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Indian Institute Of Technology Madras, India, jerinre@gmail.com
Indian Institute Of Technology Madras, India, mania@iitm.ac.in
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Ebenezar, Jerin Robins and Mani, Annamalai, "Falling Film Evaporation On A ;ermal Spray Metal Coated Vertical Corrugated Plate
Conduits" (2016). International Reigeration and Air Conditioning Conference. Paper 1575.
h<p://docs.lib.purdue.edu/iracc/1575
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International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016
Falling film evaporation on a thermal spray metal coated vertical corrugated plate conduits
Jerin Robins EBANESAR, Annamalai MANI*
Indian Institute of Technology Madras, Department of Mechanical Engineering,
Chennai, India
* Corresponding Author: mania@iitm.ac.in, +91 44 22574666
ABSTRACT
In falling film evaporation process, the heat is transferred from the condensing fluid to the liquid flowing over it.
Tube geometry and tube size have an important role on the performance of the falling film evaporators. This paper
presents a two dimensional CFD study of water falling film evaporation on a thermal spray metal coated vertical
corrugated conduits. Two-phase flow simulation is done by using a finite volume method based commercial
software, using k-ω equations with shear stress transport (SST). Sinusoidal corrugations with different porosity have
been selected for the study. Evaporation and heat transfer during falling film evaporation are included through user
defined functions (UDFs). Effect of Reynolds number, wall superheat and surface roughness on heat transfer
coefficient is presented. Numerical results are compared with the results of horizontal circular tube falling film
evaporation from literature. An enhancement of film heat transfer coefficient of at least 15% is observed for the
vertical corrugated plate conduits.
Key words
Falling film evaporation, vertical corrugated plate conduit, numerical simulation, heat transfer enhancement, thermal
spray metal coating
1. INTRODUCTION
Horizontal shell-side falling film evaporators have a significant potential to replace flooded evaporators. Compared
to flooded type evaporators, falling film evaporators need less working fluid and its small pressure drop and higher
heat transfer coefficient will make the falling film evaporators dominate over the conventional flooded type
evaporators. But, due to shell and tube configuration, the falling film evaporators are bulky like flooded tube
evaporators. Another, main problem concerning about the film evaporation over horizontal tubes are the formation
of dry patches. Dry patches causes reduction in heat transfer coefficient and sometimes the failure of the tubes also
occurs. On the other hand, vertical plate falling film evaporators are more compact, cheaper, lower fouling
resistance and higher heat transfer coefficient than that of the shell and tube configuration [2, 3, 7].
Tube geometry and tube size have an important role on the performance of the falling film evaporators. Geometry of
the tube can be varied by enhancing techniques (thermal spray metallic coating, creating grooves on the tube surface
etc.) and also by changing the shape of the tube. Enhancing the tube can provide better heat transfer coefficient
mainly because of increase in the number of nucleation sites, increase in the total surface area and the presence of
turbulence [13]. A number of experimental studies [2, 6, 7, 11] have been reported in the literature about the
enhancement techniques. Luo et al. [10] reported a better heat transfer performance by using non- circular tubes like
oval shaped and drop shaped tubes and also reported a lower dimensionless temperature and a thinner thermal
boundary layer.
Corrugated vertical plate evaporators are developing technology in the vertical plate evaporators category. Most of
the published falling film studies concern laminar and turbulent fluid flow over a horizontal tube or over a flat
vertical plate compared to corrugated vertical plate. Gonda et al. [6] conducted an experimental study on falling film
evaporation over a corrugated vertical plate. Around 50% increase in Nusselts number is obtained compared to
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International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016
smooth tube. And also Gonda et al. [6] reported that the flow regime is turbulent due to corrugated structure of the
plate. The previous work which is somewhat related to vertical corrugated plate is by Kafi et al. [7]. Their studies
are based on the evaporation of saline water over vertical smooth plate with horizontal metallic wires embedded on
it. They reported high wetting, stability and turbulent falling film due to metallic wires on the plates.
Thermal spray metal coating is a heat transfer enhancement technique, which is done by spraying molten metal on
any heat transfer surface. Studies by Abraham and Mani [1] shows that, compared to plain tubes, the performance of
thermal spray metal coated tubes are 75-150% higher. Studies by Mohammad et al. [11] shows that the metal
coating on plain tubes increases the heat transfer coefficient up to particular value, after that increase in coating
thickness will decrease the value of heat transfer coefficient.
In the present study, a numerical model is developed for falling film evaporation over a thermal spray metal coated
corrugated conduit. Fresh water is taken for the present computational study. A comparative study has been carried
out between corrugated conduit and the circular tube.
2. COMPUTATIONAL METHODS
2.1 Physical and Computational Domain
The component which is more interested in the present study is vertical corrugated plate conduits shown in figure
1(a). It is made up of two stainless steel plates which are deformed to get sinusoidal corrugations on plates and
welded together by horizontal rods to get conduits. The test section consists of a re-distributor and the corrugated
conduits. As the name implies, the main function of re-distributor is to distribute the water to the corrugated
conduits.
Figure 1(a): Physical structure of a vertical corrugated conduit
Figure 1(b) shows the computational domain used for the present study with boundary conditions. Re-distributor is
thermally insulated. The length L is taken as 33 mm, amplitude A is taken as 10.7 mm and feeder height H is taken
as 4 mm. Finite volume method based commercial software is used to carry out the heat transfer studies on falling
film evaporation on corrugated plate.
2.2 Governing Equations
Pressure based solver is employed in the present model. For turbulence modeling k-ω turbulence model with shear
stress transport (SST) is used. k-ω is well suited for simulations inside the viscous sub-layer and k-ε is well suited
for simulations away from the wall. So, this ensures that appropriate equation is used throughout the flow field. For
interface tracking, volume of fluid (VOF) method is used. Compressive scheme is used for the discretization of
volume fraction equation. The VOF solves two sets of continuity equations for liquid and vapour phase and a single
set of momentum and energy equations for combined phase of liquid and vapour.
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Figure 1(b): Computational domain with boundary conditions for the present model
( )
(
)
f f f f f f
u S
t
α ρ α ρ
∂
+ ∇ ⋅ =
∂
(1)
( )
(
)
g g g g g g
u S
t
α ρ α ρ
∂
+ ∇ ⋅ =
∂
(2)
(
)
(
)
(
)
T
u uu p u u g F
t
ρ ρ µ ρ
∂
+ ∇ ⋅ = −∇ + ∇ ⋅ ∇ + ∇ + +
∂
(3)
( ) ( )
(
)
( )
eff e
E u E P k T S
t
ρ ρ
∂
+ ∇ ⋅ + = ∇ ⋅ ∇ +
∂
(4)
f f f g g g
f f g g
E E
E
α ρ α ρ
α ρ α ρ
+
=
+
(5)
f f g g
ρ α ρ α ρ
= +
(6)
f f g g
µ α µ α µ
= +
(7)
eff f f g g
k k k
α α
= +
(8)
2.3 Phase change Model
The main challenge of simulation of two-phase flow is considering the heat and mass transfer during phase change.
Several phase change models are proposed in literature. The commonly used phase change models for evaporation
and condensation are based on model by Lee [15] and model by Tanasawa [16]. From literatures [5, 8, 14] reported
that interfacial temperature obtained by means of Lee and Tanasawa numerical technique will not be exactly the
saturation temperature. The empirical constants used in Lee model and in the Tanasawa model does not have any
physical limits. Therefore, excessively small values of these empirical constants lead to a significant deviation
between interfacial and saturation temperature. However, too large values cause convergence problems and
therefore optimal values must be found.
Third phase change model, which is used in the present study, is called sharp interface model, which uses the
Rankine – Hugoniot jump condition for energy conservation at the interface. This model is purely theoretical and
does not depend upon any empirical constants. The interfacial heat flux jump and mass flux can be calculated by
using equations (9) and (10) respectively.
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International Refrigeration and Air Conditioning Conference at Purdue, July 11-14, 2016
(
)
"
i eff i
q k T n
= − ∇ ⋅
(9)
(
)
"
eff i
fg
k T n
m
h
− ∇ ⋅
=
ɺ
(10)
Mass and energy source terms calculated from sharp interface model is given in equations (11) and (12)
respectively.
(
)
"
eff g
g f g
fg
k T
S S m
h
α
α
∇ ⋅∇
= − = ∇ =
ɺ
(11)
e f fg
S S h
=
(12)
2.4 Grid and Time-step size
Mesh and time independence studies are carried out. The mesh size used for the present model is 140336. Boundary
layer meshing method is used and a y
+
value of less than 5 is taken for the calculation of first layer thickness.
Structured mesh is used for the entire domain. The convergence criteria used for the present model is 10
-6
for energy
equation and 10
-4
for both continuity and momentum equation. The time step used for the present study is 10
-4
s.
3. RESULTS AND DISCUSSION
3.1 Heat Transfer Coefficient
For the calculation of local film evaporative heat transfer coefficient, value of wall heat flux is calculated at various
locations after a steady film is formed and equation (13) is used to calculate the local film heat transfer coefficient.
For finding the average heat transfer coefficient area weighted average of wall heat flux is calculated and is given in
the equation (14). Equation (15) and (16) give the average film heat transfer coefficient and average Nusselts
number respectively.
( )
( )
0
f
y
w
w sat w sat
T
k
y
q x
h x
T T T T
=
∂
−
∂
= =
− −
(13)
( )
0
0
L
s
w
L
s
q x dA
q
dA
=
∫
∫
(14)
w
w sat
q
h
T T
=
−
(15)
1
2
3
2
f
u
f f
h
N
k g
µ
ρ
=
(16)
In order to validate the present numerical solution an experimental study by Gonda et al. [6] from literature is
selected. Geometry shape, dimensions (L= 22.7mm and A= 5mm) and the operating conditions except the heating
method are same as that of the experimental studies. The dimensions above mentioned are used only for validation
of the present numerical model. L= 33mm and A= 10.7mm are used for the remaining parametric study. Figure (2)