Energy and Power En gi neering, 2011, 3, 181-189
doi:10.4236/epe.2011.32023 Published Online May 2011 (http://www.SciRP.org/journal/epe)
Investigation on Numerical Modeling of Water Vapour
Condensation from a Flue Gas with High CO2 Content
Hamid Nabati
School of Sustainable Development of Society and Technology, Mälardalen University,
Västerås, Sweden
Received February 2, 2011; revised April 7, 2011; accepted April 11, 2011
Abstract
In this paper, condensation of water vapor from a mixture of CO2/H2O is studied numerically. To simplify
the study and focus on the physical model, a simple vertical plate was chosen. Two condensation models are
developed and numerical approach is considered to implement these models. The main objective in the cur-
rent paper was to study the capability of numerical modeling in prediction of complex process. Results
showed that developed condensation models in combination with numerical approach can predict the trends
in condensation behavior of binary mixture very well. Results from this study can be developed further to be
used in design of condensers which are suitable for oxy-fuel power plants.
Keywords: Condensation, Two Phase Flow, Numerical Modeling, CO2 Capturing, Oxy-Fuel Power Plants
1. Introduction
Oxy-fuel power plants are one of the recently promising
processes for clean energy production with CO2 captur-
ing and condensers for separation of water vapour from
flue gas are essential components in these new proposed
power plants.
As the combustion process in the oxy-fuel power
plants is performed with fuel and pure oxygen, the re-
sulting flue gas consists mostly of H2O and CO2.The
water vapour separation process from the flue gas im-
pacts the thermal efficiency of the plant and the opera-
tional cost; thus the precise design of such CO2/H2O
condenser systems is a vital demand in the industry [1-3].
Currently there are commercialized condensers in the
market that most of them are installed for separation of
air and water or for condensation of nearly pure water
steams and thus far the condensers for separation of wa-
ter vapor and CO2 are not off the shelf products yet.
Considering the specific characteristics of such condens-
ers for application in the CO2/H2O separation, makes
them as special process heat exchangers in the industry.
Despite of wide referring to this kind of condenser in
different proposed Oxy fuel cycles, the required design
data are not available yet and there is a demand for more
studies to achieve the desired efficiency for CO2 captur-
ing and steam separation and basic studies on condensa-
tion of water vapour from a flue gas with high CO2 con-
centration could provide such useful technical data for
designers.
Naturally, condensation happens whenever the vapour
temperature is decreased by cooling until it reaches the
saturation temperature Tsat at the operational pressure and
usually this takes place when vapor is brought into con-
tact with a solid surface whose temperature Ts is less than
saturation temperature of the vapor. However condensa-
tion can also occur in a gas or on the interface of a liquid
and a gas. When condensation occurs in a gas, the liquid
droplets usually suspend in the gas. As it is more com-
mon in the industry to operate and control surface con-
tacts condensers and also based on what is shown for
oxy-fuel CO2 capturing, in the current study the conden-
sation on solid surfaces with focus on film condensation
is considered.
It is a common practice in the literatures to accept film
condensation in heat exchanger design [4-6]. In this
process, the condensate forms a liquid film is formed on
the solid surface. This liquid film slips down under the
influence of gravity. The thickness of the liquid film in-
creases gradually with more vapors condensation on the
film in the flow direction. Liquid covers the surface and
eventually a liquid film takes place between vapour and
solid surface. This liquid film resists against heat transfer
flow. It means that released heat from vapour condensa-

182 H. NABATI
tion at the vapour-liquid interface must transmit through
this layer before it approaches the cooling solid surface.
Moreover, the presence of even a small quantity of
non-condensable gas significantly affects the heat trans-
fer resistance in the region of the vapour-liquid interface.
Experimental studies show that the non-condensable
gases existence in the mixture has an unfavorable con-
sequence on condensation process [7,8]. As an example,
the presence of less than 1 percent (by mass) of air in
steam decreases the condensation heat transfer coefficient
more than half [4]. Vapour carries the non-condensable
gas towards the vapour-liquid interface and it accumu-
lates there. Thus special consideration should be applied
when condensation from CO2/H2O mixture is studied. In
this case a large portion of gas stream is occupied by
CO2 which is a non-condensable gas in the normal con-
dition. This is one of the cases that are referred as
multi-component (n > 2) mixture condensation where n
represents the number of components. The CO2/H2O flue
gas is a binary (n = 2) mixture that its phase equilibrium
characteristics is important in flue gas condenser design
and operation.
Condensation of water vapor from CO2/H2O flue gas
mixture on a vertical smooth surface is shown schemati-
cally in the Figure 1.
Referring to this figure, the condensation behavior can
be explained as the following:
When water vapor starts to condense, only the non-
condensable gas part in the mixture remains in the vicin-
ity of the interface surface. This gas layer acts as an ob-
stacle between vapor and surface, and makes it difficult
for the vapor to penetrate and reach the surface. Conse-
quently, the efficiency of the condensation process is
reduced.
There are limited works about surface condensation
which have been performed either experimentally or
numerically. Recently, some studies have been per-
formed on vapour condensation from mixture of non-
condensable gases and steam. However, nowadays, the
main idea is to use available tools (like numerical meth-
ods) to develop robust and reliable methods which can be
used to simulate the heat and mass transfer in condensa-
tion process.
Three main categories of condensation models are
available: models with experimental correlations, models
using Nusselt theory (based on heat and mass transfer
analogy) and mechanistic models based on the boundary
layer equations [9]. The main advantage of the first
group models is their simplicity and therefore they can
be easily adopted for numerical modeling. Also they can
be used for initial verification of CFD condensation
modeling. However they are bounded to a very limited
set of data. The second group models are also suitable to
Figure 1. Water vapour condensation on a smooth vertical
plane from a mixture containing non-condensa ble gas.
be implemented in the numerical simulation and they
give more realistic results. The last group models are
consistent with the numerical treatment of governing
equations. But at the moment, implementation of such
models requires high expenses because of their high de-
gree of complexity. These are the best models that
probably will be implemented in high accuracy CFD
codes in future. This work evaluates two condensation
models through a numerical simulation and propose the
optimum model based on available two-phase flow mod-
els and apply it in a numerical scheme with the help of
Fluent© software to study water vapour condensation
from a mixture containing mainly H2O and CO2. Also
effect of fin installation on the condensation surface is
partly studied.
2. Physical Model for Binary System
Condensation
As it was stated before, if any quantity of non-condensable
gas exists in the mixture, there would be major effects on
the heat and mass transfer resistance in the liquid-vapour
interface. The non-condensable gas is carried towards the
interface and accumulates there. This accumulation
causes the partial pressure of gas at the interface became
greater than its partial pressure in the binary mixture.
This effect produces a driving force for non-condensable
gas to diffuse again toward the bulk. This diffusive mo-
tion is contrary to water vapour diffusion toward liq-
uid-vapour interface. Also when the vapor which is
mixed with a non-condensable gas is condensing, only
the non-condensable gas remains in the vicinity of the
liquid-gas surface. This gas layer forms a resisting wall

H. NABATI
183
between condensing liquid and vapor and makes it hard
for the vapor to contact with the surface. Therefore vapor
should diffuse through this layer first before reaching the
surface. These effects reduce the condensation process
efficiency. These conditions are worse for the CO2/H2O
condenser, where the concentration of CO2 is much
higher than water vapour. The accumulation of CO2 in
the vicinity of condensation layer makes a barrier to re-
maining water vapour in the flue gas stream and de-
creases the effectiveness of condensation process.
In the mixture of CO2/H2O, the partial pressure PA, of
component H2O is that pressure which would be exerted
by H2O alone in the mixture appropriate to the concen-
tration of H2O in the flue gas at the same temperature.
Here A represents H2O to simplify the proceeding equa-
tions. Since P = ΣPA, then the partial pressure, PA, is
proportional to the mole fraction of H2O in the vapour
phase.
s
at
AAA
PxP (1)
The most known correlation that is used to relate the
partial pressure in the vapour phase to the concentration
of component A in the liquid phase is the Rault’s law.
This law states that the partial pressure PA is related to
the mole fraction xA and saturation pressure of pure
component A at the same temperature:
s
at
AAA
PxP

 (2)
where xA represents mole fraction of component A in the
liquid phase. During mass transfer process, water vapour
travels from high concentration region to region where it
has a low concentration. Just as thermal energy diffuses
from region of high temperature to low temperature re-
gion (following the temperature gradient), the mass
transfer follows the concentration gradient. Fick’s law of
diffusion represents that diffusion mass flux of any spe-
cies in a multi-components stream has direct proportion
to the species concentration gradient. This law can be
expressed as:
i
iim
m
Dm 

  J (3)
i
J
is the total mass flux of species i and gets the unit
of (kg/m2·s). Effective diffusivity, Dim is an indicator of
diffusion intensity of species i into a mixture. Diffusivity
coefficient is a function of composition, temperature and
pressure and for gases is typically on the order of 10–5
near the room temperature. The Chapman-Enskog corre-
lation is one of the known formulas which is based on
kinetic theory and takes into account all the molecular
effects precisely [9]. The correlation is:

3
72
2
1.8583 1011
AB
AB
AB D
T
D
M
M p 




 (4)

AB is the average molecular diameter in Å and is
equal to (

A +

B)/2. MA and MB are molecular
components A and B. D can be obtained from
cor l
weight of
available
reations in literatures [4,10,11]. Table 1 shows the
required data for diffusivity calculation.
Considering the steady state behavior at the all loca-
tion in the flow field and referring to Figure 1, the en-
ergy balance implies that the heat transfer from the flue
gas to the condensation film plus the latent heat of con-
densation should be equal to the heat which is passing
through the condensation film. As the temperature level
is the place that condenser is going to be used is some-
thing about 100˚C (more or less), the radiation from flue
gas to the film can be neglected.
The first attempt to analyze the film condensation
process was done by Nusselt with some simplifying as-
sumptions like laminar film flow, stationary vapour and
conduction heat transfer trough the film. Based on the
analysis, he proposed the following correlation for the
mean value of heat transfer coefficient over the whole
vertical surface [12]:


1
34
0.943 ff gfgf
film
ghk
h
 
f filmS
TT
L











A number of attempts have made to improve the Nus-
selt theory and modify it to suit the real pro
condensate in a real condensation process always is
co
(5)
cess. The
oled down further to a temperature which is less than
saturation temperature and higher than the cooling wall
temperature. Rohsenow [13] showed that this effect can
be accounted by using modified latent heat defined as:
For the water vapour content in the flue gas, there is
superheat state and the vapor should be cooled down to
Tsat before the condensation occurs. In this case the
modified latent heat can be written as:


,
0.63
1
,
P
film filmS
fg fg
fg
CTT
hh h
 




Ps
at
fg
CTT
h
 




(7)
Considering the definition for modified late
convective heat transfer coefficient through the con-
densing film (hfilm) can be written as [4]:
M (kg/kmol)
nt heat, the
Table 1. Required data for diffusivity calculation [10].
Species
 /kB (K)  (Å)
Air 78.6 3.711 28.96
HO 363 2.655 18.02
2
CO2 195.2 3.941 44.01

184 H. NABATI


1
4
3
0.94 ff fgf
ilm
f
k
TTL







(8)
All the liquid properties should be calculated at aver-
age temperature (Tsat + Ts)/2.
The heat transfer from flue gas to interface
tween flue gas and condensing film consists of two parts:
fir
3gh

g

f
h
s
at S




layer be-
stly, heat which passes the diffusion layer directly and
reach to the interface (sensible heat) and secondly the
latent heat of the vapour which reaches the interface and
condenses. With an assumption that the liquid-vapor
interface has a temperature between saturation and sur-
face temperatures and also considering the constant
temperature for the liquid film interface, the energy bal-
ance equation is written as following:


or
totfilmconv condens
totsff s
 
f
cond f
hT T hTT
 
  
qqq q
hTThTT


 (9)
And condensation film flow rate is given by:


condfgfsfs
mhhATT

 
 (10)
sfer coef-
fic der-
ing the mass transfer and is calculated
automatically using wall functions. So it is
he
2] and is simple to be implemented in the numerical
our atmos-
here using the saturation condition is calculated and
h∞ in (9) represents the convective heat tran
ient between flue gas and condensation film consi
in the CFD code
not explained
re and details can be found in the user guide [13]. The
last coefficient in (9) is the most challenging part in
condensation modeling. In the current paper, two differ-
ent condensation models are implemented and compared
together which are explained in the following sections.
2.1. Model I: Based on Nusselt Theory
The first condensation model is based on Nusselt theory
[1
code Firstly, the heat transfer in a pure vap
p
then effect of non-condensable gas is introduced by a
degradation factor. The following formula is derived
with this methodology:

 
1
34
1
ff gfg
condncsat f
f
ghk
qf TT
TTL
 



  



(11)
23
1 0.9464.9894.135
1
1 15.48
ncncnc nc
nc
nc
f
yy
y
y
y


 


 



(12)
The condensation flow rate is calculated using the
modified latent heat,
f
g
h

:
cond fgcond
mhq


 (13)
2.2. Model II: Based on Diffusion Boundary
Layer Theory
nsfoefficient (h) is given
by following correlation [4]:
This model is originally developed by Peterson [15]. The
condensation heat traer ccondens
22
,ABfgp gv
L
cond
Sh
hLR
TT
vf
DhC M



 

 


 
(14)
ShL is the average Sherwood number for the whole
condensing plate which is given by [4]:
1 1
3 2
0.664Sh R
LL
e Sc (15)
 issteam and non-condensable gas conc
the vicinity of interface and defined as [4]:
entration in
,
,
,
1
ln 1
nc mean
nc int
nc mean
x
x
x








,ln
erface
steam meannc
xx
x




(16)
3.1. Governing Equations
The governing equations for conversation of mass, mo-
mentum and energy given by [17] can be formulated by
sing the tensor notation. The flue gas mixture and con-
Newtonian fluids. The
ployed to solve the proc-
, momentum and conti-
ies are solved in a struc-
,mean 

, nc interface

3. Numerical Approach
u
densation layer are considered as
luent© CFD code has been emF
ess governing equations. Energy
uity equations for each specn
s atf 
The degradation factor is calculated based on experi-
mental works and here the following correlation is im-
plemented [15]:
tured or unstructured mesh using finite volume method.
Most of the following explanations on governing equa-
tions have been derived from available literatures [14],
[17].
3.1.1. Continuity Equa ti o n
If conservation equation is applied to a species and then
rearranged in a general form, the following equation is
obtained:

H. NABATI
185
 
iiii
yy S
t


J (17)
Si represents mass source term for species i and calcu-
volume. Diffusive flux for lated based on mixture unit
each species i
J
was previously presented by (3).

n
qqqqqpq
m
t
 


u (18)
1 p
where αq represents volume fraction of qth phase:
Volume of the phase in a celldomain
Volume of the celldomain
  (19)
3.1.2. Moment um Equation
This equation is based on second law of N
represents that for each fluid particle, rate of momentum
.
Transient term + Convection term = Pressure force +
Body force + Shear force + Inter-phase forces
mentum exchange + other external forces
Or in the mathematical form:
ewton and
change is equal to sum of all forces on that particle
and mo-
 

q qqqqqq
n
qqq pqpqqqqq
t
pRm
 
 
 



uuu
guF
(20)
1p

p
q
m
 is the mass transfer rate from phase q to phase p.
The momentum equation can be simplified for different
flons.
3.1.3. Multiphase Species Transport Equation
General multiphase species transport equation for s
i which belongs to mixture of the qth phase is expressed
as following:
ws based on the flow conditio
pecies
 

ii
qqq qqqq
n
i
yy
t
 
 
u
(21)
1pq q p
p
ij ji
qq qi
Sm m

 

J
3.1.4. Energy Equation
The energy conservation equation is based on enthalpy
equations for all phases. This equation is representing in
g
where the i
q
y represents the mass fraction of the spe-
cies i in the qth phase and Si is the volumetric rate of
mass increase (could be also a negative value) for com-
ponent i.
the followinform [14]:
 


1
n
qqpqpqpqqpqp
p
SQ
mhmh 

 

uq
(22)
q
qq qqqqq q
p
hh
tt
 



u
qq q
Here hq is the specific enthalpy of the qth phase and
q

is the phase stress-strain tensor. Explanations on
other terms in energy equ ation can be found in [14].
3.1.5. Mass Transfer Consid er ations
In the Fluent©, contributions due to mass transfer are
added only to the momentum, species and energy equa-
tions and no source term is added to other scalars
tu
w
ma
in-
ut the appropriate model for condensation and sink of
tion.
The later model has been used to primary study how
model output. Fins are con-
idered as a simple rectangles attached to the cooling
dary layer section. Two adiabatic inlet and
ou
like
©
rbulence [14]. More detail can be found in the Fluent
ebsite or user manuals. No general model exist for
ss transfer and it depends on the case like evaporation,
boiling or condensation, The UDF should be used to
p
mass is imposed into the continuity equa
3.2. Simulation Model
Two 2D models were used to study the described water
vapour condensation model, when mixture contains high
CO2 concentration (Figure 2). First model is a simple
vertical plate and the second one is a vertical plate with
same dimension as the first one which is equipped with
some fins.
fins affect on condensation
s
wall. Copper was selected as the material for fins. The
generated meshes for both models are structured map
element meshes. Meshes were generated several times to
assure a mesh dependent solution. Also meshes were
refined in the areas close to walls to get accurate results
in the boun
tlet sections were considered to ensure that the correct
flow condition in the condensation zone was achieved.
Figure 2. 2D models that are used for condensation study.

H. NABATI
186
For simulation start up, first the interface temperature
is approximated and condensing film properties and heat
transfer coefficient has been determined in first cells
adjacent to the cooling wall. Condensation mass flow
rate and heat flux are calculated then based on the equa-
tion that described in the former sections. Then the heat
balance calculation is performed and new film interface
temperature is calculated. This procedure continuous
until the good agreement between old and new film in-
terface is achieved.
4. Investigated Cases
Two main cases are considered: Simple flue gas channel
and flue gas channel fitted with pin fins internally. In the
first case, two condensation models are implemented and
compared. The first model is based on Nusselt theor
a
as
available correlation from literature
8,18]). Following correlation is proposed by Dehby [8]:
y
nd the latter is based on diffusion boundary layer theory
described in section 2. Then based on this study, the
selected condensation model is selected and imple-
mented in the second case to study the effect of fins in
thermo-hydraulic behavior of condensation process.
5. Validity of Models
First model was run with a binary mixture of air and wa-
ter vapor. This is done first to validate the model and
compare results with
([


2438 458.3log
S
nc
TT
Px

 

(23)
Correlation is valid within these ranges:
0.3 m < L < 3.5 m; 1.5 atm. < Ptot < 4.5 atm.;
10˚C < (T∞ – TS) < 50˚C
Heat transfer coefficient dependency on mass fraction
of air at inlet is illustrated in Figure 3. As it is observed,
the trend of both numerical condensation models is simi-
ar to the experimental correlation result. Even thoug
0.05
L3.7 28.7
condens
hP

h
eling results differ slightly,
firms that presented models
1) Errors produced by measuring system (categorized
as experimental errors).
2) Intrinsic numerical errors caused by computational
procedures such as truncations (modeling errors).
fication and
assumptions (modeling errors).
l
experimental data and mod
he presented diagram cont
are relatively capable to predict the condensation behav-
ior of such condensers.
Some reasons for slight discrepancies between experi-
mental and modeling results can be identified as follow-
ings:
3) Errors resulted from modeling simpli
Figure 3. Verification of model validity (air/water vapour
mixture).
To minimize the CFD modeling errors, mesh depend-
ency of the solution was examined by solving the flow
and temperature fields for different mesh configurations
made of different cells. These profiles were compared in
several sections for all configurations to be sure that the
maximum difference in the flow field properties between
the coarser and finer meshes are less than 1% and the
final mesh lead to mesh-independent solutions. Based on
these results, the flue gas mixture then changed from
Air/H2O to CO2/H2O and appropriate material properties
supplied to the model to make it more suitable for
Oxy-fuel process.
6. Results and Discussion
Presented results in the current section include outpu
h a validation of reference case to examine the
ondensation models and then it followed by a different
ca
wever the predicted results from
e first condensation model (based on Nusselt theory (or
)) stand higher. Both
odel show that total heat transfer decreases rapidly
t
data obtained from different simulations. The modeling
started wit
c
se containing pin-fins. Results obtained for this model
are presented in Figures 4 to 8. Several checks were
performed in order to verify accuracy of the generated
results. The contour plots for velocity, temperature and
pressure were observed separately to confirm that the
results satisfy the boundary conditions and also they are
independent of grid size.
A comparison of two condensation model is presented
in Figure 4. The relation between total heat transfer co-
efficient and CO2 mass fraction are illustrated here.
As the CO2 mass fraction increases, both models intend
to give closer results. Ho
th
heat and mass transfer analogy
m
with any increase in CO2 concentration. A rough conclu-
sion from figure is that 1% increase in CO2 mass fraction
decrease the heat transfer coefficient about 1%.
Figure 5 illustrates prediction of condensation rate.
The trend of condensation rate is consistent with theory.
As the CO2 mass fraction increases, the condensation

H. NABATI
187
Figure 4. Comparison of two condensing models in mean
heat transfer coefficient prediction (CO2/H2O mixture).
Figure 5. Comparison of condensation rate for two con-
densation models.
rate decreases more sharply. The reason is that firstl
ecame more difficult.
Results also showed that average heat transfer coeffi-
cient is more sensitive to inlet velocity at low speeds.
Figure 6 shows the results that are obtained with model
based on diffusion boundary layer theory. It can be seen
that at velocities more than 1.5 m/s, the velocity effects
is negligible. However, when the CO2 mass fraction is
lower at the inlet, velocity can be an affecting parameter
as well. The trend was found to be same for lower CO2
fractions.
Effect of flue gas inlet temperature on mean heat
transfer coefficient is depicted in Figure 7. Also here for
higher inlet temperatures, rate of heat transfer coefficien
ature with less heat removal. Subse-
uently the rate of condensation would be higher at
mparison of total heat transfer
co
y
there is less water content in the flow gas and secondly
the diffusion of water vapour toward the cooling surface
b
t
change is less. It is natural, as water vapour reach to
saturation temper
q
lower inlet temperature.
Second case that was considered in this study was a
vertical plate which was equipped with some pin fins.
Figure 8 shows the co
efficient in the simple condensing plate and surface
Figure 6. Average heat transfer coefficient vs inlet flue gas.
Figure 7. Relation between inlet temperature and total heat
transfer coefficient.
Figure 8. Comparison of total heat transfer coefficient be-
tween simple case and pin-finn e d surface
ible. It means that models that are
eveloped here are not really accurate to predict the ex-
act heat transfer coefficient in more complicate geome-
tries. The reason is that the model just look into the cell
adjacent to wall and the geometry is not accounted at all.
Especially the correlations that were implemented are
developed for vertical case and some surfaces of pins are
with pin fins. Figure shows that the difference in coeffi-
cient values is neglig
d

H. NABATI
188
horizontal.
7. Conclusions
Simulating results have been presented for two conden-
sation models and two different geometries. The physics
of the problem and the heat transfer characteristics have
been discussed for these models. The aim was to evalu-
ate numerical modeling capabilities to predict water va-
pour condensation from a flue gas that contains high
concentration of CO2. The results are summarized as
followings:
e to experimen-
ture. However at higher inlet temperatures
nd velocities the sensitivity to these parameters de-
oefficient was estimated by calculat-
ppreciated
an
9.
1) Both models are capable to predict the trends i
condensation process. However, the model based on
oundary layer theory shows closer valu
n
b
tal correlation. The effect of the CO2 presence in the flue
gas as a non-condensable gas was predicted correctly by
both models.
2) Heat transfer coefficient decreases as a consequence
of the increase in CO2 mass fraction for constant wall
temperature as a result of the higher resistance to diffuse
from the flue gas bulk to the boundary layer.
3) The total heat transfer rate depends on inlet velocity
and tempera
a
creases.
4) Heat transfer c
ing the interface temperature. However, it was found that
it is possible to get approximately same results by as-
suming this temperature equal to wall temperature. This
assumption facilitates the numerical efforts.
5) A brief description of the technical approach that
was implemented for current study is:
Modeling surface contact condensers with Fluent© re-
quires the Eulerian model. This Eulerian multiphase
model is an advanced model of Fluent and requires quite
a bit of experience to handle. In addition, modification of
these model to suit condensation process, which itself is
a very complex process, would require both, good under-
standing of the physical process and good knowledge of
model inside the Fluent. The accurateness of the nu-
merical modeling results is determined by the empirical
correlations specified to model the condensation process.
In the industry, there is a practice to model the process
with some correlations available in the open literature
and then tweak various parameters to results which are
close to the experimental results. Such a tuning is neces-
sary in numerical modeling as well for most of the cases,
as the general correlations may not yield accurate results
for a specific set up. It is advisable that designing a con-
denser just based on Numerical results may be a difficult
and expensive task.
8. Acknowledgements
Fluent Inc.’S solver capabilities are highly a
d I hereby knowledge use of it in the current paper.
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omenclature
- surface area [m2]
p - specific heat [JkgK–1]
- diameter [m]
- effective mass diffusivity [m2·s–1]
- external force vector
- acceleration of gravity [m.s–2]
- heat transfer coefficient [W·m2·K–1]
- specific enthalpy in energy equation [j·kg–1]
- evaporation latent heat [J·kg–1]
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N
A
C
d
D
F
g
h
h
hfg
f
g

h - modified latent heat of evaporation (sub-
ffect) [J·kg–1] cooling e
f
g
h - modified latent heat of evaporation (sub-
g effect) [J·kg–1]
·s–1]
–1·K–1]
S
Sc
Sh
Greek symbols
α - volume fraction
 - steam and non-condensable gas concentration
 - dynamicviscosity [Pa·s]
 - density [kg·m–3]
 - mean molecular diameter [Å]

cooling-superheatin
J - total mass flux [kg·m–2
[W.mK - heat conductivity
L - length [m]
·mol–1] M - molecular weight [kg
–1
m
 - mass flow rate [kg·s]
P - pressure [Pa]
Q - intensity of heat exchange between phases
–1
[j·s ]
R - reaction term in momentum equation
- source term in governing equations
- Schmidt number (Sc =
 /(  .d))
- Sherwood number
T - temperature [K]
u - velocity vector
se molar fraction
x - vapour pha
x' - liquid phase molar fraction
y - mass fraction
- phase stress-strain tensor
Subscripts
conv. - convection
g ase
ies
erent phases
t
s bulk
cond. - condensation
f - liquid phase, film
- gas ph
i - species i
L - dimensional length
Mean - average
nc - non-condensable spec
p,q - representative of diff
s - wall condition
sa - saturation condition
v - vapour
tot - total
∞ - flue ga
Superscripts
ave - averaged
i - species