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Pag. 35
Thermo-hydraulic design of a helical coil heat exchanger for ethanol
cooling
Diseño térmico-hidráulico de un intercambiador de calor de serpentín para el enfriamiento de
etanol
Amaury Pérez Sánchez
1
* ; Heily Victoria González
2
; Arlenis Cristina Alfaro Martínez
3
; Elizabeth Ranero González
4
;
Eddy Javier Pérez Sánchez
5
Received: 25/07/2024 – Accepted: 15/11/2024 – Published: 01/01/2025
Research
Articles
X
Review
Articles
Essay
Articles
* Author for correspondence.
Abstract.
The helical coil configuration is very effective for heat exchangers because they can accommodate a large heat transfer area in a small space, resulting in
high heat transfer coefficients. This paper deals with the thermo-hydraulic design of a helical coil heat exchanger to cool an ethanol stream coming from the
top of a rectification column, by using a classical, well-known calculation methodology. Several parameters were determined such as the overall heat transfer
coefficient (65.88 W/m
2
.K); the spiral total surface area (10.75 m
2
); the actual number of turns of coil (91) and the height of cylinder (4.12 m). The values of
the pressure drop were 290,344 Pa and 0.097 Pa respectively, which are below the limits set by the heat exchange process. The pumping power required for
the chilled water (coil-side fluid) stream was 375.21 W, while the pumping power required for the ethanol stream can be considered negligible.
Keywords.
Helical coil heat exchanger, pressure drop, pumping power, spiral surface area, Actual turns of helical coil.
Resumen.
La configuración de serpentín helicoidal es muy efectiva para intercambiadores de calor debido a que pueden acomodar un área de transferencia de calor
elevada en un pequeño espacio, resultando en altos coeficientes de transferencia de calor. Este artículo trata acerca del diseño térmico-hidráulico de un
intercambiador de calor de serpentín para enfriar una corriente de etanol proveniente del tope de una columna de rectificación, mediante el empleo de una
metodología de cálculo clásica bien conocida. Varios parámetros fueron determinados tales como el coeficiente global de transferencia de calor (65,88
W/m2.K), el área superficial total de la espiral (10,75 m2); el número real de vueltas del serpentín (91) y la altura del cilindro (4,12 m). Los valores de la
caída de presión fueron de 290 344 Pa y 0,097 Pa, respectivamente, los cuales están por debajo de los límites fijados por el proceso de intercambio de calor.
La potencia de bombeo requerida para la corriente de agua fría (fluido que circula por el serpentín) fue de 375,21 W, mientras que la potencia de bombeo
requerida para la corriente de etanol puede considerarse despreciable.
Palabras clave.
Intercambiador de calor de serpentín, caída de presión, potencia de bombeo, área superficial de la espiral, vueltas reales del serpentín.
1. Introduction.
Nowadays, due to the increase in energy saving demand in many engineering fields of the modern industry such as heating,
ventilation, air conditioning and waste heat recovery, heat exchangers that are more efficient, and have smaller sizes and lower
costs are desired, while heat transfer enhancement have been introduced to improve its overall thermo-hydraulic performance
[1].
Heat exchangers are widely used in mechanical devices which exchange heat from one type of fluid to another. They are mainly
used in heat transfer applications, such as power plants, refrigeration, electronics, air conditioning, chemical and petrochemical
processes, automobile devices, and so on [2]. Heat exchangers can improve industrial production efficiency and ensure
equipment safety [3], and come in a variety of shapes and sizes, depending on the application: shell and tube, double pipe, spiral
or straight, plate type, finned type, helical, among others [2].
Due to their compact structure and high heat transfer coefficient, the helical coil tube heat exchanger (HCHX) has been
extensively studied as one of the passive heat transfer enhancements [3].
An HCHX consists of a helical coil fabricated out of a metal pipe that is fitted in the annular portion of two concentric cylinders,
as shown in Figure 1. The fluids flow inside the coil and the annulus with heat transfer taking place across the coil wall. The
dimensions of both cylinders are determined by the velocity of the fluid in the annulus needed to meet heat-transfer requirements.
1
University of Camagüey; Faculty of Applied Sciences; amaury.perez84@gmail.com ; https://orcid.org/0000-0002-0819-6760 , Camagüey, Cuba.
2
University of Camagüey; Faculty of Applied Sciences; heily.victoria@reduc.edu.cu ; https://orcid.org/0009-0007-9319-6506 , Camagüey, Cuba.
3
Center of Genetic Engineering and Biotechnology of Camagüey; arlenis.alfaro@cigb.edu.cu ; https://orcid.org/0000-0003-2975-6867 , Camagüey, Cuba.
4
University of Camagüey; Faculty of Applied Sciences; eliza.eddy2202@gmail.com ; https://orcid.org/0000-0001-9755-0276 , Camagüey, Cuba.
5
Company of Automotive Services S.A.; Commercial Department; eddyjavierpsanchez@gmail.com ; https://orcid.org/0000-0003-4481-1262 , Ciego de
Ávila, Cuba.
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Pag. 36
Fig. 1. A helical coil heat exchanger.
Helically coiled exchangers offer certain advantages over the typical heat transfer equipment. Among them it can be mentioned
higher film coefficients and heat transfer rate through the tube wall from one fluid to the other, as well as more effective use of
available pressure drop, which result in efficient and less-expensive designs. True counter-current flow fully utilizes available
logarithmic mean temperature difference, while helical geometry permits handling high temperatures and extreme temperature
differentials without highly induced stresses or costly expansion joints. High-pressure capability and the ability to fully clean the
service-fluid flow area also add to the exchanger’s advantages.
When fluid flows through a helically coiled tube, the curvature of the coil induces centrifugal force [4], which in turn can produce
a longitudinal secondary flow in the helically coiled tube, resulting in higher heat transfer efficiency than the value obtained
from the straight tubes [3], that is, the centrifugal force induced due to the curvature of the tube results in the secondary flow
known as Dean Vortex superimposed on the primary flow which enhances the heat transfer [5]. Fluid flow in a helical tube is
characterized by the Dean number, which is a measure of the geometric average of inertial and centrifugal forces to the viscous
force ratio, and thus is a measure of a magnitude of the secondary flow [4]. In addition, the coil pitch would influence flow
torsion, while depending on the Dean number, the secondary flow pattern within a coiled tube can strongly enhance its heat
transfer rate [6].
Helically coiled tubes are useful for various industrial processes such as combustion systems, heat exchangers, solar collectors,
and distillation processes because of their simple and effective means of enhancement in heat and mass transfer [7], as well as
because they can accommodate a large heat transfer area in compact space, with high heat transfer coefficient [5]. In general
they can be used as coolers, heaters, condensers or evaporators [5].
HCHX are broadly used in heating and cooling applications such as heat recovery system, food industries, nuclear power plant,
chemical processing, solar water heater, and refrigeration and air-conditioning units because of their simple and effective means
of enhancement in heat and mass transfer The HCHX showed increase in the heat transfer rate, effectiveness and overall heat
transfer coefficient over the straight tube heat exchanger on all mass flow rates and operating conditions [7].
The merit of the HCHX is that its tube can contact the fluid flowing in the shell side directly, resulting in good heat transfer
performance. Therefore, using helical coils in heat exchangers is an effective way for heat transfer enhancement in industries
and households [8], although the pressure drop is increased across the heat exchanger, frequently for the coil-side fluid.
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Pag. 37
In the design of HCHXs, heat transfer performance and pressure loss are significant indicators to consider. It is important to
reduce the pressure loss in the helical tube and enhance the heat transfer performance between the shell and tube sides to improve
the thermo-hydraulic performance of the helical coil heat exchanger. However, there are many influencing factors on both
indices, such as the size of the helical tube, coil pitch, coil diameter, the position of the inlet and outlet streams, and the flow
direction, etc. [8]. Heat transfer on HCHX depends largely on the coil size, tube size, mass flow rate, type of thermal fluids and
number of turns [7].
Several authors have carried out the design and performance analysis of HCHX. In this sense, [2] numerically investigated the
heat transfer performance of a helical heat exchanger using various water-based nanofluids and considering multiple head-ribbed
geometries with different coil revolutions. The numerical results were validated against experimental correlations and a published
numerical study, thus obtaining as a result that the helical heat exchanger with 2 head ribbed and 30 coil revolutions is the most
effective among all the cases and is selected for the nanofluid study. Furthermore, the heat transfer rate could be enhanced by
20%–80% utilizing 2 rib head geometry and by 17%–66% using 30 coil revolutions. Likewise, [8] employed the Computational
Fluid Dynamics (CFD) software, ANSYS FLUENT to predict the thermo-hydraulic performance of an HCHX, including the
overall heat transfer coefficient and Fanning friction factor. Using different sizes of the HCHX, comparing the CFD results with
experimental data or correlations available in the literature revealed that both results on thermo-hydraulic performance agreed
well. Then the Taguchi method was used coupled with grey relational analysis to optimize the HCHX design with the
improvement of thermo-hydraulic performance. Among the selected three factors in the optimization process, it was found that
the coil pitch and coil diameter were the two most important factors in influencing the thermo-hydraulic performance of HCHXs,
while the outer diameter of the helical tube had little impact. Similarly, [1] carried out a three-dimensional study of a shell and
helically corrugated coiled tube heat exchanger considering exergy loss, where various design parameters and operating
conditions such as corrugation depth, corrugation pitch, the number of rounds, and inlet fluid flow rate on the coil and shell sides,
were numerically investigated to examine the heat exchanger hydrothermal performance.
Taguchi analysis was also used to analyze the hydrothermal parameters by considering the interaction effects of them. The results
obtained in this study showed that increasing the inlet fluid flow rate on the coil side, corrugation depth and the number of rounds
increases both heat transfer and pressure drop, while the most effective parameter that influence on the thermal and hydrodynamic
performance of the heat exchanger is the fluid flow rate on the coil side. Also, [3] performed an intelligent optimization scheme
on the whole shell and helically coiled tube heat exchanger, where a genetic algorithm was used to automatically determine the
coiled pitch, coiled diameter, tube diameter, and flow parameters, in order to maximize the heat transfer rate per thermal surface
area by combining the optimization design, structural design, meshing, and numerical calculation. At the same time, the
optimization results with and without the pressure drop constraint were compared. The field synergy principle (FSP) was used
to explain the cause of the improved performance of the heat exchanger, while the theory of entropy production minimization
was employed to evaluate the overall thermal performance. In another study, [5] carried out the analytical and experimental
analysis of heat transfer for a finned tube coil heat exchanger immersed in a thermal storage tank, where this tank is equipped
with three helical-shaped heating coils and cylindrical-shaped stratification device.
Calculations of thermal power of water coil were made, and correlations of heat transfer coefficients in curved tubes were
applied. In order to verify the analytical calculations, the experimental studies of heat transfer characteristic for coil heat
exchanger were also performed. Other authors [9] designed HCHX with two different shell configurations, that is, with and
without a central core, while both configurations has a copper helical coil. The design was done by using CATIA V5 R2015, and
the performance of both the configurations were analyzed and compared by means of Fluid flow (Fluent) in ANSYS for CFD
simulations. Saydam [10] designed, fabricated, and experimentally analyzed a prototype phase change material (PCM) heat
exchanger with a helical coil tube for its thermal storage performance under different operational conditions. Paraffin wax was
used as PCM and an ethylene glycol-water mixture was used as heat transfer fluid (HTF).
Different HTF inlet temperatures, flow directions, and flow rates were tested to find out the effects of these parameters on the
performance, including charging and discharging time, of the thermal storage unit. In the work carried out by [11] a supercritical
heat exchanger of helical coil type was first designed and then evaluated under real operational conditions. Three heat transfer
correlations available from the literature were employed for the design of the heat exchanger. These heat transfer correlations
were derived for different working fluids and conditions than the tested organic Rankine cycles. Therefore, to account for the
uncertainties of the heat transfer correlations the heat exchanger was oversized by 20%. Finally, performance evaluation of the
constructed heat exchanger was performed at supercritical working conditions (laboratory conditions) by examining the influence
of several different parameters. [6] proposed a computational fluid dynamics (CFD) methodology to investigate the effects of
different Dean (De) number and pitch size on the thermal-hydraulic characteristics in a helically coil-tube heat exchanger with
high-temperature helium (He) flowing in the shell side and low-temperature water in the coiled tube.
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Pag. 38
Three values of De number and four sizes of pitch are considered herein. Based on the simulation results, the complicated
phenomena occurred within a helically coiled-tube heat exchanger can be reasonably captured, including the flow acceleration
and separation in the shell side, the turbulent wake around the rear of a coiled tube, the secondary flow within the tube, and the
developing flow and heat transfer behaviors from the entrance region, etc. [12] performed an experimental investigation of the
natural convection heat transfer from helical coiled tubes in water. The outside Nusselt number was correlated to the Rayleigh
number using different characteristic lengths, and the relationship obtained was based on a power law equation. The constants
in the equation were presented for each of the different characteristic lengths used. The best correlation was using the total height
of the coil as the characteristic length.
The developed models were then used to develop a prediction model to predict the outlet temperature of a fluid flowing through
a helically coiled heat exchanger, given the inlet temperature, bath temperature, coil dimensions, and fluid flow rate. [13]
designed and modeled several unique tube configurations to examine the thermal and hydraulic performance of a helical tube
heat exchanger both experimentally and numerically. For cold and hot side tube designs, the numerical investigation is completed
using three-dimensional modeling, and the findings are confirmed using experimental data with Reynolds numbers ranging from
16,000 to 25,000. The findings showed that, as compared to the uniform tube distribution, the novel tube arrangements have a
greater overall heat transfer coefficient, and the performance of heat transfer is dramatically improved, although variations in
pressure drop and pumping power are only a little affected.
Other authors presented and successfully implemented a simple mathematical methodology to model the shell and coil heat
exchanger [4]; analyzed the performance of a helical coil heat exchanger operating at subcritical and supercritical conditions
[14]; introduced an experimental study of horizontal shell and coil heat exchangers in order to determine the effect of coil torsion
on heat transfer and pressure drop of shell and coil heat exchangers [15] and determined the convective heat transfer coefficient
in both helical and straight tubular heat exchangers under turbulent flow conditions [16].
In certain chemical processing plant it’s desired to cool down a stream of ethanol coming from the top of a rectification column,
and for that a vertical helical coil heat exchanger was selected as the preferred equipment due to space limitations and the need
of achieving a high heat transfer rate. In this context, the present work deals with the design of a helical coil heat exchanger using
a well-known, classical calculation methodology, where several parameters are determined such as the actual number of coil
turns, calculated spiral total tube length, height of cylinder, spiral total surface area, the pressure drop of both fluids and the
pumping power required.
2. Materials and methods.
2.1. Problem definition.
It’s desired to cool 750 kg/h of an ethanol stream from 90 ºC to 30 ºC using chilled water at 2 ºC as the cooling medium.
The following data are available for the coil, core tube and shell (Figure 2):
• Shell inner diameter (
i
D
): 0.46 m.
• Core tube outer diameter (
K
D
): 0.34 m.
• Average spiral diameter (
H
D
): 0.40 m.
• Tube outer diameter (
o
d
): 0.030 m.
• Tube inner diameter (
i
d
): 0.025 m.
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Pag. 39
Fig. 2. Geometric parameters of the helical coil heat exchanger.
The outlet temperature of the chilled water should not be higher than 10 ºC, while the fouling factors for the water and ethanol
are 0.000176 and 0.000352 K.m
2
/W, respectively [17]. The chilled water will be located inside the coil, while the ethanol will
flow inside the shell, and both fluids will circulate at countercurrent flow inside the designed helical coil heat exchanger (Figure
2). The coil material is 316 stainless-steel thus having a thermal conductivity of 16.3 W/m.K [18] and the tube pitch, which is
the spacing between consecutive coil turns (measured from center to center) (
p
) can be taken as
o
d5.1
. The pressure drop
of the shell-side and coil-side fluids must not exceed 0.5 Pa and 300,000 Pa, respectively. Design a suitable helical coil heat
exchanger for this heat transfer service.
Fig. 3. Schematic view of the proposed helical coil heat exchanger.
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Pag. 40
2.2. Design methodology.
The equations and correlations reported by [4] [19] [20] were employed to design the helical coil heat exchanger, where several
important design parameters are determined such as the overall heat transfer coefficient, the required heat exchange area, the
spiral total tube length, the actual number of turns of helical coil, the height of cylinder, as well as the calculated pressure drops
and the required pumping power for both fluids.
2.3. Thermal design of the helical coil heat exchanger.
Step 1. Initial data required:
• Mass flowrate of shell-side fluid (
shell
m
).
• Inlet temperature of hot fluid (
1
T
).
• Outlet temperature of hot fluid (
2
T
).
• Inlet temperature of cold fluid (
1
t
).
• Outlet temperature of cold fluid (
2
t
).
• Fouling factor of hot fluid (
h
R
).
• Fouling factor of cold fluid (
c
R
).
• Maximum allowable pressure drop for coil-side fluid (
)( Acoil
P
).
• Maximum allowable pressure drop for shell-side fluid (
)( Ashell
P
).
• Thermal conductivity of coil material (
W
k
).
• Shell inner diameter (
i
D
): 0.46 m.
• Core tube outer diameter (
K
D
): 0.34 m.
• Average spiral diameter (
H
D
): 0.40 m.
• Tube outer diameter (
o
d
): 0.030 m.
• Tube inner diameter (
i
d
): 0.025 m.
• Tube pitch (
p
).
Step 2. Average temperature of both fluids:
• Ethanol:
2
21
TT
T
+
=
(1)
• Chilled water:
2
21
tt
t
+
=
(2)
Step 3. Physical properties of both fluids at the average temperatures determined in the previous step:
The physical properties showed on Table 1 must be determined for both fluids:
Table 1. Physical properties of both fluids.
Physical property
Hot fluid
Cold fluid
Units
Density
h
c
kg/m
3
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Pag. 41
Viscosity
h
c
Pa.s
Heat capacity
h
Cp
c
Cp
kJ/kg.K
Thermal
conductivity
h
k
c
k
W/m.K
Source: Own elaboration.
Step 4. Heat load (
Q
):
Taking the data for the hot fluid (ethanol):
( )
600,3
21
TTCpm
Q
hshell
−
=
(3)
Step 5. Required mass flowrate of chilled water (
c
m
):
( )
600,3
12
−
=
ttCp
Q
m
c
coil
(4)
Step 6. Cross-sectional area of coil (
coil
A
):
4
2
i
coil
d
A
=
(5)
Step 7. Volumetric flowrate of coil-side fluid (
coil
q
):
600,3
c
coil
coil
m
q
=
(6)
Step 8. Velocity of coil-side fluid (
coil
v
):
coil
coil
coil
A
q
v =
(7)
Step 9. Reynolds number of coil-side fluid (
coil
Re
):
c
ccoili
coil
vd
=Re
(8)
Step 10. Prandtl number of the coil-side fluid (
coil
Pr
):
000,1Pr
=
c
cc
coil
k
Cp
(9)
Step 11. Nusselt number of the coil-side fluid (
coil
Nu
):
• For
coil
Re
> 8,000
33.08.0
PrRe023.0
coilcoilcoil
Nu =
(10)
Step 12. Coil-side heat transfer coefficient (
coil
):
i
ccoil
coil
d
kNu
=
(11)
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Step 13. Heat transfer coefficient inside coiled tube based on inside diameter [
)(SPcoil
]:
+=
H
i
coilSPcoil
D
d
5.31
)(
(12)
Step 14. Heat transfer coefficient inside coiled tube based on the outside diameter of the coil [
)(SPacoil
]:
o
i
SPcoilSPacoil
d
d
=
)()(
(13)
Step 15. Outer spiral diameter (
Ho
D
):
oiHo
dDD −=
(14)
Step 16. Inner spiral diameter (
Hi
D
):
okHi
dDD +=
(15)
Step 17. Shell-side flow cross-section (
shell
A
):
( ) ( )
2222
4
HiHoKishell
DDDDA −−−=
(16)
Step 18. Volumetric flowrate of shell-side fluid (
shell
q
):
600,3
h
shell
shell
m
q
=
(17)
Step 19. Flow velocity of the shell-side fluid (
shell
v
):
shell
shell
shell
A
q
v =
(18)
Step 20. Reynolds number of shell-side fluid (
shell
Re
):
h
hshello
shell
vd
=Re
(19)
Step 21. Prandtl number of the shell-side fluid (
shell
Pr
):
000,1Pr
=
h
hh
shell
k
Cp
(20)
Step 22. Nusselt number of the shell-side fluid (
shell
Nu
):
33.06.0
PrRe196.0
shellshellshell
Nu =
(21)
Step 23. Heat transfer coefficient of shell-side fluid
(
shell
):
o
hshell
shell
d
kNu
=
(22)
Step 24. Coil wall thickness (
W
s
):
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Pag. 43
2
0 i
W
dd
s
−
=
(23)
Step 25. Overall heat transfer coefficient (
U
):
ch
W
W
shellSPacoil
RR
k
s
U
++++
=
11
1
)(
(24)
Step 26. Logarithmic Mean Temperature Difference
(
LMTD
):
• For countercurrent flow:
( ) ( )
( )
( )
12
21
1221
ln
tT
tT
tTtT
LMTD
−
−
−−−
=
(25)
Step 27. Effective mean temperature difference (
T
):
t
FLMTDT =
(26)
Where
t
F
is the temperature correction factor = 0.99 [20].
Step 28. Spiral total surface area (
A
):
000,1
=
TU
Q
A
(27)
Step 29. Spiral total tube length (
L
):
( )
2
2
pDnL
H
+=
(28)
Step 30. Theoretical number of turns of helical coil (
N
):
n
L
d
A
N
o
=
(29)
Step 31. Actual number of turns of coil (
N
rounded to the next highest integer) (
n
):
Step 32. Calculated spiral total tube length (
'L
):
nLL ='
(30)
Step 33. Height of cylinder (
H
):
o
dpnH +=
(31)
2.4. Pressure drop.
Step 34. Factor
E
:
+=
2
1
H
H
D
p
DE
(32)
Step 35. Friction factor for flow inside the coil (
f
):
27.0
2/1
25.0
03.0
Re
3164.0
+=
wi
coil
E
d
f
(33)
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Pag. 44
Where
27.0
w
= 1 as suggested by [4]
Step 36. Drag coefficient on coil surface (
D
C
):
+=
25.0
2/1
25.0
Re095.01
Re
3164.0
shell
H
o
shell
D
D
d
C
(34)
Step 37. Pressure drop for the coil side fluid (
coil
P
):
2
'
2
ccoil
i
coil
v
d
L
fP
=
(35)
Step 38. Volume available for the flow of fluid in the annulus (
shell
V
):
( )
'
44
222
LdnpDDV
oKishell
−−=
(36)
Step 39. Shell side equivalent diameter (
e
D
):
'
4
Ld
V
D
o
shell
e
=
(37)
Step 40. Pressure drop for the shell side fluid (
shell
P
):
2
2
hshell
e
Dshell
v
D
H
CP
=
(38)
2.5. Pumping power.
Step 41. Pumping power required for the coil side fluid (
coil
P
):
cp
coil
coil
coil
m
P
P
=
600,3
(39)
Where
coil
m
is given in kg/h and
p
= 0.8 [21].
Step 42. Pumping power required for the shell side fluid (
shell
P
):
hp
shell
shell
shell
m
P
P
=
600,3
(40)
Where
shell
m
is given in kg/h and
p
= 0.8 [21].
3. Results.
3.1. Design parameters of the helical coil heat exchanger.
Table 2 shows the initial data required to design the helical coil heat exchanger, which are included in Step 1.
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Pag. 45
Table 2. Initial data required to design the helical coil heat exchanger.
Parameter
Symbol
Value
Unit
Mass flowrate of shell-side fluid
shell
m
750
kg/h
Inlet temperature of hot fluid
1
T
90
ºC
Outlet temperature of hot fluid
2
T
30
ºC
Inlet temperature of cold fluid
1
t
2
ºC
Outlet temperature of cold fluid
2
t
10
ºC
Fouling factor of hot fluid
h
R
0.000352
K.m
2
/W
Fouling factor of cold fluid
c
R
0.000176
K.m
2
/W
Maximum allowable pressure drop for coil-side fluid
)( Acoil
P
300,000
Pa
Maximum allowable pressure drop for shell-side fluid
)( Ashell
P
0.5
Pa
Thermal conductivity of coil material
1
W
k
16.3
W/m.K
Shell inner diameter
i
D
0.46
m
Core tube outer diameter
K
D
0.34
m
Average spiral diameter
H
D
0.40
m
Tube outer diameter
o
d
0.030
m
Tube inner diameter
i
d
0.025
m
Tube pitch
2
p
0.045
m
1
As reported by [22].
2
Taken as
o
d5.1
Source: Own elaboration.
Step 2. Average temperature of both fluids.
• Ethanol:
T
= 60 ºC
• Chilled wáter:
t
= 6 ºC
Step 3. Physical properties of both fluids at the average temperatures calculated in the previous step.
Table 3 presents the physical properties of both fluids at the average temperatures calculated in the previous step, as reported by
[18].
Table 3. Physical property of both fluids.
Physical property
Ethanol
Chilled water
Unit
Density
753.22
999.94
kg/m
3
Viscosity
0.000584
0.001445
Pa.s
Heat capacity
2.781
4.203
kJ/kg.K
Thermal conductivity
0.159
0.572
W/m.K
Source: Own elaboration.
Table 4 exhibits the results of the parameters included in steps 4 to 33.
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Pag. 46
Table 4. Results of the parameters included in steps 4 to 33.
Step
Parameter
Symbol
Value
Unit
4
Heat load
Q
34.76
kW
5
Required mass flowrate of chilled water
coil
m
3,721.63
kg/h
6
Cross-sectional area of coil
coil
A
0.00049
m
2
7
Volumetric flowrate of chilled water
coil
q
0.0010
m
3
/s
8
Velocity of chilled water
coil
v
2.04
m/s
9
Reynolds number of chilled water
coil
Re
35,292
-
10
Prandtl number of the chilled water
coil
Pr
10.62
-
11
Nusselt number of the chilled water
1
coil
Nu
217.93
-
12
Coil-side heat transfer coefficient
coil
4,986.24
W/m
2
.K
13
Heat transfer coefficient inside coiled tube based on inside
diameter
)(SPcoil
6,076.98
W/m
2
.K
14
Heat transfer coefficient inside coiled tube based on the outside
diameter of the coil
)(SPacoil
5,064.15
W/m
2
.K
15
Outer spiral diameter
Ho
D
0.43
m
16
Inner spiral diameter
Hi
D
0.37
m
17
Shell-side flow cross-section
shell
A
0.0377
m
2
18
Volumetric flowrate of ethanol
shell
q
0.0003
m
3
/s
19
Flow velocity of the ethanol
shell
v
0.008
m/s
20
Reynolds number of ethanol
shell
Re
309.54
-
21
Prandtl number of ethanol
shell
Pr
10.21
-
22
Nusselt number of ethanol
shell
Nu
13.15
-
23
Heat transfer coefficient of ethanol
shell
69.70
W/m
2
.K
24
Coil wall thickness
W
s
0.0025
m
25
Overall heat transfer coefficient
U
65.88
W/m
2
.K
26
Logarithmic Mean Temperature Difference
LMTD
49.57
ºC
27
Effective mean temperature difference
T
49.07
ºC
28
Spiral total surface area
A
10.75
m
2
29
Spiral total tube length
L
1.257n
-
30
Theoretical number of turns of helical coil
N
90.78
-
31
Actual number of turns of helical coil
n
91
-
32
Calculated spiral total tube length
'L
114.38
m
33
Height of cylinder
H
4.12
m
1
Equation (10) is valid to use to determine the Nusselt number of chilled water since
coil
Re
> 8,000.
Source: Own elaboration.
3.2. Pressure drop.
Pressure drop increases as fluid flow velocity through the heat exchanger is increased, as does the convection heat transfer
coefficient; a good design is therefore always a compromise of sufficiently heat transfer characteristics with acceptable pressure
drop.
Table 5 displays the results of the parameters included in steps 34-40, valid to determine the pressure drop of both streams.
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Pag. 47
Table 5. Results of the parameters calculated in steps 34-40.
Step
Parameter
Symbol
Value
Unit
34
Factor
E
E
0.40
m
35
Friction factor for flow inside the coil
f
0.0305
-
36
Drag coefficient on coil surface
D
C
0.0836
-
37
Pressure drop for the chilled water
coil
P
290,344
Pa
38
Volume available for the flow of fluid in the annulus
shell
V
0.228
m
3
39
Shell side equivalent diameter
e
D
0.085
m
40
Pressure drop for the ethanol
shell
P
0.097
Pa
Source: Own elaboration.
3.3. Pumping power.
Table 6 presents the results of the pumping power required for both fluids.
Table 6. Pumping power required for both fluids.
Step
Parameter
Symbol
Value
Unit
41
Pumping power required for the chilled water
coil
P
375.21
W
42
Pumping power required for the ethanol
shell
P
0.000034
W
Source: Own elaboration.
4. Discussion.
4.1. Design parameters of the helical coil heat exchanger.
According to the results of Table 4, the heat load had a value of 34.76 kW, while about 3,721.63 kg/h (1.03 kg/s) of chilled water
will be necessary to meet the required heat exchange duty. The Reynolds number of chilled water was 35,292, which is 114
times above the Reynolds number of ethanol (309.54). This is due to the relatively high value of the shell-side flow cross-section
(0.0377) and the small value of the volumetric flowrate of ethanol (0.0003 m
3
/s), which in turn decreases the value of the flow
velocity of ethanol (0.008 m/s), thus decreasing the Reynolds number of ethanol (
shell
Re
). The smaller value of the ethanol
density (753.22 kg/m
3
), as compared to the density of chilled water (999.94 kg/m
3
), also affects the small value obtained for
shell
Re
. It’s worth stating that the mass flowrate of chilled water is about five times higher than the mass flowrate of ethanol,
which therefore influences in the large difference obtained for the Reynolds number of both streams.
The Nusselt number of the chilled water (217.93) is about 17 times higher than the Nusselt number for ethanol (13.15). This is
mainly due to the small value of the Reynolds number obtained for ethanol as compared to the Reynolds number of chilled water.
This also influences in that the heat transfer coefficient for the chilled water (5,064.15 W/m
2
.K) is about 73 times higher than
the heat transfer coefficient for ethanol (69.70 W/m
2
.K), although the correlations used to determine these heat transfer
coefficients for both fluids are relatively different with each other. Moreover, the values obtained of the Prandtl number for both
fluids are almost the same (10.62 for chilled water and 10.21 for ethanol), thus this parameter doesn’t affect the calculated values
of the heat transfer coefficient for both fluids.
The overall heat transfer coefficient (
U
) had a value of 65.88 W/m
2
.K, which can be classified as low mainly due to the small
value obtained of the heat transfer coefficient for the ethanol stream. The rather small value obtained for
U
influences in the
relatively high values obtained for the spiral total surface area (10.75 m
2
), the theoretical number of turns of helical coil (90.78)
and the height of cylinder (4.12 m). Finally, the calculated spiral total tube length was 114.38 m, while 91 turns of helical coil
will be needed for the designed heat exchanger.
In a previous study [23] carried out, a helical coil heat exchanger was designed to cool an acetone stream, where a similar
methodology that the one used in this work was applied. In this paper, the acetone mass flowrate is 300 kg/h, while about 1,287
kg/h of chilled water at an inlet temperature of 2 ºC were needed to accomplish the heat transfer duty of cooling the acetone from
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Pag. 48
70 ºC to 30 ºC. It was obtained a heat transfer coefficient for the chilled water of 1,684.30 kcal/h.m
2
.ºC (1,958.84 W/m
2
.K) which
is about 68 times higher than the heat transfer coefficient for acetone (28.73 W/m
2
.K). Also, the Reynolds number of the chilled
water (the coil-side fluid) was 11,211, which is 17 times higher than the Reynolds number of acetone (the shell-side fluid).
Likewise, the value obtained for the overall heat transfer coefficient was 23.88 kcal/h.m
2
.ºC (27.77 W/m
2
.K) which can be
considered low.
Finally, it was required a heat transfer area of 6.60 m
2
, an actual number of turns of helical coil of 53 and a cylinder height of
2.58 m. In general terms, the values of the parameters overall heat transfer coefficient, heat transfer area, actual number of turns
of helical coil and cylinder height are higher in the present study as compared to that obtained in [23] due fundamentally to the
higher mass flowrate handled for the hot stream. The results found in [23] agree and ratify the results obtained in this study
regarding the values of the heat transfer coefficients and the Reynolds numbers for both streams, as well as the validity of the
calculated design parameters.
4.2. Pressure drop.
As shown in Table 5, the pressure drop for the coil-side fluid (chilled water) had a value of 290,344 Pa, while the value of this
parameter for the shell-side fluid (ethanol) was 0.097 Pa. Both values are below the limits established by the process (300,000
Pa and 0.5 Pa for water and ethanol, respectively). The high value obtained of the pressure drop for the coil-side fluid is due to
the small value of the tube inner diameter (0.025 m), as well as the relatively high values of the calculated spiral total tube length
(114.38 m), the velocity of chilled water (2.04 m/s) and the density of this fluid (999.94 kg/m
3
).
Similarly, the low value of pressure drop obtained for the shell-side fluid is owed mainly to the very low values of the ethanol
velocity (0.008 m/s) and the drag coefficient on coil surface (0.0836), as well as to the relatively high value of the shell side
equivalent diameter (0.085 m). The same results were obtained in [23], that is, a higher pressure drop was obtained for the coil-
side fluid (chilled water: 16,188 Pa) as compared to the pressure drop of the shell-side fluid (acetone: 0.2 Pa). This also agrees
with the findings of [4], which reported that the pressure drop at the shell side is significantly smaller than that at the coil side.
Likewise, it can be observed that the higher value obtained for the pressure drop corresponds to the coil-side fluid since it has
the highest value of the Reynolds number, which agrees with the reported by [13] and [24]. Also, in [4] it was determined that
the pressure drop of both the shell-side and coil-side fluids increase with the increment of the mass flow rate.
4.3. Pumping power.
Regarding the values of Table 6, it will be necessary 375.21 W of pumping power for the chilled water, while the required
pumping power for the ethanol can be considered negligible. This is owed mainly to the very small value of the calculated
pressure drop obtained for this fluid.
5. Conclusions.
The thermo-hydraulic design of a helical coil heat exchanger was carried out in order to cool an ethanol stream coming from the
top of a rectification column and by using a classical, well-known calculation methodology. Several design parameters were
determined such as the overall heat transfer coefficient (65.88 W/m
2
.K), the spiral total surface area (10.75 m
2
), the spiral total
tube length (114.38 m), the actual number of turns of helical coil (91) and the height of cylinder (4.12 m). The pressure drop of
the coil-side fluid (chilled water) and the shell-side fluid (ethanol) were 290,344 Pa and 0.097 Pa, respectively, which are below
the limits established by the heat exchange process for both streams. The pumping power required for the chilled water had a
value of 375.21 W, while the pumping power for the ethanol stream can be neglected due to its very low value.
6.- Author Contributions.
1. Conceptualization: Amaury Pérez Sánchez.
2. Data curation: Yerelis Pons García, Elizabeth Ranero González.
3. Formal analysis: Amaury Pérez Sánchez, Daynel Basulto Pita, Eddy Javier Pérez Sánchez.
4. Acquisition of funds: Not applicable.
5. Research: Amaury Pérez Sánchez, Yerelis Pons García, Eddy Javier Pérez Sánchez. 6.
6. Methodology: Amaury Pérez Sánchez, Daynel Basulto Pita, Elizabeth Ranero González.
7. Project administration: Not applicable.
8. Resources: Not applicable.
9. Software: Not applicable.
10. Supervision: Amaury Pérez Sánchez.
11. Validation: Amaury Pérez Sánchez .
12. Writing - original draft: Eddy Javier Pérez Sánchez, Elizabeth Ranero González.
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Pag. 49
13. Writing - revision and editing: Amaury Pérez Sánchez, Yerelis Pons García.
7.- References.
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[23] Pérez, E. J. Pérez, A. Heredia, and L. Pazos, "Diseño de un intercambiador de calor de serpentín para el enfriamiento de acetona," Nexo, vol. 32, no. 1, pp.
61-74, 2019. https://doi.org/10.5377/nexo.v32i01.7988
[24] S. A. Nada, W. G. E. Shaer, and A. S. Huzayyin, "Heat transfer and pressure drop characteristics of multi tubes in tube helically coiled heat exchanger,"
JP Journal of Heat and Mass Transfer, vol. 9, no. 2, pp. 173-202, 2014.
Nomenclature.
A
Spiral total surface area
m
2
coil
A
Cross-sectional area of coil
m
2
shell
A
Shell-side flow cross-section
m
2
D
C
Drag coefficient on coil surface
-
Cp
Heat capacity
kJ/kg.K
i
d
Tube inner diameter
m
o
d
Tube outer diameter
m
e
D
Shell side equivalent diameter
m
Universidad de
Guayaquil
INQUIDE
Ingeniería Química y Desarrollo
https://revistas.ug.edu.ec/index.php/iqd
ISSN – p: 1390 –9428 / ISSN – e: 3028-8533 / INQUIDE / Vol. 07 / Nº 01
Facultad de
Ingeniería Química
Ingeniería Química y Desarrollo
Universidad de Guayaquil | Facultad de Ingeniería Química | Telf. +593 4229 2949 | Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 50
H
D
Average spiral diameter
m
Hi
D
Inner spiral diameter
m
Ho
D
Outer spiral diameter
m
i
D
Shell inner diameter
m
K
D
Core tube outer diameter
m
E
Factor
m
f
Friction factor for flow inside the coil
-
t
F
Temperature correction factor
-
H
Height of cylinder
m
k
Thermal conductivity
W/m.K
W
k
Thermal conductivity of coil material
W/m.K
L
Spiral total tube length
m
'L
Calculated spiral total tube length
m
LMTD
Logarithmic Mean Temperature Difference
°C
m
Mass flowrate
kg/h
n
Actual number of turns of coil
-
N
Theoretical number of turns of helical coil
-
Nu
Nusselt number
-
p
Tube pitch
m
P
Pumping power
W
Pr
Prandtl number
-
coil
P
Pressure drop
Pa
)( A
P
Maximum allowable pressure drop
Pa
q
Volumetric flowrate
m
3
/s
Q
Heat load
kW
R
Fouling factor
K.m
2
/W
Re
Reynolds number
-
W
s
Coil wall thickness
m
t
Temperature of cold fluid
°C
t
Average tempereature of cold fluid
°C
T
Temperature of hot fluid
°C
T
Average temperature of hot fluid
°C
T
Effective mean temperature difference
°C
U
Overall heat transfer coefficient
W/m
2
.K
v
Velocity
m/s
shell
V
Volume available for the flow of fluid in the annulus
m
3
Greek symbols
Heat transfer coefficient
W/m
2
.K
)(SPcoil
Heat transfer coefficient inside coiled tube based on inside
diameter
W/m
2
.K
)(SPacoil
Heat transfer coefficient inside coiled tube based on the
outside diameter of the coil
W/m
2
.K
Density
kg/m
3
Viscosity
Pa.s
p
Isentropic efficiency of the pump
-
Universidad de
Guayaquil
INQUIDE
Ingeniería Química y Desarrollo
https://revistas.ug.edu.ec/index.php/iqd
ISSN – p: 1390 –9428 / ISSN – e: 3028-8533 / INQUIDE / Vol. 07 / Nº 01
Facultad de
Ingeniería Química
Ingeniería Química y Desarrollo
Universidad de Guayaquil | Facultad de Ingeniería Química | Telf. +593 4229 2949 | Guayaquil – Ecuador
https://revistas.ug.edu.ec/index.php/iqd
Email: inquide@ug.edu.ec | francisco.duquea@ug.edu.ec
Pag. 51
Subscripts
1
Inlet
2
Outlet
c
Cold
coil
Coil-side fluid
h
Hot
shell
Shell-side fluid
