Effect of ventilation on the
around a sphere
G. K. Suryanarayana, G. E. A. Meier
flowfield
Experiments in Fluids 19 (1995) 78 88 V Springer-Verlag 1995
78
Abstract The flowfield around a sphere with and without
ventilation was investigated in a wind tunnel over a range of
Reynolds numbers in an incompressible flow. At supercritical
Re, the pressure drag of a sphere can be nearly nullified by
venting only 2% of the frontal area of the sphere to the base
through a smooth internal duct. The drag reduction is achieved
by increased pressures in the separated flow region close to the
base. At high Re, the vent flow breaks through the near wake
and brings about symmetry in the global flowfield. When the
internal shear is increased by using a rough internal duct, the
base pressure is unchanged, but the external flow is accelerated
to velocities beyond that achieved by the potential flow around
the basic sphere. The findings can be explained by a flow model
in which the near wake is aerodynamically streamlined by
a pair of counterrotating vortex rings at the base. A roughness
element can be made to partially destroy the vortex system at
the base and result in a steady asymmetric wake. A 1.2 mm
diameter wire placed at 70" was found to overtrip the boun-
dary layer and completely destroy the vortex system.
Simultaneously, the turbulent separation is advanced and the
drag increased.
At subcritical Re, ventilation marginally increases static
pressures all over the surface. Since the large pressure
Received: 7July 1994~Accepted: 2 ]uly 1995
G. K. Suryanarayana
Experimental Aerodynamics Division,
National Aerospace Laboratories,
Bangalore, India
G. E. A. Meier
DLR Institute for Experimental Fluid Mechanics,
D-37073 Gi3ttingen, Germany
Correspondence to: G. K. Suryanarayana
The work reported was carried out under a study grant from the
German Academic Exchange Service (DAAD) in Bonn. The authors
wish to thank the Director of DAAD in Bonn for the same. Thanks are
due to Dr. F. R. Grosche and colleagues at DLR in G6ttingen who
assisted in the design, fabrication and wind tunnel testing of the
sphere model. Thanks are also due to Prof. D. G. Mabey, visiting
Professor, Imperial College, London for useful discussions. The many
useful discussions with the research advisors of the first author viz.,
Dr. P. R. Viswanath of National Aerospace Laboratories and Prof. A.
Prabhu of Indian Institute of Science, Bangalore are acknowledged
with thanks. The support given by the Head, Experimental
Aerodynamics Division, National Aerospace Laboratories is thankfully
acknowledged.
differential between the windward and leeward sides is not
reduced, the internal flow has a rapid acceleration to a velocity
close to that of the free stream. The reverse flow associated with
the near wake forces the vent flow to rest within itself and the
wake profile is unchanged. The main features of subcritical
flow around the basic sphere are retained in spite of
ventilation. The upstream effects of ventilation are greater for
subcritical flow than for supercritical flow.
1
Introduction
Air flow around a bluff body such as a sphere or a cylinder
causes a stagnation region on the windward side and a low
pressure region surrounding the separated flow on the leeward
side. When these two regions are interconnected or ventilated
through an internal duct, a jet flow from the base is auto-
matically set up by the external pressure distribution. The
shear generated at the external and internal surfaces results in
opposing vorticities. A constructive interaction between the
two can result in a base pressure increase or a drag reduction.
The concept of ventilation is different from that of the
well-known Base-bleed. Ventilation is a passive technique for
a natural management of the pressure field around a bluff body
and involves a feedback of downstream flow changes to the
upstream flow parameters. Further, the magnitude of the jet
velocity at the base is of the order of free stream velocity. In
base bleed, the bleed velocity is usually a fraction of the free
stream velocity in order that the device drag is small. Base
bleed results in a forced flowfield governed by the energy input
into the system. Wood (1964, 1967) and Bearman (1967) have
studied the effect of base bleed on an airfoil with a blunt
trailing edge. According to them, base bleed delays the onset of
instabilities in the shear layer and thereby increases the vortex
formation distance. The delay is shown by dimensional
analysis to result in a base pressure increase and a consequent
drag reduction. This effect was found to be greater when the
width of the jet is large as compared to that of the base. The
base pressure monotonically increased up to a certain value of
the blowing moment coefficient and for higher blowing the
effect was negative. More recently, Zhdanov and Eckelmann
(1990, 1991, 1992) have observed that the maximum base
pressure achieved is a function of the bleed rate as well as width
of the jet. For models with narrow slot, the maximum base
pressure occurs at much the same momentum flux density of
the jet as for wider slots and reports that thick and thin jets
may not have identical effects. Wong (1985) has reported
stabilisation of the wake by base bleeding a cylinder in a water
tunnel. In this experiment, the stagnation flow around a hollow
cylinder was vented into its base using a concentric inner
cylinder at
Re
varying from 2000 to 3000. Measurement of
forces was not made. In this experiment however, the internal
flow passes around an annulus and undergoes large pressure
changes resulting in a large reduction in the vent mass flow
which is an important parameter.
The concept of ventilation of a sphere was first reported by
Meier et al. (1990) in which a drag reduction of the order of
10% was observed from tests on vented spheres in free fall at
a subcritical
Re.
It was also observed from interferograms of
flow around vented cylinders that a divergent internal vent
collapses the near wake into a twin-eddy like structure at
moderate Re. A convergent or parallel internal vent resulted in
a flip-flop behaviour of the jet inside the near wake. Drag
reduction of the order of 50% to 60% due to ventilation at
supercritical
Re
from direct force measurement in a wind
tunnel was reported by Meier et al. (1991) and Suryanarayana
et al. (1992). At low (subcritical)
Re,
no significant drag
reduction was observed. Results from force measurements and
flow visualisations are reported by Suryanarayana et al. (1993)
based on wind tunnel and water tunnel experiments. A drag
reduction of 50% to 60% was measured for parallel, convergent
or divergent internal vents. A possible model of the flow at high
Re
around a vented sphere was also proposed. It was reported
that venting at high
Re
has the effect of aerodynamically
streamlining the base, like a splitter plate. It must however be
noted that efforts to find a three-dimensional equivalent of
a splitter plate behind a two-dimensional cylinder have not
succeeded. Maxworthy (1969) introduced a cylinder in the
wake of a sphere and found that the base pressure did not
change until the cylinder was moved very close to the base.
This is because of the fact that the three-dimensional flow
allows for circumferential communication of pressure signals
unlike a two-dimensional flow.
Dimensional analysis of the flow around the vented sphere
shows that the drag depends on
Re, (AP/q)
and
(d/D)
where
AP
is the differential pressure across the duct, q the dynamic
pressure, d the diameter of the internal duct, D the diameter of
the sphere and
Re
the Reynolds number based on D. In the
earlier experiments of Suryanarayana et al. (1993), values of
0.15 and 0.10 for the ratio of diameters were found to result in
the same amount of drag reduction. Since the present work was
aimed at verifying the earlier results by pressure measurements
rather than optimise the diameter ratio, a value of 0.15 was
chosen for the tests.
The present work is mainly an extension of the earlier work
of Suryanarayana et al. (1993) and hence an extensive reference
of the same will be made. The main objective was to obtain the
pressure distribution on the sphere with and without
ventilation over a range
of Re.
Additionally, the development of
flowfield around the vented sphere, wake profiles and internal
velocity profiles were also obtained. In this paper, the results
will be discussed and compared with the data available in the
literature on the basic sphere. Pressure distribution on the
basic sphere was obtained by closing the vent holes using
a curved flat plate at the entry and an adhesive tape at the rear.
The work reported forms a part of the doctoral thesis of the
first author.
2
Description of the vented sphere, experimental set-up and
instrumentation
The vented sphere consists of two asymmetric parts turned out
of Aluminium alloy. The bigger part is provided with a smooth
entry which is matched to an internal duct open at the base.
The smaller part can be fixed to the bigger one as a covering
shell and rigidly fixed. Provision is made in the bigger part to
accommodate a scanivalve and a supporting sting. When the
two parts are assembled, the vented sphere has an outer
diameter of 200 mm. The internal diameter of the duct is
30 mm. A final polishing after assembly of the two parts
provided a very smooth surface with a mirror finish. The vented
area corresponds to 2.25% of the frontal area of the sphere.
Figure 1 shows the constructional details and a schematic of the
model which was designed using CATIA Software at the DLR
Institute of Experimental Fluid Mechanics, G6ttingen, Germany.
The sphere was asymmetrically fixed to a support sting at
a location of 150 ~ from the stagnation point of the basic sphere
as shown in Fig. 1. The sting has a diameter of 10 mm up to
a distance of 100 mm behind the sphere and then increases to
25 mm up to a length of 600 mm. Justification for asymmetric
mounting of the sphere is included along with the results and
discussions. The sting was held at the downstream end using
a heavy sector arrangement fixed rigidly to the ground.
Distance between the base of the sphere and the sector was
nearly 600 mm.
Experiments were conducted in the i m wind tunnel at DLR.
The wind tunnel is a closed circuit open jet facility driven by
a propeller with variable speed control. A nozzle with a
rectangular exit of dimensions 0.75 m x 1 m provides the jet
flow. Length of the test section is about 1.25 m and the free
stream turbulence intensity
(Tu)
0.15%. The maximum free
stream velocity is 55 m/s. A traverse mechanism can be fixed
on a truss work above the test section to move a probe to any
desired position within the test volume. Figure 2 shows
a photograph of the vented sphere installed in the test section
of the 1 m wind tunnel. Thirty holes of diameter 0.4 mm were
drilled at various locations normal to the surface along a spiral
for measurements of surface pressures as shown in Fig. 1. The
spiral shape was chosen to avoid any interference among
pressure ports. Helical symmetry in the flow was assumed for
interpretation of results. Ten holes of the same size were drilled
on the internal duct for measurement of wall pressures. All the
pressure ports were connected to a 48 port Scanivalve
manufactured by Pressure Systems Inc., USA. Static pressures
were measured using a SETRA pressure transducer of range
140 mm of water (13.5 mBar) with atmospheric pressure as the
reference. The free stream velocity was determined from the
pressure difference between the atmosphere and the settling
chamber using a similar transducer of range 127 mm of water
(12.3 mBar). A 1.2 mm wire rolled into a ring was fixed at 70 ~
in order to trip the boundary layer.
A static pressure tube of diameter 3 mm and length 370 mm
was introduced from the rear vent hole using the traverse
mechanism and traversed along the centreline from upstream
to downstream for measurement of static pressures. A SETRA
transducer of range 63.5 mm of water (6.1 mBar) with atmo-
spheric reference pressure was used for this purpose. For
measurements of internal velocity profiles, a 3 mm diameter
79
80
w wr..l i I I I G11 "if I~I
Fig. la-c. Constructional details and distribution of pressure ports.
a Model constructional details; b isometric view of the vented sphere;
c distribution of pressure ports
Fig. 2. Installation photograph of the vented sphere model
Prandtl tube was positioned 50 mm upstream of the base inside
the sphere using the traverse mechanism, Total pressure
obtained from the tube and the wall static pressure measured
on the duct were used for measurement of velocity. The probe
was also traversed along horizontal and vertical planes inside
the duct. Total pressure was measured using a SETRA
transducer of range 140 mm water (13.5 mBar) and static
pressures measured using a similar transducer of range
63.5 mm water (6.1 mBar). The Prandtl tube was traversed
along the downstream centreline up to two sphere diameters
and pressures recorded. Wake of the sphere was scanned using
the Prandtl tube at two diameters behind the base along
a horizontal plane. A delay time of 4 seconds was chosen for
the scanivalve ports and the pressure signals from the static
and total pressure tubes were integrated over 10 seconds.
3
Results and discussions
3.1
Effect of ventilation on the pressure distribution
Figure 3 shows the pressure distribution obtained with (vented
sphere) and without venting (basic sphere) the sphere at
subcritical Re and comparison of the data on the basic sphere
from literature. It is apparent that venting leads to increased
1.0
0.8
0.6
0.4
0.2
~. 0
L~
-0.2
-0.4
-0.6
-0.8
,,i,t, ' , ' , ,
I0
I I I I I I I
2 40 60 80 1 O0 120 140 160
0 o
180
1 .Or
0,8-
0.6-
0.4
0.2
l~
d
-0.2.
-0.4
-0.6
-0.8
Symbol Configuration Description
-1.0"t
o Vented Sphere Present Result at Re = O.B x 10 5
l
Basic Sphere Present
Result at Re = O.B x 105
Fage (1936) Re = 1.1 x 10 s
9 Msxworthy (1969) j Re = 0.6 x 10 ~
Achenbach (1972) I Re = 1.62 x 105 0
Fig. 3. Effect of venting on pressure distribution at subcritical
Re
pressures all over the surface, from the stagnation ring at
the front (8.2 ~ to the base (171.2~ Thus, a decrease in
drag as a result of base pressure increase is nearly nullified
by increased drag due to windward static pressures. Thus,
a ventilation of the present kind is unlikely to reduce the drag
at low Re.
Figure 4 shows the pressure distribution at supercritical
Re
with and without venting the sphere and comparison with data
from literature on the basic sphere. Venting leads to increased
pressures on the windward side almost up to 90 ~ A laminar
separation bubble occurs over nearly 10 ~ after about 100 ~ as
evidenced by the plateau in the pressure curve of both the
vented and basic spheres. Reattachment of turbulent shear
layer occurs at about 110 ~ and a rapid pressure recovery takes
place thereafter. The occurrence of laminar separation bubble
in this range of
Re
can be noticed in the oil-flow pattern also.
The vented sphere shows lower pressures (or increased
velocities) up to about 125 ~ as compared to the basic sphere.
The most interesting feature occurs beyond 125 ~ when venting
increases the pressure and makes the pressure distribution in
the base region uniform and positive. Beyond the turbulent
separation on the basic sphere at 135 ~ , the separated flow
shows large pressure gradients. Venting is seen to marginally
delay the turbulent separation.
According to Taneda (1978), the separated turbulent shear
layer behind a sphere at high
Re
rolls up into a three-
dimensional horse shoe vortex structure with a pair of counter
rotating streamwise vortices as shown in Fig. 5. The entire
structure rotates randomly about a streamwise axis. As a result,
the basic sphere at high
Re
experiences an unsteady
aerodynamic force whose direction is arbitrary. Dallmann and
Schewe (1987) have identified the various critical points
t
I
/
/
I
!
i 4JO i
20 60
"~--SEPARATION
BUBBLE
I I I
120 140 160 80 100 180
8 ~
Symbol Configuration Description
Basic
Theory (Potential)
9
Basic Present Result for
Re = 6.7 x 10 ~
0 Vented Present Result for Re = 8.3 x 105
o
Basic Fage
(1936), Re = 4.2 x 10 ~
c,
Basic Achanbach
(1972), Re = 11.4 x 10 s
Fig. 4. Effect of venting on pressure distribution at supercritical
Re
associated with such a flow based on topological con-
siderations of three-dimensional separated flows. According
to Suryanarayana et al. (1993), ventilation of the sphere at
high Re causes the separated shear layer to roll up as a base
vortex ring primarily due to its entrainment by the secondary
vortex ring which is formed by the vent flow close to the base as
shown in Fig. 5. The combined effect of the vortex rings is to
provide an aerodynamic streamlining at the base. The
occurrence of a pressure plateau in the separated flow region as
in a subcritical flow confirms the absence of large scale flow
oscillations in the wake as visualised on a laser light sheet in
the referred work. Figure 6 shows the increase of base pressure
(at the last measurement point at 160 ~ ) due to venting as
compared to that of the basic sphere from the present
measurements over a range of
Re.
Integration of the pressure distribution
(Cd=
S1.72L8
Cp
sin 2OdO) shows that in the supercritical range
of
Re,
the pressure drag of the vented sphere is nearly zero.
This is because of the base pressure increase (base thrust)
which nearly compensates the drag due to windward static
pressures as shown by the pressure distribution in Fig. 4. The
net drag on the vented sphere would then be due to skin
friction due to internal and external flows and a pressure drag
due to the radius of the vent hole, all of which are expected to
be very small.
81
82
a
Base vortex ring
~ Secondary vortex ring
.
Free stagnation ring
Fig. 5a-c. Structure of the wake behind a sphere with and without
venting, a Basic sphere at high
Re
(Taneda, S., ].F.M. 85, 1978);
b vented sphere at subcritical
Re;
c vented sphere at supercritical
Re
0.3"
L)
0.2-
0.1
O
-0.1
-0.2
-0.,"
-0.4
" Measurement Uncertainty ~I
_
-l
r
.,~,i / o-~_.,.,
1 2 3 4 5 6 7 8 9
Re
xl0 -s
Symbol I
Configuration
9 Basic Sphere
0
Vented Sphere
Fig. 6. Variation of base pressure with Re for basic and vented spheres
The earlier study of Suryanarayana et al. (1993) reported
a drag reduction of 50% to 60% in the supercritical range and
hardly any change at lower
Re
from direct measurement of
force in a wind tunnel using an external balance. Correction
due to the support system was estimated by supporting the
sphere from an alternate support through which the effect of
the sphere wake on the original support system was identically
simulated. It was assumed that the correction factor would be
the same for both the vented and the basic spheres. The pre-
sent measurements indicate that the pressure drag, which
corresponds to nearly 90 to 95% of the total drag (Achenbach,
1972) is nullified. The discrepancy is due to underestimation of
the support drag in the earlier work when the sphere was
vented. Aerodynamic streamlining due to ventilation results
in higher dynamic pressures in the wake and hence the tare
drag correction due to the support system would be higher
for the vented sphere than that for the basic sphere. If the same
correction factor is used, the resulting figure is an under-
estimate of the actual reduction achieved.
3.2
Comparison of results on the basic sphere
Figures 3 and 4 also show comparisons of the present results
on the basic sphere with those of Fage (1936), Maxworthy
(1969) and Achenbach (1972) at subcritical and supercriti-
cal
Re
respectively. The discrepancies in the results can be
attributed to four factors viz., small variations in
Re,
model
support position,
Tu
and the model surface roughness. Each of
these factors can play an important role as discussed below:
When the separated laminar shear layer starts reattaching
on the surface, the drag curve starts sinking and reaches
the minimum drag condition. At higher
Re,
the drag starts
increasing again. Therefore, the pressure distribution can show
large changes even for small changes in velocity in this range
of
Re.
A reasonable agreement is seen between the present data and
that from literature as shown in Fig. 3, even though the present
results are for an asymmetric support whereas the others
except Maxworthy (1969) are all for symmetric rear supports.
This observation is consistent with that of Raithby and Eckert
(1968) who have studied the effects of a cross flow support and
a conventional rear support on the surface flow over a sphere.
This feature is essentially because of the fact that in subcritical
flow, separation of the laminar boundary layer occurs at about
82 ~ without a turbulent reattachment. A support fixed
downstream of it lies in the separated flow region and does not
strongly influence the windward flow. Since the present support
system is at 150 ~ which is well downstream of laminar as well as
turbulent separation, it does not have a significant influence on
the results. Further, in the earlier experiments, it was found that
the reduction in drag due to ventilation was unaffected when the
vented sphere was rotated about the asymmetric sting axis.
Figure 4 shows comparison at supercritical
Re
with those of
Fage (1936) and Achenbach (1972). Good agreement is shown
with the data of Fage almost up to the point of turbulent
reattachment of the flow. Turbulent separation is indicated at
about 145 ~ in Fage's results whereas at about 135 c in the
present results. Whereas a clear pressure gradient in the
separated flow region is indicated in the present results, data in
the region from 150 '~ to 175 are not reported by Fage. The data
of Achenbach (1972) which are for a slightly higher
Re
agree
well with the present data only up to 70 ~ . The value of
minimum
Cp
achieved is higher than that shown by the present
data as well as that by Fage (1936). Large differences are shown
by Achenbach's results at locations beyond 90 <, apparently
because of the higher
Re
as well as
Tu
of 0.45% as compared to
the
Tu
of 0.15% for the present results. This is also suggested
by the absence of laminar separation bubble and the advanced