NH Kim, JP Cho, Air-side Performance of Louver-finned Flat Aluminum Heat Exchangers at a Low...

ORIGINAL

Air-side performance of louver-finned flat aluminum heatexchangers at a low velocity region

Nae-Hyun Kim Æ Jin-Pyo Cho

Received: 19 May 2007 / Accepted: 12 September 2007 / Published online: 25 October 2007

� Springer-Verlag 2007

Abstract The heat transfer and pressure drop character-

istics of heat exchangers having louver fins were

experimentally investigated. The samples had small fin

pitches (1.0–1.4 mm), and experiments were conducted up

to a very low frontal air velocity (as low as 0.3 m/s). Below

a certain Reynolds number (critical Reynolds number), the

fall-off of the heat transfer coefficient curve was observed.

The critical Reynolds number was insensitive to the louver

angle, and decreased as the louver pitch to fin pitch ratio

(Lp/Fp) decreased. Existing correlations on the critical

Reynolds number did not adequately predict the data. The

heat transfer coefficient curves crossed over as the Rey-

nolds number decreased. Possible explanation is provided

considering the louver pattern between neighboring rows.

Different from the heat transfer coefficient, the friction

factor did not show the fall-off characteristic. The reason

was attributed to the form drag by louvers, which offsets

the decreased skin friction at low Reynolds numbers. The

friction factor increased as the fin pitch decreased and the

louver angle increased. A new correlation predicted 92% of

the heat transfer coefficient and 94% of the friction factor

within ±10%.

List of symbols

A heat transfer area (m2)

cp specific heat (J /kg s)

Cr heat capacity ratio, dimensionless [Eq. (6)]

D ideal transverse distance (m)

Dh hydraulic diameter (m)

FD depth of fin array in flow direction (m)

Fe flow efficiency, dimensionless [Eq. (18)]

Fp fin pitch (m)

f airside friction factor, dimensionless [Eq. (15)]

fi tube-side friction factor, dimensionless [Eq. (10)]

H fin height (m)

h heat transfer coefficient (W/m2 K)

j Colburn j factor, dimensionless [Eq. (14)]

k thermal conductivity (W/m K)

Ll louver length (m)

Lp louver pitch (m)

_m mass flow rate (kg /s)

N actual transverse distance (m)

NTU number of transfer units, dimensionless [Eq. (7)]

Pf fin pitch (m)

Pr Prandtl number, dimensionless

Q Heat transfer rate (W)

ReLp Reynolds number based on Lp, dimensionless

¼ VmaxLp

m

� �

Re�Lp critical Reynolds number, dimensionless

ReDhtube-side Reynolds number based on

Dh, dimensionless

S1 Non-louvered inlet and exit fin length (m)

S2 Re-direction louver length (m)

t tube wall thickness (m)

T temperature (K)

Tp tube pitch (m)

tf fin thickness (m)

U overall heat transfer coefficient (W/m2 s)

Vmax maximum airside velocity (m/s)

Greek symbols

a louver angle (degree)

b flow angle (degree)

N.-H. Kim (&) � J.-P. Cho

Department of Mechanical Engineering, University of Inchon,

#177 Dohwa-Dong, Nam-Gu, Inchon 402-749, South Korea

e-mail: [email protected]

123

Heat Mass Transfer (2008) 44:1127–1139

DOI 10.1007/s00231-007-0346-4

choi

강조

e thermal effectiveness, dimensionless [Eq. (5)]

DP pressure loss (Pa)

g fin efficiency, dimensionless [Eq. (12)]

go surface efficiency, dimensionless [Eq. (11)]

q density (kg/m3)

m kinematic viscosity (m2/s)

r contraction ratio of the cross-sectional area,

dimensionless

Subscripts

c heat exchanger core

exp experimental

i tube-side

in inlet

f fin

m mean

max maximum

min minimum

o airside

out outlet

pred predicted

t tube

1 Introduction

Fin-and-tube heat exchangers have been widely used as

condensers or evaporators in a household air-conditioning

system. In the forced convective heat transfer between air

and refrigerant, the controlling thermal resistance is on the

air-side. To improve the air-side performance, rigorous

efforts have been made, which include a usage of high

performance fins and of small diameter tubes, etc. How-

ever, fin-and-tube heat exchangers have inherent short-

comings such as the contact resistance between fins and

tubes, the existence of a low performance region behind

tubes, etc. These short-comings may be overcome if fins

and tubes are soldered, and low profile flat tubes with high

performance fins are used. Brazed aluminum flat-tube heat

exchangers with louver fins could be the choice, although

the price could be higher due to additional brazing process.

Flat tube heat exchangers have been used as condensers of

automotive air conditioning units for more than ten years,

and they are replacing fin-and-tube condensers of the res-

idential air-conditioning units. The possibility of replacing

the residential fin-and-tube heat exchangers by flat tube

heat exchangers has been studied by Webb and Jung [1].

They showed that, for the same air-side thermal capacity,

the flat-tube geometry requires less than half the heat

exchanger volume compared with the fin-and-tube coun-

terpart. The advantage of flat-tube heat exchangers has

further been studied by Webb and Lee [2]. They compared

the thermal performance of flat tube condenser having

866 fins per meter with that of the fin-and-tube condenser

having 7.0 mm round tubes and 1,024 fins per meter. The

flat tube condenser was shown to reduce the material up to

50%. One major challenge for the application of the flat

tube condenser to the residential air-conditioner is the

reduced frontal air velocity. The frontal air velocity of the

residential system is much lower (0.5–1.5 m/s) than that of

the automotive system (2–5 m/s), where most of the flat

tube heat exchanger technology is based. The thermal

performance of the louver fin is known to significantly

decrease as the flow velocity decreases.

Although louvered surfaces have been used since the

1950s, the flow characteristics have not been unveiled until

the pioneering work by Davernport [3]. He showed that,

through flow visualization study, the flow did not pass

through the louvers at low Reynolds numbers. At high

Reynolds numbers, however, the flow became nearly par-

allel to the louvers. He speculated that, at low air velocities,

the developing boundary layers on adjacent louvers

became thick enough to effectively block the passage,

resulting in nearly axial flow through the array. Achaichia

and Cowell [4] further confirmed that, through heat transfer

tests on flat tube heat exchangers having louvered plate

fins, the Stanton numbers approached those of the duct flow

at sufficiently low Reynolds numbers. At high Reynolds

numbers, the data were parallel to those of the laminar

boundary layer for a flat plate. Two types of flow were

identified within the louvered plate fin array—‘‘duct

directed flow’’ and ‘‘louver directed flow’’. The amount of

either flow depended on the louver geometry such as fin

pitch, louver pitch, louver angle as well as Reynolds

number. Webb and Trauger [5] conducted flow visualiza-

tion experiments using large scale models and introduced

the ‘‘flow efficiency’’, which implies the ratio of the louver

directed flow to the total flow. The flow efficiency

increased as the Reynolds number increased or the fin pitch

decreased. The role of vortex shedding in louver geometry

has been investigated by DeJong and Jacobi [6]. The

shedding started at the last downstream louver, and moved

upstream as the Reynolds number increased. The critical

Reynolds number, where the vortex shedding started,

decreased as the louver angle increased and the fin pitch

decreased.

Significant efforts have also been devoted to numeri-

cally analysis to obtain detailed flow structures over the

louver array. Achaichia and Cowell [7] modeled one louver

in the fully developed region assuming periodic boundary

conditions. Their results confirmed the existence of duct

directed flow at low Reynolds numbers and louver

directed flow at high Reynolds numbers. Atkinson et al. [8]

conducted time-dependent two- and three-dimensional

numerical study. The results showed vortex shedding from

the trailing edges. Three-dimensional model predicted the

1128 Heat Mass Transfer (2008) 44:1127–1139

123

data better than the two-dimensional model. Tafti et al. [9]

investigated the flow transition in a louver fin geometry by

conducting time-dependent two-dimensional analysis. The

initial instability was observed at the exit louver, and

moved upstream as the Reynolds number increased. The

findings were in close agreement with the experimental

results by DeJong and Jacobi [6].

Following the pioneering study by Davernport [10], many

investigations have been made on the air-side heat transfer

and pressure drop characteristics of louver fin–flat tube heat

exchangers. The previous experimental studies are sum-

marized in Table 1. Davernport [10] provides data on 32

one-row samples, where louver dimensions were systemat-

ically varied (0.94 £ Lp/Pf £ 2.24, 8� £ a £ 36�) for two

louver lengths (12.7 and 7.8 mm). The Reynolds number

ranged 300 £ ReLp£ 4,000. However, it should be noted that

the fin corrugation pattern of Davernport [10] is not com-

mon. Their fin geometry had adjacent fins inclined at a

significantly larger angle to each other (Z-shape) than is the

case with the more common pattern (U or V-shape). Dav-

ernport [11] provides j and f correlations based on the data.

Sunden and Svantesson [12] tested 6 one-row samples

having 0.26 £ Lp/Pf £ 0.91, 14� £ a £ 34� for 100 £ ReLp700,

and proposed j and f correlations based on their own data.

Webb and Jung [1] provides data for 6 one-row samples

having 0.48 £ Lp/Pf £ 1.0, a = 30� for 100 £ ReLp£ 2,000.

Chang and Wang [13] tested 27 samples having 0.60 £ Lp/Pf

£ 0.85, a = 28� for 100 £ ReLp£ 800, and reported that

Shanoun and Webb [14] analytic model predicted the heat

transfer and friction data successfully. Significant amount of

data have been provided by Kim and Bullard [15] (45

samples, 0.26 £ Lp/Pf £ 0.91, 14� £ a £ 34�) for 100 £ ReLp

£ 500. The heat transfer coefficient increased as the louver

angle increased. However, above a critical louver angle, the

heat transfer coefficient decreased with the increase of the

louver angle. The friction factor continuously increased with

the increase of the louver angle. Multiple regression corre-

lations were proposed based on their own data. Achaichia

and Cowell [4] tested 15 samples having 0.24 £ Lp/Pf £ 0.85,

22� £ a £ 30� for 30 £ ReLp£ 1,000, and proposed j and f

correlations from their own data. Achaichia and Cowell’s

sample had louvered plate fins on flat tubes, different from

the traditional flat tube geometry, which has folded louver

fins between flat tubes.

The literature survey reveals that most of the studies

have been conducted for the Reynolds number (based on

louver pitch) larger than 100. Only Achaichia and Cowell’s

[4] samples were tested up to Reynolds number of 30. For a

household air-conditioner, the frontal air velocity is

between 0.5 and 1.5 m/s with corresponding Reynolds

number between 60 and 200 (for 1.7 mm louver pitch). It

has been revealed by many investigators that, as the Rey-

nolds number decreases, more flow tends to be duct-

oriented, which significantly decreases the heat transfer

coefficient. This situation may be remedied if the fin pitch

is decreased or louver pitch is increased. Smaller the fin

pinch (or lager the louver pitch), more flow is expected to

follow the louver. Table 1 reveals that most of the previous

studies have been conducted at small values of Lp/Pf. The

Lp/Pf of Achaichia and Cowell [4] is less than 1.0. The

present samples have small fin pitches (1.0–1.4 mm) and

large louver length (1.7 mm) with corresponding Lp/Pf

from 1.21 to 1.70. In addition, in the present study,

experiments were conducted at frontal air velocities as low

as 0.3 m/s (with the corresponding Reynolds number as

small as 40). The effect of fin pitch and louver angle has

also been investigated.

2 Experiments

2.1 Heat exchanger samples

A total of 12 heat exchangers having three different fin

pitches (1.0, 1.2, 1.4 mm) and four different louver angles

(15�, 19�, 25�, 27�) were tested. The louver pitch was fixed

at 1.7 mm. The samples consisted of 24 steps of louver fins

brazed to flat tubes as illustrated in Fig. 1. The height and

width of the samples were 254 and 400 mm, respectively.

The tube-side was circuited in a serpentine fashion with

Table 1 Summary of previous studies on the air-side performance of flat-tube heat exchangers having louver fins

Investigators LP (mm) Fp (mm) a (degree) LP/Fp ReLp

Davernport [10] 1.5–3.0 1.0–1.6 8–36 0.94–2.24 300–4,000

Achaichia and Cowell [4] 0.8–1.4 1.7–3.3 22–30 0.24–0.85 30–1,000

Sunden and Svantesson [12] 0.8–1.5 1.5–2.0 14–34 0.26–0.91 100–700

Webb and Jung [1] 1.0–1.4 1.4–2.1 30 0.48–1.0 100–2,000

Chang and Wang [13] 1.3–1.9 1.8–2.2 28 0.60–0.85 100–800

Kim and Bullard [15] 1.7 1.0–1.4 15–29 1.21–1.70 100–500

This study 1.7 1.0–1.4 15–27 1.21–1.70 30–1,000

Heat Mass Transfer (2008) 44:1127–1139 1129

123

two tubes per pass. With this circuitry, tube-side flow was

maintained turbulent. Maintaining turbulent flow in the

tube-side is important because the tube-side thermal

resistance needs to be minimized for an accurate assess-

ment of the airside heat transfer coefficient. In addition to

this, tube-side flow mal-distribution problem, which might

exist for a multiple tube configuration, was eliminated.

Dimensional details of the flat tube and the louver fin are

provided in Fig. 2 and Table 2.

2.2 Test apparatus and procedures

A schematic drawing of the apparatus is shown in Fig. 3.

It consists of a suction-type wind tunnel, water circulation

and control units, and a data acquisition system. The

apparatus is situated in a constant temperature and

humidity chamber. The airside inlet condition of the heat

exchanger is maintained by controlling the chamber

temperature and humidity. The inlet and outlet dry and

wet bulb temperatures are measured by the sampling

method as suggested in ASHRAE Standard 41.1 [16]. A

diffusion baffle is installed behind the test sample to mix

the outlet air. The waterside inlet condition is maintained

by regulating the flow rate and the outlet temperature of

the constant temperature bath situated outside of the

chamber. Both the air and the water temperatures are

measured by pre-calibrated RTDs (Pt-100X sensors).

Their accuracies are ±0.1 K. The water flow rate is

measured by a mass flow meter, whose accuracy is

±0.0015 l/s. The airside pressure drop across the heat

exchanger is measured using a differential pressure

transducer. The air flow rate is measured using a nozzle

pressure difference according to ASHRAE Standard 41.2

[17]. The accuracy of the differential pressure transducers

is ±1.0 Pa. The wind tunnel is equipped with multiple

nozzles, and an appropriate one is selected depending on

the air velocity.

During the experiment, the water inlet temperature

was held at 45�C. The chamber temperature was main-

tained at 21�C with 60% relative humidity. Experiments

were conducted varying the frontal air velocity from 0.3

to 3.5 m/s. The energy balance between the airside and

the tube-side was within ±2% for the air velocity larger

than 1.0 m/s. It increased to ±5% at the air velocity of

0.3 m/s. All the data signals were collected and con-

verted by a data acquisition system (a hybrid recorder).

The data were then transmitted to a personal computer

for further manipulation. An uncertainty analysis was

conducted following ASHRAE Standard 41.5 [18], and

the results are listed in Table 3. The major uncertainty on

the friction factor was the uncertainty of the differential

pressure measurement (±10%), and the major uncer-

tainty on the heat transfer coefficient (or j factor) was

that of the tube-side heat transfer coefficient (±10%).

The uncertainties decreased as the Reynolds number

increased.

2.3 Data reduction

The total heat transfer rate used for the calculation of air-

side heat transfer coefficient was obtained from the

mathematical average of Qo and Qi.

Fig. 1 Schematic drawing of the test sample

Dh: 1.307mm

20.0

2.00.4

0.5

1.4

R1

R0.6

TP

HLl

AA

FD

FP

LP

S2S1

α

Dh: 1.307mm

20.0

2.00.4

0.5

1.4

R1

R0.6

TP

HLl

AA

FD

FP

LP

S2S1

α

Fig. 2 Geometric dimensions of the test sample


123

Table 2 Geometric dimensions of test samples

Samples FD (mm) a (degree) FP (mm) LP (mm) Ll (mm) H (mm) TP (mm) S1 (mm) S2 (mm)

1 20 15 1.0 1.7 6.4 8.15 2.0 1.82 1.0

2 20 19 1.0 1.7 6.4 8.15 2.0 1.82 1.0

3 20 25 1.0 1.7 6.4 8.15 2.0 1.82 1.0

4 20 27 1.0 1.7 6.4 8.15 2.0 1.82 1.0

5 20 15 1.2 1.7 6.4 8.15 2.0 1.82 1.0

6 20 19 1.2 1.7 6.4 8.15 2.0 1.82 1.0

7 20 25 1.2 1.7 6.4 8.15 2.0 1.82 1.0

8 20 27 1.2 1.7 6.4 8.15 2.0 1.82 1.0

9 20 15 1.4 1.7 6.4 8.15 2.0 1.82 1.0

10 20 19 1.4 1.7 6.4 8.15 2.0 1.82 1.0

11 20 25 1.4 1.7 6.4 8.15 2.0 1.82 1.0

12 20 27 1.4 1.7 6.4 8.15 2.0 1.82 1.0

Fig. 3 Schematic drawing

of the apparatus


123

Q ¼ ðQo þ QiÞ=2 ð1Þ

where Qo and Qi are heat transfer rates of air and water

sides, respectively.

Qo ¼ _mocp;oðTo;out � To;inÞ ð2Þ

Qi ¼ _micp;iðTi;in � Ti;outÞ: ð3Þ

The UA value was obtained from the effectiveness and

NTU method assuming unmixed-unmixed cross flow [19].

e ¼ 1� expNTU0:22

Crexpð�CrNTU0:78Þ � 1� ��

ð4Þ

where

e ¼ Q=Qmax ð5Þ

Cr ¼ ð _mcpÞmin=ð _mcpÞmax: ð6Þ

The UA value was obtained from the following

equation.

UA ¼ ð _mcpÞminNTU: ð7Þ

The airside heat transfer coefficient ho was then

calculated by subtracting the water-side and wall

resistances from the total thermal resistance.

1

gohoAo¼ 1

UA� 1

hiAi� t

ktAtð8Þ

where go is the overall surface effectiveness of the louver

fin, ‘‘t’’ is the thickness of the tube wall, and the subscripts

‘‘o’’ and ‘‘i’’ stand for the air and tube sides, respectively.

Note that the tube-side heat transfer area, Ai includes the

internal web surfaces. The tube-side heat transfer

coefficient, hi was evaluated from the Gnielinski [20]

semi-empirical correlation.

hi ¼ki

Dh;i

� �ðReDh;i � 1; 000ÞPriðfi=2Þ

1:0þ 12:7ffiffiffiffiffiffiffiffifi=2

pðPr

2=3i � 1Þ

ð9Þ

where

fi ¼ 1:58 lnðReDh;i � 3:28Þ ��2

: ð10Þ

During the experiment, the tube-side Reynolds number

was maintained at 6,500, which was the maximum value

obtainable from the present experimental set-up. Due to the

small hydraulic diameter of the flat tube, it was very hard to

increase the tube-side Reynolds number within permissible

pressure loss. At the tube-side Reynolds number 6,500, the

tube-side thermal resistance was within 5% of the total

thermal resistance.

The surface efficiency go was obtained from Eq. (11).

go ¼ 1� Af

Aoð1� gÞ: ð11Þ

The fin efficiency is given by Schmidt [21] as

g ¼ tan hðmlÞml

ð12Þ

where

m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ho

kf tf1þ tf

FD

� �s

l ¼ H

2� tf

: ð13Þ

The heat transfer coefficient is traditionally presented as

the Colburn j factor.

ReLp¼ VmaxLp

mð14Þ

j ¼ ho

qoVmaxcpoPr2=3

o ð15Þ

where Vmax is the maximum velocity in the core of the heat

exchanger. The Vmax is obtained when all the flow passes

through louvers. All the fluid properties were evaluated at

an average air temperature. The core friction factor was

calculated from the measured pressure drop.

f ¼ Ac

Ao

qm

qin

2DPqin

ðqmVmaxÞ2� ðKc þ 1� r2Þ � 2

qin

qout

� 1

� �"

þð1� r2 � KeÞqin

qout

�: ð16Þ

In Eq. (16), Kc and Ke are coefficients for pressure loss

at the inlet and outlet of the heat exchangers, and were

evaluated at ReDh = ? from Figs. 4, 5 of Kays and London

[22].

Table 3 Experimental uncertainties

Parameter Max. Uncertainties

Temperature ±0.1 K

Differential pressure ±1 Pa

Water flow rate ±1.5 · 10–6 m3/s

ReDc ±2%

f ±10%

j ±12%


123

3 Results and discussions

Figure 4 shows the heat transfer coefficients and friction

factors for four different louver angles. Each graph con-

tains data for three different fin pitches except for 15�louver angle where fin pitch 1.4 mm data are missing. The

sample was spoiled during preparation. Figure 4 shows two

distinct regimes. At high Reynolds numbers, the j factor

increases as the Reynolds number decreases. At low

Reynolds numbers, however, it decreases as the Reynolds

number decreases. This fall-off of the j factor has also been

reported by Achaichia and Cowell [4, 7]. As noted by many

investigators [3, 4, 5], more flow tends to follow the duct as

the Reynolds number decreases, which results in the

decrease of the heat transfer coefficient. Davernport [3]

conjectured that, at low Reynolds numbers, the laminar

boundary layer on louvers becomes sufficiently thick to

effectively block off the gaps between adjacent louvers.

The critical Reynolds numbers at which the fall-off of j

factor curve occurs are listed in Table 4. The critical

30 100 1000 2000

a) α = 15 ° b) α = 19 °

c) α = 25 ° d) α = 27 °

0.01

0.1

30 100 1000 20000.01

0.1

j

f

j

f

ReLp

α = 19o

1.0 mm1.2 mm1.4 mm

α = 15o

1.0 mm 1.2 mm

ReLp

30 100 1000 20000.01

0.1j

f

ReLp

α = 27o

1.0 mm 1.2 mm 1.4 mm

30 100 1000 20000.01

0.1

1

j

f

ReLp

α = 25o

1.0 mm 1.2 mm 1.4 mm

Fig. 4 The j and f factors of present samples showing the effect of fin pitch

FLOW

IDEAL STREAMLINE

ACTUAL STREAMLINE

Fig. 5 Illustration of the flow

efficiency


123

Reynolds number has also been investigated by Cowell

et al. [23]. They defined the critical Reynolds number as

the one obtained when the flow angle (b) has dropped to

95% of its maximum value (bmax). The bmax is the limiting

value of b at high Reynolds numbers, and was obtained

from their previous numerical results [7]. The flow angle bis illustrated in Fig. 5. The resulting equation for the crit-

ical Reynolds number obtained by Cowell et al. [23] is

Re�Lp¼ 4; 860=½0:936� 1:76=ðLp=FPÞ þ 0:995a� ð17Þ

where a is the louver angle. The critical Reynolds number

has also been identified by Webb and Trauger [5] through

the flow visualization test. They noted that the flow angle is

dependent on the louver geometry and the Reynolds

number. Then, they introduced the ‘‘flow efficiency’’ to

correlate the data.

Fe ¼N

Dð18Þ

where N is the actual transverse distance and D is the ideal

transverse distance. The flow efficiency is illustrated in

Fig. 5. If all the flow passes the through the louvers, it would

be displaced the lateral distance D. Actual flow path is

displaced a lateral distance N. Webb and Trauger noted that,

below a certain Reynolds number, the flow efficiency

decreased as the Reynolds number decreased. Above the

value, which they defined as the critical Reynolds number,

the flow efficiency was independent of the Reynolds number.

Webb and Trauger developed the following equation for the

critical Reynolds number

Re�Lp¼ 828ða=90Þ�0:34: ð19Þ

Note that the critical Reynolds number by Eq. (19) is

only dependent on the louver angle.

The critical Reynolds numbers have been calculated

from both correlations, and they are summarized in

Table 4. Table 4 reveals that the critical Reynolds numbers

obtained from present j factors are insensitive to the louver

angle, and decrease as the Lp/Fp decreases. When the

present data are compared with the predictions by Cowell

et al. [23] and Webb and Trauger [5] correlations, a large

discrepancy is noted. Predicted values reveal strong

dependency on the louver angle and relative independency

on Lp/Fp. The present data show an opposite trend—strong

dependency on Lp/Fp and relative independency on the

louver angle. Note that the present louver fin has Lp/Fp

values from 1.21 to 1.70, which lie outside of the appli-

cable range of Webb and Trauger (Lp/Fp up to 1.31) and

Cowell et al. (Lp/Fp up to 1.0) correlations. Table 4 shows

that the Webb and Trauger correlation predicts much larger

Re�Lpvalues compared with the present heat transfer results

or the Cowell et al. predictions. The reason may partly be

attributed to the small number of louver rows of Webb and

Trauger’s samples. Their samples consisted of five rows of

louvers. Recent study by Springer and Thole [24] and

Beamer et al. [25] revealed that, as fewer rows of louvers

are used, the flow is forced to become duct-directed

because of the end-wall effects. Duct-directed flow will

delay the fall-off of the j factor curve. Springe and Thole

[24] recommended samples of more than 19 rows for a

proper flow visualization test.

Kim and Kim [26] conducted flow visualization tests for

two louver geometries having Lp/Fp larger than 1.0 (Lp/Fp

= 1.0 and 1.4, a = 27�). Tests were conducted in a water

tunnel using four times scaled-up models. The test section

comprised of 14 louver arrays. The flow efficiencies were

obtained from the flow visualization results, and they are

reproduced in Fig. 6. This figure shows that the flow effi-

ciency decreases slightly as the Reynolds number

decreases for ReLplarger than 100. Below ReLp

of 100,

however, it drops significantly, suggesting the critical

Reynolds number of approximately 100. This value is in

approximate accordance with the critical Reynolds num-

bers obtained from the heat transfer tests (first row of

Table 4). Figure 6 also shows that the flow efficiency

slightly increases as Lp/Fp increases. Also shown in the

graph are the predictions by Cowell et al. [23] and Webb

[27] correlation. Webb [27] updated the Webb and Trauger

[5] flow efficiency correlation. Figure 6 shows that Cowell

et al. correlation generally predicts the trend of the data,

although some overprediction is noticed. Webb correlation

reasonably predicts the data above the critical Reynolds

number. However, the fall-off of the data is not predicted.

Figure 4 shows that the effect of fin pitch is prominent at

low Reynolds numbers, and decreases as the Reynolds

Table 4 The critical Reynolds numbers predicted by Cowell et al. [22] and Webb and Trauger[5]

Investigators Fp = 1.0 mm (Lp/Fp = 1.70) Fp = 1.2 mm (Lp/Fp = 1.42) Fp = 1.4 mm (Lp/Fp = 1.21)

15� 19� 25� 27� 15� 19� 25� 27� 15� 19� 25� 27�

Present heat transfer test %140 %140 %140 %140 %100 %110 %130 %130 %70 %70 %70 %70

Cowell et al. [22] 328 258 196 182 332 261 198 183 336 264 200 184

Webb and Trauger [5] 1,522 1,405 1,280 1,247 1,522 1,405 1,280 1,247 1,522 1,405 1,280 1,247


123

number increases. In addition, one can clearly notice the

cross-over of j factor curves. It has been shown by Webb

and Trauger [5] that the flow efficiency increases as the fin

pitch decreases, which will yield a high heat transfer

coefficient. This is true for high Reynolds numbers. Fig-

ure 4 shows that, for high Reynolds numbers, the j factor

increases as the fin pitch decreases. For low Reynolds

numbers, however, the trend is reversed. The j-factor

decreases as the fin pitch decreases. This is an unexpected

result. Careful review of Achaichia and Cowell [4] data,

however, reveals the same trend. Their sample 3 (Fp =

1.65 mm, Lp = 1.4 mm) yielded lower j factor than that of

sample 6 (Fp = 2.15 mm, Lp = 1.4 mm). Then, why the j-

factor decreases as the fin pitch decreases? Figure 7 shows

louver patterns for three different fin pitches at 27� louver

angle. For a given louver angle, different fin pitch yields

different transverse gap between the upstream and down-

stream louvers, as illustrated in Fig. 7. For the fin pitch

1.0 mm, louvers on the lower row almost align with those

on the upper row yielding very small gap between louvers.

This gap increases as the fin pitch increases. It is known

that louvers enhance the heat transfer through repeated

growth of laminar boundary layer, followed by its dissi-

pation in the wake region [28]. If the thermal and the

velocity boundary layers from the upstream louver are not

fully dissipated in the wake region, the heat transfer per-

formance of the downstream louver will be deteriorated.

For the fin pitch of 1.4 mm, the gap between neighboring

louvers appears wide enough that the flow approaching the

downstream louver is not likely to be affected by the wake

from the upstream louver. For the free-stream velocity of

1.0 m/s, the boundary layer thickness at the trailing edge of

the present louver (width 1.7 mm) is approximately

0.9 mm. For the smallest fin pitch of 1.0 mm, where there

is virtually no gap, the downstream louver will be buried in

the boundary layer from the upstream louver. In this case,

the thermal performance will be deteriorated. This may

explain the effect of fin pitch at low Reynolds numbers.

With increasing Reynolds number, the boundary layer gets

thinner, and the downstream louver will eventually be

situated outside of the boundary layer even with the

smallest fin pitch. Then, the heat transfer coefficient will

increase as the fin pitch decreases.

Different from the j factor, the friction factor curve does

not show the fall-off characteristic. It continuously

increases as the Reynolds number decreases. For high

Reynolds numbers, most of the flow will be aligned with

louvers, and the skin friction will constitute most of the

pressure drop. For low Reynolds numbers, however, most

of the flow will follow the duct. In this case, a form drag by

louvers should be added to the skin friction. This may

explain the continual increase of the friction factor with

decreasing Reynolds number. The form drag does not

contribute to the heat transfer from louvers. Figure 4 shows

that the friction factor increases as the fin pitch decreases.

Same trend has been reported by Achaichia and Cowell [4]

and Chang and Wang [13]. As noted by Achaichia and

Cowell, more flow will be louver-directed for decreased fin

pitch, which will lengthen the travel distance of the flow,

and eventually increase the friction factor.

In Fig. 8, the data are re-plotted for different fin pitches.

Each graph shows the effect of louver angle. Figure 7

shows that the louver angle has minor influence on the j

factor for Fp = 1.4 mm. For smaller fin pitches, the j factor

increases as the louver angle increases. It has been shown

through flow visualization [5] that the flow efficiency

increases as the louver angle increases, which will yield a

high heat transfer coefficient. The effect of louver angle is

likely to decrease as the fin pitch increases. For a very large

fin pitch, for example, the flow will be duct-directed, and

louvers will behave like roughness elements on a surface.

In this case, the effect of louver angle will be negligible.

For Fp = 1.0 mm, j factors cross over at the Reynolds

number of approximately 140. Below the Reynolds

ReLp

0 50 100 150 200 250 300 350 400 450 500 5500.4

0.5

0.6

0.7

0.8

0.9

1.0

Lp/Fp=1.0Lp/Fp=1.4

Fe Cowell et al.

Webb

Fig. 6 Flow efficiency of the louver geometries having large values

of Lp/Fp

Fp = 27 °α

1.0 mm

1.2 mm

1.4 mm

Fig. 7 A graph showing louver patterns for the louver angle 27�


123

number, the sample having lower louver angle yield higher

heat transfer coefficient. This result appears, at first,

uncommon. Careful review of the louver pattern, however,

provides a clue to this uncommon behavior. In Fig. 9,

louver patterns for different louver angles are provided.

Figure 9 shows that the gap between upstream and

downstream louvers decreases as the louver angle increa-

ses, yielding virtually no gap at 27� louver angle. In this

case, the downstream louver will be buried in the boundary

layer from the upstream louver, which will decrease the

heat transfer coefficient. Figure 8 shows that the friction

factor increases as the louver angle increases. Same trend

has been reported by Achaichia and Cowell [4] and Chang

and Wang [13]. As noted by Achaichia and Cowell, more

flow will be louver-directed for increased louver angle,

which will lengthen the travel distance of the flow, and

eventually increase the friction factor.

The literature shows several correlations which predict

the heat transfer coefficients and friction factors of louver

finned heat exchangers. The present data are compared

with the predictions by Davernport[11], Achaichia and

Cowell [4], Sunden and Svantessen [12], Chang and Wang

[29], Chang et al. [30] and Kim and Bullard [15] correla-

tions, and the results are shown in Fig. 10. The statistical

data are summarized in Table 5. The analytical model by

Sahnoun and Webb [14] was also assessed. For the heat

transfer coefficient, Achaichia and Cowell [4] correlation

and Sahnoun and Webb model [14] reasonably predict the

data except for the low Reynolds number range. At low

Reynolds numbers, the data are overpredicted. The reason

may be attributed to the extrapolation of the correlation or

the model. The Achaichia and Cowell correlation is

applicable for the Reynolds number larger than 150 as

reported by themselves. The Sahnoun and Webb model

includes the flow efficiency correlation, which was devel-

oped from the flow visualization data by Webb and Trauger

[5]. The flow visualization test was conducted in a water

tunnel for the Reynolds number range 400�ReLp� 4,000.

Kim and Bullard [15] correlation overpredicts the

ReLp\ 100 data, and underpredicts the ReLp

[ 100 data.

Figure 10 shows that the Davernport correlation highly

30 100 1000 20000.01

0.1

1j

f

ReLp

Fp = 1.0mm

15o 19o

25o 27o

a) Fp = 1.0 mm

b) Fp = 1.2 mm

c) Fp = 1.4 mm

20 100 1000 20000.01

0.1

1

j

f

ReLp

Fp = 1.2mm

15o 19o

25o 27o

30 100 1000 20000.01

0.1

1

j

f

ReLp

Fp = 1.4mm

19o 25o

27o

Fig. 8 The j and f factors of present samples showing the effect of

louver angle

α Fp = 1.0mm

15 °

19 °

25 °

27 °

Fig. 9 A graph showing louver patterns for the fin pitch 1.0 mm


123

underpredicts the data, and the Chang and Wang correla-

tion overpredicts the data. Note that the present samples

have very small fin pitches, which most of the previous

correlations do not cover. Figure 10 shows all the corre-

lations underpredict most of the present friction factors

except for the Achaichia and Cowell [4] correlation, which

overpredicts the data.

Since none of the existing correlations adequately pre-

dicted the data, an attempt was made to develop a new

correlation. Figure 4 shows that, for ReLp[ 150, the

present j factor increases as the Reynolds number decreases

and the fin pitch decreases. The trend is reversed for

ReLp£ 150. Thus, different correlations were developed for

the corresponding Reynolds number ranges. A multiple

regression procedure was carried out to correlate the data.

The potentially significant variables are a flow variable

ðReLpÞ and louver fin parameters (a, Fp, Lp, etc.). The final

correlation is as follows:

ReLp[ 150 : j ¼ 0:705Re�0:477

Lp

a90

� �0:271 Lp

Fp

� �0:155

ð20Þ

ReLp\150 : j ¼ 0:0311Re0:183

Lp

a90

� �0:0475 Lp

Fp

� ��1:25

ð21Þ

entire Reynolds number : f ¼ 8:42Re�0:560Lp

a90

� �0:493

� Lp

Fp

� �0:535

: ð22Þ

Note that, for the j factor, the exponents of the Reynolds

number and (Lp/Fp) have different signs for different

Reynolds number ranges. The present correlations are

compared with the data, and the results are listed in

0 200 400 600 800 1000 12000

1

2

j exp/j

pred

ReLp

ReLp

Davenport[11] Achaichia and Cowell[4] Sunden and Svantesson[12] Chang and Wang[27] Sahnoun and Webb[14] Kim and Bullard[15] Present study

a) jexp/jpred

b) fexp/fpred

0 200 400 600 800 1000 12000

1

2

3

4

5f ex

p/f pre

d Davenport[11] Achaichia and Cowell[4] Sunden and Svantesson[12] Chang and Wang[27] Sahnoun and Webb[14] Kim and Bullard [15] Present study

Fig. 10 The present data

compared with existing

correlations


123

Table 5. The present correlation predicts 92% of the heat

transfer coefficient and 94% of the friction factor within

±10%. Figure 10 shows that the prediction is excellent

even for the low Reynolds number range.

4 Conclusions

In this study, the heat transfer and pressure drop charac-

teristics of heat exchangers having louver fins were

experimentally investigated. The samples had small fin

pitches (1.0–1.4 mm), and experiments were conducted up

to very low frontal air velocities (as low as 0.3 m/s). Listed

below are the major findings.

(1) The critical Reynolds number, where the fall-off of j

factor curve occurs, is insensitive to the louver angle,

and decreases as the Lp/Fp decreases. Existing

correlations on the critical Reynolds number do not

adequately predict the data.

(2) For high Reynolds numbers, j factors increase as the

fin pitch increases. For low Reynolds numbers,

however, the trend is reversed yielding cross-over of

j factor curves. Possible explanation is provided

considering the louver pattern at different fin pitches.

(3) The j factor increases as the louver angle increases.

At the small fin pitch (Pf = 1.0 mm), however, the

cross-over of j factor curves occurred.

(4) Different from the j factor, the friction factor does not

show the fall-off characteristic. The reason may be

attributed to the form drag by louvers, which offsets

the decreased skin friction at low Reynolds numbers.

The friction factor increases as the fin pitch decreases

and the louver angle increases.

(5) A new correlation predicts 92% of j factors and 94%

of f factors within ±10%.

References

1. Webb RL (1992) Air-side performance of enhanced brazed alu-

minum heat exchangers. ASHRAE Trans 98(2):391–410

2. Webb RL, Lee H (2001) Brazed aluminum heat exchangers for

residential air-conditioning. J Enhanc Heat Transf 8:1–14

3. Davernport CJ (1980) Heat transfer and fluid flow in louvered

triangular ducts. PhD thesis, Lanchester Polytechnic, UK

4. Achaichia A, Cowell TA (1988) Heat transfer and pressure drop

characteristics of flat tube and louvered plate fin surfaces. Exp

Therm Fluid Sci 1:147–157

5. Webb RL, Trauger PE (1991) Flow structure in the louvered fin

heat exchanger geometry. Exp Therm Fluid Sci 4:205–217

6. DeJong NC, Jacobi AM (2003) Localized flow and heat transfer

interactions in louvered fin arrays. Int J Heat Mass Transf

46:443–455

7. Achaichia A, Cowell TA (1988) A finite difference analysis of

fully developed periodic laminar flow in inclined louvered arrays.

In: Proceedings of second UK national heat transfer conference.

Glassgow, pp 883–888

8. Atkinson KN, Drakulic R, Heikal MR, Cow ell TA (1998) Two

and three dimensional numerical models of flow and heat transfer

over louvered fin arrays in compact heat exchangers. Int J Heat

Mass Transf 41:4063–4080

9. Tafti DK, Wang G, Lin W (2000) Flow transition in a multi-

louvered fin array. Int J Heat Mass Transf 43:901–919

10. Davernport CJ (1983) Heat transfer and flow friction character-

istics of louvered heat exchanger surfaces, in Heat Exchangers:

Theory and Practice, Hemisphere Pub, pp 387–412

11. Davernport CJ (1983) Correlation of heat transfer and flow fric-

tion characteristics of louvered fin. AIChE Symp Ser 79:19–27

12. Sunden B, Svantessen J (1992) Correlation of j and f factors for

multi-louvered heat transfer surfaces. In: Proceedings of third UK

national heat transfer conference, pp 805–811

13. Chang YJ, Wang CC (1996) Air-side performance of brazed

aluminum heat exchangers. J Enhanc Heat Transf 3(1):15–28

14. Sahnoun A, Webb RL (1992) Prediction of heat transfer and

friction for the louver fin geometry. J Heat Transf 114:893–900

15. Kim MH, Bullard CW (2002) Air-side thermal hydraulic per-

formance of multi-louvered fin aluminum heat exchangers. Int J

Refrigeration 25:390–400

16. ASHRAE Standard 41.1 (1986) Standard method for temperature

measurement, ASHRAE

17. ASHRAE Standard 41.2 (1987) Standard method for laboratory

air-flow measurement, ASHRAE

18. ASHRAE Standard 41.5 (1975) Standard measurement guide,

engineering analysis of experimental data, ASHRAE

19. Incropera FP, Dewitt DP (1990) Fundamentals of heat and mass

transfer, 3rd edn. Wiley, London

Table 5 Comparison of existing correlations with the present data

Investigators ±10

(%)

±30

(%)

±50

(%)

±100

(%)

Standard

deviation (%)

Davernport [11]

jexp/jpred 3.8 9.1 24.2 100.0 35.8

fexp/fpred 0.0 0.5 1.08 12.4 58.3

Achaichia and Cowell [4]

jexp/jpred 58.4 88.7 96.2 100.0 19.3

fexp/fpred 0.0 0.0 44.7 100.0 145.0

Sunden and Svantesson [12]

jexp/jpred 28.0 81.7 93.6 100.0 27.3

fexp/fpred 3.8 28.0 77.4 100.0 27.5

Sahnoun and Webb [14]

jexp/jpred 74.2 87.1 91.9 100.0 24.3

fexp/fpred 0.5 2.2 6.5 76.3 45.4

Chang and Wang[27]

jexp/jpred 0.0 65.1 88.2 100.0 58.2

Chang et al. [28]

fexp/fpred 5.9 28.0 72.0 100.0 27.6

Kim and Bullard [15]

jexp/jpred 5.3 85.6 95.8 100.0 23.0

fexp/fpred 23.0 64.7 96.2 98.4 21.4

This study

jexp/jpred 91.9 100.0 100.0 100.0 6.7

fexp/fpred 93.5 100.0 100.0 100.0 5.6


123

20. Gnielinski V (1976) New equations for heat and mass transfer in

turbulent pipe flows. Int Chem Eng 16:359–368

21. Schmidt TE (1949) Heat transfer calculations for extended sur-

faces. J ASRE Refrig Eng 4:351–357

22. Kays WM, London AL (1984) Compact heat exchangers, 3rd

edn. McGraw-Hill Pub, New York

23. Cowell TA, Heikal MR, Achaichia A (1995) Fluid flow and heat

transfer in compact louvered fin surfaces. Exp Therm Fluid Sci

10:192–199

24. Springer ME, Thole KA (1998) Experimental design for flow

field studies of louvered fins. Exp Therm Fluid Sci 18:258–269

25. Beamer HE, Ghosh D, Bellows KD, Huang LJ, Jacobi AM (1998)

Applied CFD and experiment for automotive compact heat

exchanger development, SAE 980426

26. Kim NH, Kim HJ (2007) Flow efficiency in louvered fin geom-

etries having large louver pitch to fin pitch ratio. Int J Air Cond

Refrig (submitted)

27. Webb RL (1991) Letters to the editor. Exp Therm Fluid Sci 4:374

28. DeJong NC, Jacobi AM (1997) An experimental study of flow

and heat transfer in parallel plate arrays: local, row by row and

surface average behavior. Int J Heat Mass Transf 40(6):1365–

1378

29. Chang YJ, Wang CC (1997) A generalized heat transfer corre-

lation for louver fin geometry. Int J Heat Mass Transf 40(3):533–

544

30. Chang YJ, Hsu KC, Lin YT, Wang CC (2000) A generalized

friction correlation for louver fin geometry. Int J Heat Mass

Transf 43:2237–2243


123

NH Kim, JP Cho, Air-side Performance of Louver-finned Flat Aluminum Heat Exchangers at a Low...

Documents

Transcript of NH Kim, JP Cho, Air-side Performance of Louver-finned Flat Aluminum Heat Exchangers at a Low...