International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Numerical investigation on pre-heating of coal water slurry
in shell-and-tube heat exchangers with fold helical baffles
Simin Wang a, Juan Xiao a, Shupei Ye a, Chen Song a, Jian Wen b,⇑
a
b
School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China
School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history:
Received 2 February 2018
Received in revised form 5 May 2018
Accepted 10 June 2018
Keywords:
Shell-and-tube heat exchanger
Fold helical baffle
Coal water slurry
Non-Newtonian fluid
Bingham model
Pre-heating process
a b s t r a c t
Pre-heating process of coal water slurry (CWS) in Integrated Gasification Combined Cycle (IGCC) systems
is beneficial to enhance the energy efficiency. In this paper, shell-and-tube heat exchangers with fold
helical baffles (STHXsFHB) were firstly used as pre-heating exchanger. Using numerical simulation
method, the flow and heat transfer performance of STHXsFHB with different helical angles and overlapped degrees was investigated. CWS with concentration of 62 wt% was shell-side fluid, which is characterized as non-Newtonian fluid and simulated with Bingham model. The numerical results show the
temperature of CWS rises obviously, both Nusselt number and friction coefficient increase with helical
angle at same shell-side mean velocity, Nuf1/3 decreases when helical angle increases. Nusselt number
and friction coefficient have a negative correlation with overlapped degree, and Nuf1/3 with 50% overlapped degree is 13.8–33.1% and 3.9–8.8% higher than that with 1% and 30% overlapped degree, respectively. The variation of Nusselt number and friction coefficient versus helical angle and overlapped degree
of CWS differs from thermal-hydraulic performance of Newtonian fluid in STHXsFHB. It is also found that
the comprehensive performance of STHXsFHB is superior to shell-and-tube heat exchangers with segmental baffles.
Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
Integrated gasification combined cycle (IGCC) is a promising
power generation process due to the advantages such as higher
efficiency, lower emissions, products flexibility, higher fuels flexibility and lower water requirement compared with conventional
coal-based power generation systems [1–3]. IGCC is made up of
two parts, coal gasification and combined cycle, where coal gasification plays an important role. There are two series coal gasification technology according to different coal-feeding system, one of
which is wet feeding using coal water slurry (CWS), and the other
is dry feeding employing pulverized coal.
Coal water slurry feeding system has obvious advantages of
simple technology, without dust explosion and dust emissions,
nevertheless, the energy efficiency of coal water slurry feeding system is less than that of pulverized coal feeding system. Therefore,
pre-heating process of coal water slurry was proposed to improve
the energy efficiency of coal gasification with the reduction of coal
and oxygen consumption [4–8]. However, there are only a few
studies that have introduced the type of pre-heater in details for
⇑ Corresponding author.
E-mail address: jianwen@mail.xjtu.edu.cn (J. Wen).
https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.060
0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
pre-heating process. Aiuchi et al. [5] and Roffe et al. [6] both adopt
tubular heat exchanger, but the pre-heating sources were different,
the former used alkyl diphenyl as the heating medium, and the latter selected the electric resistance heating. Using tubular heat
exchanger, the blockage easily occurs when coal water slurry flows
in a tube. Therefore, the configuration and performance of heat
exchanger for pre-heating process are focused on.
The shell-and-tube heat exchangers with helical baffles
(STHXsHB) were proposed by Lutcha and Nemcansky [9], which
have plenty of advantages, for example: reducing shell-side fouling, applying to high viscous fluid, enhancing heat transfer performance and avoiding flow-induced vibration [10–13], and gradually
take the place of shell-and-tube heat exchangers with segmental
baffles (STHXsSB). It is found that there have been a lot of experimental and numerical investigations on effects of structural
parameters (helical angle and overlapped degree) [14–16], optimization method [17–19], baffle type [20–26] and heat transfer
medium [27–28] on thermal-hydraulic performance for shelland-tube heat exchangers with helical baffles. Particularly, Wang
et al. [21] proposed a new type of shell-and-tube heat exchangers
with fold helical baffles (STHXsFHB) that can effectively eliminate
leakage zones between adjacent baffles. However, few studies have
been conducted on the flow and heat transfer of non-Newtonian
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Nomenclature
A
Am
B
cp
Di
D1
D
d0
E
e
f
h
k
keff
L
l
m
N
Nu
P
Dp
Q
Ri
Re0
T
heat transfer area, m2
minimum flow sectional area, m2
helical pitch, m
specific heat, Jkg1K1
inner diameter of shell, m
diameter of tube bundle, m
rate of deformation tensor
outer diameter of tubes, m
total energy per mass unit, J
overlapped degree
friction coefficient
heat transfer coefficient, Wm2K1
turbulence pulsation kinetic-energy, m2s2
effective thermal conductivity, Wm1K1
effective length of tubes, m
vertical dimension from overlapped point to shell, m
mass flow rate, kgs1
number of tubes
Nusselt number
pressure, Pa
pressure drop in shell side, Pa
heat transfer rate, W
radius of shell, m
generalized Reynolds number
temperature, K
fluid, and the convection heat transfer of non-Newtonian fluid is
widely found in daily life and industrial production. Coal water
slurry is a typically high-viscosity and non-Newtonian fluid, hence,
STHXsHB is a good choice for coal water slurry in pre-heating
process.
Existing literature demonstrates that the most studies have
paid attention to the application of non-Newtonian fluid to tube
side of heat exchangers or plate heat exchangers. Pawar et al.
and Pimenta et al. studied on non-Newtonian fluid in helically
coiled tube heat exchanger, the heat transfer coefficient and friction coefficient were obtained using experiment method and computational fluid dynamics analysis [29–32]. Rennie et al.
numerically studied the effect of non-Newtonian power law fluid
on the heat transfer and the pressure drop for laminar flow in
double-pipe helical heat exchanger, and obtained the correlations
between Nusselt number and Péclat number [33]. The performance
of flow and heat transfer of a non-Newtonian fluid for the plate
heat exchanger was presented using the numerical simulation
method, and the effect of structural parameters for plate heat
exchanger was investigated [34]. Bahiraei et al. [35–38] studied
the thermal-hydraulic performance of non-Newtonian nanofluid
in double-pipe heat exchanger and chaotic channel. The volume
concentration and particle size of non-Newtonian nanofluid were
selected as optimization variables to maximum heat transfer and
minimum pressure drop in annuli with different radius ratios
[39]. However, investigation on shell-side flow and heat transfer
performance is challenging when non-Newtonian fluid flows in
shell side of shell-and-tube heat exchangers. He et al. [40] have
studied the performance of Carboxymethyl cellulose (CMC) with
power low model in vertical heat exchanger combined helical baffles with elliptic and circular tubes, but few studies show that the
thermal-hydraulic performance of non-Newtonian fluid characterized by Bingham model for shell-and-tube heat exchangers.
Combining the non-Newtonian characteristics and the problem
urgently to be solved in pre-heating process of coal water slurry,
investigating the flow and heat transfer performance of coal water
DTm
tp
ui
ue
V
!
v
logarithmic mean temperature, K
tube pitch, m
velocity in x, y, z direction, ms1
mean velocity in shell side, ms1
volume flow rate, m3h1
velocity vector, ms1
Greek symbols
b
helical angle, °
c_
shear strain rate, s1
e
turbulent pulsating kinetic energy dissipation rate,
kgm1s1
g
non-Newtonian viscosity, Pas
gp
Bingham plastic viscosity, Pas
k
thermal conductivity, Wm1K1
l
dynamic viscosity, Pas
leff
effective viscosity, Pas
q
fluid density, kgm3
s
shear stress, Pa
s0
yield stress, Pa
s
stress tensor
Subscript
1, 2, w inlet, outlet, wall
slurry for shell-and-tube heat exchangers with fold helical baffles
is significant using numerical simulation method. Plenty of
research on the heat transfer characteristics and rheological model
of coal water slurry has been reported [41–44]. In this paper, the
thermal-hydraulic performance will be simulated while 62 wt%
coal water slurry flows through the shell side of shell-and-tube
heat exchangers with fold helical baffles. The Nusselt number
and friction coefficient in the shell side will be presented, in addition, the effects of geometry parameters (helical angle and overlapped degree) for shell-and-tube heat exchangers with fold
helical baffles on shell-side Nusselt number and friction coefficient
will be studied. Comprehensive performance comparison will be
conducted between two types of shell-and-tube heat exchanger
with different baffles, namely fold helical baffles and segmental
baffles.
2. Mathematical method
2.1. Physical model
The geometrical model of shell-and-tube heat exchangers with
fold helical baffles is shown in Fig. 1. There are two key structural
parameters for fold helical baffles, namely helical angle and overlapped degree. Helical angle b is angle between the normal lines
of fold helical baffles and the axis of cylindrical shell. Overlapped
degree e is expressed as, e = l/Ri, where l is vertical dimension from
overlapped point to shell and Ri is radius of cylindrical shell. As
shown in Fig. 2, the tube bundle of STHXsFHB is presented, and
the parameters in details are shown in Table 1. The shell-side
diameter of shell-and-tube heat exchangers with fold helical baffles is 250 mm and tube bundle is 2420 mm in length. The tube
bundle is composed by 40 tubes with the diameter of 19 mm and
tubes are arranged squarely with the tube pitch of 25 mm. Besides,
12 spacer tubes are set to fix baffles and increase flow disturbance
of shell side, in which there is no fluid. Parameter modeling was
used in the modeling process.
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2.3. Meshing
There is only one domain in shell-and-tube heat exchangers
with fold helical baffles, due to the tube wall is constant temperature. The computational domain was meshed with unstructured
tetrahedral grids owing to complicated configuration in shell side.
Before the numerical simulation, the grid independence test was
conducted in order to improve the accuracy of the calculation,
where the helical angle is 18°, overlapped degree is 50% and the
shell-side volume flow rate is 18 m3h1. As shown in Fig. 3, it
can be clearly found that the deviations of shell-side heat transfer
coefficient and pressure drop are both within the acceptable range
when the mesh elements increase to 17,293,033. For kinds of geometrical models of STHXsFHB with different helical angle and
overlapped degree, the grid number is 1.6 107–1.8 107.
2.4. Governing equations and numerical method
Fig. 1. Schematic diagram of fold helical baffle.
The numerical solution is based on Navier-Stokes equations,
and the renormalization group (RNG) k-e model is adopted as turbulence model which is derived using a statistical technique
named renormalization group theory. Therefore, the governing
equations for impressible non-Newtonian fluid including continuity, momentum, energy, k and e can be expressed as follows
[20,34]:
Continuity equation:
r ðq!
vÞ¼0
ð3Þ
Momentum equation:
r ðq!
v!
v Þ ¼ rp þ r ðsÞ
Fig. 2. Tube bundle of STHXsFHB.
Item
Specification
Item
Specification
Shell diameter/mm
250
Tube bundle length/mm
Tube diameter/mm
Tube pitch/mm
2420
19
25
Layout pattern
of tubes
Helical angle/°
Overlapped degree
Number of tubes
Square
arrangement
18–40
1–50%
40
To simplify numerical simulation, assumptions are demonstrated as follows: (1) the thickness of baffles, tubes and shell are
all neglected; (2) the leakage zones between baffles and shell
and those between baffles and tubes are neglected; (3) the fluid
flow is turbulent and in steady state and the heat loss to the
environment is totally ignored; (4) the shell-side fluid is nonNewtonian fluid with Bingham plastic model with constant
density, specific heat and thermal conductivity.
s ¼ gðDÞD
where g is the non-Newtonian viscosity, D is the rate of deformation tensor.
Specifically, a non-Newtonian fluid for Bingham plastic model is
characterized by a nonzero shear stress when the strain rate is
zero, therefore, the non-Newtonian viscosity can be described by:
s
g ¼ _0 þ gp
c
c_ ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
D:D
2
where s, s0, gp, and c_ are the shear stress, yield stress, Bingham
plastic viscosity and shear strain rate, respectively. In this paper,
the Bingham model fitted by Xie [45] using the CWS with concentration of 62 wt% is adopted, which is shown by the following correlating equation.
s ¼ 60:06 þ 0:2026c_
ð2Þ
ð7Þ
129
1100
128
1050
h / W⋅m-2⋅K-1
1000
ð1Þ
ð6Þ
where c_ is defined as follows:
2.2. Rheological model
Plenty of literatures indicated that the coal water slurry follows
the Bingham plastic model well [41,42], and the rheological model
can be expressed as follows:
ð5Þ
h
ΔP
127
950
126
900
125
850
124
800
123
750
122
121
700
6.0x106 9.0x106 1.2x107 1.5x107 1.8x107 2.1x107
Mesh elements
Fig. 3. Grid independence test.
ΔP / kPa
Table 1
Specifications of tube bundle.
s ¼ s0 þ gp c_
ð4Þ
are the static pressure and the stress tensor, respecwhere p and s
is calculated by:
tively. In addition, s
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S. Wang et al. / International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
Energy equation:
220
r ½!
v ðqE þ pÞ ¼ r ðkeff rT þ seff !
vÞ
ð8Þ
200
where E is the total energy per mass unit, keff is the effective thermal
conductivity, and T is the temperature.
Turbulent kinetic energy k equation:
180
ð9Þ
160
ΔP / Pa
@
@
@
@k
þ Gk qe
ðqkui Þ ¼
ak leff
ðqkÞ þ
@t
@xi
@xj
@xj
Turbulent energy dissipation e equation:
@
@
@
@e
ðqeÞ þ
ðqeui Þ ¼
ae leff
@t
@xi
@xj
@xj
where
leff ¼ l þ lt ; lt ¼ qC l ke ;
2
140
120
100
e
e2
þ C 1e Gk C 2e q
k
k
C ð1g=g Þ
C 2e ¼ C 2e þ l 1þbg3 0 ;
80
ð10Þ
60
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
g ¼ 2Xij Xij ke ;
40
0.5
@uj
1 @ui
ij ¼ 2 ð @x @x Þ.
j
i
X
The empirical constants for the RNG k-e model are recommended to use as following values: C 1e ¼ 1:42; C 2e ¼ 1:68;
C l ¼ 0:0845; g0 ¼ 4:38;b ¼ 0:012; ak ¼ ae ¼ 1:393.
The coal water slurry flows through the shell side of shell-andtube heat exchangers with fold helical baffles in order to prevent
blocking. Uniform velocity and temperature are used to the shell
inlet, the shell-side volume flow rate is from 12 m3h1 to 52
m3h1, and the shell-side inlet temperature of coal water slurry
is 293 K, meanwhile, atmospheric static pressure is applied to the
shell outlet. The temperature of tube wall is fixed to 393 K, and the
conditions of helical baffles are coupled wall, while other walls are
non-slip, impermeable and adiabatic. The solution strategy is
based on finite volume method, and the governing equations are
iteratively solved by SIMPLE velocity-pressure coupling algorithm.
The second-order upwind scheme is adopted to calculate the convection terms. The convergence criterion is that the normalized
residuals are less than 1 104 for mass, momentum equations,
and 1 106 for other equations.
2.5. Model validation
In order to validate the accuracy of numerical model and solution method, the numerical results are compared with the theoretical value using the calculated method from Ref. [46,47], where the
tube diameter is 11.4 mm and 1000 mm in length, the thickness of
tubes is neglected. The tube-inlet velocity of CWS (62 wt%) is
0.5–3.0 ms1, the temperature is 300 K and zero relative pressure
was used to tube outlet. The temperature of tube wall is fixed to
600 K. As shown in Figs. 4 and 5, the heat transfer coefficient and
1400
1300
Numerical data
Theoretical value
h / W⋅m-2⋅K-1
1200
Numerical data
Theoretical value
1.5
2.0
Tube-inlet velocity /
2.5
3.0
m⋅s-1
Fig. 5. Comparison of pressure drop between numerical data and theoretical value.
pressure drop obtained from numerical simulation is in good
agreement with the theoretical value. The errors of heat transfer
coefficient are 6.81–8.69% with an average one of 7.98%, those of
pressure drop are 0.67–4.54% with an average deviation of 2.99%
when the tube-inlet velocity varies from 0.5 ms1 to 3.0 ms1.
Therefore, it can be concluded that the numerical method adopted
in this study is reliable.
3. Data reduction
The shell-side heat transfer coefficient can be given by [20]:
h¼
Q
A DT m
ð11Þ
where Q is the heat transfer rate in shell side, A is the heat transfer
area, and DTm is the logarithmic mean temperature, which can be
expressed as following equations:
Q ¼ cp mðT 2 T 1 Þ
ð12Þ
A ¼ N pd0 L
ð13Þ
DT m ¼
ðT 2 T w Þ ðT 1 T w Þ
ln½ðT 2 T w Þ=ðT 1 T w Þ
ð14Þ
where cp, m are the specific heat and mass flow rate of coal water
slurry, and N, d0 and L are the number, outer diameter and effective
heat transfer length of tubes, respectively. Meanwhile, the subscripts1, 2 and w respectively represent inlet, outlet and tube wall.
Nusselt number in shell side is calculated as follows:
Nu ¼
1100
1.0
hd0
k
ð15Þ
where h is the heat transfer coefficient in shell side, d0 is the outer
diameter of shell, and k is the thermal conductivity.
Pressure drop in shell side is defined as:
1000
900
DP ¼ P 1 P 2
800
ð16Þ
Denoting helical pitch as B, where:
700
pffiffiffi
B ¼ 2 2ð1 eÞDi tan b
600
ð17Þ
Minimum flow sectional area at shell centerline is defined as:
500
0.5
1.0
1.5
2.0
2.5
3.0
Tube-inlet velocity / m⋅s-1
Fig. 4. Comparison of heat transfer coefficient between numerical data and
theoretical value.
ðD1 d0 Þðt p d0 Þ
Am ¼ 0:5B Di D1 þ
tp
ð18Þ
where Di, D1, tp are inner diameter of shell, diameter of tube bundle,
and tube pitch, respectively.
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S. Wang et al. / International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
Mean velocity in shell side is given by:
ue ¼
V
Am
ð19Þ
where V is shell-side volume flow rate.
Friction coefficient in shell is defined as:
f ¼
2 DP B
qu2e L
ð20Þ
Nuf1/3 is a non-dimensional number, which is selected as criteria to evaluate comprehensive performance due to the pump
power is proportional to the third power of the velocity, and
Nuf1/3 can show a qualitative magnitude of the heat transfer
performance to the flow resistance in the same pump power condition. And the performance evaluation criteria number is given by
following expression, if the value of PEC is larger than 1.0, the comprehensive thermal-hydraulic performance of heat exchanger is
superior.
ðf =f o Þ
1=3
Fig. 7. Contour of apparent viscosity (Z = 0.55 m).
ð21Þ
14
where Nu and Nuo are parameters for different shell-and-tube heat
exchangers, and the same to f and fo. The subscript o refers to the
reference heat exchanger before heat transfer enhancement.
14
Velocity
Apparent viscosity
12
12
4. Results and discussion
4.1. Physical field analysis
4.1.1. Rheological property
Figs. 6 and 7 show the contour of shear strain rate and apparent
viscosity contour of coal water slurry at cross-section (Z = 0.55 m)
of STHXsFHB (helical angle is 18°and overlapped degree is 50%). As
seen from Fig. 6, the shear strain rate is higher adjacent to the centre of shell on account of coal water slurry mainly flows through
the centre. Fig. 7 represents the apparent viscosity, and it illustrates that apparent viscosity of coal water slurry simulated with
Bingham model increases with the decrease of shear strain rate
at the same position, where the apparent viscosity at centre of shell
is smaller than other location. At the same time, it is clearly said
that coal water slurry displays shear-thinning or pseudo-plastic
rheological property.
The plots of velocity and apparent viscosity versus X position
are shown in Fig. 8. It is revealed that indirect relationship between
velocity and apparent viscosity. The velocity is maximum close to
Fig. 6. Contour of shear strain rate (Z = 0.55 m).
Velocity / m⋅s-1
10
10
8
X=-0.125m
X=0m
X=0.125m
8
6
6
4
4
Y=0 m Z=0.55m
2
2
0
0
-0.15
-0.10
-0.05
0.00
0.05
0.10
Apparent viscosity / Pa⋅s
PEC ¼
Nu=Nuo
0.15
X/m
Fig. 8. Velocity and apparent viscosity versus X position (Y = 0 m and Z = 0.55 m).
X = 0, and apparent viscosity is smaller. The results correspond to
the Figs. 6 and 7. Furthermore, the velocity and apparent viscosity
are both approximately symmetric with the X position. Apparent
viscosity is uniform when X varies from 0.05 m to 0.05 m, but
the value is uneven when X varies within 0.125 m to 0.05 m
and 0.05–0.125 m, which is possibly generated by the spiral flow
at margin of shell for shell-and-tube heat exchangers with fold
helical baffles.
4.1.2. Flow and heat transfer performance
The streamline and temperature distribution at cross-section
(X = 0 m) of shell-and-tube heat exchangers with fold helical baffles are respectively given as Figs. 9 and 10, where helical angle
is 18° and overlapped degree is 50%. Fig. 9 indicates the coal water
slurry flows in the form of central leakage and spiral flow in shell
side, and the flow rate is larger at central leakage that has a direct
effect on heat transfer performance. However, due to the fold helical baffle is improved based on plain helical baffle, the triangle
leakage zones between two adjacent baffles obviously decreases,
and the blocking triangle leakage zones forces the coal water slurry
flows to shell center where the effective heat transfer areas of
tubes are larger. As shown in Fig. 10, it is observed that the temperature of coal water slurry increases smoothly and evenly from the
inlet to outlet in shell side. During the process of flowing, coal
water slurry in shell side exchanges heat with the tube wall. Eventually, the temperature of outlet is obviously higher than that of
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S. Wang et al. / International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
Fig. 9. Streamline (X = 0 m).
Fig. 10. Temperature contour (X = 0 m).
inlet, which means the pre-heating of coal water slurry using shelland-tube heat exchanger with fold helical baffles is efficient.
What’s more, the temperature in central region is lower than that
in marginal region of shell side, and the reason is that there are
four spacer tubes with adiabatic wall in central region of shell side.
34
33
32
Nu
4.2. Configuration parameters analysis
35
31
30
4.2.1. Effect of helical angle b
The helical angle determines the inclination angle of fold helical
baffle, which has an effect on tangential velocity of coal water
slurry in shell side. The STHXsFHB with different helical angles
(b = 18, 27, 35, 40) were investigated. Figs. 11 and 12 show the
variation of Nusselt number and friction coefficient versus mean
velocity in shell side when overlapped degree is 50%. When mean
velocity of shell side increases for a certain helical angle, it can be
clearly seen that Nusselt number increases and friction coefficient
reduces. However, the slope of Nusselt number and friction coefficient decreases gradually with the increasing of mean velocity.
Hence, there is an optimal mean velocity for shell-and-tube heat
exchangers with different fold helical baffles. For instance, the Nusselt number and friction coefficient both keep steady when mean
velocity is 1.04 ms1, where helical angle is 40°and overlapped
degree is 50%.
In addition, as described in Fig. 11, Nusselt number increases as
the increase of helical angle at the same mean velocity, that is to
say, a larger helical angle is beneficial to effective heat transfer.
18° 50%
27° 50%
35° 50%
40° 50%
29
28
27
26
0.2
0.4
0.6
0.8
ue /
1.0
1.2
1.4
1.6
m⋅s-1
Fig. 11. Nusselt number versus mean velocity at different helical angles.
The reasons can be explained as follows. A larger helical angle
leads to a longer helical pitch (Eq. (17)) and a larger minimum flow
sectional area at the shell centerline (Eq. (18)). Therefore, the coal
water slurry exchanges heat fully with more central tubes at the
same mean velocity. Fig. 12 illustrates that friction coefficient also
increases obviously when the helical angle varies from 18° to 40° at
the same mean velocity in shell side. The results differ from Ref.
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S. Wang et al. / International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
80
34
70
33
18° 50%
27° 50%
35° 50%
40° 50%
f
50
40
32
31
Nu
60
30
20
29
10
28
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
27
1.6
0.2
ue / m⋅s-1
4.2.2. Effect of overlapped degree e
As shown in Figs. 14 and 15, the effect of overlapped degree e on
Nusselt number and friction coefficient is presented when helical
18
18° 50%
27° 50%
35° 50%
40° 50%
14
12
10
8
6
0.2
0.4
0.6
0.8
ue /
1.0
0.6
0.8
1.0
1.2
1.4
1.2
1.4
m⋅s-1
Fig. 13. Nuf1/3 versus mean velocity at different helical angles.
1.6
Fig. 14. Nusselt number versus mean velocity at different overlapped degrees.
120
100
27° 1%
27° 30%
27° 50%
80
f
[48] when Newtonian fluid flows through the shell side of
STHXsFHB. In Ref. [48], the shell-side working fluid is conductive
oil, whose viscosity is regarded as a constant in numerical simulation and the viscosity is lower compared with coal water slurry.
Nusselt number and shell-side pressure drop both decrease with
the increasing of helical angle under the same shell-side inlet
velocity. However, coal water slurry is a shear-thinning fluid, the
apparent viscosity varies at different shear strain rate, which flows
through the central leakage zones within the calculated conditions,
therefore, the larger helical angles contribute to heat exchange.
And larger helical angles lead to lower velocity in shell side of
shell-and-tube heat exchanger with fold helical baffles under same
volume flow rate. Hence, the higher apparent viscosity is generated, which causes larger friction resistance.
The effect of helical angle b on Nuf1/3 for STHXsFHB with shellside mean velocity is displayed as Fig. 13. It is noteworthy that
Nuf1/3 increases when mean velocity increases. What’s more,
Nuf1/3 has a negative correlation with helical angles, that is, the
comprehensive performance of STHXsFHB with small helical angle
is higher than that with large helical angles at a same mean velocity of coal water slurry. Although the Nusselt number is lower with
small helical angle, the growth rates that are different between
Nusselt number and friction coefficient lead to high Nuf1/3.
16
0.4
ue / m⋅s-1
Fig. 12. Friction coefficient versus mean velocity at different helical angles.
Nu⋅f -1/3
27° 1%
27° 30%
27° 50%
30
60
40
20
0
0.2
0.4
0.6
0.8
ue /
1.0
1.2
1.4
m⋅s-1
Fig. 15. Friction coefficient versus mean velocity at different overlapped degrees.
angle is 27°. In this paper, the overlapped degree of STHXsFHB varies from 1% to 50%. When mean velocity is same, the Nusselt number and friction coefficient both reduce with the increase of
overlapped degree. As given in Fig. 14, with the calculated mean
velocity, the Nusselt number with 1% and 30% overlapped degree
are 3.3–14.5% and 1.7–9.4% higher than that with 50% overlapped
degree when mean velocity varies from 0.44 ms1 to 1.02 ms1,
respectively. Similarly, when overlapped degree increases from
1% to 50%, Fig. 15 shows that friction coefficient decreases by
37.3–61.5% compared with 1% overlapped degree. The same explanation conducted to analyze the change of helical angle is adopted,
the increase of overlapped degree means that the minimum flow
sectional area at centerline increases, hence, the heat transfer performance in STHXsFHB with small overlapped degree is superior.
And due to the large volume flow rate generated if the mean velocity is same, the flow resistance characteristic is inferior. However,
the results in Ref. [48] show that Nusselt number and pressure
drop increase with the increasing of overlapped degree when
shell-side fluid in STHXsFHB is Newtonian fluid, the same reasons
of the effect on helical angles can be used to explain.
Fig. 16 shows the variations of Nuf1/3 versus mean velocity in
shell side for STHXsFHB with different overlapped degree. It is
1354
S. Wang et al. / International Journal of Heat and Mass Transfer 126 (2018) 1347–1355
5. Conclusions
16
Nu⋅f -1/3
In this paper, shell-and-tube heat exchanger with fold helical
baffles was applied to preheating process of coal water slurry for
the first time. The coal water slurry is a typical non-Newtonian
fluid simulated with Bingham model, the investigation on flow
and heat transfer performance in shell side of STHXsFHB is significant. Hence, visualization research of physical field for coal water
slurry in shell side was conducted using numerical simulation
method. In addition, the effect of configuration parameters (helical
angle and overlapped degree) on Nusselt number, friction coefficient and Nuf1/3 was investigated. At last, comprehensive performance of STHXsSB and STHXsFHB was compared. The main
conclusions are listed as follows.
27° 1%
27° 30%
27° 50%
14
12
10
8
6
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ue / m⋅s-1
Fig. 16. Nuf1/3 versus mean velocity at different overlapped degrees.
1.52
1.50
Fold helical baffles-segmental baffles
PEC
1.48
1.46
1.44
1.42
1.40
12
16
20
24
28
32
36
V / m3⋅h-1
Fig. 17. PEC versus shell-side volume flow rate.
observed that Nuf1/3 increases with the increase of overlapped
degree at the same mean velocity. When mean velocity varies from
0.44 ms1 to 1.02 ms1, Nuf1/3 with 50% overlapped degree is
13.8–33.1% and 3.9–8.8% larger than that with 1% and 30%, respectively. Hence, comprehensive performance is superior at larger
overlapped degree.
1. Coal water slurry simulated with Bingham model is a pseudoplastic fluid, the viscosity of coal water slurry is lower at central
shell than other locations. Besides, non-Newtonian fluid flows
through central leakage easily from the description of streamline in shell side, and the temperature rising is obviously for
purpose of preheating process of coal water slurry.
2. Nusselt number grows gradually and friction coefficient declines with the increasing of mean velocity in shell-side. Nusselt
number and friction coefficient both tend to be steady, and
plots illustrate that a suitable mean velocity can be obtained
for shell-and-tube heat exchangers with different fold helical
baffles.
3. At a certain mean velocity in shell side, Nusselt number and
friction coefficient both increase with the increasing of helical
angle, however, Nuf1/3 reduces when helical angle varies from
18° to 40°. The comprehensive performance is superior at lower
helical angle with 18°.
4. Under the same shell-side mean velocity, Nusselt number and
friction coefficient are both negatively correlated with overlapped degree, while Nuf1/3 has a positive relationship with
overlapped degree. The flow and heat transfer performance of
STHXsFHB with 50% overlapped degree is the highest among
the simulated heat exchangers.
5. In comparison, the effect of helical angle and overlapped degree
on Nusselt number and friction coefficient of coal water slurry
differs from that of Newtonian fluid in STHXsFHB. And comprehensive performance of SHTXsFHB is effectively improved
against to SHTXsSB, which is conducive to the selection of different shell-and-tube heat exchanger.
6. The experiment of coal water slurry in shell-and-tube heat
exchangers will be conducted in further work, and the empirical
correlation of Nusselt number and friction coefficient will be fitted for preheating of coal water slurry characterized by Bingham model.
4.3. Comprehensive performance of STHXs with different baffles
Conflict of interest
Fig. 17 shows the performance evaluation criteria number of
flow and heat transfer along with volume flow rate in shell side
for shell-and-tube heat exchangers with different baffles, where
plate spacing of segmental baffles is equal to the helical pitch of
fold helical baffle with 27° helical angle and 50% overlapped
degree. It is clear that PEC between STHXs with fold helical baffles
and STHXs with segmental baffles is higher than 1.0 within the calculated volume flow rate. Compared with the shell-and-tube heat
exchanger with segmental baffles, the comprehensive performance
of shell-and-tube heat exchanger with fold helical baffle is
improved by 44.8–48.8% with an average value of 46.2%. Therefore,
the comprehensive performance of STHXsFHB used to pre-heating
process of coal water slurry is enhanced significantly compared
with STHXsSB.
We declare that we do not have any commercial or personal
relationships with other people or organizations that can inappropriately influence our work.
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 51676146) and the Fundamental Research Funds
for the Central Universities (No. xjj2018202).
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