Dans ce présent travail nous étudions l'humidification d'un flux d'air dans un procédé de dessalement à travers l'évaporation du film liquide tout en considérant l'eau pure et l'eau de mer. Pour atteindre les objectifs, une méthode implicite de différence finie est utilisée pour résoudre les équations gouvernantes couplées dans les phases liquide et gazeuse. L'influence des conditions d'entrée du film liquide, y compris la salinité, sur l'humidification du flux d'air dans un tube vertical est étudiée

Charef, Adil

Feddaoui, M.

Labsi, Nabila

Nait, Alla, A.

Najim, Monssif

I-Revues

23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
 
Gas flow humidification enhancement by 
evaporating seawater liquid film 
 
M. NAJIMa, M. FEDDAOUIa, A. NAIT ALLAa, Adil CHAREFa, Nabila 
LABSIb 
 
a. Laboratoire Génie de l’Energie, Matériaux et Systèmes (LGEMS) 
ENSA, Agadir, Maroc + monssif.najim@edu.uiz.ac.ma 
b. Equipe Rhéologie et Simulation Numérique des Ecoulements, Alger, Algérie 
Université des Sciences et de la Technologie Houari Boumediene + nabilalabsi@yahoo.fr 
 
Résumé : 
 
Dans ce présent travail nous étudions l'humidification d’un flux d'air dans un procédé de dessalement 
à travers l'évaporation du film liquide tout en considérant l'eau pure et l'eau de mer. Pour atteindre les 
objectifs, une méthode implicite de différence finie est utilisée pour résoudre les équations gouvernantes 
couplées dans les phases liquide et gazeuse. L'influence des conditions d'entrée du film liquide, y 
compris la salinité, sur l'humidification du flux d'air dans un tube vertical est étudiée. 
 
Abstract : 
 
The purpose of this study is to investigate the humidification of air flow in a desalination process through 
studying liquid film evaporation with considering pure water and seawater. To achieve the goals, an 
implicit finite difference method is used to solve the coupled governing equations in both liquid and gas 
phases. The influence of inlet conditions of liquid film, including salinity, on the air stream 
humidification in a vertical tube is studied. 
 
Mots clefs : Desalination, evaporation, seawater, liquid film, salinity, heat 
and mass transfer 
 
1 Introduction 
 
The demand on freshwater and drinkable water is increasing. Thus, Mediterranean countries have to 
deal with a growing pressure on their water resources. Indeed, the desalination of seawater or brackish 
water is one of the best solutions to defeat against water rarity. In fact, solar desalination technologies 
are being considered and many solar devices have been developed based on liquid films evaporation. 
Studying such process allows to determinate the best solutions for desalination plants to not only have 
a low capital costs but also lower operating costs.  
Many studies have been done to study the liquid film evaporation process. Earlier, Yan [1] has studied 
the effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel. 
It was found that the heat transfer between film interface and gas stream is dominated by the transport 
of latent heat and it is greater five times then the sensible heat transport. An experimental and numerical 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
study was also done by Cherif et al. [2]. The experiment revealed that the evaporation takes place in the 
majority of both channel walls surfaces. To understand the combined buoyancy effects of thermal and 
mass diffusion on the turbulent mixed convection tube flows, Feddaoui et al. [3] have conducted a 
detailed numerical study reporting the best conditions to have a better heat transfer, in particular, a 
higher gas flow Reynolds number, a higher heat flux or a lower inlet water flow. Then multiple studies 
have been realized, in the same context and goal, but considering a variety of liquids (ethylene glycol, 
propylene glycol, methane…) and boundary conditions (fully or half heated or insulated wall, tube or 
channel) [4–8].  For studies related to seawater, Yang et al. [9] carried out an experimental study of 
falling film evaporation outside horizontal tubes. It was concluded that in the evaporation heat transfer 
experiment, replacing the seawater experimental results with pure water’s is applicable in desalination. 
Recently, Najim et al. [10] have studied the salinity effect on heat and mass transfer along a vertical 
tube and showed that pressure reduction have a great impact on film evaporation among other effects. 
 
Throughout this literature review, the characteristics of heat and mass transfer are mainly studied for 
pure liquids and little attention is paid to saline water films. The aim of this study is to analyze the heat 
and mass transfer phenomenon during the evaporation of a saline liquid film along a vertical tube under 
low pressure. A comparison of liquid film salinity, temperature and flow rate effects on evaporation is 
done. In the following, we present the studied problem, the numerical method and the main results. 
 
2 Analysis 
2.1 Problem formulation 
 
The geometry of the present study is a vertical tube heated by a uniform heat flux Qw where a falling 
liquid film is heated and evaporated. The liquid films enters with inlet temperature TL0, inlet mass flux 
Γ0 and inlet salinity S0 while the gas flow enters with inlet temperature TG0 and inlet velocity u0. The 
length and radius of the tube are L=3m and R=0.01m respectively. 
 
 
Figure 1 : Geometry of the studied problem 
 
To mathematically formulate the problem, the following assumption are done: 
 The flow in the two phases is considered laminar, incompressible and axisymmetric. 
 The problem is two dimensional and steady, 
 The thermodynamic and thermophysical properties of air and air–water vapour mixture are function 
of both local temperature and concentration. 
 The film surface is in thermodynamic equilibrium and smooth. 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
 Heat transfer by radiation, viscous dissipation, effect of the surface tension and other secondary 
effects are negligible. 
 The axial diffusion of heat, momentum, and mass were assumed to be negligible   
 
2.2 Governing equations 
 
With respect of the mentioned assumptions, the steady state governing equations of the liquid flow are: 
 
- Continuity equation: 
1
( ) ( ) 0L L L Lu r v
x r r
 
 
 
   (1) 
- Momentum equation: 
1
( ) ( ) ( )L
L L L L L L L L
udp
u u v u r
x r dx r r r
g   
  
    
     (2) 
- Energy equation: 
1
( ) ( ) ( )L
L L L L L L pL L L
T
u Cp T v C T r
x r r r r
  
  
 
     (3) 
Similarly for the gaseous phase, the governing equations are: 
- Continuity equation:  
1
( ) ( ) 0g g g gu r v
x r r
 
 
 
   (4) 
- Momentum equation: 
0
1
( ) ( ) ( ) ( )
g
g g g g g g g g
udp
u u v u r g
x r dx r r r
    
  
     
     (5) 
- Energy equation: 
1
( ) ( ) ( ) [ ( ) ]
g
g g g g g g pg g g g v pg pa g
T w
u Cp T v C T r D C C T
x r r r r r r
   
    
   
       (6) 
- Species diffusion equation:  
1
( ) ( ) ( )g g g g g v
w
u w v w r D
x r r r r
  
   
 
     (7) 
 
The pure component data are approximated by polynomials in term of temperature and mass fraction. 
For further details, the thermophysical properties are available in [11]. To consider the salinity in 
thermophysical properties, many modifications are done respecting the correlations described in [12]. 
 
2.3 Boundary and interface conditions 
 
The boundary conditions used in this numerical study are as follows: 
- At the tube inlet (x=0) : 
0 0 0
0 0 0 0
 ;  0; ;  ;
   ;  ;  ;
G G G G G
L L
T T v u u w w
p p T T S S
   
     
  (8) 
- At the tube wall r=R 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
0 ; LL L L W
T
v u q
r


  
   (9) 
- At the tube center (r=0) : 
Gv 0 ; 0; 0; 0
gG
uT w
r r r
 
   
    (10) 
 
The interfacial matching conditions specified at 𝑟 =  𝑅 − 𝛿 are described as follows: 
 
 Continuities of velocity and temperature: 
   , , ;  I G I L I I G Lu x u u T x T T      (11) 
 Continuity of shear stress 
, ,
  I
L I G I
u u
r r
  
    
          (12) 
 Heat balance at the interface implying: 
, ,
   I fg
L I G I
T T
m h
r r
 
    
        
 (13) 
 
2.4 Numerical solution method 
 
The set of the non-linear coupled parabolic equations mentioned above 1-7, are solved using a numerical 
finite difference method. Taking into account the appropriate boundary conditions, a fully implicit 
numerical scheme in which the axial convection terms are approximated by the backward difference 
and the radial convection and diffusion terms by the central difference is employed to transform the 
governing equations into finite-difference equations. The transformed equations are written in form of 
a tridiagonal matrix equation system, which can be solved by Thomas algorithm [13]. A special care 
was taken to correctly discretize the equations at the interface and to ensure the accuracy of the 
numerical computation, by generating a non-uniform grid in both axial and radial directions. 
Accordingly, the grid is refined at the interface and tube inlet. The in-house code is validated by 
comparing our solutions to the results of Yan’s study [14] for the case of laminar and turbulent liquid 
film. 
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0
20
40
60
80
100
120
140
160
180
200
Re
L
=500
Re
L
=2000
Re
L
=5000
Q
w
=2500W/m², water film
 
N
u
x
2x/(R.Re)
 Study of Yan [14]
 Present study
 
Figure 2 : Comparison of local total Nusselt number 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
0.00 0.05 0.10 0.15 0.20 0.25 0.30
5
6
7
8
Re
L
=500
Re
L
=2000  S
h
x
2x/Re/R
 Study of Yan[14]
 Present study
Q
w
=2500W/m², water film
Re
L
=5000
 
Figure 3 : Comparison of local Sherwood number 
 
3 Results and discussion 
 
In this study, calculations are specifically performed for saline and pure water films. The following sets 
of conditions are selected in the computation: the dry air enters at TG0=20°C; Re=2000 and 0.25 atm 
along the vertical tube. The liquid flow rate is varied and the inlet liquid temperature is TL0=60°C.  
A first study is done in order to determinate the best conditions for evaporation. For that, the total 
evaporating rate ?̅̇?𝑒𝑣 is presented in the figure 4. When increasing the inlet mass flow, three different 
behaviors of total evaporating rate are revealed. The first behavior is where ?̅̇?𝑒𝑣  decreases by increasing 
inlet mass flow and the difference between the seawater and pure water is negligible. This behavior is 
identified for the lowest liquid film temperature (TL0=20°C). In the second behaviour, ?̅̇?𝑒𝑣  increases 
with increasing the inlet mass flow (case with TL0=60°C).  While for the third behavior, a slight variation 
of ?̅̇?𝑒𝑣 occurs for TL0=45°C. In the last two cases, the seawater presents higher total evaporating rate 
comparing to pure water. Because of the high heat of vaporization, pure water film evaporates slowly 
and absorbs more heat. 
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
 m
e
v
(x
1
0
-3
 k
g
.m
-2
.s
-1
)
T
L0
=20°C
T L0
=60
°C
 

0
(x10
-3
 kg/(m.s))
 Purewater
 Seawater
 P=0.25 atm; T
0
=20°C; Q
w
=5000 W.m
-2
T
L0
=45°C
.
 
Figure 4 : Total evaporating rate in function of inlet mass flow at different conditions 
 
To establish the following results we have chosen the case where evaporation is important: TL=60°C. 
As plotted in figure 5, latent heat flux decreases from the inlet to a defined distance xi (inversion 
distance) where it begins to increase. Moreover, when increasing the inlet mass flow of the liquid the 
distance xi becomes bigger, and the latent heat flux becomes smaller. The distance xi increases from 0.5 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
to 1.5 m. the examination of the figure shows also that salinity enhance latent heat transfer, especially 
for high inlet mass flows.  
0.0 0.5 1.0 1.5 2.0 2.5 3.0
3500
3750
4000
4250
4500
4750
5000
5250
5500
P=0.25 atm; T
0
=20°C; Q
w
=5000 W.m
-2
,T
L0
=60°C
 
 
g/(m
.s)
 
 g/
(m.s
)
Q
L
(W
/m
²)
x(m)
 Seawater
 Pure water


 g/(m.s)
 
Figure 5 : Axial evolution of latent heat flux for different inlet mass flow of liquid 
 
The figure 6 shows the variation of sensible heat flux along the tube. It is clear that pure water presents 
high sensible heat fluxes comparing to seawater. The difference increase as the fluid goes to the outlet. 
This is due to the thermal conductivity that becomes smaller with salinity increasing (figure 7). In fact, 
as the fluid flow downstream along the tube, the amount of the evaporated water increases, so the ratio 
of salt in the liquid flow increases and therefore, the salinity increases too. It is worth noting that latent 
heat flux is dominating this process of evaporation since it is much larger then sensible heat flux. To 
explain the effect of salinity, we refer to the liquid film thickness: with high salinity, the density of the 
liquid increases comparing to pure water, this means that with the same inlet mass flow rate 𝛤0, the 
saline water has a bigger film thickness leading to an extra energy stored in the liquid film. 
0.0 0.5 1.0 1.5 2.0 2.5 3.0
20
25
30
35
40
45
50
55
60
P=0.25 atm; T
0
=20°C; Q
w
=5000 W.m
-2
,T
L0
=60°C
 


 g
/(
m
.s
)
 

 
g
/(
m
.s
)
Q
S
(W
/m
²)
x(m)
 Seawater
 Pure water

  g/(m.s)
 
Figure 6 : Axial evolution of sensible heat flux for different inlet mass flow of liquid 
 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
30 35 40 45 50 55 60 65 70 75 80
0.615
0.620
0.625
0.630
0.635
0.640
0.645
0.650
0.655
0.660
0.665
 

L
(w
.m
-2
.K
-1
)
T(°C)
 Pure water
 S=10 g/kg
 S=39 g/kg
 
Figure 7 : Thermal conductivity of liquids with different salinities in function of temperature 
 
Attention is turned now to mass transfer by evaluating the evaporating flux presented in figure 8. When 
increasing the salinity (seawater) or the inlet mass flux, the evaporation mass flux increases too. Notice 
that the salinity impact becomes significant and increases as the liquid film goes to the outlet of the tube. 
The evaporation mass flux increases continuously along the tube. Consequently, air stream 
humidification increases. 
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
 
 
g/(
m.
s)
 
 g
/(m
.s)
 

 g/
(m
.s)
m
e
v
 (
x
1
0
-4
 k
g
/(
m
².
s
)
x(m)
 Seawater
 Pure water
 
Figure 8 : Variation of evaporation mass flux for different liquid inlet mass flows along the tube 
 
4 Conclusion 
 
The behavior of seawater in the case of the evaporation in vertical tube has been investigated 
computationally. The effects of inlet mass flow and temperature of liquid film on heat and mass transfer 
are reported. In the realized study, the following conclusions are demonstrated: 
- The latent heat flux is bigger whereas the sensible heat flux is smaller in the case of seawater 
- Air stream humidification is enhanced by the use of seawater 
- The humidification of the air stream when increasing the inlet mass flow rate depends on TL0: for inlet 
liquid film temperature less than 45°C it decreases, otherwise humidification increases. 
 
23ème Congrès Français de Mécanique                              Lille, 28 Août au 1er Septembre 2017 
 
 
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Gas flow humidification enhancement by evaporating seawater liquid film

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Gas flow humidification enhancement by evaporating seawater liquid film

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