numerical and experimental study on temperature crossover in shell and tube heat exchangers

7/29/2019 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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International Journal of Food Engineering, Vol. 7 [2011], Iss. 4, Art. 7

http://www.bepress.com/ijfe/vol7/iss4/art7

DOI: 10.2202/1556-3758.2217


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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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Jiang and Deng: Temperature Crossover in Shell and Tube Heat Exchangers

Published by Berkeley Electronic Press, 2011


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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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(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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numerical and experimental study on temperature crossover in shell and tube heat exchangers

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