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Experimental study of thermalhydraulic performance of cam-shaped

tube bundle with staggered arrangement

Hamidreza Bayat a,, Arash Mirabdolah Lavasani b, Taher Maarefdoost a

a Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran.b Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 20 February 2014

Accepted 2 June 2014

Available online 22 June 2014

Keywords:

Heat exchanger

Tube bundle

Experimental heat transfer

Cam-shaped tube

Cross-flow

a b s t r a c t

Flow and heat transfer from cam-shaped tube bank in staggered arrangement is studied experimentally.

Tubes were located in test section of an open loop wind tunnel with two longitudinal pitch ratios 1.5 and

2. Reynolds number varies in range of 27,000 6 ReD 6 42,500 and tubes surface temperature is between

78 and 85 C. Results show that both drag coefficient and Nusselt number depends on position of tube in

tube bank and Reynolds number. Tubes in the first column have maximum value of drag coefficient,

while its Nusselt number is minimum compared to other tubes in tube bank. Moreover, pressure drop

from this tube bank is about 9293% lower than circular tube bank and as a result thermalhydraulic

performance of this tube bank is about 6 times greater than circular tube bank.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

Study of flow and heat transfer around single and multiple bluffbodies has wide engineering applications such as heat exchangers,

cooling towers, and electronic cooling. There are several authors

who published books about flow and heat transfer phenomena

around bluff bodies such as Kays and London [1], Hoerner [2],

Zukauskas and Ulinskas [3], Zukauskas and Ziugzda [4], and

Zdravkovich [5,6].

Traub [7]reported that turbulence grids lead to an enhance-

ment in heat transfer of plain tube bundles. Stanescu et al. [8]

found that increasing ReD decreases the optimal spacing of cylinder

to cylinder. Wilson and Bassiouny[9]suggested to choose longitu-

dinal pitch ratioa 6 3 for circular tube bank, in order to have best

performance and compactness. The studies of Mandhani et al. [10]

showed that decreasing value of porosity and increasing values of

Prandtl and Reynolds numbers, average value of Nusselt number of

circular tube bundle increases. Yoo et al. [11] found that average

Nusselt number of second and third tubes in staggered tube bank

is higher than first tube. Gupta et al. [12] optimized coil finned

tube heat exchanger, by choosing a suitable mean diameter of shell

and appropriate clearance for a given fin diameter. Hassan [13]

found that in a small tube bundle for decreasing pressure the pitch

over tubes should be widened.

One of the aspects in studying flow and heat transfer from mul-

tiple bodies is in heat exchangers where reducing pressure drop

and increasing heat transfer is of interest to many scientists. There

are several studied about flow and heat transfer from non-circular

tubes [1422]. Rocha et al. [14] showed that compare to circulartubes plate fin heat exchangers, elliptic one performed better due

to lower pressure drop and higher fin efficiency. Matos et al.

[15,16]also found that elliptic tubes perform more efficiently than

circular one. Ibrahim and Gomma[17]concluded that elliptic tube

bank at zero angle of attack has the maximum thermal perfor-

mance. Ibrahim and Moawed [18]found that in an elliptic tubes

with longitudinal fins, the position of fin on elliptic tubes, effects

on friction factor and heat transfer. Bouris et al. [19]reported that

in in-line tube bank, deposition rate for elliptic-shaped tubes is 73%

lower than circular tubes. Nouri-Borujerdi and Lavasani[20,21]

experimentally measured flow and heat transfer characteristics

around single cam-shape tube. Moawed [22] experimentally inves-

tigated forced convection from outside surface of helical coiled

tube.

Furthermore, several authors used vortex generator in order to

increase thermal performance of heat exchanger [2325]. Joardar

and Jacobi [23] reported that adding vortex generator enhanced

heat transfer with modest pressure drop penalties. However, Wu

and Tao [24] and Wu et al. [25] showed that it is possible to

enhance heat transfer with reduction in pressure drop by using

longitudinal vortex generator.

Compare to other works on literature streamlined-shaped tube

bundle, has higher thermalhydraulic performance and need less

pumping power due to low hydraulic resistance. Because cam-

shaped tube compare to circular tube has lower drag coefficient

[20,21] andhigher heat transfer of staggeredtube bundlecompared

http://dx.doi.org/10.1016/j.enconman.2014.06.009

0196-8904/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +98 937 1681530.

E-mail address: hrb.mech@gmail.com(H. Bayat).

Energy Conversion and Management 85 (2014) 470476

Contents lists available at ScienceDirect

Energy Conversion and Management

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n c o n m a n

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to in-line tube bundle, the purpose of this study is to experimen-

tally investigate the flow and heat transfer characteristics around

cam-shaped tube bundle in staggered arrangements subject to

cross flow of air.

2. Experimental setup

The cross section profile of the cam-shaped tube is represented

in Fig. 1. These tube are comprised of two circles with two arcs seg-

ments tangent to them and are made of commercial steel plate

with 0.7 mm of wall thickness. Identical diameters of tubes areequal tod = 8 mm, D = 16 mm and distance between their centers

isl = 15.75 mm.

A test tube with length of 31 cm was made, in order to measure

drag coefficient of cam shaped tube in tube bank. To measure the

static pressure on the tube surface by using a digital differential

pressure meter, fourteen holes with diameter of 1 mm were drilled

on the surface of test tube. Four test tubes with length of 22 cm

were made for measuring heat transfer. In order to decrease heat

transfer from these surfaces the two ends of test tubes were insu-

lated by using elastomeric thermal tube insulation.

Fig. 2shows fourteen cam-shaped tubes located at wind tunnel

test section. The space between two tandem tubes is defined by

longitudinal pitch SL and the space between side-by-side tubes is

defined by transverse pitchST. In this study transverse pitch ratioisST/Deq= 1.25 and longitudinal pitch ratios areSL/Deq= 1.5 and 2.

Fig. 3shows an open circuit low speed wind tunnel where the

experiments were performed. A pitot static tube is used to measure

the free stream velocity in front of the frame cross section. The air

velocity varied from 9 to 15 m/s by controlling a variable speed

motor.

Toheat up thetubes, a pumpcirculates hot waterbetweena tank

and the tubes. An electric heating element supplies the hot water

and a control valve regulates the hot water at the tube inlet. Water

temperature is measured at the inlet and outlet of the tubes using

type-k thermocouple wires and saved at interval times of one sec-

ond by using data logger. A glass tube flow meter measures the flow

rate with 1% uncertainty in full-scale flow. A steady state condition

is reached between 5 and 15 min, depending on the ambient tem-peratureand freestreamvelocity,and thendata collection is started.

To estimate the pressure drag and heat transfer from the cam

shaped tubes compared to that of a circular tube with various

cross sections, it is important to select an appropriate reference

length. Deq is the diameter of an equivalent circular tube whose

circumferential length is equal to that of the cam-shaped tube.

Based onFig. 1, the equivalent diameter is obtained byDeq= P/p=22.44 mm wherePis perimeter of cam shape tube.

For understanding flow characteristic better, Reynolds number

is defined with two equations. First, for comparing heat transfer

from each tube in tube bank with single tube in crossflow, Rey-

nolds number is calculated by Reeq= U1Deq/m. Second, since thespeed of fluid varies along its path in tube bank, a reference veloc-

ity base on minimum free area available for fluid flow is being used

for calculating of ReD= UmaxDeq/m. There are two correlations for

Nomenclature

C circumferential length (mm)CD drag coefficientcp,i pressure coefficientd small diameter (mm)D large diameter (mm)

Deq equivalent diameter,Deq=C/p(mm)f friction factorh heat transfer coefficient (W m2 K1)j Colburn factor, Nu/(RePr1/3)k thermal conductivity (W m1 K1)L tube length (cm)l distance between centers (mm)_m mass flow rate (kg s1)NL number of transverse rowsP pressure (Pa)_Q heat transfer rate (W)SD diagonal pitch, (m)SL/Deq longitudinal pitch ratioST/Deq transverse pitch ratioReeq Reynolds number, (U1Deq/t)ReD Reynolds number, (UmaxDeq/t)Nu Nusselt Number, (hDeq/k)

T temperature (K)U velocity (m s1)Umax maximum velocity, (

STSTD

U) (m s1)_Vw volume flow rate (L s

1)

Greeki density (kg m3)t fluid kinematic viscosity (m2 s1)g thermalhydraulic performancer Afree flow area/Afrontal areah hole angle (degree)

Subscriptsave. averagecam cam-shaped tubeeq equivalenti inleto outlets surface

w water1 free stream

Fig. 1. Schematic of a cam-shaped tube: (a) pressure drag, (b) heat transfer testtube.

H. Bayat et al. / Energy Conversion and Management 85 (2014) 470476 471

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calculating maximum velocity in staggered tube bundle [26]; if

2(SD D) < (ST D), maximum velocity is calculated from

Umax= STU1/(2(ST D)), otherwise it is calculated from Umax=

STU1/(ST D). In the present work the second correlation is used

for calculating maximum velocity, where Reynolds number base

on minimum free area varies in range of 27,000 6 ReD 6 42,500.

Quarmby and Al-Fakhri[27]showed that forL/Deq> 4 this ratio

has little effect on the heat transfer as a result the test tube for

measuring heat transfer was made with L/Deq= 8.

The pressure drag coefficient CD is determined experimentally

from pressure distribution over the cam shaped-tube surface,

including the large and small circles as well as two tangent arcs

between them byCD fP14

i1cp;iCoshiDSig=Deq, where the pressure

distribution on the cam shaped is expressed in dimensionless form

by the pressure coefficientcp;i pip1=0:5qU21.

According to Fig. 1,pi is the static pressure which was measured

by a differential pressure meter at the location of the holes drilled

perpendicular to the tube surface.P1andU1are the pressure and

velocity of the air free stream respectively and q is air density.Friction factor f is determined by calculating pressure drop

across tube bank. WhereDPis the difference between the pressure

at inlet and the exit of the cam shaped tube bank and NLis number

of transverse rows.

f DP

0:5NLqU2max

1

The mean Nusselt number is determined as follows:

NueqhDeqk

_mwCp;wTwi Two

pLkTs T1 2

where _mw qw_Vw whichCp,w,qw and _Vw are specific heat, density

and volume flow rate of water respectively, temperature of tube

surface is defined by TS= (Twi+ Two)/2.

The thermo physical properties of air such as k is calculated at

film temperature which is the average of surface and free stream

temperature, Tf= (Ts+ T1)/2.

After measuring Nueq for all tubes in tube bank, the average

Nusselt number of tube bank was calculated by the following

equation.

Nuave:

1

NNueq

3

where Nis number of tubes in a row of tubebank. Heat transfer per-

formance against the friction factor of cam defines by Nuave:=f.

Thermal hydraulic performance shaped tube bank base on cir-

cular tube bank is defined by efficiency index g which has beenproposed by Webb[28].

g Nuave:cam:=Nuave:cir:

fcam:=fcir:4

Yan and Sheen[29]suggested a factor AGF or area goodness

factor for comparing heat exchanger base on their frontal area

and desired duty. Heat exchanger which has higher AGF is better

because it requires less frontal area.

AGF r2

J=f 5

In Eq.(5),ris ratio of free flow area to frontal area of tube bankandj is Colburn factor, Nu/(RePr1/3).

3. Uncertainty analysis

Wind tunnel experiments are subjected to different sources of

uncertainty such as instrumentation, data acquisition, and data

analysis. Therefore, uncertainties of results are estimated with

theory of Moffat[30], a final result,R, is typically the combination

of different measured variables, vi, where R=f(v1,v2,. . .v3). The

contribution of the uncertainty in each variable can be estimated

by:

URR

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidv1

v1

2

dv2

v2

2

dvn

vn

2s 6

As an example, uncertainty of Nusselt number was calculated

by the following equation:

UNueq

Nueq

UQwpLkTsT1

2

Qw

pLkTsT12UT1

" #2

Qw

pLkTsT12UTs

" #28