# Experiments and Modelling Techniques for  Heat and Mass Transfer in Light Water Reactors

Authors: W. Ambrosini; M. Bucci; N. Forgione; A. Manfredini; F. Oriolo
Journal: Science and Technology of Nuclear Installations
 (2009)

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## Abstract

The paper summarizes the lesson learned from theoretical and experimental activities performed at the University of Pisa, Pisa, Italy, in past decades in order to develop a general methodology of analysis of heat and mass transfer phenomena of interest for nuclear reactor applications. An overview of previously published results is proposed, highlighting the rationale at the basis of the performed work and its relevant conclusions. Experimental data from different sources provided information for model development and assessment. They include condensation experiments performed at SIET (Piacenza, Italy) on the PANTHERS prototypical PCCS module, falling film evaporation tests for simulating AP600-like outer shell spraying conditions, performed at the University of Pisa, experimental data concerning condensation on finned tubes, collected by CISE (Piacenza, Italy) in the frame of the INCON EU Project, and experimental tests performed in the CONAN experimental facility installed at the University of Pisa. The experience gained in these activities is critically reviewed and discussed to highlight the relevant obtained conclusions and the perspectives for future work.


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## Body

## 1. Introduction

The capability to correctly model heat and mass
transfer phenomena has a key role in the analysis of postulated accidents in
present nuclear reactors and designs conceived for future deployment. In
particular, steam condensation and water evaporation in the presence of
noncondensable gases have been the subject of extensive studies in the past
decades, mainly aiming to close the problem from the modelling point of view.This
effort was performed in many countries, particularly, in connection with the
design of third generation reactors based on passive mechanisms for removing
decay heat from the reactor vessel and the containment. Downscaled experimental
facilities were set up reproducing basic heat and mass transfer phenomena
occurring during normal and off-normal operations in such plants in order to
collect relevant data (see e.g., [1–4]). In Europe,
the objective of a more in depth understanding of these phenomena was attained also
by projects financed in different EU framework programs, as those included in
the INNO and CONT clusters of FP-4 [5] and in the FP-5 SCACEX Project [6].The University of Pisa  had an active part in these activities, contributing both by model development
and assessment and by original experiments on both evaporation and condensation.
The research started on the modelling side, with the analysis of available
theories and techniques for evaluating condensation and evaporation rates in
reactor systems [7]. In addition to empirical engineering
correlations, the analogy between heat and mass transfer, in the different
forms appearing in literature, was adopted as the basic tool for predicting
mass transfer rates. Then, experimental data from different sources provided
the relevant information for model development and assessment. In particular,
the following:
(i)
condensation experiments performed at SIET (Piacenza, Italy) on the PANTHERS-PCC prototypical
passive containment cooling system modules were addressed by a 1D
model [8];(ii)
falling film evaporation tests for simulating outer
shell spraying conditions similar to those envisaged in AP600 reactor, were
performed at the University of Pisa by the EFFE experimental facility and were
simulated by both simplified models and a CFD code
[9, 10];(iii)
condensation on finned tubes was then considered,
adopting experimental data collected by tests performed at CISE (Italy)
in the frame of the INCON EU Project [11];(iv)
experimental tests were carried out and are still running
in the CONAN experimental facility installed at the University of
Pisa [12] to study condensation in the
presence of noncondensable gases, also in the frame of the EU Severe Accident
Research Excellence Network (SARnet) of Excellence [13].The experience gained in these different steps allowed refining modelling
techniques ranging from simple engineering correlations to 1D and CFD models. In
particular, the suitability of the analogy between heat and mass transfer was
assessed in correlating both evaporation and condensation data [9, 10, 12, 14]. The
further step of applying CFD models in
predicting heat and mass transfer was aimed to develop up-to-date modelling
tools for light water reactor containment analysis [13, 15, 16]; this represents one of the most
challenging aspects to be coped with in the years to come, in order to take
full profit of the experimental information collected in the last decades, making
a reasonable use of the increased capabilities of computational means.The paper summarizes the relevant conclusions obtained in the above mentioned
steps, trying to point out the lesson learned in relation to the available
methodologies for evaluating heat and mass transfer in conditions of interest for
nuclear reactor applications.


## 2. Prediction of Condensation in  a Prototypical PCCS Module

In support to the design of components of the General
Electric SBWR reactor [17], SIET set up a facility named
PANTHERS-PCC in order to evaluate the effect of noncondensable gas build-up in
the tubes of the SBWR passive containment
cooling system condenser [18, 19].The PCC
test loop consisted of a pool tank housing the full-scale prototype, made of
two equal modules submerged in water (see Figure1). The number of vertical tubes in each module was
248, having 5.08 cm (2 inches) outer
diameter and being connected with upper and lower headers. The air-steam
mixture was introduced in the condenser at prescribed values of air and steam
flow rates, pressures, and temperatures. The steam condensed partly on the inner walls of the tubes and was collected in
the lower header and routed to a drain tank; the latter represents the gravity
driven coolant system pool of the full scale reactor. Coherently with the
mechanisms envisaged to occur in the SBWR reactor, air accumulating in the gas
space of the drain tank was discharged to a vent tank, maintained at a slightly
lower pressure than the PCC inlet and outlet, thus, simulating the behavior of
the pressure suppression pool in the SBWR. The experimental facility preserved
the elevation of the full-scale plant, in order to correctly simulate the
expected gravity driven phenomena.Figure 1
PANTHERS-PCC test facility.Different
series of tests were performed in the facility aiming at simulating the main characteristics
of the SBWR design basis accidents. The tests involved different degrees of
superheating of the air-steam mixture and different air mass fractions; the
effect of level in the water pool was also tested.The 1D model adopted by the University of Pisa
in this frame [8] was developed in order to simulate
both filmwise condensation and falling film evaporation. A schematic
representation of the geometrical and operating conditions assumed in the model
in the case of film condensation in tubes is reported in Figure 2. The model makes use of a complete nonequilibrium
two-fluid approach, solving separate steady-state mass, energy, and momentum
balance equations for each phase, discretized by a finite difference scheme. Several
tens of control volumes were adopted to axially discretize the PCC tubes.Figure 2
Physical model adopted for film condensation in tubes.The Rohsenow boiling heat transfer correlation [20] was adopted on the outer side of the
heat exchanger tubes, as in many tests the outer fluid temperature was very close to saturation and
boiling conditions could be envisaged. The modelling of the gas-liquid interfacial
heat and mass transfer, having the greatest importance in order to evaluate the
overall efficiency of the heat exchanger, relied on the analogy between heat
and mass transfer, adopting different heat transfer correlations. In
particular, in a base model, the classical Dittus and Boelter
correlation [21] was adopted in the forms
(1)Nug,i,∞=0.023Reg,i0.8Prg0.3,Shg,0,∞=0.023Reg,i0.8Scg0.3.
The asymptotic values of the heat transfer
coefficients, applicable in long tubes, were then corrected taking into account
entrance effects according to a correlation suggested by Bonilla [22]. Once the corrected Sherwood number
at low mass transfer rate, Shg,0, was calculated, the condensation heat transfer was
evaluated by the following relationship:
(2)qcond′′=hlvShg,0DvgρgDhln(1+Bm),Bm=ωv,i−ωv,b1−ωv,i,
taking into account the suction effect by the
classical formulation derived from the solution of the Stefan's problem [23]. Similarly, the Ackerman correction
for the heat transfer coefficient [24] was adopted.As found in previous experiences of code applications by other researchers (see
the discussion in [8]), two variants of the model were
introduced, adopting a correlation by Banerjee and Hassan [25] and taking into account evidence
from experiments pointed out by Almenas and Lee [26],
concerning the dependence of heat transfer coefficients on system pressure. In
particular, as in the Banerjee and Hassan [25] model, a minimum value of the
Nusselt number was imposed adopting the formulations:
(3)Nug,i,tu=0.023Reg,i0.8Prg0.3,Nug,i,min=5.5(pp0)1.2,Nug,i=[(Nug,i,tu)3+(Nug,i,min)3]1/3,
with p0=0.1MPa.The obtained results showed an increasingly better behavior in predicting the trend
of condenser efficiency by applying the basic model, the Banerjee and Hassan [25] model and the final proposed model, which
implemented the suggestion by Almenas and Lee [26]
expressed in (3).
The overall performance of the model in predicting condensation efficiency,
also as a function of pressure, is described in Figure 3, showing that the final proposed model was able to
predict with good accuracy the observed experimental data.Performance of the adopted model in predicting condensation
efficiency as observed in PANTHERS-PCC tests.
(a)(b)


## 3. Falling Film Evaporation

The EFFE experimental facility [27] was set up in order to provide
separate effect data on falling film evaporation in conditions similar to those
envisaged for the outer surface of the AP600 safety envelope after a postulated
loss of coolant accident. The facility consisted in a 0.6 m wide, two-meter-long
stainless steel plate, heated on the back side by 100 modular electric heaters.
The heaters were arranged in three groups, supplied by the three phases of an
electrical transformer, in order to separately control heat flux in the film
inlet, middle, and outlet sections [9, 10].The plate was mounted over a frame allowing to rotate it from the completely
vertical to the completely horizontal position (Figure4(a)), in order to allow for simulating the conditions
occurring along the vertical part of the AP600 containment shell and in the
upper dome. A water spray system, located at the top of the plate (labelled Distr in Figure 4(b)), allowed for distributing in a uniform fashion
the falling film on the heated surface; a transparent screen (Pp),
located approximately at a distance of 10 cm from the heated surface, contributed to
enclose the evaporating region into a square channel. A countercurrent air flow
was forced in the channel by a blower (Bl) located at the bottom of the
plate itself, thus, reproducing conditions similar to those occurring in the
external AP600 containment flow paths owing to natural draft. The overall
evaporation rate was measured in different ways, in order to allow for
cross-checking the measured values; the most accurate measurement was achieved
by the rate of decrease of water level in the reservoir (Mv), obtained
by continuously acquiring a differential pressure signal between the bottom of
the vessel and the external atmosphere.EFFE Experimental Facility.
(a)
Front view of the plate(b)
Flow diagramThe experimental facility was operated in the frame of the EU DABASCO Project [5], devoted to acquire experimental data on containment
phenomena. Both dry (i.e., pure forced convection) and wet (i.e., film
evaporation) tests were performed, aiming to compare the average Nusselt number
data obtained in the former with corresponding averaged Sherwood numbers
obtained in the latter. Film flow rates from 20 to 100 g/s were adopted,
together with velocities of the countercurrent air flow up to nearly 9 m/s and
plate temperatures from 50 to 90°C.The obtained heat and mass transfer experimental data showed a general coherence
with the analogy between heat and mass transfer, as shown in Figure5, reporting average values of the Nusselt and the
Sherwood numbers for corresponding tests at 50 and 60°C of nominal plate
temperature. As it can be noted, the heat transfer correlation obtained from
dry tests approaches the classical correlation for heat transfer in closed
ducts multiplied by a coefficient larger than unity, accounting for the limited
length of the pipe and for the effect of the thrust generated by the blower
located at channel inlet; on the other hand, wet test data, in terms of
Sherwood number exhibit a similar behavior, supporting the applicability of the
analogy between heat and mass transfer. This conclusion was confirmed by data
at higher plate temperatures (from 70 to 90°C)  [10].Figure 5
Comparison of dry and wet test data in the experimental test series
at 50°C and 60°C of plate temperature
in the EFFE experiments [6].Computational domain and discretization of the channel of the EFFE
experimental facility for the FLUENT code.
(a)
Computational domain(b)
discretizationThe availability of experimental data on falling film evaporation offered a first
opportunity to apply computational fluid dynamics in simulating heat and mass
transfer in a flow duct [15]. The adopted model, quite similar to
the ones to be used later on for filmwise condensation, exploited the opportunities
offered by the FLUENT code [28] to simulate the near-wall region with
models having different degrees of low-Reynolds number capabilities. In
particular, the RNG k-ε
model was adopted with the two-layer standard model available in the CFD code,
making use of detailed discretizations close to the walls. In particular, a 2D
46×46, 90×90 or 180×180 grid was chosen with a refined distribution
of meshes close to the lateral walls and at the channel inlet. The falling film
was not modelled, due to its minor role in determining heat and mass transfer;
the evaporating wall was therefore assumed as a still interface at the measured
average temperature. Water vapour concentration at the wall was assumed to be at the value
corresponding to saturation at the wall temperature.Since the evaporating wall could not be assumed permeable to vapour, as it should be
for a transpiration problem in which vapour is continuously blown from the film
into the gas-steam mixture, equivalent mass and energy sources were assumed to exist
in the first mesh layer close to the wall, having a thicknessΔ in the order of 10−4 m.
This approach, subsequently used also for simulating film condensation, makes
use of the available user defined functions to assume volumetric sources given
by
(4)Sm=m˙i′′/Δ=−ρg,iDvg1−ωv,i∂ωv∂y|i/Δ
for mass, and
(5)Sh=Smhv
for energy.The results obtained
for the dry and wet experimental tests, whose boundary conditions are reported
in Table1, showed a tendency to underestimate heat transfer and
evaporation rates (see Table 2 for the case Vin=0). This effect could be attributed to the location
of the blower close to the channel inlet, possibly impressing a transversal
component to the inlet velocity. As a matter of fact, the calculations
performed with a 45°C
degree inclination of the inlet flow rate (see Table 2 for the case Vin=Uin) showed powers and evaporation rates more
coherent or even in excess with the measured values confirming the possibility
that such an effect plays a role in the performed experiments.Table 1
Boundary conditions for the dry and wet EFFE tests
addressed by FLUENT calculations [15].
Air flowTest no.Average plate temperature (°C)Inlet temperature (°C)Relative humidity (%)Mean inlet velocity (m/s)DryDTI57.820.847.60.87DT256.921.247.54.25DT357.524.043.37.47WetWTI60.323.530.90.78WT260.823.634.64.07WT360.525.038.27.24Table 2
Results obtained by the FLUENT
calculations for the dry and wet EFFE tests [15].
Thermal power (kW)Total evaporation rate (g/s)Test no.Exp.Calc. (Vin=0 m/s)Calc.   (Vin=Uin)Exp.Calc. (Vin=0 m/s)Calc. (Vin=Uin)DryDTI0.350.240.32———DT21.170.831.14———DT31.591.191.72———WetWTI2.822.383.081.190.921.20WT29.608.5611.783.713.334.58WT315.3412.8618.465.725.007.18


## 4. Condensation on Finned Tubes

The proposal made in the early 90s by ENEL, Italy, the Italian
electrical utility, of a double containment equipped with a completely passive
heat removal system [29], stimulated a renewed interest for
condensation on finned heat exchangers. In fact, the proposed design included a
number of compact heat exchangers made of arrays of inclined finned tubes,
connected through a natural circulation loop to an external heat exchanger.As the efficiency of this system had to be clearly proven in front of safety
requirements, an experimental campaign was then carried out by ENEL in
cooperation with different Europe an partners.
The activity involved an extensive testing of major components, including the
internal heat exchanger, the intermediate loop, and the external pools. In
particular, CISE performed an extensive campaign on both smooth and finned single
tubes in natural convection conditions [30]; in addition, both CISE and PSI [31] performed functional tests on compact finned tube heat
exchangers, making use of different modalities. Figure 7 shows sketches of the experimental apparatuses
adopted by CISE in this purpose.Sketches of the experimental apparatuses adopted by CISE
for single tubes and full compact heat exchanger mock-ups [11].
(a)(b)This new experimental information allowed the University of Pisa to set up
models for finned tube condensation, testing different heat transfer
correlation and applying the heat and mass transfer analogy. The main
characteristics of the models were the following.(i)
Based on available correlations for heat transfer in
free or forced convection on finned tubes and compact heat exchangers, the
analogy between heat and mass transfer was applied in the form(6)Nu=f(Re,Gr,Pr,geometry)⇒Sh0=f(Re,Gr,Sc,geometry),
where f represents the particular heat transfer correlation identified for the
application and Sh0 represents the Sherwood
number at low mass transfer rate, to be corrected by the classical logarithmic
relationship derived by the solution of the Stefan problem:
(7)Sh=hmDρgDvg=Sh0ln(1+Bm)Bm,
the corresponding mass transfer rate was
calculated as
(8)m˙i′′=hmBm=hmωv,i−ωv,b1−ωv,i.(ii)
Since in the case of condensation, the presence of a
finned surface raises the problem of evaluating the overall surface efficiency
and also the effect of “bridging” (or flooding) of the fins with liquid
condensate, it was necessary to include models for both these effects; in
particular, the Beatty and Katz model [32] was used to combine the heat
transfer coefficients of the finned and unfinned surfaces based on the film
condensation Nusselt theory for flat plates; in addition, the Rudy and Webb
model [33] was initially adopted for evaluating
the possible effect of efficiency reduction due to bridging, but it was later recognized
that this phenomenon played a minor role in the experiments and it was finally
neglected; in the final form of the model, also the thermal resistance of the liquid
film at the condensing surface was neglected, since it was found to introduce a
very weak effect.Figures8 and 9 show the results obtained for both the case of single-finned
tubes in natural convection and for compact-finned tube heat exchangers with
natural draft (CISE) and forced convection (PSI). As it can be noted, also for
this relatively more complicated case, the application of the analogy between
heat and mass transfer showed to be successful enough as to provide a good
comparison with the reference base of data.Figure 8
Results obtained for natural convection condensation on single-finned
tubes by the Tsubouchi and Masuda model [34].Figure 9
Results obtained for condensation on compact-finned tube heat exchangers
making use of the Nir model [34].


## 5. Filmwise Condensation onto a Flat Plate

Recently, the University of Pisa  undertook experiments on filmwise condensation in the CONAN experimental
facility installed at its laboratories [12, 13, 16, 35]. As shown in
Figure 10, the experimental facility includes
three loops.
(i)
The primary loop, containing a square cross-section (0.34 m× 0.34 m), two-meter-long test
channel, facing a 4.5 cm thick aluminium plate (0.34 m × 2 m, in width and length) on
which condensation takes place; the loop presently operates at atmospheric
pressure and the steam content in the air-steam mixture circulated in the
facility is controlled by the electrical power fed to the steam generator
(capable of 60 kW).(ii)
The secondary loop provides the needed cooling on the back
side of the cooling plate, by circulating relatively cold water in a narrow
channel (5 mm of depth); the measurements of the secondary coolant conditions on the back
side of the plate represent important information to be provided for modelling,
relying on the measured inlet and outlet secondary coolant temperature and flow
rate to evaluate the heat transfer coefficient and the average secondary fluid
temperature.(iii)
The tertiary loop, interfaced with the secondary one
through a mixing vessel, accomplishes with the function to remove heat from the
test section, by extracting a prescribed flow of warm water from the vessel and
replacing it with a same flow of colder water from a large reservoir.
The relevant measurements available in the facility
include the primary air-steam mixture flow rate (corresponding to channel
velocities in the range from 1.5 to 3.5 m/s), dry-bulb and wet-bulb tempe ratures, the local tempe
rature close to the surface and within
the thickness of the cooled plate (from 30 to 70°C) and the overall
condensate flow rate, as collected by a gutter.Figure 10
Flow diagram of the CONAN experimental facility.In addition to comparing the results of the measurements in terms of local
Sherwood numbers with available engineering correlations (see Figure11),
the experimental data were compared with the
predictions obtained by the FLUENT code in which a 2D model very similar to the
one adopted in the case of the evaporation tests described above (see
Section 3) was used. In making use of the model, a conjugated heat transfer approach
was successfully implemented, by discretizing the cooled plate and simulating
heat conduction through it, in addition to condensation on the gas-side surface
(Figure 12). Also in this case, the RNG k-ε
model was used with a two-layer treatment near the wall. Appropriate sinks of
mass and energy are introduced near the wall to simulate the steam suction. The
overall good agreement obtained in the general comparison with data (Figure 13) encouraged to improve the measurement techniques and
to analyze in greater detail the phenomena and the observed slight
discrepancies with experimental data.Figure 11
Comparison of a set of experimental data from the CONAN facility
with an engineering correlation [16].Figure 12
Discretization adopted in the analysis of CONAN experiments
by the FLUENT code with conjugated heat transfer.Figure 13
Comparison of a set of experimental data from the CONAN
with FLUENT code predictions [35].In particular, specific tests performed in the CONAN facility were
proposed as Step 1 of a condensation benchmark organized by the University of
Pisa in the frame of the EU SARnet of
Excellence [13]. Several participants applied their
CFD condensation models in predicting the observed behavior, obtaining in
general a good agreement with experimental results.Figures14 and 15 illustrate the results obtained by the University of Pisa
in the application of the FLUENT code to the 5 proposed tests. As it can be
noted from Figure 14, the overall condensation rate is slightly underestimated,
a feature that resulted common with other code results. This behavior can be
explained considering Figure 15, that shows a corresponding underestimate of the
local heat flux at the entrance of the test channel. Possible 3D effects as
well as some degree of nonuniformity in the inlet mixture velocity can be
considered as possible causes of this slight discrepancy.Figure 14
Results for the overall condensation rate obtained by the University of Pisa
in the Condensation Benchmark Step-1.Figure 15
Results for the local heat flux obtained by the University of Pisa
in the Condensation Benchmark Step-1.


## 6. Conclusions

The experience gained in simulating heat and mass
transfer phenomena relevant for light water nuclear reactor applications
provides a suitable basis to draw conclusions about the present capabilities of models in predicting
evaporation and condensation in the presence of noncondensable gases.As a first remark, it can be noted that, at both the level of engineering models and
of CFD codes, evaporation and condensation can be dealt with by quite the same
approaches, obtaining similar accuracy. On one side, the classical treatment of
mass transfer on the basis of the definition of appropriate coefficients to be
multiplied by a suitable
driving force, making use of the analogy between heat and mass transfer,
appears very effective. Once an applicable heat transfer correlation is
selected for the addressed geometry, the analogy assures a reasonable degree of
reliability of the corresponding mass transfer model. As a matter of fact, the
step of selecting the heat transfer correlation is the one that differentiates
the various applications discussed in this paper, ranging from rectangular channels
with a falling film, to circular heat exchanger pipes and compact-finned tube
heat exchangers. The diversity of the addressed geometries, in which the
adopted approach proved to be effective, suggests a reasonable level of
reliability.In this respect, it must be also recognized that the role of the analogy between heat
and mass transfer, though particularly evident in the case of the engineering
correlation approach, is a key one also in CFD models. In fact, the adoption of
constant values of the turbulent Prandtl and Schmidt numbers in defining the
turbulent diffusivities on the basis of the eddy viscosity reveals the use of
this assumption also in the case of mechanistic models having low Reynolds
number capabilities. Therefore, even while using sophisticated two-equation
turbulence models, we often still rely on the analogy between heat and mass
transfer, something to be attentively considered when extrapolating our
modelling experience to different fluids or operating conditions, for which
this approach may be not completely justified or successful.The effectiveness of computational fluid-dynamic techniques in providing plenty of
detailed local data, to be compared with experimental information, is quite
evident, though their suitability for practical applications can be matter of discussion. In this respect, we can
identify two separate orders of problems.(i)
On one side, even for simple geometries, refining the
meshes close to the walls, in order to fully exploit low-Reynolds number
capabilities, may be too costly, requiring a huge number of finite volumes or
elements and a corresponding increase of computational effort.(ii)
On the other side, complex geometries, like the finned-tubes
heat exchangers, may anyway require great detail to be described making the use
of CFD models, resulting particularly expensive for production calculations.It seems therefore that CFD must be considered as a very powerful tool for
obtaining relatively accurate results, though it is still not always completely
affordable for studying system behavior in cases like complex experimental
apparatuses or full-scale reactor plants. In this respect, the job of
engineering models and correlations seems not yet to be completed, not only for
quick guesses of heat and mass transfer rates, but also for inclusion in system
analyses, requiring to model simultaneously many interacting phenomena.As noted in the conclusions about the SARnet Benchmark [13],
at least for simple geometries efforts can be spent in providing CFD codes with
models suitable to reasonably predict mass transfer phenomena without introducing an
unaffordable number of nodes in the near-wall region. This could be achieved by
the use of specialized wall functions allowing for a realistic description of
boundary layers. Though a
proposal in this aim is already available, dealing by wall functions with
intrinsically complicated phenomena as mixed convection may be challenging
enough; some sort of compromise modelling should be then achieved, while
waiting for increased computing power allowing for adopting more fundamental
and mechanistic approaches.


## Nomenclature

Latin Letters
B:Width [m]Bm:Driving force for mass transfer in terms of mass fractionsDvg:Vapor diffusion coefficient in the gas mixture [m2/s]Dh:Hydraulic diameter [m]g:Gravity [m2/s]Gr:Grashof numberh:Specific enthalpy [J/kg]hlv:Latent heat of evaporation [J/kg]hm:Mass transfer coefficient [kg/(m2s)]j:Node numberL:Length [m]m˙″i:Interfacial mass flux [kg(m2s)]Nu:Nusselt numberp0:Reference pressure [Pa]Pr:Prandtl numberq′′:Heat flux [W/m2]Re:Reynolds numberSh:Energy volumetric source [W/m3]Sm:Mass volumetric source [kg/(m3s)]Sc:Schmidt numberT:Temperature [K]U:X-component of fluid velocity [m/s]V:Y-component of fluid velocity [m/s]W:Mass flow rate [kg/s]x:Longitudinal coordinate [m]y:Transversal coordinate [m]Greek Letters
Δ:Node thickness [m]ρg:Gas mixture density [kg/m3]ω:Mass fractionSubscripts
b:Bulkcond:Condensationf:Liquidg:Gas mixturei:Interfacein:Inletmin:Minimumtu:Turbulentv:Vapor (steam)w:Wall0:At low mass transfer rate∞:Asymptotic value



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*Source: 738480-2009-03-18.xml*