surface, but also the vapor flow flied
inside the bubble. In regions away from the bubble, heat
conduction would be the dominant factor. Velocity and
temperature field, heat flux, bubble contour, and departure
diameter were calculated for different fluids by the authors.
Mukherjee and Kandlikar (2007) presented a static contact
angle model and a dynamic contact angle model based on
contact line velocity and the sign of the contact line velocity
which have been used at the base of a vapor bubble growing
on a heated wall. The complete Navier-Stokes equation was
solved and the liquid-vapor interface was captured through
the Level-Set technique. The effects of dynamic contact angle
on bubble dynamics and vapor volume growth rate were
compared with results obtained with the static contact angle
model.
Hazi and Markus (2009) used the lattice-Boltzmann approach
to simulate heterogeneous boiling on a horizontal plate in
stagnant and slowly flowing fluid. They found that the bubble
departure diameter is proportional to gl/2 and the release
frequency scales with g3/4 in a stagnant fluid, where g is the






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


gravitational acceleration. Simulation results showed no
dependence between the bubble departure diameter and the
static contact angle, but the bubble release frequency
increased exponentially with the latter.
Numerical researches about bubble growth mostly based on
pool boiling. However, the character of bubble growth in
subcooled flow boiling is quite different from that of the
pool boiling. The bubble growth process in subcooled flow
boiling is affected by the thermal characteristics of heating
wall and mainstream liquid, etc. Due to the existence of the
mainstream liquid velocity, the motion characteristic of
bubble interface and the flow field around the bubble are
more complex than that of pool boiling. Thus, distortion and
deformation of the bubble may occur which will lead to
characterized features during the growth,
In present paper, based on the characteristic of bubble
growth process in subcooling flow boiling, a bubble growth
model is proposed and a numerical simulation is performed
to understand the process of bubble growth. The simulation
results well reflect bubble growth process as a dynamic
result of evaporation and condensation which agree the
experimental results very well, and the relationship between
the vapor-liquid interface motion and velocity field inside
the bubble also presented here.

Nomenclature

E energy
F surface tension force

hf, latent heat, kJ-kg :
the net mass flow rate per unit area,
G kg-m --s-'
M mass per mole, kg-mol :
p pressure, Pa:
q heat flux, kW- m -;
r ~bubble radius, m:
R universal gas constant, J-mol -K :
S the mass source term:
t time, s:
T temperature, K
u velocity, m-s~'
x, y coordinate axis:
micro-layer thickness under the bubble
8 bottom, m:
a surface tension coefficient, N/m
coefficient of the vapor-liquid
interface.
oc. volume fraction:
p density, kg-m
thermal conductivity of liquid,
?L W-m -K-1
AT the temperature difference, K.
Subscripts
1 liquid:
v ~vapor:
w wall;


saturated
evaporation
condensation:
ith fluid component


2 Numerical simulation methods
The VOF formulation relies on the fact that two or more
fluids (or phases) are not interpenetrating. For each additional
phase that was added to model, a variable is introduced: the
volume fraction of the phase in the computational cell. In
each control volume, the volume fractions of all phases sum
to unity. The fields for all variables and properties are shared
by the phases and represent volume-averaged values, as long
as the volume fraction of each of the phases is known at each
location. This paper investigates the bubble growth process
by VOF model (Fluent Inc., 2005, Hirt and Nichols, 1981)
and UDF interface of the CFD software Fluent.
2.1 VOF model
Generally, a VOF algorithm (Hirt and Nichols, 1981) solves
the problem of updating the phase volume fraction field
given the fixed grid, the velocity field and the phase volume
fraction are determined in previous time step. In
two-dimensional problem, the interface is considered to be a
continuous and piecewise smooth line. The problem is
reduced to the reconstruction of an approximation of the
interface in each cell, knowing only the volume fraction of
each phase in the cell itself and in the neighboring cells.
During all simulation cases in present work, a piecewise
linear interface calculation (PLIC) (Yongs, 1984) interface
reconstruction method has been used for interpolation in a
cell. In the existing CFD code, this scheme is the most
accurate one and it is applicable for general unstructured
meshes as used here, this interpolation scheme assumes that
the interface between two fluids has a linear slope within
each cell and this linear shape is used for the calculation of
the advection of the fluid through the cell interfaces.
In VOF model, the kth fluid's volume fraction in the cell is
denoted as ak then the following three conditions are
possible:
ak= 0: the cell does not contain the kth fluid;
ak = 1: the cell is full of the kth fluid:
0 kth fluid and one or more other fluids.

In present model, there are two phases: vapor and
liquid. When ac, 1, it represents vapor bubble region; when
ai= 1, it is liquid region. When 0 bubble interface exiting in this region. Based on the local
value of ak, the appropriate properties and variables will be
assigned to each control volume within the domain.
(1) Continuity equation
In VOF model, the volume fraction of each fluid ack is
calculated by tracking the interface between different phases
throughout the solution domain. Tracking of the interfaces
between different phases present in the system is
accomplished by solving continuity equations of the phase
volume fraction for phases. A physical interpretation can be
given by various terms in this continuity equation .For the
vapor phase, this equation has the following form:






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


6a Sm
.'+uVa =
at p4 (1)
where S,, is the mass source term of vapor in the bubble
growth process, which can be estimated by Eq. (8) and
(10) through the UDF interface.
(2) Momentum equations

S(pu) + V (puu) = -Vp+ V -[(Vu +Vu )] +pg +F

(2)
Where F is the surface tension force, which can be
estimated through CSF (continuum surface force) model
(Brackbill, et al., 1992) as following:
= P zVax


(3) Energy equation

t(pE)+ V (u(pE + p)) = V -(iVT)+ Sq 4
(4)

The physical properties of p and ?L (effective thermal
conductivity) are shared by both of the two phases. Source
term SEq COntains contributions from all other volumetric
heat sources.

(4) Vapor-liquid interfacial density
The properties appearing in the transport equations
are determined by the presence of the component phases in
each control volume (Fluent Inc., 2005). In a two-phase
system, for example, if the phases are represented by the
vapor and liquid, and if the volume fraction of the second
phase has been tracked, the density in each cell would be
given by:
p = alpt + (1 a)p, (5)

2.2 UDF procedures
The User Defined Functions (UDF) interface of the
commercial CFD code of Fluent (Fluent Inc., 2005) is
employed to simulate the heat and mass transfer of the
phase change. UDF subroutine allows us to customize
Fluent to fit particular modeling needs. UDF is a function
that user program can be dynamically loaded with the
Fluent solver to enhance the standard features of the code.
They are defined by DEFINE macros which are supplied
by Fluent Inc. They can access data from the Fluent solver
using predefined macros and functions. Present UDF
programs are based on following described bubble
generation theories of micro-layer evaporation to simulate
the bubble growth.
3 Bubble growth physical models in sub-cooled
flow boiling
3.1 Bubbles growth process in subcooled flow
boiling
The channel is vertically arranged, and the fluid flows
vertically from bottom in y-direction. The temperature of
the mainstream region T1 is lower than that of the liquid
saturation temperature Ts corresponding to local pressure.
Tw is the temperature of single-side heated wall which is
higher than Ts. There is a temperature boundary layer close
to heating wall. In this region, the liquid temperature is
higher than saturation temperature but lower than the


Ssuperheated liquid layer
T1 >Ts

subcooled liquid region
( T1


t; vapor bubble

Y IMicro-layer region


heakting wall


flow direction


Fig.1 Schematic diagram of bubble growth model
heating wall temperature, i.e, T, < T1 < Tw. There is a liquid
micro-layer region near the bottom of bubble which
temperature is higher than T,. (3 is the contact angle of the
bubble with the heating wall. The bubble on the heating wall
grows up with growing times goes by to, tl, t2.
At the initial time, to, bubble radius is relatively small.
The whole bubble is submerged in superheating liquid layer.
The heat and mass supplied for bubble growth are derived
from the liquid micro-layer evaporation at the bottom of
bubble and superheating liquid around bubble surface. As
the bubble diameter increasing, at the time of tl, the top of
bubble pass through the superheating boundary layer, and
enters the subcooled mainstream region. Consequently, the
condensation will occur at the top of the bubble. At this
period, as the mass into the bubble caused by evaporation at
the bottom and the interface exceeds the condensation mass
at the bubble top, the bubble continues to grow up. At the
time of t2, the bubble diameter is greatly larger. Because a
large portion of bubble top region is submerged in
subcooled mainstream liquid, condensation effect becomes
significant and bubble growth rate will be gradually slowed.
When the condensation mass of vapor is approximately
equivalent to the mass adding into the bubble by
evaporation at the bottom and the interface, the bubble
growth rate will slow down to zero and bubble diameter
remains unchanged.
3.2 Bubble growth model
Based on above analysis, there are four assumptions in
current model: i) there is a very small initial bubble existed
on heating wall which radii will be estimated through
classic bubble nucleation theory; ii) the vapor in the
growing bubble is ideal gas; iii) the temperature at the initial
bubble growth time is equal to saturation temperature Ts
corresponding to the working pressure; iv) the pressure in
the initial bubble is based on Yong-Laplace equation:
P, =P; +--
r (6)
where, o is surface tension coefficient, N/m.
3.2.1 Micro-layer liquid evaporation model on the bottom of
growing bubble
Experimental results (Tong and Tang, 2001) showed that
there is a liquid micro-layer exists at the bottom of bubble






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

vapor-liquid interface region can be defined by:

y'm~hip(12)
It should be aware that m is the mass source term of the
continuity equation and the heat flux q is the energy source
term of the energy equation according to VOF model,
Wm-3
3.3 Geometry and boundary conditions
















Fig.2 Schematic of the geometry structure
In present work, a single bubble growth process has
been simulated in subcooled flow boiling in a narrow
channel. Due to the symmetrical characteristic in the wide
side of the bubbles, it can be simplified to a
three-dimensional geometry structure Fig.2 (a). In the
simulation geometry structure model, the vertical
rectangular narrow channel has a inlet section of 2 mmx2
mm, and length of L=10 mm.
Based on the assumption of the bubble growth model,
there is a small bubble on heating wall at the initial stage of
the simulation. The diameter of the small bubble is
calculated by the Han and Griffith correlation equation (Han
and Giffith, 1965).

s(T, T, ) 12 I(T, -rlr TrT
r.=3 (Tw T, ) 1 -3(Tw T, )Z h. p,

In this paper, rmin is ranged from 20 pLm to 50 pLm in the
subcooling flow boiling.
Mesh around the bubble has been refined to obtain the
details of bubble growth, According to mesh sensitivity
testing, the number of meshes 120000 is suitable for
simulation. The heating wall temperature keeps constant
while the other wall is adiabatic. The inlet of the channel is
set as velocity-inlet condition, and the outlet is set as
pressure-outlet condition. The viscous model is the laminar
model.

4 Results and Discussion
4.1 Bubble growth curve
The varying bubble diameters with time in different working
conditions are simulated. Based on the numerical results,
analysis about bubble growth curve in different simulation
condition with p=0.102-0.132 MPa ATw=1-10 K, ATi-8-16 K,
u=0.10-0.60 m-s ', (3=850 has been performed.
Fig.4 depicts the impacts of wall superheating on bubble
growth. With other working conditions remained unchanged,
the bubble growth rate would increase with raising wall
superheated. According to micro-layer evaporation model,
higher wall superheating lead to themore micro-layer
evaporation intensity. Thus, the bubble growth rate would


during bubble growth, and it is very important to the process.
The convectional heat transfer through this layer can be
ignored due to its small thickness. Thus, the heat flux
through the micro-layer liquid can be estimated as:
T, T
6 (7)
where, ?L is the thermal conductivity of the liquid,
W-m-2-K ; Tw is the temperature of the heating wall, K; T,
is the vapor temperature of growing bubble, K; 8 is the
micro-layer thickness under the bubble bottom, m.
The mass transferring from the micro liquid layer to
vapor bubble can be estimated by:
G = q / h (8)
where hf, is the latent heat, kJ/kg; q is the heat flux through
the micro-layer, kW-m respectively. G is the net mass
flow rate per unit area, kg-m-2S,
Because Fluent is the CFD soft ware which based
on the FVM(Finite Volume Method),the mass source
which is added to the continuity equation is the mass flow
rate per volume, kg-m-3S-1


cell1 (9)
Where, Aell, is the area of a face in the jth cell, Veli3 is the
volume of the jth cell. m is the mass source to vapor bubble
volume fraction in the jth cell of vapor bubble.
3.2.2 Interfacial bubble heat and mass transfer
model
Vapor-liquid interface is quite important to bubble growth.
When the radius of bubble is relatively small, the whole
bubble is submerged in superheated liquid layer. Heat will
transfer to bubble from the superheated liquids through the
bubble interface, and the diameter will be increased
consequently. When the diameter of bubble increases to a
certain scale, the bubble interfacial area will be divided into
two parts; one is submerged in the superheated liquid layer
where the heat would be transferred from the superheated
liquid to the bubble; the other one is submerged in
subcooled liquid where the vapor in the top of bubble would
be condensed and the heat would be transferred from bubble
to the subcooled liquid through the interfacial areas.
Under the conditions of thermodynamic equilibrium, the
mass transfer mechanism representing evaporation
coefficient will be not distinguished from the ones of the
condensation coefficient; and ones often have the
simplification of oeGo, (Mareka and Straub, 2001). For
a curved interface, an analogous equation can be deduced
(Marek, 1996, Marek and Straub, 2001):
G=4e M ,T)P, (10)
4-3geV27cR J~J

When G>0, the net mass from liquid will enter into the
bubble through the vapor-liquid interface; when G <0, the
net mass from bubble will enter into the liquid through the
interface.

thz = a, G J
cellJ-(11)
m is the mass transfer rate proportional to vapor bubble
volume fraction in the jth cell of vapor-liquid interface
region.
The heat flux due to the phase change in the jth cell of






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

large amount of heat and mass is transferred from the
micro-layer to the bubble. The bubble grows fast as a
hemisphere. The value of bubble diameter increases from
0.2 mm to 0.54 mm. After 0.4 ms, the pressure inside
bubble decreases quickly, bubble growth in the stage is the
1.2
p =0.13 MPa
1 u =0.25 m-s'
ATw=8 K
0 .8



S0.6

S12 K
0.2 -e- 16 K



O 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Time (ms)
Fig.6 The subcooling of mainstream impact on bubble growth


become higher.

p=0.13 MPa
u=0.15 m~s
0. Tf=12 K





0.4 -l K 6 4

--3 K -M 1K


00.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Time (ms)
Fig.4 the wall superheating impact on bubble
growth

p=0.12 MPa
ATw=8 K
0.6-Ay=5K




~04-%-0.1(m/s)
S0.2 -e-r 0.3 (m/s)
-&0.6 (m/s)



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Time (ms)
Fig.5 The velocity of mainstream impact on bubble growth
Fig.5 shows the impacts of the liquid subcooling on bubble
growth. With increasing liquid subcooling, bubble growth
rate would slow down significantly at the later bubble
growth stage. It can be explained by that the condensation
intensity will be enhanced at the bubble top, which lead to
a decline in bubble growth rate. It also indicates that the
bubble growth process is a dynamic consequence resulted
from evaporation and condensation.
Fig.6 depicts the effect of the mainstream velocity on
bubble growth. Under the same conditions, the velocity of
mainstream has a mild impact on the bubble growth
comparing with the mainstream subcooling. It can be
explained that with thinner superheated liquid layer under
high-speed condition, bubble growth rate would become
slower than that of low speed circumstance.
4.2 Bubble shape evolution during bubble growth and
detaclunent process
The evolution of bubble shape in subcooling flow boiling
would be impacted by a couple of factors. In this paper, the
section through the central of bubble in X-Y plane is
selected, in order to make a better analysis of bubble shape
and physical filed around growing bubble.
Figure shows the evolution process.with p=0.102 MPa,
AT,,=10K,ATfll5K,u=0.20 m-s ', B=850. Comparing with
Fig.6, the numerical results agree well with typical
consecutive image of bubble evolution in visualization
experiment of subcooling flow boiling. Figure 8 is the
curve of bubble diameter in the time of bubble growth and
detaclunent.
As shown in Fig.7, there is a growing bubble at the
nucleation site on the heating wall. The nucleation site
coordinate is z=x=0.0 m, y=0.005 m. At the initial time of
bubble growth (0.1-0.4 ms), due to high pressure in the
bubble, bubble growth is in the stage of inertial control. A


-ow~n
1 6on.=




-
bln
n..


.


IEOson.. In70...






.. r



59nun em -05um




., ~ n .. ~ Wo




-. x x .. x .


Fig.7 The evolution of bubble shape in bubble growth and
detaclunent processing working condition p=0.102 MPa,
AT =10 K, ATfl5 K ,u=0.20 m-s ',B=850
o.s
bubble growth period bubble departure period
0.7


0.6 bubble departue
0. fomnuclearnsit
0.4
bubble departure
,0.3 fom heating wall
0.2
0.1


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8
Time (ms)
Fig.8 The bubble diameter in bubble growth and
detaclunent process on working condition p=0.102
MPa,AT,,=10 K ATf l5 K,u=0.25 m-s ',=850






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

1.2 ms, the bubble growth is in the thermal diffusion control
stage. The bubble growth rate is relatively low and stable.
The pressure inside the bubble fluctuates from 1500 Pa to
2000 Pa. From 1.2 ms to 2.6 ms, bubble is in detaching.
Because of the intensive condensation of a departing bubble
caused by subcooled liquid, the bubble diameter
dramatically decreases and the pressure inside bubble drops
rapidly also.
2500- -*gague pressure
2250 -\ lnsidebubble
S2000
1750
S1500
S1250

750
500
002040608 1 12141618 2 222426
Time (ms)
Fig.10 presents the pressure evolution inside a bubble
during bubble growth and detachment
4.4 Velocity field of growing bubble












Figure 11 the velocity vector field at t=1.0 ms, t=2.8 ms.
According to the analysis of the pressure filed around a
bubble, eddies is formed by the pressure discrepancy around
the bubble. As shown at = 1.0 ms, eddies can be observed on
both sides of the growing bubble. The eddy accelerates
contraction of the vapor-liquid interface at bottom of bubble,
which leads to bubble shape changing from ellipsoid to
approximate sphere. As the eddies transfer sub-cooled liquid
to the heating wall on both sides of bubble, the
micro-convection in the vicinity of bubble is enhanced,
which would increase heat transfer significantly. At t=2.8
ms, the difference of the fluid velocity on both sides of the
departing bubble is quite evident, which accelerates bubble
departing from the heating wall.


o is





-*- 2ms --- 4ms
0 6ms -*- 8ms
o as oms -*1 2ms


O 0 0001 0 0002 m00003 0 0004 0 0005

Fig.12 the velocity cuve along the center-line of a
bubble at different bubble growth time.
It shows that along the center-line of bubble, from iner side
of the bubble to the mainstream liquid region around the


thermal diffusion control. As the condensation intensity
gradually enhances at the top of bubble, bubble growth rate
becomes much slower than that of former. From 0.6 ms to
0.8 ms, bubble expands slowly in hemisphere shape.
However, with increased bubble diameter, the force
balance acting on the growing bubble has been broken. As
the result, the shape of bubble evolves from a
hemispherical to an ellipse at the time of t= 1.0 ms. At
t=1.2 ms, bubble diameter increases to the maximum value
0.71 mm. After that Bubble begins to detach from
nucleation point. From 1.2 ms to 2.6 ms, the shape of
bubble evolves from ellipse to spherical and bubble
diameter decreased gradually. Bubble remains as a roughly
sphere until it lifts off from the heating wall.
4.3 Pressure distribution evolution during bubble growth
0 0056F


0 0056 ~


xim
Fig.9 the pressure distribution of bubble growth at 0.4
ms and 1.0 ms.
As shown in Fig.9, in the bubble growth process, the
pressure are identical in different region inside vapor
bubble. The pressure inside the bubble is higher than that
of the flow liquid around the bubble. Farther away from
the bubble, the pressure of the flow liquid becomes much
higher. At t=0.4 ms, the value of gauge pressure inside
bubble is 1930 Pa. Away from the top of bubble, there is a
flow liquid region with the minimum pressure, which
gauge pressure value is 1880 Pa. At t=1.0 ms, the value of
gauge pressure inside bubble is 1539 Pa. The minimum
pressure of flow liquid region is at the two sides of the
growing bubble.
Fig.10 presents the pressure evolution inside a bubble
during bubble growth and detachment. As a whole trend,
the pressure inside the bubble is decreased continuously.
From 0.1 ms to 0.6 ms, the bubble growth is in the inertial
control stage. Bubble expands rapidly lead to the
dramatically pressure drop inside bubble. From 0.6 ms to






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


Conclusion
In this paper, a bubble growth model has been proposed for
single bubble in subcooled flow boiling, and a numerical
simulation of bubble growth process is realized by VOF
model and UDF interface through CFD software Fluent.
The factors such as velocity of mainstream, subcooling of
mainstream, the superheating of heating wall and
vapor-liquid contact angle have been considered to
understand the mechanism of bubble growth. The bubble
growth curve also has been obtained: the simulation results
agree the experimental results with relative error within
+25%. The results can be concluded as following:
1. The process of bubble growth in subcooled flow
boiling is a dynamic result of evaporation and condensation.
With increasing wall superheating, the rate of the bubble
growth would be accelerated; with higher mainstream
liquid subcooling, the growth rate of later stage would be
easier decreased.
2. The evolution of bubble shape is a quite
complicated process. At the initial time of bubble growth, a
large amount of heat and mass transfers through the
micro-layer into the bubble and the bubble grows fast and
expands rapidly as a hemisphere. As the condensation
gradually enhances at the top of bubble, bubble growth rate
becomes much slower than that of before. With increasing
bubble diameter, the change of forces balance acting on a
growing bubble has taken place. Thus, the shape of bubble
evolves from hemispherical to ellipse.
3. During bubble growing, the pressure inside the
bubble will be decreased and it is identical in different
region inside vapor bubble, and it will be higher than that of
the flow liquid around the bubble. Farther away from the
bubble, the pressure of the flow liquid becomes much higher
and a flow liquid region with the mnummum pressure will
exist in the vicinity of growing bubble.
4. Few eddies will exist on both sides of the growing
bubble. The eddies accelerate contraction of the
vapor-liquid interface at the bottom of the bubble, which
result to bubble shape changing with bubble growth and
detachment process and enhances the of micro-convection
heat transfer in the vicinity of bubble. With increase of
bubble growth time, the velocity inside the bubble gradually
reduces.
5. During bubble growing, a super-heated flow liquid
region will be presented near the heating wall. In this region,
the temperature gradient which does not change with the
growth time is very large. With the increase of the distance
from the heating wall, the flow liquid temperature decreases.
Because of the convection heat transfer, temperature of the
subcooled liquid region far from the heating wall increases
with the bubble growth process.

Acknowledgements
The authors are grateful for the support of the National
Science Foundation of China (No.50406012) and the
support of the Researching Foundation of the Laboratory of
Bubble Physics and Nature Circulation of China under
contract of 9140C37101020802.

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7th International Conference on Multiphase Flow
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