Acta Polytechnica


https://doi.org/10.14311/AP.2022.62.0352
Acta Polytechnica 62(3):352–360, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence

Published by the Czech Technical University in Prague

THEORETICAL AND EXPERIMENTAL STUDY OF WATER
VAPOUR CONDENSATION WITH HIGH CONTENT OF

NON-CONDENSABLE GAS IN A VERTICAL TUBE

Jakub Krempaský∗, Jan Havlík, Tomáš Dlouhý

Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Energy Engineering,
Technická 4, Prague 6 16607, Czech Republic

∗ corresponding author: jakub.krempasky@fs.cvut.cz

Abstract. This article deals with the possibility of separating water vapour from flue gases after
oxyfuel combustion using condensation processes. Those processes can generally be described as
condensation of water vapour in the presence of non-condensable gases. Hence, the effect of non-
condensable gas (NCG) on the condensation process has been theoretically and experimentally analysed
in this study. The theoretical model was developed on the basis of the heat and mass transfer analogy
with respect to the effect of the NCG, the flow mode of the condensate film, the shear stress of the
flowing mixture, subcooling and superheating. Subsequently, an experimental analysis was carried
out on a 1.5 m long vertical pipe with an inner diameter of 23.7 mm. The mixture of vapour and air
flowed inside the inner tube with an air mass fraction ranging from 23 % to 62 %. The overall heat
transfer coefficients (HTC) from the theoretical model and experimental measurement are significantly
lower than the HTC obtained according to the Nusselt theory for the condensation of pure water
vapour. The overall HTC decreases along the tube length as the gas concentration increases, which
corresponds to a decrease in the local condensation rate. The highest values of the HTC are observed
in the condenser inlet, although a strong decrease in HTC is also observed here. Meanwhile, there is
a possibility for an HTC enhancement through turbulence increase of the condensing mixture in the
condenser outlet. Results also showed that the heat resistance of the mixture is several times higher
than the heat resistance of the condensate film. The developed theoretical model based on heat and
mass transfer analogy is in good agreement with experimental results with the standard deviation
within +25 % and −5 %. The model is more accurate for lower NCG concentrations.

Keywords: Condensation, non-condensable gas, vertical tube, experimental, theoretical.

1. Introduction
One of the promising CCS technologies is oxyfuel
combustion. The use of CO2 captured from oxyfuel
combustion technology for other technological pur-
poses and for storage requires a sufficient purity of
the product. After emissions cleaning, suitable op-
tions for final drying of flue gases are condensation
processes in condensing heat exchangers. The aim
is to dry the flue gas formed by oxyfuel combustion,
which is consists of steam and a high proportion of
non-condensing gases (especially CO2 and O2). The
drying is necessary for the final purification of CO2
prior to its further use. This process can generally be
described as the condensation of water vapour with
a high content of non-condensable gases.

Condensation of water vapour with the presence
of non-condensable gas (e.g. CO2) is a widely stud-
ied topic and its recognition dates back to 1873 [1].
Up to now, the main focus has been on condensa-
tion of water vapour with a small fraction of air in
tube condensers [2, 3]. Such cases can be found in
various technological processes such as refrigeration,
condensers in power plants, geothermal power plants
and various processes in chemical and process indus-

try. This field of study has been investigated by many
authors and, today, represents a well-covered topic.
However, there are areas where the content of air
during the vapour condensation can be higher or dif-
ferent gas than air is present. For instance, it can
be: CCU/S technologies, desalination of water, latent
heat recovery from flue gas or LOCA accidents [2–4].
Therefore, studying condensation in tube condensers
with respect to new technological challenges has a
potential for commercial applications and system im-
provement.

Chantana [5] conducted an experimental and the-
oretical study of water vapour condensation in the
presence of air in a vertical tube. The water vapour
content in the gas vapour mixture was very low. The
theoretical model was developed on the basis of the
heat and mass transfer analogy. The results showed
that the condensation of the vapour and roughness
of the film surface cause a disruption of the gas layer
accumulated near the phase interface, which increases
the HTC. A detailed description of the processes at
the vapour-liquid interface is also introduced in [6, 7].
Maheswari [8], in his work, studied the influence of
the water vapour and air mixture’s Reynolds number
on the HTC in a vertical tube. He concluded that the

352

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vol. 62 no. 3/2022 Theoretical and experimental study of water vapour condensation . . .

Semi-theoretical Theoretical

Method Correction anddegradation factor
Heat and mass

transfer analogy
Diffusion layer

model
Boundary layer

model

Description
Empirical equations

based on
experimental data.

Based on similarities
between momentum,

energy, heat, and
mass transfer
equations and

empirical coefficients.

Based on Fick’s law
of molecular diffusion.

Vapour diffuses
through the layer of
non-condensable gas
to phase interphase.

Description of
condensate film layer
and boundary layer

with initial and
boundary conditions.

Accuracy
and output

Low accuracy, simple
output.

Moderately high
accuracy, usually
iteration involved.

Moderately high
accuracy, usually
iteration involved.

High accuracy,
various results, too

complex for practical
application.

Table 1. Overview of theoretical models for film-wise condensation with non-condensable gas.

HTC of the film can be lower than the HTC of the
mixture in the case of high Reynolds number of the
mixture. No and Park [9] conducted experiments in
vertical and horizontal tubes. The most important
observation was that the waviness of the film decreases
the accumulation of gas near the phase interface, and
thereby effectively increases heat transfer. The effect
of gas velocity on the flow of the liquid film in the ver-
tical tube is also studied in the work of the Kracik [10],
where the effect of shear stress of the flowing gas on
the liquid film is analysed experimentally and theoret-
ically with three different diameters of the inner tube.
Kuhn [11] created three theoretical models developed
on degradation factor, heat and mass transfer anal-
ogy, and mass transfer modelling and compared them
with results from an experimental measurement. The
standard deviations of the HTC were 6.4 %, 8.4 % and
17.6 % for water vapour with air and 3.2 %, 6.1 % and
17.6 % for water vapour with helium according to the
mass transfer modelling, diffusion layer modelling and
degradation factor, respectively.

This article focuses on research of the process of
condensation of water vapour from flue gases from
oxyfuel combustion. In this study, the effect of non-
condensable gas (NCG) on vapour condensation in
a vertical tube condenser is theoretically and experi-
mentally analysed.

2. Theoretical modelling
2.1. Summary of available theoretical

models
There are several methods to calculate heat trans-
fer during the condensation of water vapour in the
presence of NCG in a vertical tube. In general, the-
oretical models for such phenomena are governed by
the film condensation model, which was first described
by Nusselt in 1916 [12]. Theoretical models based on
the theory of film-wise condensation are usually di-
vided into two groups, semi-theoretical and theoretical.

Semi-theoretical models use, to some extent, experi-
mentally established coefficients and data, which are
incorporated into the theoretical analysis. The first
option is correction and degradation factors, which
modify the standard theory for the condensation of
pure vapour. The second option is models based on
heat and mass transfer analogy. Meanwhile, theo-
retical models are not based on experimental data,
but on the description of the boundary layer near
the phase interphase. The general summary of the
theoretical models is shown in Table 1 [3, 11, 13]. The
degradation factor is the simplest method for the de-
termination of HTC; however, it gives less accurate
results. While the theoretical models are quite com-
plex and can give very accurate results, their practical
use is quite complicated.

2.2. Developed theoretical model
A theoretical model based on the heat and mass trans-
fer analogy was developed for a vertical double-pipe
condenser in which the condensing water vapour flows
downwards in the inner tube and the cooling water
flows in counter-current in the outer tube. Detailed
descriptions of semi-theoretical models based on heat
and mass transfer analogy can be found in the liter-
ature [5, 14, 15]. Herein, the condenser was divided
into 15 segments where local heat transfer was deter-
mined. The overall HTC in the condenser is given
by the heat transfer coefficients of several layers as
shown in Figure 1 and described with Equation (1).
One segment is shown in Figure 2.

Heat transfer of the condenser can be determined
by a temperature difference and a corresponding HTC
of the certain layer. The overall condenser power can
be calculated from the temperature difference of bulk
mixture temperature TSAT and cooling water temper-
ature TK with the overall HTC of the condenser K.
The heat transfer from the condensing mixture to the
phase interface is given by the temperature difference
of the bulk mixture TSAT and phase interface TF,SAT
and HTC of condensing mixture α̈G. This is equal

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J. Krempaský, J. Havlík, T. Dlouhý Acta Polytechnica

Figure 1. Heat and mass resistances during condensation [14]. Figure 2. Analytical model.

to the heat transfer from the phase interface with
temperature TF,SAT to the coolant flow with temper-
ature TK with corresponding HTC k′. Two dots in
HTC of condensing mixture α̈G indicates that heat is
transferred not only by conduction which is given by
αG but also by mass flow of condensing vapour, which
is given by mass transfer coefficient βG.

The heat flux between the gas-vapour mixture and
the cooling water is determined by the heat and mass
transfer resistances and the temperature difference of
the fluids in the condenser.

q̇ = α̈G(TSAT − TF,SAT )
= k′(TF,SAT − TK )
= k(TSAT − TK ) (1)

The fundamental assumption in the model is that
the condensate flows on a vertical wall in an annu-
lar film, similarly to the Nusselt condensation theory
with HTC αF . The vapour condenses on the film
surface, while the gas accumulates near the phase in-
terface. This forms another layer of non-condensable
gas through which the vapour diffuses towards the
phase interface. Heat flux, which is transferred from
the gas-vapour mixture, can be divided into sensible
heat given by HTC αcv and latent heat given by αc,
as described by Equation (2). The mass transfer resis-
tance occurs only in the mixture since the condensate
film is formed only by water with a temperature at
the wall TW,F .

q̇ =
1

1
αF

+
1

αcv + αc

(TSAT − TW,F ) (2)

The convective heat flow q̇G transferred from the
gas to the liquid film is calculated with respect to the
mass transfer that occurs with heat transfer according
to the Ackermann correction factor ET (Equation (3))
with Equation (4) and Equation (5), where ΦT is a
non-dimensional mass flow, ṅ local molar flux, c̃pG
molar specific heat capacity and αG convective HTC
of the mixture.

q̇ = αGET (TSAT − TF,SAT ) (3)

ET =
ΦT

1 − exp (−ΦT )
(4)

ΦT =
ṅc̃pG
αG

(5)

The latent heat corresponds to the vapour trans-
ferred through the gas layer to the phase interface.
This can be determined by applying the heat and
mass transfer analogy. Mass transfer is based on the
same formal relation as heat transfer replacing the
Nusselt number N u with the Sherwood number Sh
and the Prandtl number P r with the Schmidt number
Sc as shown in Equations (6) and (7). The relation
between mass and heat transfer can then be described
by the Lewis number Le according to Equation (8)
with molar density of the gas nG. The mass trans-
fer coefficient is then applied to calculate the local
condensing flow according to the diffusion of concen-
tration (Equation (9)) where ṙv is the relative molar
flow of the vapour, ỹv,F is the molar concentration
of vapour at the phase interface, ỹv,B is the molar
concentration of vapour in the bulk mixture, and ṅv
is the local vapour molar flux.

N u = CReαP r0.6 (6)

Sh = CReαSc0.6 (7)

αG = nGβGc̃pGLe0.6 (8)

ṅ = nGβG ln
( ṙv − ỹv,F

ṙv − ỹv,B

)
, (9)

where:
ṙv =

ṅv
ṅ

. (10)

During the calculation of the heat balance at cer-
tain parts of the condenser, it is necessary to know
the condensation temperature of the vapour on the
phase interface TF,SAT . This temperature is calcu-
lated from Equation (10), including mass and energy
balance. This equation is solved iteratively with the
initial estimation of the film temperature at the phase

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vol. 62 no. 3/2022 Theoretical and experimental study of water vapour condensation . . .

Figure 3. Schematic diagram of experimental setup.

interface with ṄF being the film molar flux and TF
being the film temperature.

ṄF c̃pF
dTF
dA

+ k′(TSAT − TF,SAT ) = ṅ∆h̃v

+ αGET (TSAT − TF,SAT ) (11)

Overall results are given by an arithmetic ratio of
results from given segments. The overall condensa-
tion performance of the heat exchanger is calculated
according to the steps shown below. Two parameters
must be estimated at the beginning – the condensa-
tion temperature of the vapour on the film surface
and the outlet temperature of the cooling water. The
temperature of the film surface has to be estimated
in each segment, while the temperature of the cooling
water has to be estimated only in the outlet segment.
The temperature of the cooling water at other points
is given by the energy balance corresponding to the
condensation and convection of the air-vapour mix-
ture in the given segment. The HTC of the cooling
water was experimentally determined by pure water
vapour tests. The effects of the film flow mode, the
shear stress of the flowing mixture, and the subcooling
and superheating are included according to [14].
(1.) Input of initial values (mixture and cooling wa-

ter inlet parameters – temperature, pressure, mass
flow).

(2.) Estimation of the outlet temperature of cooling
water.

(3.) Estimation of the saturation temperature at the
phase interface of vapour.

(4.) Calculation of fluid thermodynamic properties
according to [15].

(5.) Calculation of heat and mass transfer coefficients
αG; βG.

(6.) Calculation of the local condensation rate and
HTC of the film αF .

(7.) Calculation of saturation temperature at the
phase interface using the Ackermann correction fac-
tor.

(8.) Check if the calculated saturation temperature on
the phase interface corresponds to the estimated (if
not, back to step 3 – an adjustment of the saturation
temperature on the phase interface is necessary).

(9.) Calculation of the condenser power, heat transfer
coefficient, outlet cooling water temperature for a
given segment.

(10.) Repeat the calculation from the beginning until
the last segment is calculated.

(11.) Check if the calculated outlet temperature of the
cooling water corresponds to the estimated temper-
ature (if not, back to Step 2 – the adjustment of
cooling water outlet temperature).

(12.) Results and average values.

3. Experimental apparatus
A schematic diagram of the experimental apparatus
used for the theoretical model validation is shown in
Figure 3. The system is designed as an open loop
comprised of three parts: main test section; water

355



J. Krempaský, J. Havlík, T. Dlouhý Acta Polytechnica

vapour and air supply section; cooling water section.
The main test section comprises a vertical double-pipe
heat exchanger made of two concentric stainless steel
tubes. The mixture of water vapour and air enters the
heat exchanger at the top and is directed vertically
downwards through a calming section before flowing
into the inner vertical tube. The cooling water flows
upwards in the annulus. The heat exchanger is in
counter-current configuration. The inner tube of the
heat exchanger is 2000 mm long with an inner diame-
ter of 23.7 mm and a wall thickness of 1.6 mm. The
outer tube is 1500 mm long, with an inner diameter of
29.7 mm and a wall thickness of 2 mm. The tube ma-
terial is stainless steel 1.4301 (AISI 304). The annulus
created from these two concentric tubes is 1.6 mm
in width. Stainless steel pins are used as spacers at
three circumferential positions to keep the annulus
concentric.

The steam generator was placed on the platform
weight scale, which measured the amount of vapour
generated. The generator produced steam steadily at
a rate controlled by the power input to the electrical
immersion heaters. In the first stage of the experi-
ments, air was chosen as the NCG and blown in the
mixing point by a compressor. The volume flow rate of
air was measured by a rotameter. The pressure of the
air was measured using a U-tube water manometer.
The mixing chamber of water and air was designed
so that any possible condensate occurring during the
mixing of the vapour and air was flowing back to the
steam generator. The flow rate of the cooling water
was controlled by a regulating valve. Non-condensing
gases in the water circuit were vented from the system
through a manual gate valve at the exit of the con-
denser. Microfiber insulation and rubber foam were
wrapped around the heat exchanger to prevent any
potential heat loss. Four thermocouples were placed
in condenser tapings measuring the inlet and outlet
temperature of the cooling water and the inlet and
outlet temperature of the water vapour-air mixture.
All experiments were performed under atmospheric
pressure. Measurements were conducted after the
steady state of the system was reached.

4. Results and discussion
4.1. Theoretical analysis
The theoretical model was developed to predict the re-
sults from experimental measurements and analyse the
condensation process. Six different air mass concentra-
tions in the mixture were tested in the model, ranging
from 23 % to 62 %. The condensation of the vapour –
air mixture differs in several parameters as compared
to condensation of pure vapour. As water vapour con-
denses along the condenser tube, the concentration of
vapour in the mixture changes. Therefore, the HTC,
the condensation rate, the saturation temperature,
and most of the driving parameters change along the
condense tube.

Figure 4. Overall HTC along condenser length.

Figure 5. Air concentration in the mixture along
condenser length.

The local HTC of the condenser along the tube
length for all tests is shown in Figure 4. A rapid
decrease in the HTC in the condenser inlet was cal-
culated for the model for all cases of the condenser.
As the vapour condenses along the condenser tube,
several factors change, which leads to a reduction in
vapour condensation and heat transfer; these factors
are: increase of air concentration; decrease of veloc-
ity and Reynolds number of the mixture; increase of
film thickness. As air concentration increases and the
local condensation rate decreases, the overall HTC
decreases rapidly in the condenser inlet. In the con-
denser outlet, HTC does not change so much since
the local heat transfer is low and the amount of con-
densed vapour is also very small. Correspondingly,
the HTC in the condenser outlet is very low because
of the high concentration of air, which forms a gas
layer next to the condensate film and prevents the
vapour from reaching the phase interface. This can be
seen in Figure 5, where the air concentration along the
tube length is shown for all measurements. A strong
increase in air concentration is observed at the begin-
ning, and slow degradation is seen at the end as a
result of a lower local condensation rate. The overall
HTC of the condenser is determined by the heat re-
sistance of certain parts of the condenser, as shown
in Figure 2 and Equation (11), with the inner radius
of the inner tube r1, inner radius of the outer tube
r2, wall thermal conductivity λW , and HTC of the

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vol. 62 no. 3/2022 Theoretical and experimental study of water vapour condensation . . .

Tests
1 2 3 4 5 6

Air mass concentration x [-] 23 % 26 % 41 % 51 % 60 % 62 %
Air flow Ṁa [kg/h] 0.58 0.58 1.37 2.04 2.63 2.04
Water vapour flow Ṁp [kg/h] 1.97 1.68 2.01 1.94 1.77 1.24
Condensate flow ṀKON [kg/h] 1.98 1.68 1.87 1.58 1.16 -
Cooling water flow ṀK [kg/s] 0.0213 0.0213 0.0213 0.0165 0.0213 0.0281
Cooling water inlet temperature TK1 [◦C] 14.8 14.8 14.7 15.0 14.6 16.0
Cooling water outlet temperature TK2 [◦C] 32.0 29.2 30.8 30.4 25.8 22.2
Mixture inlet temperature Tp1 [◦C] 94.9 93.9 91.1 82.9 82.1 76.4
Mixture outlet temperature Tp2 [◦C] 43.6 40.6 74.6 66.5 64.6 61.3

Table 2. Measured values for all six tests.

cooling water ∝K .

1
r1k

=
1

r1∝̈G
+

1
r1 ∝F

+
ln r2

r1

λW
+

1
r2 ∝K

(12)

Since the heat resistance of the cooling side and
the tube wall of the condenser is quite low, the over-
all HTC is determined by the heat resistance of the
condensing side. During the condensation of water
vapour without non-condensing gases, the main heat
resistance is usually formed by the condensate film
on the cooling surface. This is quite well described
by the Nusselt theory. In the case of the presence
of NCG, the heat resistance is formed not only by
the condensate film but also by the heat resistance of
the mixture. The magnitude of heat resistance in the
condensate film and the mixture depends on several
parameters, mainly the concentration of air in the
mixture, the flow of the condensate film, the flow of
the mixture and the subcooling of the film. Due to
the high amount of NCG in the mixture and low Re
of the mixture, the heat resistance on the condensing
side, in presented tests, was formed mainly by the
heat resistance of the mixture. This can be seen in
Figure 6 where the HTC of the film and the mixture
are compared. The HTC of the condensate film is
several times higher than the HTC of the mixture,
therefore, the heat transfer is strongly affected by the
heat and mass transfer in the gas-vapour mixture.
Although the HTC of the film decreases along the
condenser length as a result of the increase in film
thickness, the HTC of the mixture is at least ten times
lower and, in some cases, it is lower even more than
two hundred times. This supports the claim that the
HTC of the film can be neglected in some cases, since
the overall HTC is formed mostly by the HTC of the
mixture.

It can also be seen that it is quite difficult to fully
condensate the vapour out of the mixture. Since
the HTC decreases significantly at the end of the
condenser, a very large condensation surface would be
necessary to fully separate the vapour and the non-
condensable gas. The initial gas concentration is not
so crucial when the vapour must be fully condensed,

Figure 6. Comparison of HTC of film and gas –
vapour mixture.

as the HTC is approaching similar parameters at the
end of the condenser for all runs.

4.2. Experimental results
Experimental measurements with a mixture of wa-
ter and air were conducted in the experimental loop
with a vertical double-pipe condenser. The tests were
carried out for six different air concentrations. The
evaluation of experimental data was determined from
the mass and energy conversion equations. The mea-
sured parameters and values are shown in Table 2.

The evaluation of the HTC for water vapour con-
densation is usually done according to the Nusselt’s
condensation theory. However, in the case when NCG
is present, a deviation occurs between results from
Nusselt’s theory and experimental measurements. In
Figure 7, a comparison between the results from ex-
perimental measurements and the results predicted
with the Nusselt’s theory for the mean HTC of the
film is shown. As it can be seen, the Nusselt theory
cannot be used by itself for a result prediction when
NCG is present in the condensing mixture. There-
fore, it might be useful to use one of the theoretical
models presented in the previous section. In Figure 8,
the measured amount of condensate captured during
the tests is shown. With increasing air inlet concen-
tration, the ratio of condensed vapour significantly

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J. Krempaský, J. Havlík, T. Dlouhý Acta Polytechnica

Figure 7. Condensing side HTC comparison obtained
from the experiments, developed theoretical model and
Nusselt theory.

Figure 8. Dependence of the condensed vapour and
the air concentration in the mixture.

decreases. It was observed that in the case of the
inlet air mixture concentration of 20 %, almost all the
vapour condensed. This is in accordance with the
results from the theoretical model.

4.3. Comparison of results from
experiments and the theoretical
model

The predicted results from the theoretical model were
compared with the results from the experimental mea-
surements. The results were compared with the overall
condenser power and are shown in Figure 9. The heat
rejected by the cooling water, determined by the ex-
periments and calculated from the theoretical model,
is in good agreement with the standard deviation
within +25 % and −5 %. In the case of a lower NCG
concentration, the theoretical model can predict, with
a very high accuracy, the overall condenser power;
however, at a higher NCG concentration, the model is
less accurate. Another option to compare experimen-
tal and theoretical data is through the overall HTC,
which is shown in Figure 7. The HTC predicted from
the theoretical model for lower values of air inlet con-
centration are lower than those measured during the
experiment. Although this might not be so accurate,
since the overall HTC from the model is calculated
as an arithmetic ratio of local values. Another reason

Figure 9. Comparison of condenser power of theoret-
ical model and experiments.

why the HTCs from the theoretical model and experi-
mental measurements differ might be the disturbance
of the NCG layer by other phenomena. These might
occur during condensation and were not considered
in the presented model. In [16, 17], the suction effect,
which occurs during the condensation of vapour in
the presence of NCG, was analysed and it was con-
cluded that it can improve HTC by even 20 %. The
formation of mist can also improve HTC [18, 19]. This
occurs when the mass transfer resistance in the mix-
ture is much higher than the heat transfer resistance.
However, the clear influence of the suction effect and
the formation of mist on the HTC has not yet been
determined. Therefore, including these phenomena in
the model is rather difficult and unclear, even though
it might be viable to do so, since it might improve the
accuracy of the results predicted from the theoretical
models.

5. Conclusions
Four theoretical methods for the determination of the
HTC and heat transfer during condensation of vapour
with gas are usually recommended in the literature:
degradation and correlation factor, heat and mass
transfer analogy, diffusion layer and boundary layer
model.

For the theoretical model, based on heat and mass
transfer analogy, it was observed that the overall HTC
of the condenser decreases as the air concentration
increases, also, as the Reynolds number of the mixture
decreases, and/or the film thickness increases. An in-
crease in air concentration has the strongest influence
on the HTC. This is observed because of the mass
transfer resistance of the vapour due to the layer of
NCG near the phase interface. Increasing Re number
of the mixture or disturbing this layer of NCG near the
phase interface might, therefore, increase the HTC of
the condensing mixture. The HTC of the film during
the condensation of vapour in the presence of a high
content of NCG can be several times higher than the
HTC of the mixture. Neglecting the HTC of the film
might not produce a significant error in calculation
and can simplify the theoretical modelling. A signifi-
cant decrease in film HTC is also seen at the beginning

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vol. 62 no. 3/2022 Theoretical and experimental study of water vapour condensation . . .

of the condenser, which corresponds to local condens-
ing flow. A rapid decrease in HTC is observed mainly
in the condenser inlet, while in the condenser outlet,
HTC is very low and does not change significantly. It
was also observed that an effort to condensate all the
vapour content out of the mixture leads to a much
larger condensing surface, since the HTC is very low at
the end of the condenser. Increasing the HTC in the
condenser outlet can, therefore, rapidly increase the
condenser power and might contribute to condensing
a larger portion of the vapour out of the mixture.

An experimental measurement of water vapour con-
densation in the presence of high concentration of air
was carried out in a counter-current vertical double-
pipe condenser. Air mass concentration ranged be-
tween 23 % and 62 %. A significant decrease in the
HTC on the condensing side can be seen in the model
and experiment as compared to results from Nusselt
theory. Therefore, using the Nusselt theory for vapour
condensation in the presence of NCG is not suitable.

The results of the theoretical model and the ex-
perimental measurements were compared regarding
the cooling power of the condenser. The results from
the theoretical model and experiments are in good
agreement with the standard deviation within +25 %
and −5 %. Therefore, the heat and mass transfer anal-
ogy might predict the power of the condenser and the
HTC of vapour condensation in the presence of large
amount of NCG with a sufficient accuracy. A larger
accuracy is observed for a low NCG concentration
than for a higher NCG concentration. Precaution
is, therefore, recommended when using the model for
a higher NCG concentration. Obtained results are
valid for all vertical geometries when the width of the
condensate film is negligible compared to the cross
section of the flow. In addition, studying other factors
that might influence the condensation of vapour in the
presence of NCG, such as the suction effect and mist
formation, can enhance the accuracy of the heat-mass
transfer model. Experiments to determine the effect
of NCG on water vapour condensation have been per-
formed, so far, for an artificially prepared mixture of
water vapour and air, also because of the availabil-
ity of relevant literature references. Another goal of
the research is to verify the process of water vapour
condensation from a mixture with CO2 to apply this
method for drying flue gas from oxyfuel combustion.

List of symbols
a Air
A Heat exchanger area [m2]
C Geometric dimensionless number in empirical

equation
c̃p Molar specific heat capacity [J kg−1 K−1]
ET Ackermann factor [–]
∆h̃v Molar heat of condensation [J mol−1]
HTC Heat transfer coefficient [W m−2 K−1]
k Overall heat transfer coefficient [W m−2 K−1]

k′ Heat transfer coefficient between phase interface and
coolant [W m−2 K−1]

K Cooling water
Le Lewis number
n Molar density [mol m−3]
ṅ Local molar flux [mol m−2 s−1]
Ṅ Molar flux [mol s−1]
NCG Non-condensable gas
N u Nusselt number [–]
p Vapour
P r Prandtl number
q̇ Heat flux [W m−2]
r1 Radius of inner tube [m]
ṙv Relative molar flow [–]
r2 Radius of outer tube [m]
Re Reynolds number [–]
Sc Schmidt number [–]
Sh Sherwood number [–]
ỹ Molar concentration [–]

Greek symbols
α Heat transfer coefficient [W m−2 K−1]
α̈G Heat transfer coefficient of condensing side

[W m−2 K−1]
β Mass transfer coefficient [m s−1]
λ Thermal conductivity [W m−1 K−1]
ΦT Non-dimensional mass flow [–]

Subscripts
1 Inlet
2 Outlet
a Power products in empirical equation
B Bulk
c Condensation
cv Convection
F Film
F,SAT Film saturation
i Inner
KON Condensate
G Gas
SAT Saturation
v Vapour
W Wall

Acknowledgements
This work was supported by the Ministry of Educa-
tion, Youth and Sports under OP RDE grant number
CZ.02.1.01/0.0/0.0/16_019/0000753 “Research centre for
low-carbon energy technologies”.

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	Acta Polytechnica 62(3):352–360, 2022
	1 Introduction
	2 Theoretical modelling
	2.1 Summary of available theoretical models
	2.2 Developed theoretical model

	3 Experimental apparatus
	4 Results and discussion
	4.1 Theoretical analysis
	4.2 Experimental results
	4.3 Comparison of results from experiments and the theoretical model

	5 Conclusions
	List of symbols
	Acknowledgements
	References