Flow over a Magnetically Suspended Cylinder in an Axial Free Stream

Flow over a Magnetically Suspended Cylinder
in an Axial Free Stream
Hiroshi Higuchi 1
Syracuse University, Syracuse, NY, 13244
Hideo Sawada. 2
Japan Aerospace Exploration Agency, Tokyo, 182, Japan
and
Pieter van Langen 3
University of Twente, Enschede, The Netherlands
AIAA-2005-1078
Axial flow over cylinder of varying fineness ratio (length to diameter ratio) was examined in air with the
magnetically suspension and balance system to avoid interference of model support. Above a moderately large
fineness ratio, the shear layer separated from the leading edge reattaches on the side surface and the streamwise
growth of the boundary layer causes the increased drag coefficient. As the fineness ratio is reduced, the shear layer
from the leading edge does not attach resulting in increased drag coefficient. Development of associated flowfield
was investigated in the fineness ratio raging from near unity to 8, and the Reynolds number from 6x10 4 to 1.8x10 5 .
I. Introduction
FLOW over a circular cylinder in an axial flow represents a canonical configuration to be applicable to aircraft
fuselages, missiles and road vehicles, etc. The drag coefficient of the cylinder aligned with the flow is listed in various
handbooks and textbooks (see, for example, Ref. 1). However, the original source dates back to Hoerner 2 who in turn
quoted Eiffel’s experiment 3 . Hoerner gives a compilation of data in Fig. 3-12 in his book. The present investigators
decided to take a new look into this problem involving this very well-defined geometry, with key parameters being the
length-to-diameter ratio (fineness ratio) and the Reynolds number. The resulting flow field, however, involves the
separated shear layer from sharp edges that may or may not attach at a given fineness ratio to form the boundary layer
development. The flow at the end is accompanied by the eventual flow separation followed by a recirculation region
and three-dimensional wake structure.
Since the flows about the front face, in the boundary layer and the wake of the axisymmetric body are all critical, the
traditional model support poses certain difficulties. In order to avoid any interference from model sting or other
support, the present experiment has been conducted using the 60 cm x 60 cm Magnetic Suspension and Balance
System at the Institute of Space Technology and Aeronautics, Japan Aerospace Exploration Agency. Precise model alignment
is easily implemented, and the instantaneous forces and moment acting on the entire body are directly measured as a
part of feed-back control system without introducing unnecessary interference or flow disturbance due to a
conventional force balance. In addition, the mean and turbulent wake velocity profiles were measured and the
momentum balance was checked against the measured drag. A new, more definitive set of drag coefficient variation in
the wide range of fineness ratio has been obtained, and the effect of the shear layer reattachment is investigated further
in detail with flowfield measurements.
1 Professor, Department of Mechanical and Aerospace Engineering, 141 Link Hall; hhiguchi@syr.edu, Associate Fellow.
2 Subgroup Leader, Innovative Testing and Fundamental Aerodynamics Subgroup, Aerodynamic Research Group, the Institute
of Space Technology and Aeronautics, Member .
3 Undergraduate Student, Department of Engineering Technology.
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American Institute of Aeronautics and Astronautics

II. Experimental Set Up
A. Magnetic Model Suspension, Force Balance and Wind Tunnel
The experiment was conducted using the Magnetic Suspension and Balance System at the Institute of Space
Technology and Aeronautics, Japan Aerospace Exploration Agency (formerly the National Aerospace Laboratory). The system
was developed by the second author and is described in Ref. 4. Figure 1 shows schematically the coil arrangement used
in the system, and specifications of the individual coils are listed in Table 1. The position and attitude of the model
were monitored by two CCD cameras oriented perpendicular to each other. Two colors and filters were used to
separate reflected lights in two directions. The position was controlled at a feedback frequency of 248Hz. The magnet
current was calibrated against known force applied through pulleys and weights for each model. The calibration was
repeatable within 0.02%. The models were made of aluminum alloy and housed a rod-shaped magnet along their
centerline. The balance system was installed in the subsonic wind tunnel with a 60cmx60cm test section. The available
flow speed ranges from 10 to 35 m/s. The free stream turbulence level was less than 0.05%. The measured flow angle
at the center is 0.05 degree in downwash and 0.15 degree about z-axis shown in Fig. 1. Further detail of the MSBS and
the wind tunnel can be found in Ref. 4.
model
coil # turn number size purposes
0,9 50 620 x 620 drag
1,3,5,7 97 + 97 200 x 200 lift,
pitch moment
side force ,
yawing moment,
rolling moment
130V, 120A in continuous mode … 3 units
130V, 60A in continuous mode … 4 units
5 DOF for models with a main magnet only
6 DOF for special models with pair magnets
2,4,6,8 100 200 x 200
coil drive
units
control
Table 1 Specifications of the 60cm MSBS (Ref. 4)
position sensing camera
Fig. 1 MSBS coil arrangement (not to scale,
only one camera is shown)
B. Test Models
Figures 2 illustrates cylindrical models supported magnetically in the test section. In addition to the model edges, the
sensing cameras use a vertical stripe in the middle to detect the model position and attitude. Instantaneous model position
was monitored and held within ±0.2mm. In order to provide a wide range of the fineness ratio, models with different
diameters were used. One had 45mm diameter and shared the same center section enclosing the magnet. By changing the end
caps of different lengths, nine fineness ratios between 4.13 and 8.13 were achieved. Second set of model had a diameter of
85mm and the third 110mm. These larger diameter models provided the fineness ratio down to 1.272. An additional model of
25mm diameter and fineness ratio of 6 was also used. The Reynolds number based on the diameter ranged from 60,000 to
100,000.
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American Institute of Aeronautics and Astronautics

Fig. 2(a) A magnetically supported 45mm diameter cylinder model
Fig. 2(b) A magnetically supported 85mm diameter cylinder model
III. Results and Discussion
A. Wake behind magnetically supported cylinder
The mean velocity distribution behind the L/D=5.02 model is presented in both vertical (z) and horizontal (y)
directions in Fig. 3. The distance is measured from the trailing edge of the model. An earlier test employed the PIV
system on loan and the results indicated excellent results in the wake while limiting the illumination away from the
position sensing cameras. Results from another PIV measurement in water will be also discussed oater. However, these
velocity measurements relied on a more conventional total head probe as well as a hot-wire probe. Naturally, the
results are limited to regions where these instrumentations are applicable. Figure 3 nonetheless demonstrates excellent
flow axisymmetry measured with the total head probe. The results clearly benefited from the absence of the model
support in the present system. The symmetry of the flow and the repeatability of the measurements are further
illustrated in Fig. 4 by vertical and horizontal probe traverses.
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American Institute of Aeronautics and Astronautics

80
u/U
65
50
35
20
5
z(mm)
-10
-25
-40
-55
-70
1.00 -1.02
0.98 -1.00
0.96 -0.98
0.94 -0.96
0.92 -0.94
0.90 -0.92
0.88 -0.90
0.86 -0.88
0.84 -0.86
0.82 -0.84
0.80 -0.82
-85
-70
-55
-40
-25
-10
5
20
35
50
65
80
-85
y(mm)
Figure 3 Mean axial velocity (u/U) distribution in the wake of the 45mm diameter cylinder,
L/D=5.02 at x/D= 6.11 (Re D =100,000)
1.05
1.00
0.95
y traverse
y traverse (mirror image)
z traverse (mirror image)
z traverse
u/U
0.90
0.85
0.80
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
y/D or z/D
Figure 4 Mean velocity profiles along 2 axes in the wake
a 45mm diameter L/D=5.02 axial cylinder at x/D= 6.11
The streamwise variation of the mean velocity in the wake was measured behind the 25mm diameter cylinder
with a single hot wire probe, and the results are shown in Fig. 5. When the virtual origin of the wake was taken to be
1.3D downstream of the trailing edge, the velocity defects shown in Figs. 4 and 5 followed the established x^(-1/3)
law for axisymmetric wakes.
1.0
u/Umain
0.8
0.6
0.4
z=1mm
x=0.04D
x=2D
x=4D
x=10D
0.2
0.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
y/D
Figure 5.
Velocity distributions across the wake of 25mm diameter cylinder (L/D=6)
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American Institute of Aeronautics and Astronautics

(y - D/2)/delta
2.0
1.5
1.0
0.5
L/D=4.13 (45Dia.) delta=32.5mm
L/D=5.02 (45Dia.) delta=32.5mm
L/D=6.00 (25Dia.) delta=19.0mm
L/D=8.13 (45Dia.) delta=41.0mm
0.2
0.0
0 0 0 0 1 1 1 1
u/U
Figure 6. u/U vs.[y-(D/2)]/δ, effect of fineness ratio)
(Re D =50,000 for 25mm dia, 100,000 for 45mm dia.)
2.0
1.5
L/D=4.13 (45Dia.) delta=32.5mm
L/D=5.02 (45Dia.) delta=32.5mm
L/D=6.00 (25Dia.) delta=19.0mm
L/D=8.13 (45Dia.) delta=41.0mm
(y - D/2)/delta
1.0
0.2
0.5
0.0
0 0 0 0
0.8
u rms /U
Figure 7. u rms /U vs. .[y-(D/2)]/δ, effect of fineness ratio
The boundary layer leaving the cylinder at the trailing edge was further investigated for various fineness ratios.
The mean velocity profiles and the turbulence intensity normalizes by the boundary layer thickness are shown in Fig.
6 and Fig. 9, respectively. Ota 4 investigated the boundary layer over a sting-mounted sharp-edged cylinder, and his
velocity profiles at x/D=3.1, 5.1, and 7.1 from the leading edge are very consistent with the present data at the
trailing edge (L/D=4.13-8.13). Ota’s experiment corresponds to Re D =5.62x10 4 and the Reynolds number for the
measurements in Figs. 6 and 7 was 5x10 4 for the 25mm cylinder and 1x10 5 for the 45mm cylinder. The oil flow
visualization and Ota’s measurement indicated a separation bubble from the leading edge ending with flow
reattachment approximately at 1.5-1.6 diameter downstream. The mean velocity profiles further downstream of the
reattachment are indicative of a developing turbulent boundary layer. The turbulent intensity profiles are also in
general agreement between the two experiments, though the present data are at a somewhat higher level. The power
spectrum density in the immediate wake shear layer showed the distribution typical of turbulent boundary layer
devoid of any spectral peak, but at x/D=4, a spectral peak was evident at Strouhal number fD/U=0.185 which was
indicative of a helical mode wake oscillation.
C. Force Measurement
The magnetic balance was calibrated against the known weight for each model. The uncertainty of the drag
coefficient measurement at Reynolds number 10 5 , for example, was estimated to be ±0.005.
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American Institute of Aeronautics and Astronautics

1.00
0.95
L/D = 4.13
L/D = 6.13
L/D = 8.13
CD
0.90
0.85
0.80
0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Reynolds number (million)
Fig. 8
Drag coefficient versus Reynolds number at 3 large fineness ratios.
Figure 8 shows that the measured drag coefficients for 3 fineness ratios are nearly constant over the range of Reynolds
number between 60,000 and 100,000. On the other hand, the fineness ratio has shown a clear influence on the drag
coefficient as shown at the top of Fig. 9. In order to estimate the contributions to the total drag from the front face pressure,
the base pressure and the boundary layer drag, Fig. 9 shows the total drag, the momentum loss based on the boundary layer
measurement (see Fig 7), and the estimated skin friction drag. The skin friction drag was simply estimated from the empirical
formula for the flat plate turbulent boundary layer (1/5 th power to the Reynolds number based on the length.) Here, the
separated flow at the front corner is considered to attach at 1.5 diameter downstream, based on the oil flow visualization,
which is consistent with Ota’s observation 5 . The differences among the three lines are, in effect, estimates of the front
pressure and the base pressure, respectively, and they are nearly independent of the fineness ratio.
1.0
total drag (measured)
CD based on momentaum thickness
friction drag
0.8
C D = 0.0182(L/D) + 0.7809
base drag
0.6
C D
0.4
C D = 0.0197(L/D) + 0.4331
forebody pressure drag
0.2
0.0
Fig. 9.
C D = 0.0167 (L/D) - 0.0071
friction drag
0 1 2 3 4 5 6 7 8
L/D
Drag coefficient based on momentum thickness versus fineness ratio
(simple line fit is also given.)
9
Figure 10 summarizes the present measurements and historical as well as classical data. The first experiment by
Eiffel 5 was conducted by dropping the test models from the Eiffel tower along a guide cable. The second Eiffel data 3
were collected in his wind tunnel with models cable-mounted in the test section. Apparently Hoerner used Eiffel’s
second data (not as listed in his book) and subtracted the estimated skin friction and presented the data. It is of interest
that these Hoerner’s data have been quoted for many decades in many articles, reference books and textbooks, not
necessarily after critical evaluation. Robertson et al. 7 carried out new wind tunnel measurements to study the effect of
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American Institute of Aeronautics and Astronautics

1.2
1.1
1.0
Eiffel 1913 (30cm Dia.)
Eiffel 1913 (15cm Dia.)
Roberson
JAXA/NAL(45Dia)
JAXA(85Dia)
JAXA(110Dia)
Cd
0.9
0.8
0.7
0.6
0 1 2 3 4 5 6 7 8 9
L/D
Fig. 10. Drag coefficient variations with fineness ratio (The present data are all at Re D =1x10 5 )
the free stream turbulence on the flow reattachment and the drag at small fineness ratios. Original technical results are
given, for example in Ref. 7, but summary of data is listed in Roberson and Crowe’s textbook 8 for Re D >10 4 are used in
this figure. The present series of experiment are expected to provide modern, more definitive results on how the
flowfield and drag vary with the wide range of fineness ratio.
D. Discussion of results and additional flowfield measurement in water.
The lower drag coefficients obtained in the fineness ratio L/D=1-2 is expected to represent flow reattachment on the
side surface. Oil flow visualization was conducted on the long magnetic suspended model of the 45 mm diameter. The
reattachment line was located near 1.6-1.7 diameters downstream of the leading edge. In order to obtain better
ascertain the flowfield, an additional set of experiment was conducted in a Syracuse University water channel. In lieu
of the magnetic suspension system, the model was sting-mounted from downstream. The sting diameter was kept small
(635mm) compared to the model diameter of 77mm. The cross-flow strut was also kept sufficiently far downstream.
The velocity vector field was measured using a DANTEC particle image velocimeter (PIV) system at reduced
Reynolds number between 10,000 and 30,000. Seeding was provided by 20µm PSP particles uniformly mixed in the
flow. Figure 11 shows the mean velocity vector field together with a short model of the fineness ratio of 0.67. One can
clearly see that the separating shear layer remains separated forming a large reverse flow region in the wake. Figure 12
on the other hand shows the mean velocity vector past a long cylinder of L/D=3. The separating and reattaching shear
layer and the recirculating flow within the separation bubble are clearly seen in the measurement. Even though Ota
used the hot wire anemometer on a rear-mounted cylindrical model and its use in the vicinity of this type of separating
flow may be of suspect, the deduced streamlines and the location of the flow reattachment are in very good agreement
with the current PIV measurement. The behavior of the boundary layer development subsequent to the flow
reattachment and the drag variation with the fineness ratio are in accordance with the velocity profile measurement in
Fig. 7 and Fig. 10, respectively. At an intermediate fineness, L/D=1.5, the time averaged separated shear layer attached
in the immediate vicinity of the trailing edge as shown in Fig. 13. At higher Reynods number of 20,000 and 30,000, the
shear layer was found to attach slightly upstream, indicating the higher sensitivity to the Reynolds number. This is
close to the region where the drag coefficient reaches its minimum with respect to the fineness ration as shown in Fig.
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American Institute of Aeronautics and Astronautics

10. Roberson et al 7 applied as high as 10% free stream turbulence and observed the reduction of drag due to earlier
reattachment of separated shear layer at L/D=1. Koenig and Roshko 9 placed a disk ahead of the cylinder to control the
separating shear layer and reattachment. Preliminary numerical simulations with the implicit LES method 10 showed
general qualitative agreement with the present experiment but the size of the leading edge separation bubble was
over-predicted.
1000
pix
900
800
70 0
600
50 0
400
300
200
10 0
0
Image size: 1280×1024 (0,0), 8-bits (frame 1)
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Analog inputs: -10 000; -10 000; -10 000; -10 000
0 10 0 200 300 400 500 600 700 800 900 1000 110 0 pix 1200
Figure 11. Mean velocity field (PIV) and the model (L/D=1.67) at Re D =10,000.
550
500
450
400
350
300
250
200
150
10 0
50
Statistics vector map: Masked vectors, 79×127 vectors (10033)
Size: 1280×1024 (0,0)
A l i t 7 280 7 217 7 236 7 192
0 50 10 0 150 200 250 300 350 400 450 500 550 600 650 70 0 750 800 850 900 950 1000 10 50 110 0 1150 12 0 0 pix 12 50
Figure 12. Mean velocity above the L/D=3 cylinder at Re D =10,000
400
pix
350
300
250
200
150
10 0
50
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Size: 1280×1024 (0,0)
Burst#; rec#: 1; 1 (1) Date: 11/5/2004 Time: 12:07:13:375AM
350 400 450 500 550 600 650 700 750 800 850 900 950 pix 1000
Figure 13. Mean velocity above the L/D=1.5 cylinder at Re D =10,000
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0 10 0 200 300 400 500 600 70 0 800 900 10 0 0 110 0 pix 1200
1000
pix
900
800
70 0
600
50 0
400
300
200
10 0
0
Vector map: Masked vectors, 79×63 vectors (4977), 497 rejected, 323 substituted
Burs t#; rec#: 7; 1 (7), Date: 11/3/2004, Tim e: 01:02:16:812PM
Analog inputs: 10 000; 10 000; 10 000; 10 000
Figure 14. Instantaneous velocity vector over the L/D=3 cylinder model, Re D =10,000
Even though the mean velocity profiles of the separating and reattaching flow looks well-defined in velocity vector
as well as in mean streamlines (not shown for brevity), it is worthwhile to note the complex flowfield involved. Figure
14 is an instantaneous velocity vector used to compute the averaged velocity profile in Fig. 12, and it shows large-scale,
convoluted eddy motion that will be pertinent in investing the possible control of the shear layer at wide Reynolds
number range and turbulence level.
The PIV measurement of the wake behind the sting-mounted model was also performed in water. When the wake
flow was measured with the sting placed upstream, a disturbance from the upstream was detectable in the
instantaneous velocity field. The flowfield measurements in the wake using a PIV system behind a magnetic suspended
model are of critical importance and are being scheduled.
IV. Conclusion
The drag coefficient variation of circular cylinder placed in an axial flow was obtained over a wide range of fineness
ratio. In order to avoid flow interference with any model support and to insure axisymmetry of the flow, the
experiment was conducted using a magnetic suspension and balance system. The flow field in the wake, boundary
layer as well as the behavior of the separated shear flow from the leading edge was studied to collaborate the measured
drag variation.
Acknowledgements
The present study was supported by the Japan Society for Promotion of Science, Ministry of Education and Culture,
Japan. Authors acknowledge assistance of Mr. Tetsuya Kunimasu and Dr. Shinichi Suda during the JAXA experiment.
Author PVL performed the water channel experiment at Syracuse University with author HH and they thank Prof.
Harry Hoeijmakers at Twente University for his arrangement.
References.
1 Blevins, R.D., Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Company, NY, 1984.
2 Hoerner, S. F., Fluid Dynamic Drag, published by author, 1958, p.3-12.
3 Eiffel, G., “The Resistance of the Air and Aviation,” (translated by J. C. Hunsaker), London: Constable Co., Boston: Houghton,
Mifflin & Co. 1913.
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American Institute of Aeronautics and Astronautics

4 Sawada, H., Kunimasu, T., “Status of MSBS Study at NAL,” 6 th International Symposium on Magnetic Suspension Technology,
Oct. 7-11 2001, Tulin, Italy, pp.163-168.
5 Ota, T., ”An Axisymmetric Separated and Reattached Flow on a Longitudinal Blunt Circular Cylinder” Journal of Applied
Mechanics, June 1975, pp. 311-315.
6 Eiffel, G., “Recherches Expérimentales sur la Résistance de l'Air Exécutées à la Tour Eiffel,” L. Maretheux, Impimeur, 1907
7 Roberson, J. A., Lin, C. Y., Rutherford, G. S., and Stine, M. D., “Turbulence Effects on Drag of Sharp-Edged
Bodies,” Journal of the Hydraulic Division, Proceedings of ASCE, 1972, pp. 1187-1209.
8 Roberson, J. A. and Crowe, C. T., Engineering Fluid Mechanics, 6 th edition, John Wiley & Sons, Inc., 1997.
9 Koeing, K. and A. Roshko, A., ”Study of Geometrical Effects on the Drag and Flow Field of Two Bluff Bodies Separated by a
Gap,” J. Fluid Mech. Vol. 156, 1985, pp.167-204.
10 Higuchi, H. , Sawada, H., Suenaga, Y., Dohi, S. , and Kawamura, T. “Drag of Truncated Cylinder in Axial Flow,” Bulletin of the
American Physical Society, Vol. 49, No. 9, Nov. 2004, p.78.
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