Transverse flow over a wavy cylinder
Anwar Ahmed and Byram BaysMuchmore
Citation: Physics of Fluids A: Fluid Dynamics (1989-1993) 4, 1959 (1992); doi: 10.1063/1.858365
View online: http://dx.doi.org/10.1063/1.858365
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Transverse
flow over a wavy cylinder
Anwar Ahmed and Byram Bays-Muchmorea)
Department of Aerospace Engineering, Texas A&M
University, College Station, Texas 77843-3141
(Received 15 May 1991; accepted 13 May 1992)
Transverse flow over a wavy cylinder was investigated experimentally; surface-pressure
distributions and flow visualizations were obtained for a set of wavy cylinders with different
axial wavelengths. Significant spanwise pressure gradients were present, resulting in
three-dimensional separation lines and the formation of streamwise trailing vortex structures
near the geometric nodes. Despite the symmetry of the geometries, the separated Sow
structures near the geometric nodes were distinctly asymmetric a large fraction of time.
Integration of the pressure data revealed greater sectional drag coefficients at the
geometric nodes than at the geometric saddles.
1. INTRODUCTION
Unsteady flow fields associated with general threedimensional, bluff-body separation and transitional or turbulent wakes are still too complex to be determined using
the available computational tools. The current work is part
of a program to study the physics of such flows experimentally, with the goal of aiding in the development of engineering tools. In recent years greater attention has been
focused on the three-dimensional phenomena present in
the nominally two-dimensional flow over a right circular
cylinder. l-3 In the current work three-dimensionality was
explicitly introduced into the flow field by the wavycylinder geometry shown in Fig. 1. This geometry was
identified as a natural extension of the right-circularcylinder geometry for a study of three-dimensional separation and wake development. This paper reports on some
the salient characteristics of the wavy-cylinder flow field.
The only information available in the literature on
wavy-cylinder
flows
concerns
the attachment-line
boundary-layer behavior between nodal and saddle points
of attachment. Brown,4 Cooke and Robbins, and more
recently von Kerczek6 solved the laminar boundary-layer
equations for flow from nodal to saddle points of attachment using a variety of solution techniques. They all found
that for waviness of sufficiently small amplitude, the entire
boundary layer flows from geometric node to geometric
saddle without separation. For amplitudes greater than
this “borderline case,” the earlier works speculated significant separation would occur, disrupting the outer flow.
von Kerczek’s calculations also predicted that reversed
flow would occur (directed away from the saddle and toward the node) but that it would be limited to the bottom
of the boundary layer and not disrupt the outer flow. These
efforts were all based on various assumed forms for the
pressure distribution from nodal to saddle points of attachment, as there were no prior experimental data available
for the pressure distribution over a wavy cylinder.
‘)Present address: The Boeing Company, Seattle, Washington 98124.
II. DESCRIPTION OF EXPERIMENTS
A. Model geometries
The terminology used to describe the wavy cylinders is
shown in Fig. 1. The axial locations of maximum diameter
are hereafter termed “geometric nodes” and the axial locations of minimum diameter are termed “geometric saddles.” A right-circular cylinder and four wavy cylinder
models were used in the wind-tunnel and water-tunnel
tests. The wavy cylinders (shown in Fig. 2) are described
by the equation:
R ,ocal=Rmean-A
cos(2rZ/j).
For each of the four cylinders R,,,, was 3 1.75 mm and
A was 6.35 mm; the four different wavelengths (A> were
76.2, 101.6, 127.0, and 152.4 mm. Hereafter the cylinders
are referred to by the appropriate value of wavelength/
mean diameter (/z/D): either 1.2, 1.6, 2.0, or 2.4.
The cylinders were each slightly over 610 mm long.
Each cylinder spanned the height of the wind tunnel and
extended from the floor of the water tunnel to a point
above the waterline. The base geometry of each cylinder
(the lowest 20 mm) was slightly different as shown in Fig.
2. The spanwise-waviness geometry abruptly changed to a
constant 76.2 mm diameter cylinder for the /z/D= 1.2, 1.6,
and 2.0 cylinders while the UD=2.4
cylinder base ended
smoothly near a geometric node.
B. Wind-tunnel
tests
Boundary-layer
transition
and surface-pressuremeasurement tests were conducted in the Texas A&M 2
~3 ft low-speed wind tunnel at a Reynolds number of
20 000 based on mean cylinder diameter. Transition was
detected using a Pitot probe connected to a set of earphones; turbulent shear layers were identified by an audible
hiss reflecting rapid variations in total pressure. This
method of transition detection, despite being intrusive,
proved to be adequate and far easier to use than alternatives such as hot-film sensors, sublimating chemicals, and
liquid crystals.7-‘0
@ 1992 American institute of Physics
1959
0899-8213/92/091959-i
0$04.00
Phys. Fluids A 4 (9), September 1992
1959
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seven diameters upstream of the cylinder revealed a spanwise free-stream velocity variation of up to 1%. The pressure coefficient was calculated using C,= ( P-Pf,)/Qf,
where Q,, was calculated for each pressure tap using the
free-stream velocity measured upstream at the spanwise
location of the tap (rather than using one averaged value
for Qf,) . This procedure had a maximum effect of changing
C, by 0.02. Using the symmetry of the wavy-cylinder geometry, all data presented are averages from measurements
at positive and negative angular locations. These C, values
agreed within 0.02 (or 2% of the free-stream dynamic
pressure value) for 6 less than to 28” (see Fig. 1 for the
definition of angle 6) and within 0.04 everywhere else with
a few exceptions occurring for 6 above 60”, primarily in the
post-separation regions. Further descriptions of the wind
tunnel and instrumentation
hardware are given elsewhere.”
Geometric Node
Geometric Saddle
FIG. 1. The geometry and coordinate system of the wavy cylinders.
Surface pressures were measured using 11 pressure
taps on each wavy-cylinder model. The taps were spaced
every O-15/2,extending from one geometric saddle to a geometric node 1.51 further along the span. Because of the
symmetry of the geometry, the data were combined to give
the pressure distribution over a typical half-wavelength
with pressure measurements every 0.05d along the span.
[This procedure assumes the asymmetric separation structures near the nodes (discussed later) were either symmetric in a time-averaged sense or else had negligible effect on
the surface pressure distribution.] The pressure distribution over the entire surface of each wavy cylinder was obtained by rotating the model 360” in 4” increments.
The only corrections applied to the data were to account for a spanwise variation in free-stream dynamic pressure. A survey of the wind-tunnel test section conducted
C. Water-tunnel
tests
The flow-visualization data were obtained in the Texas
A&M University 2 X 3 ft water tunnel. The tunnel has a
test section velocity range of 61 to 610 mm/set. The empty
test-section turbulence intensity is less than 1.0% for velocities up to 305 mm/set (the highest velocity used in the
current work). The wavy-cylinder surface-flow behavior
was observed by injecting a mixture of food coloring and
water through the pressure taps described earlier. The
pressure on the dye injection line to each tap was regulated
separately to the minimum value required to produce a
visible dye line. Dye was also painted onto the surfaces of
the cylinders and allowed to dry prior to insertion in the
water tunnel. The surface-flow separation behavior was
then observed as the dye was washed away.
The behavior of the attachment-line flow for each cylinder was observed with and without a wake splitter plate
installed. The splitter plates had serpentine edges to fit the
wavy cylinder model geometries and extended seven diameters downstream from the centers of the cylinders.
The location of the separation line was determined by
projecting a laser beam from the side of the water tunnel
and measuring the distance required to move the beam
from a reference location (X=0,
see Fig. 1) to the
separation-line location. For these measurements the separation line was identified using the injected-dye streaklines.
Ill. RESULTS AND DISCUSSION
A. Attachment-line
FIG. 2. Wavy-cylinder models used in the wind-tunnel and water-tunnel
tests. From left to right the values of /z/D are 1.2, 1.6, 2.0, and 2.4. A
right-circular cylinder is also shown.
1980
Phys. Fluids A, Vol. 4, No. 9, September
1992
flow
For each cylinder tested, dye injected from the surface
showed the attachment-line location to oscillate at the von
K&man shedding frequency: dye injected near 8=0” was
carried over alternate sides of the cylinder. The oscillation
was much more dramatic for Re= 10 000 and 20 000 than
for Re=5 000. For the wavy cylinders this motion was
observed everywhere along the attachment line, from geometric node to geometric saddle, and was in phase over at
A. Ahmed and B. Bays-Muchmore
1960
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0
AttachmentLine, 0 = 0 deg.
h/D
0 = 1.2
0 = 1.6
A = 2.0
v = 2.4
-EC.2
-- = Borderline
Case
Saddle
FIG. 3. The attachment-line pressure distribution measured on each of
the cylinders. The dashed curve is the theoretical borderline pressure
distribution for the onset of attachment-line boundary-layer separation by
von Kerczek.6
(b)
least one half-wavelength. In each case it was possible to
suppress the attachment-line oscillation by inserting a
splitter plate along the wake centerline. This demonstrated
that the attachment-line oscillation was due to induced
effects of the primary wake instability, rather than a local
instability at the attachment line. These results are consistent with those previously reported for unsteadiness at the
attachment line of right-circular cylinders.12-‘7 The splitter
plates were not used in any of the other tests reported here.
The mean attachment-line pressure distributions for all
four wavy cylinders are shown in Fig. 3. The pressure
variation is fairly insensitive to the spanwise wavelength,
although there is a slight trend of increasing amplitude
with decreasing cylinder wavelength, particularly near the
geometric node. Each attachment-line pressure distribution is skewed toward the node, indicating the outer flow
acceleration is more rapid near the node than the subsequent deceleration near the saddle.
As discussed earlier, if the amplitude of the waviness is
large enough, the attachment-line boundary layer leaving
the node will not reach the saddle. The theoretical pressure
distribution (taken from Ref. 6) for the onset of boundarylayer separation along the attachment line is also shown in
Fig. 3. The data for all the cylinders tested fall well below
this “borderline case,” both in amplitude and maximum
adverse pressure gradient. The flow visualization confirmed that there were no disruptions along the attachment
line. For both the oscillating and nearly steady flow, the
spanwise flow of dye along the attachment line was di-
FIG. 4. Dye injected from the surface of the wavy cylinders at Re
= 10 OC0 at various angular locations. (a) 0=0”. (b) 0=30”.
rected from geometric node to geometric saddle for each
wavy cylinder.
B. Boundary-layer
flow
The boundary-layer region on each cylinder extended
from the attachment line near 8=0” to the primary separation line near 6=80“. Figure 4 shows streaklines produced by injecting dye from the surfaces of the A/D= 1.2
and 2.4 cylinders at Re= 10 000. The dye lines show that
for each cylinder the flow was primarily circumferential,
but did contain a spanwise velocity component directed
from geometric node to geometric saddle until just before
the separation line, where the flow turned back toward the
node. This spanwise flow was more pronounced for the
shorter wavelength cylinders. The surface-streakline patterns showed no significant variation over the Reynolds
number range tested (5000 to 20 000). The entire streakline patterns appeared to be slightly unsteady due to the
von K&man vortex shedding, significantly more so for Re
= 10 000 and 20 000. The movement did not significantly
affect the appearance of the streaklines ahead of separation.
It was expected that the boundary layers in these experiments would not transition via Tollmien-Schlichting
waves prior to separation because the test Reynolds number (Re = 20 000) was an order of magnitude lower than
A. Ahmed and B. Bays-Muchmore
1961
Phys. Fluids A, Vol. 4, No. 9, September 1992
1961
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0
Node
no
0180
Lx&&&4
2.0
000002.4
RCC
Saddle
100
75
Sepa?ation85Ang1~0
(degy
FIG. 7. The separation line locations measured for each of the cylinders
at Re=20 Ooo.
tions characteristic of turbulent boundary layers were not
present on the cylinder surfaces.
FIG. 5. Boundary-layer separation line of a right-circular
cylinder.
C. The boundary-layer
the critical Reynolds number for a “two-dimensional” cylinder. However, the spanwise flow over the wavy cylinders
introduced the possibility of transition triggered by crossflow instabilities. The Pitot-probe audible tests revealed
that the boundary layer did remain laminar up to separation for each cylinder. This result justifies the use of the
intrusive Pitot-probe technique: the presence of the probe
is expected to enhance, rather than suppress, transition
upstream in the boundary layer. Distinct frequencies were
detected above the cylinder surfaces near the separation
lines (corresponding to the separation structures described
later) but the broadband frequency total pressure fluctua-
separation
line
The structure of the separation line was observed by
painting dye onto the surface of the cylinder and allowing
it to wash off. As shown in Fig. 5, the separation line for a
right-circular cylinder was found to be very crisp and uniform (“two dimensional”) along the central 60% of the
span, in agreement with past work at subcritical Reynolds
numbers.’ As shown in Fig. 6, the wavy-cylinder separation lines were clearly three dimensional, originating at the
geometric saddles at approximately 8 = 75” and terminating
near the geometric nodes at approximately 8=92”. As seen
from the measured separation-line locations given in Fig. 7,
the distortion of the separation line was greater for the
shorter wavelength cylinders.
An interpretation of the topology of the flow field near
the wavy-cylinder boundary-layer separation line is offered
in Fig. 8 (where S and F denote saddles and foci in the
:
Ix
1
h/D
FIG. 6. Boundary-layer
1962
~&+I,
= 1.2
separation line of a wavy cylinder.
Phys. Fluids A, Vol. 4, No. 9, September
1992
I
FIG. 8. Topology of the velocity field near the wavy-cylinder boundarylayer separation line.
A. Ahmed and B. Bays-Muchmore
1962
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s
s
F
N
F
s
s
I:
S
S
@
ill
FIG. 9. Kinematically possible topologies of the surface shear-stress field
near the geometric node of wavy cylinder.
topology of the surface shear-stress field). That there exists
a saddle point of separation at each geometric saddle, and
that the boundary-layer fluid rolls up into streamwise vortical structures near each geometric node is quite clear
from the earlier figures and all of the flow-visualization
tests conducted. Less clear, due to the nature of the watertunnel flow-visualization techniques, are the details of the
singularity (or singularities) in the surface shear-stress
field at the geometric node. Several possible alternative topologies for the separating flow near the geometric node
are shown in Fig. 9 (where N denotes an ordinary node in
the surface shear-stress field). Dye patterns consistent with
each of these topologies were observed during the experiments. In cases where there appeared to be two trailing
vortices as suggested in Fig. 8, the two consistently combined into a single structure (see Fig. 6) resulting in an
asymmetric flow pattern despite the symmetric geometry.
D. Complete
surface
pressure
distributions
An overview of the mean static pressure distribution
over each of the wavy cylinders is presented in Fig. 10,
where the surface contours were determined based on linear interpolation between the data points and the mean
circumference was used in scaling the lengths of the axes.
These contour plots show that the pressure drops more
quickly and attains more negative values over the geometric saddles than over the geometric nodes. The pressure
contours indicate that the flow also separates earlier at the
geometric saddles than at the geometric nodes. Beyond the
primary separation region, especially in the range from
0= 1 lo” to 150”, the contour lines are roughly parallel to
the axes of the cylinders. From 8= 160” to 180” each cylinder shows a region of lower pressure near the geometric
node.
The circumferential pressure distributions for all of the
cylinders are plotted together in Fig. 11. At the geometric
saddle [Fig. 11 (a)] each wavy cylinder shows a more rapid
pressure drop, an earlier, higher suction peak, and an earlier separation than the right-circular cylinder. These effects become more pronounced as cylinder wavelength decreases, except for the lower suction peak visible for the
A./D= 1.2 cylinder. Halfway between geometric node and
saddle [Fig. 11 (b)] the circumferential pressure distribu-
tion for each wavy cylinder closely matches that for the
right-circular cylinder. At the geometric node [Fig. 11 (c)]
the trends from Fig. 11 (a) are reversed: the wavy cylinders
show a more ‘gradual pressure drop, to a ‘later -and less
extreme suction peak and a later separation.
In all of these figures the spanwise-averaged basepressure coefficient is slightly lower (more suction) for the
/z/D= 1.6 cylinder and slightly higher (less suction) for
cylinder. These effects are likely due to the
the A/0=2.4
cylinder end conditions; each of the wavy cylinders intersected the wind-tunnel ceiling at a different location between node and saddle. Williamson and Roshkoi8 have
shown that for a cylinder at Reynolds numbers of 105 and
302, the end conditions can have a significant effect on the
oblique nature of the von K&man vortex shedding and the
value of the base-pressure coefficient, especially within 20
diameters of the ends of the cylinder. The results of Fig. 11
indicate that the spanwise-mean base-pressure coefficient
for a wavy cylinder of aspect ratio 9.6 is more sensitive to
the geometry at the cylinder-wall interface than to the
local geometry of the waviness, even at a Reynolds number
as high as 20 000 where the wake is highly three dimensional.
The spanwise pressure gradients are shown in Fig. 12.
The attachment-line pressure distribution given in Fig. 3 is
repeated in Fig. 12(a) on the same scale as the rest of the
plots in Fig. 12. By 8=20” [Fig. 12(b)] the spanwise pressure gradient is favorable from node to saddle, and the
increase of this gradient with decreasing cylinder spanwise
wavelength is visible. The spanwise gradient grows until
8= 52” [Fig. 12(c)]. The variation of spanwise pressure
gradient with wavelength is even more pronounced ‘iii
physical dimensions than it appears to be in Fig. 12(c),
since the abscissa in the figure is nondimensionalized’ by
the spanwise wavelength. For angles between 56” and 80”
Zig
the point of minimum pressure moves from saddle to node.
The typical case of f3= 72” is shown in Fig. 12(d) . At
8 = 80” the saddle pressure has reached its plateau level,
indicating separation, and the node pressure is at its peak
and is about to start recovery. By 8=96” even the /z/D
= 1.2 wavy-cylinder node shows signs of having separated.
For 8= loo”-156” there are no discernible spanwise pressure variations. From 8 = 160”-180” there is a pressure drop
from the saddle to the node, shown for 8= 180” in Fig.
12(e).
E. Pressure-drag
calculations
Although the flow is three dimensional, it is interesting
to examine the spanwise variations in “local pressure-drag
coefficient per unit length,” cd-rocal,measured at a fixed
axial location and based on local diameter:
as well as the “mean pressure-drag coefficient per unit
length,” qmean, based on mean diameter:
1963
Phys. Fluids A, Vol. 4, No. 9, September 1992
A. Ahmed and B. Bays-Muchmore
1963
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137.222.24.34 On: Fri, 30 Jan 2015 05:34:27
s
---I&----[[;--,.2;
4”5
1
*-Q---&\~
---__-.
-Gy---- ______0s
--4:--z.
----. ---____-_--_
I=
- b.0 d.1 d.2
Saddle
Ii.5
ii.4 0-s
d.3
(a)
G
s
‘-0
,::- p ~;G-:l.&y~~-=
,’
,/--;-bo.‘---__ I’
\----;-NL---
Y
f&
-1.2 -
:
g
Node
Saddle
(cl
Node
Z/A
:
._---_
‘\-.
-. -.-_ __;_------ ____--.-_-- .*
z
\c-
./
--.
0.0
Saddle
0.1
d.3
6.2
6.4
z/x
Node
Saddle
FIG. 10. Isobars of static pressure coefficient for each of the wavy cylinders. Re=20 CEO. (a) A/D=
--2 I,“==boy
J(;;;o,’ (“FL@)
Cd-mean-
1964
Phys. Fluids A, Vol. 4, No. 9, September
Node
(d)
(b)
1992
1.2; (b) L/D=
1.6; (c) A/0=2.0;
(d) ,X/0=2.4.
This equation for cd-,, is valid for the wavy cylinders as
long as the axial length to which it is applied consists of an
integral number of half-wavelengths. The spanwise variacdSIOCd
and the value of c&meanwere evaluated using
trapezoidal integration and are shown for the A/D= 1.2
A. Ahmed and B. Bays-Muchmore
1964
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0
0
A
v
-=
h/D
= 1.2
= 1.6
= 2.0
= 2.4
cc!
h/D
0 = 1.2
0 = 1.6
A =
v =
e @ed
2.4
I
e @cd
0
0
A
v
(b)
2.0
h/D
= 1.2
= 1.6
= 2.0
= 2.4
FIG. 11. Circumferential pressure distributions for each of the wavy
cylinders at three locations along the span, Re=20 Ooo. (a) Z/l.=O.O
(the geometric saddle); (b) Z/A=O.25; (c) Z/2,=0.5 (the geometric
node).
0 (deg)
cylinder in Fig. 13. The value of cd-ioc~ at the geometric
node is over 10% greater than the value of c&mean,and the
value of c&loCalat the saddle is more than 10% less. The
local drag force per unit length is approximately 30%
greater at the geometric node than the mean value and
30% less at the geometric saddle, due largely to the spanwise variation in local diameter. The difference between
c&&al at the geometric nodes and the geometric saddles
decreases with increasing spanwise wavelength as shown in
Fig. 14. The mean pressure-drag coefficient per unit span is
given for each of the cylinders in Table I. Despite the large
spanwise pressure variations, the integrated pressure-drag
coefficient for the wavy cylinders is not significantly different from that for a right-circular cylinder. The pressure
drag is dominated by the mean level of the base-pressure
coefficient, which seems far more sensitive to the cylinder
end conditions than to the spanwise waviness of the geometries tested.
IV. CONCLUDING
REMARKS
In the current work we have explored the pressure field
and flow patterns over the surface of the wavy-cylinder
geometry. This geometry is promising as a testbed for experimental, theoretical, and numerical research in unsteady, three-dimensional, bluff-body separation and wake
development because of its simplicity and symmetry. The
significant spanwise pressure gradients suggest the use of
1965
Phys. Fluids A, Vol. 4, No. 9, September 1992
A. Ahmed and B. Bays-Muchmore
1965
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137.222.24.34 On: Fri, 30 Jan 2015 05:34:27
2
,
h/D
0 =
0 =
A =
v =
-=CO
2
2
“:
7
-~
A/D
1.2
1.6
2.0
2.4
‘c4
”
-i
62
6 T-
F
LLI‘:
c.lo
2
L
0 f-
2
2
0
N
a*
v
B A
0
v8po
-r,,
0
0
LI
0 =
0 =
A =
v =
-=CO
1.2
1.6
2.0
2.4
@
x0:
0
O
8
I,
E,
0
0
zI
I
9
I’
B
m
I
0.1
%
8
1
0.2
Saddle
@
I
0.3
i?
B
,
0.4
@
7
0. 5
0.0
1
Saddle
Node
Z/h
(at
0.1
t
8
0.2
d
-I
0.4
I
0.3
t
0.:
blad
Z/h
(d)
te
-i
6;
a
t-3
0
i
f
“a:+
Fi
9,
f,
A
0
v
v
g
0
@
q
0
0
”
n
Q
:
v
v
on
0
cl
n
I
”
v
0
i1
%
2
0.0
#
0.1
Saddle
1
0.3
0.2
1
0.4
I,
.5
0.0
Saddle
(e)
Node
Z/X
(b)
0
0.1
4
0.2
I
0.3
Z/h
d.4
0.5
Node
FIG. 12. Spanwise pressure distributions for each of the wavy cylinders at
lOCatiOns,
(a) 8=0”; (b) 6’=20”; (c) 8~52”; (d) 0~72~; (e)
various
8= 180”.
2
II
0.0
Saddle
I
0.1
8
0.3
d.2
1
0.4
Z/h
5
Ntde
(cl
1966
Phye. Fluids A, Vol. 4, No. 9, September
1992
A. Ahmed and B. Bays-Muchmore
1966
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137.222.24.34 On: Fri, 30 Jan 2015 05:34:27
TABLE
Re,=20
I. Integrated mean pressure-drag coefficients per unit span,
OCO.The values given were repeatable to within 0.01.
1.30
1.25
1.20
‘;;
Sl 15
48 .
0
1.10
1.00 I
0.00
0
(
0.10
I
I
0.20
Saddle
I
I
0.30
a
,
0.40
1
1.24
1.19
1.21
1.20
1.13
This work was conducted while the second author was
supported by Rockwell International through the Rockwell Doctoral Fellowship Program.
,
0.50
Node
Z/h
FIG. 13. Spanwise distribution of cd.iocalfor the A/D= 1.2 wavy cylinder.
The dashed line indicates the value of cd-mea”for this cylinder.
this geometry at higher Reynolds numbers as a testbed for
cross-flow transition work.
Symmetrical geometry does not ensure symmetrical
flow patterns, as illustrated by some of the shear-stress field
topologies sketched in Fig. 9. In the current tests the flow
appeared far more stable and symmetrical about the geometric saddle than the geometric node; therefore it is suggested that if the wavy-cylinder geometry is used for numerical research into the instabilities
of separation
structures, the cylinder should intercept the computational
boundaries at the geometric saddles.
The base-pressure coefficient was found to be slightly
lower (more suction) at the geometric nodes than at the
geometric saddles, suggesting a spanwise variation in the
wake structure. The separation structures and turbulent
wake of the wavy-cylinder geometry are the subjects of
work currently in progress, and will be addressed in a
forthcoming paper.
0.30
1
0.25
-
0.20
\
;0.15-
2
--~-
x 0.10 0.05
i
I
0.6
I
1.2
1
1.6
I
2.0
1
2.4
I
2.8
h/D
FIG.14. The
effect of cylinder wavelength on the spanwise variation in
cd-,ocll
= cd.local
( Acd-,,a,
cd-mean
RCC
A/D= 1.2
/z/D= 1.6
A/0=2.0
k/D=24
ACKNOWLEDGMENT
1.05
0.00
Cylinder
(node) -
cd4,1
(saddle) ).
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