Pressure Loss and Heat Transfer
Characterization of a Cam-
Shaped Cylinder at Different
Orientations
A. Nouri-Borujerdi
Professor
School of Mechanical Engineering,
Sharif University of Technology,
Tehran, Iran
e-mail: anouri@sharif.edu
Arash M. Lavasani
Professor
Science and Research Branch,
Islamic Azad University,
Tehran, Iran
e-mail: a_lavasani@iauctb.ac.ir
Pressure drag coefficient and heat transfer are experimentally in-
vestigated around a single noncircular cylinder in cross-flow un-
der angle of attack 0 deg 360 deg and Reynolds number
1.5 10
4
Re
eq
4.8 10
4
based on equivalent diameter of a cir-
cular cylinder. The results show that the trend of pressure drag
coefficient against the angle of attack has a wavy shape but the
wavy trend of the Nusselt number is smoother relative to the drag
coefficient behavior. It is found that for l / D
eq
= 0.4 and over the
whole range of the Reynolds number, the pressure drag coefficient
has a minimum value of about C
D
= 0.4 at = 30 deg, 180 deg,
and 330 deg and a maximum value of about C
D
= 0.9 at
= 90 deg and 270 deg. The corresponding value of the mean
Nusselt number to that of the equivalent circular tube is 1.05
Nu
cam
/ Nu
cir
1.08 at = 90 deg and 270 deg as well as 0.87
Nu
cam
/ Nu
cir
0.92 at = 30 deg and 180 deg.
DOI: 10.1115/1.2969259
Keywords: pressure drag, surface heat transfer, cam-shaped
cylinder, heat exchangers
1 Introduction
In contrast to the circular tubes, which cause severe separation
and large wake regions to produce high pressure drops, noncircu-
lar tubes of streamlined shapes offer high heat transfer and low
hydraulic resistance and consequently require less pumping
power.
Ota et al. 1,2 found that at Re 10
4
maximum and minimum
mean heat transfer coefficients around an elliptic cylinder with a
major axis parallel to the flow direction with axis ratios of 1:2 and
1:3 occurred in the range of 60 deg 90 deg and 0 deg
30 deg, respectively. The minimum mean heat transfer rate
was higher than that of a circular tube with equal circumferential
length. The drag coefficient was about 0.12 at Re= 4.8 10
4
and
= 0 deg and increased monotonically with and reached 1.8 at
=90 deg.
Ruth 3 measured pressure drop and heat transfer rate for a
lenticular tube bundle in the range of 10
3
Re 5 10
4
with a
transverse tube pitch-to-diameter ratio of 2. He found that the drag
was reduced by 70% in comparison with a circular tube bundle.
Merker and Hanke 4 measured heat transfer and pressure drop
along the shell-side of a tube bundle with oval-shaped tubes. They
showed that heat exchangers with oval-shaped tubes have consid-
erably smaller frontal areas on the shell-side in comparison with
circular tubes in the range of 10
3
Re 5 10
4
based on the
stream length.
Prasad et al. 5 reported heat transfer and pressure drop from
an aerofoil NACA-0024 in cross-flow for 2 10
4
Re 5 10
4
based on the equivalent diameter. They concluded that this shape
gives higher values of Stanton number to pressure drop coefficient
in comparison with a circular, lenticular, and oval tubes at Re
2 10
4
.
Badr et al. 6 numerically simulated the unsteady flow over an
elliptic cylinder with a major axis parallel to the flow direction at
different orientations. They obtained the total drag coefficient
equal to 0.8 at Re=3700 and 0.9 at Re=700 with a length ratio of
minor-to-major axis equal to 0.6. The form drag was 80–90% of
the total drag. Compared with a circular tube, the drag coefficient
was reduced between 10% and 20%.
Matos et al. 7 numerically and experimentally studied three
dimensional of staggered finned circular and elliptic tubes at
Re
L
= 852 and 1065, where subscript L is the swept length of a
fixed volume. Circular and elliptic arrangements with the same
flow obstruction cross-sectional area were compared on the basis
of maximizing the total heat transfer. The results illustrate that the
optimal elliptic tube arrangement exhibits higher heat transfer up
to 19% in comparison with the optimal circular tube arrangement.
The heat transfer gain and the relative total mass reduction of up
to 32% show that the elliptical arrangement has a potential to
deliver considerably higher global performance and lower cost.
Li et al. 8 numerically investigated the heat transfer enhance-
ment of three streamlined polymer tubes with fins of lenticular
and oval profiles. For Bi 0.3 and 2 10
3
Re 2 10
4
, the heat
transfer of oval-shaped tubes was higher than that of the circular
tubes. They showed that the teardrop tube had the highest effi-
ciency in comparison with the lenticular and oval tubes.
Bouris et al. 9 carried out experiments and numerical simula-
tions on a novel tube bundle heat exchanger with tube cross sec-
tion that contained a parabolic shape in front and a semicircular
one at the rear. The Reynolds number was in the range of 2.2
10
3
Re 4.1 10
3
based on the diameter of the bottom circu-
lar section of the tube. Their results indicate a higher heat transfer
level with 75% lower deposition rate and 40% lower pressure
drop.
Moharana and Das 10 gave an improvement on the analysis of
Li et al. 8. They analyzed conduction through shaped tubes with
a circular inner surface and a hydrodynamically shaped outer sur-
face by two different techniques. These two techniques were a
two-dimensional analysis as well as a one-dimensional approxi-
mate technique, which showed a closed agreement with the two-
dimensional analysis.
Table 1 summarizes the results of the previous works concern-
ing the pressure drag coefficient and the Nusselt number around a
streamlined single tube or tube bundle. All these noncircular tubes
have low pressure drag coefficient and high Nusselt number in
comparison with circular tubes with the same circumferential
length. Those tubes, which have cross-sectional area similar to a
teardrop, have more efficiency than those of the oval and lenticu-
lar tubes with less deposition rate of suspension materials on the
tube surface.
To give better understanding regarding the optimum shape for a
noncircular tube in which high heat transfer and/or low drag can
be achieved, this study has emphasized on cam-shaped tubes. This
shape provides ease of manufacturing and varying flow pattern
under different angles of attack in cross-flow.
Contributed by the Heat Transfer Division of ASME for publication in the JOUR-
NAL OF HEAT TRANSFER. Manuscript received January 4, 2007; final manuscript received
June 2, 2008; published online September 22, 2008. Review conducted by S. A.
Sherif.
Journal of Heat Transfer DECEMBER 2008, Vol. 130 / 124503-1 Copyright © 2008 by ASME
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