Numerical and Experimental Study on Temperature Crossover in Shell and Tube Heat Exchangers
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Transcript of Numerical and Experimental Study on Temperature Crossover in Shell and Tube Heat Exchangers
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Volume 7,Issue 4 2011 Article 7
International Journal of Food
Engineering
Numerical and Experimental Study on
Temperature Crossover in Shell and Tube
Heat Exchangers
Fuhua Jiang, South China University of Technology
Xianhe Deng, South China University of Technology
Recommended Citation:
Jiang, Fuhua and Deng, Xianhe (2011) "Numerical and Experimental Study on Temperature
Crossover in Shell and Tube Heat Exchangers,"International Journal of Food Engineering: Vol.
7: Iss. 4, Article 7.
DOI: 10.2202/1556-3758.2217
Available at: http://www.bepress.com/ijfe/vol7/iss4/art7
2011 Berkeley Electronic Press. All rights reserved.
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Numerical and Experimental Study on
Temperature Crossover in Shell and Tube
Heat Exchangers
Fuhua Jiang and Xianhe Deng
Abstract
Experimental and numerical studies were conducted to investigate the heat transfer
characteristics of five shell and tube heat exchangers (STHXs) with ratio of the length to width (L/
W) at the range of 1.85 to 9.23. Temperature crossover in counter flow STHXs is meaningful in
food processing industry. The relationship between temperature crossover and L/W is proposed
for the first time. Both the experimental and numerical results show that temperature crossover can
be achieved in STHXs with L/W4.62 and cant be achieved any more in STHXs with L/W3.08.
The results also indicate that heat transfer performance decreases with L/W decreasing. The
inherent reason of this phenomenon is analyzed by computational fluid dynamics method.
KEYWORDS: temperature crossover, temperature difference field, shell and tube heat
exchanger, uniformity factor
Author Notes: This project 20776046 is supported by National Natural Science Foundation ofChina.
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1. INTRODUCTIONS
Shell and tube heat exchangers (STHXs) are widely used in food processing
industry according to their robust geometry construction, easy maintenance andpossible upgrade. In STHXs, the ratio (outlet temperature of hot fluid to that of
cold one) indicates heat exchange depth. When outlet temperature of hot fluid islower than that of cold fluid,
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The heat transfer performance of five STHXs withL/Wranging from 1.85
to 9.23 is studied with both experimental and numerical methods in this paper. The
inherent reason why heat transfer performance decreases with L/Wdecreasing is
presented based on the numerical results. The range ofL/Wat which temperaturecrossover can be achieved has been given. In the following, the numerical approach
to deal with 10-50tube STHXs will be presented first, followed by the experimentalsetup and data processing method. The experimental and numerical results are then
reported in parallel to facilitate the comparison between two methods. Finally the
inherent reason of heat transfer performance decreases with decreasing L/W is
given.
2. SIMULATION STUDY
2.1COMPUTATIONAL DOMAIN
Fig.2.Configuration of 10tube STHX
Fig.3 Tube bundles arrangement in the shell side
Computational Fluid Dynamics (CFD) has been widely used to betterunderstand food thermal processes (Augusto and Cristianini, 2010; Augusto et al.,
2009; Chai et al., 2010). In order to quantitatively predict heat transferperformances of 10-50tube STHXs, five three-dimensional physical models have
been developed. The configuration of 10tube STHX is shown in Fig.2. As the
primary objective of this research is to study the influence ofL/Won temperature
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crossover, the tube bundle arrangement in the shell side is identical for all the five
heat exchangers. The tube numbers are 10,20,30,40 and 50 for 10-50tube STHXs,
respectively. Fig.3 shows the tube bundle arrangement in the shell side. Detailed
physical dimensions of the five STHXs are summarized in Table 1. Air is theworking fluid in the shell side and its thermo-physical properties are listed in
Table2.
Table1. Geometric parameters
Table2. Thermo-physical properties of air
2.2GOVERNING EQUATION AND BOUNDARY CONDITIONS
The renormalization group (RNG) k- model is adopted because it can provide
improved predictions of near-wall flows(Tao, 2001). The governing equations forthe mass, momentum, and energy conservations, and forkand can be expressed as
follows:
Mass:
0ii
ux
(1)
Momentum:
ki ki i i k
u pu u
x x x x
(2)
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Energy:
ii i p i
k tu t
x x c x
(3)
Turbulent kinetic energy:
i k eff i j j
kk ku Gk
t x x x
(4)
Turbulent energy dissipation:
2
*
1 2i eff k
i j j
u C G C t x x x k k
(5)
where
eff t ,
2
t
kc
, *1 1 3
1
1
OC C
,
1
22 ij ijk
E E
,1
2
jiij
j i
uuE
x x
.
The empirical constants for the RNG k-model are assigned as
following(Smith and Woodruff, 1998)
0.0845C , 1 1.42C , 2 1.68C , 0.012 , 4.38o , 1.39k .
Now boundary conditions are presented. Non-slip boundary condition is
applied on the shell surface and thermal coupled condition is applied on the tubesurface in the computational domain. The standard wall function method is used to
simulate the flow in the near-wall region. The velocity-inlet and pressure-outlet
boundary condition(Smith and Woodruff, 1998) are applied on the inlet and outletsections, respectively.
2.3SOLUTION PROCEDURE
The computational domain is discretized with unstructured tetrahedral grids, which
are generated by the commercial code GAMBIT. The region adjacent to the tube is
meshed much finer with the help of successive ratio scheme. Before anycomputational result can be deemed enough to illuminate the physical phenomenon,
it must be justified by a grid independence test. Grid independence tests have been
carried out for each mesh model to ensure the optimized computational mesh. The
follow mesh modes having approximately 515983, 1029862, 1475661, 1936078,2451194 elements are adequate for the 10-50tube STHXs, respectively.
The computer code FLUENT is used to calculate the fluid flow and heat
transfer characteristics of the STHXs. The governing equations are iterativelysolved by the finite-volume-method with SIMPLE pressure-velocity coupling
algorithm. Segregated approach is selected. It is used to solve a single variable field
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by considering all cells at the same time, and then solves the next variable field by
again considering all cells at the same time. The convective term in governing
equations are discretized by QUICK scheme with three-order precision. The
convergence criterion is that the normalized residuals are less than 10-5 for the flowequations and 10
-8for the energy equation.
3. EXPERIMENTAL STUDY
3.1EXPERIMENTAL APPARATUS AND OPERATING PROCEDURE
In the present study, heat transfer performances of 10-50tube STHXs are studied
experimentally, respectively.
Fig.4.The experimental setup
The experimental setup of the study is shown in Fig.4. The system includes
a cooling air part and a heating air part. The heating air part consists of an air pump,a volumetric flow meter, a heater, and a heat exchanger. Air is heated up by a heater
to reach a predetermined inlet temperature before entering the tube side of the heat
exchanger. Then it is pumped to the tube side to be cooled down. Finally, the cooledair is pumped out off to the environment. The cooling air part consists of an air
pump, a volumetric flow meter and the heat exchanger. The cool air is pumped to
the shell side of the heat exchanger for heat-up. Then it is pumped out off to theenvironment. To minimize heat loss of the facilities, 40mm thickness fibreglass
insulation is covered on the outer surface of the heat exchanger.
Measurements of inlet and outlet fluid temperature are carried out using
T-type thermal couples. The volumetric flow is measured with a flow meter at a
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range of 0-300m3/h. Data Acquisition System(Agilent HP3470A) records readings
of thermal couples.
The experiments are being conducted under steady state conditions. The
procedure is repeated a few times for different flow rates of the shell side rangingfrom 20 to 200m
3/h, while the flow rate of the tube is maintained constant. Prior to
each experiment, an energy balance test is conducted.. After reaching the stablecondition, temperatures are recorded by a Data Acquisition System for 10min
maintaining a span of 5s between two successive readings. At the same time, the
volumetric flow rate is recorded.
3.2DATA REDUCTION
The shell-side Reynolds number is defined by equation (6)
s s s
ss
de u
Re
(6)
Where su is the mean velocity at the minimum transverse area; sde is the
characteristic dimension which takes the value of tube diameterd; s is the fluid
density.
Before each experiment was carried out, a heat balance test was conducted.
The difference of heat duties between the hot air and cool air needs to be within5.0%. The heat balance equation is
s t
ave
5.0%Q Q
Q
(7)
s t
ave 2
Q QQ
(8) s s s p,s s,in s,outQ v c T T (9) t t t p,t t,in t,outQ v c T T (10)
where sQ and tQ are heat transfer rate of the shell side and the tube side; s,inT and
s,outT are shell-side temperature at the inlet and outlet; t,inT and t,outT are tube-side
temperature at the inlet and outlet, respectively.p,sc and p,tc are special heat of the
cool air and hot air. The thermodynamic and transport properties of the hot air and
cool air are calculated according to average temperature values of the inlet andoutlet for the section.
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2 1LMTD
1
ln
T TT
TT
(12)
1 , ,t out s inT T T , 2 , ,t in s out T T T (13)
Heat transfer coefficient of the shell side is calculated with traditional Wilson plots
technique. The shell-side Nusselt numbers is computed by the following equation:
ss
s
h dNu
(14)
3.3EXPERIMENT UNCERTAINTY
The experimental uncertainty of the present work is determined by using the
method presented by Kline and McClintock. The uncertainty calculation method
involves calculating derivatives of the desired variable with respect to individualexperimental quantities and applying known uncertainties. According to the
reference, the experimental uncertainty is defined as follows:
1 2 n
2 2 2
R
1 2 n
x x x
R R RW W W W
x x x
(15)
Where 1 2, ,..., nR f x x x and nx is the variable that affects the results ofR .
For10-50tube STHXs, the uncertainties of Nusselt number are 1.8%.
4. RESULTS AND DISSCUSSIONS
4.1MODEL VALIDATION
In order to verify the experimental setup, 10 tube STHX is used to investigate heat
transfer characteristics firstly. The heat transfer measurements of the present workare compared with the data from Bell-Delaware method(Bell, 1988).
The overall heat transfer coefficient,Km, is defined as
ave
m
LMTD
QK
A T
(11)
where A is the surface area, and LMTDT is the log mean temperature difference,which is determined by
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Fig.5. Comparison of experiment results of Nusselt number with the data from Bell-Delaware
method for10tube STHX
The comparison of experimental results of Nusselt number in the shell sidewith the data from Bell-Delaware method for 10tube STHX is presented in Fig.5. It
can be seen that the difference between the present experimental data and the
classical one is within 6%. The present experimental results are in great agreement
with the data from Bell-Delaware method. It indicates that the experimental setup isreliable for the experimental research of 10-50tube STHXs.
4.2EXPERIMENTAL RESULTS
As temperature crossover can be achieved or not is determined by many factors, in
order to simplify the problem, heat transfer performances of 10-50tube STHXs areanalyzed at the condition that average velocity is 10m/s both in the shell side and
the tube side.
Table3. Experimental and numerical results
The comparison between experimental results of the outlet temperature inthe shell side and tube side and the data from the numerical results for 10-50tube
STHXs is shown in Table3. It is seen from the table that the differences between the
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present experimental data and the numerical results are within 7%. The numerical
results are in good agreement with the data from experiments. It indicates that the
simulation method is reliable.
From table3, it can be observed that whenL/W4.62, the outlet temperatureof the cold air ( s,outT ) is higher than that of the hot air ( t,outT ), that means
temperature crossover can be achieved at the STHX with L/W4.62. But when
L/W3.08, outlet temperature of the cold air is lower than that of the hot air, whichmeans temperature crossover cant be achieved any more. The outlet temperature
of the cold air will equal to that of the hot air in STHX withL/Wat the range of 3.08
to 4.62.
Fig.6. Heat transfer coefficient of 10-50tube STHXs
Fig.6 illustrates the comparison of experimental results of heat transfercoefficient with the data from simulations for 10-50tube STHXs, respectively. It
can be seen that the deviation between the present experimental measurements and
the numerical results is within 7%. The present experimental results are in good
agreement with the numerical results. From Fig.6, it also can be clearly observedthat heat transfer coefficients decrease with the increase of tube numbers in STHXs.
In other words, heat transfer coefficients decrease withL/Wdecreasing. The reason
for this phenomenon appears to be as follows, the ratio of the cross flow area to the
whole area is 19.5% for 10tube STHX, but for 50tube STHX the ratio is 97.5%. Asthe heat transfer efficient is higher when hot air and cold air exchange heat in
counter flow than in cross flow, the heat transfer coefficient will be getting smallerwhen cross flow proportion is getting larger.
The inherent reason why heat transfer coefficient decrease with L/W
decreasing is distributions of temperature difference field (TDF) in 10-50tube
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STHXs become more and more uneven. It agrees with the principle of uniformity
of temperature different field (Guo et al., 2002).
Fig.7. Partition of sub-elements in 10tube STHX
A STHX can be divided into a lot of small elements (named sub-element)
and each sub-element is a small STHX. In Fig.7, 10-50 tube STHXs are dividedinto numbers of the sub-elements with dimensions of 13mm100mm13mm in x,
y and z directions. Numbers of sub-elements in 10-50tube STHXs are 10121,
20121, 30121, 40121, 50121, respectively. Each sub-element isnumbered sequentially in x, y and z directions having a unique three-dimensional
coordinate (i, j, k). For example, the sub-element departed from the 10tube STHX
in Fig.7 is representative of (1, 1, 1). As there is only 1 sub-element in z direction,
k=1 for all sub-elements, so the three-dimensional coordinate (i, j, k) can besimplified as two-dimensional coordinate (i, j). Then the sub-element departed
from the 10tube STHX in Fig.7 is representative of (1, 1). There is a characteristic
hot fluid temperature [ ,tT i j ] and a characteristic cold fluid temperature [ ,sT i j ]for each sub-element. Their difference [ T ] is named local characteristic
temperature difference. The aggregate of these local characteristic temperature
differences forms a temperature difference field of the heat exchanger.
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(a)
(b)
(c)
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Jiang and Deng: Temperature Crossover in Shell and Tube Heat Exchangers
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(d)
(e)
Fig.8. TDF in 10-50 tube STHXs (a) 10tube (b) 20tube (c) 30tube (d) 40tube (e) 50tube
Fig.8 shows temperature difference fields acquired by the numerical
method in 10-50tube STHXs. From Fig.8, it can be observed that the localtemperature difference is almost uniform and the temperature difference is in the
range of 17.15-29.61K for 10tube STHX. But for 50tube STHX, the local
temperature difference is very uneven and the temperature difference ranges from 0
to 21.09K. The uniformity characteristics for 20-40tube STHXs are between10tube STHX and 50tube STHX. Temperature difference becomes more and more
non-uniform withL/Wdecreasing.
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A parameter is defined as the uniformity factor of TDF.
1 1
2
1 1
[ , , ]
[ , , ]
M N
t s
i j
M N
t s
i j
T i j T i j
N T i j T i j
(16)
Where ,tT i j and ,sT i j are the temperature distributions in the tube side and the
shell side, respectively; M and N are the numbers of sub-elements in length andwidth directions. The uniformity factor of TDF in reality is at the range of 0-1, and
the more non-uniform the TDF, the smaller the uniformity factor of TDF.
Table4. Uniformity factor of TDF in five STHXs
Table 4 presents uniformity factors of TDF in 10-50tube STHXs. It isclearly observed that the uniformity factor of TDF decreases withL/Wdecreasing.
Thats because the uniformity factor of TDF decreases (Guo et al., 1996).
5. CONCLUSIONS
The heat transfer characteristics of 10-50tube STHX have been studied onexperimental and numerical method. Heat transfer coefficients and outlet
temperatures of the hot air and the cold air in five STHXs are reported. Temperaturedifference fields and uniformity factors of TDF acquired by the numerical method
in 10-50tube STHXs are depicted, respectively.
The conclusions are as follows:(1)The heat transfer coefficient decreases withL/Wdecreasing. The reason
why heat transfer coefficient decrease with L/W decreasing is temperature
difference fields become less and less uniform. The uniformity of the temperature
difference field is in favour of increasing heat exchanger effectiveness.(2)At the condition that average velocity is 10m/s in both the shell side and
the tube side, temperature crossover can be achieved in STHXs withL/W
4.62. ButwhenL/Wof STHXs is smaller than 3.08, temperature crossover cant be achievedany more. =1 will be achieved in STHX withL/Win the range of 3.08 to 4.62.
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