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OCR for page 655
24eh Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
PIV Measurements of the Cross-Flow Wake of a Turning
Submarine Model (ONR Body-1)
T. C. Fu, P. Atsavapranee, D. E. Hess
(Naval Surface Warfare Center, Carderock Division, USA)
ABSTRACT
Particle Image Velocimetry (PIV), a quantitative flow
visualization technique, was utilized to characterize
the flow field around a sting-mounted captive model
in a steady turn. The submarine model (ONR Body-
1) was also instrumented with block gages, yielding
force and moment data in tandem with the detailed
map of the cross-flow velocity field. The near wake
flow field is observed to be dominated by complex
interactions of large-scale vertical structures from the
hull separated flow and the tip vortices from the sail
and various control surfaces.
INTRODUCTION
The wake of a maneuvering submarine represents a
highly complex three-dimensional flow field,
dominated by interactions of large-scale vertical
structures from the separated flow around the body
and the trailing flow structures from the sail and
various control surfaces. As a submarine progresses
through a maneuver, the local flow incidence angle
changes in an unsteady manner, further complicating
the flow interactions. In a steady turn, for instance,
the asymmetric flow separation over the hull creates
a pair of body vortices on the leeward side.
Additionally, the sail and the control surfaces of the
submarine create tip vortices, whose location and
strength depend upon characteristics of the local flow
field and the control surface deflections. The
complex interaction of these various vertical
structures presents a particular difficulty in the
prediction of such flows using computational fluid
dynamics (CFD). Detailed measurements of the flow
field not only provide validation data for CFD codes
but also give physical insights into this complex flow
field.
Though flow field measurements of a free-
runn~ng radio-controlled model (RCM) in a
maneuver using particle image velocimetry (PIV) can
be preformed, there is a substantial associated
increase in the complexity and cost. Steady turn
conditions, being somewhat easier to compute and
interpret, offer a reasonable starting point. The
.
present study utilized a captive model sting mounted
on a rotating arm (towing carriage) with the speed,
yaw, pitch, roll and turning rate fixed through the
duration of a turn. Force and moment data, as well as
the velocity field data, were measured concurrently,
allowing for more complete validation of CFD codes.
The test conditions, including yaw, speed, rudder and
rudder angle, were chosen to match those measured
from the RCM while performing a steady turning
maneuver
A PIV system was previously built and used
in the Rotating Arm Basin in 1994, to measure
vertical structures from a turning submarine (Liu &
Fu, 1994~. Although this test successfully
demonstrated the potential of PIV technology in such
an application, it also revealed the limitations of the
technology at that time. Transitioning PIV from
small-scale laboratory applications to large-scale
facilities or field measurements involves a number of
technical issues related to the deployment of a
complex measurement system in a relatively remote
and uncontrolled environment. These technical
issues include laser power limitation and delivery
technique, feasibility of utilizing scientif~c-grade
instruments in a submerged environment,
experimental physical arrangement and layout, and
image acquisition and analysis issues. Since then,
affordable higher power lasers, fiber optics delivery
systems, digital cameras, image acquisition systems
and analysis software have all became incorporated
into state-of-the-art PIV systems, addressing the
limitations encountered in the 1994 test. Utilizing a
PIV system developed and built by the Johns
Hopkins University (Bertuccioli et al, 1999; and
Sinha & Katz, 2000) a similar test was performed.
The PIV measurements taken in this study provide
detailed cross-flow velocities in a static measurement
plane on the leeward side of the model as it passes by
in a turn. Since the maneuver is steady, the time
series of velocities in the measurement plane are
equivalent to instantaneous "snapshots" of the cross
flow velocity field at several axial locations relative
to the model (see Figure 1~. Note that the
measurement planes, as represented in Figure 1, are
oriented in a changing fashion at successive stations
OCR for page 656
Figure 1: Laser sheet position (data planes) relative to
the model as it passes through the turn.
along the model, due to the fact that the model, which
is pitched, rolled and yawed, passes through a static
measurement plane along a circular arc. Also, note
that PIV measurements are taken using two cameras.
The measurement plane for the first camera (situated
inboard and closer to the model) is shown in red.
The measurement plane for the second camera is
shown in light green. The area of overlap between
the first and second camera is shown in yellow. Only
data from the inboard camera will be shown in this
paper. The location for each measurement plane, in
model coordinates, is defined as a vector from the
model reference point to the center of the
measurement plane. The measurement plane
orientation is defined as a unit vector, in model
coordinates, normal to each measurement plane.
Both the locations and the orientations of the
measurement planes from the inboard camera are
listed in Table 1.
PARTICLE IMAGE VELOCIMETRY
Particle image velocimetry (PIV) is a flow-field
measurement technique that provides an
instantaneous distribution of two velocity
components over an entire two-dimensional
measurement plane. Fluid velocity is measured by
tracking the mean motion of a group of small
neutrally buoyant particles dispersed within the fluid,
assuming that necessary care is taken to ensure that
the particles faithfully track the flow. In a typical
PIV implementation, the working fluid is seeded with
microscopic tracer particles, and a selected plane of
measurement is illuminated twice with a pulsed laser
light sheet. The two exposures of the particle field
are either recorded together in one double-exposed
image or separately in two single-exposed frames.
Table 1. Locations (hi, ye, zip and orientations (x2,
Y2, z2) of the inboard set of measurement planes, in
model coordinates (fit). The left column represents the
plane number, starting from the rightmost plane as
shown in Figure 1.
Plar~e
#
~ .
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
. x,
2.979
2.591
2.202
1.812
1.422
1.032
0.643
0.255
-0.130
-0.512
-0.891
-1.266
-1.635
-2.000
-2.358
-2.710
-3.054
-3.391
-3.720
-4.040
Yl
0.158
0.111
0.079
0.064
0.064
0.080
0.112
0.159
0.223
0.301
0.396
0.506
0.630
0.770
0.924
1.093
1.277
1.473
1.684
1.907
Z1
-0.106
-0.118
-0.130
.
-0.144
-0.157 .
-0.171
-0.186
-0.201
-0.217
-0.233
-0.250
-0.266
-0.284
-0.301
-0.319
-0.337
-0.356
-0.375
-0.393
-0.412
X2
-0.230
-0.238
-0.246
-0.253
-0.259
-0.266
-0.272
-0.277
-0.282
-0.286
-0.290
-0.294
-0.297
-0.299
-0.301
-0.303
-0.304
-0.304
-0.304
-0.304
Y2
-0.200
-0.190
-0.180
-0.170
-0.160
-0.149
-0.138
-0.127
-0.116
-0.104
-0.093
-0.081
-0.069
-0.057
-0.045
-0.032
-0.020
-0.008
0.005
0.017
Z2
-0.001
-0.002
-0.002
-0.003
-0.003
-0.004
-0.005
-0.005
-0.006
-0.006
-0.007
-0.007
-0.008
-0.009
-0.009
-0.009
-0.010
-0.010
-0.011
-0.011
For PIV using double-exposed images, such
as in the present application, a means of shifting the
second exposure from the first is used to eliminate
the directional ambiguity arising from the inability to
distinguish the sequence of exposure within a pair.
During vector-map analysis, each image is
subdivided into small interrogation windows. For
each interrogation window of the double-exposed
image, an auto-correlation function is calculated.
The location of the peak of the correlation function
represents the mean displacement of the tracer
particles in each interrogation window. The average
velocity in the window can then be readily calculated
by dividing the mean particle displacement by let, the
time separation between the two illumination pulses.
OCR for page 657
Comprehensive reviews of PIV techniques may be
found in the literature (Adrian, 1991 & Grant, 1997~.
EXPERIMENTAL SETUP
ONR Body-1 Model and Sting
The submarine model used in this study is NSWCCD
Model 5484 with a length of 5.18 m. (17.0 ft.), a
diameter of 0.47 m. (1.55 ft.) and configured as
"ONR Body-1." ONR Body-1 is an unclassified
generic submarine shape composed of an
axisymmetric body, sail and 4 identical stern
appendages. The sail has a NACA 0014 section with
an aspect ratio of 0.27. It is faired to the hull and
located at x/L=0.2. The stern appendages, all identical
in shape and size, are NACA 0018 foils with an
aspect ratio of 1.2. A boundary layer trip wire, with
an OD of 1.5 mm. (0.06 in.), was mounted at
x/L=0.05. Particle injectors were also located just
upstream of the trip wire (see Figured. The
injectors were not used while data was being
recorded, but instead were used to seed the flow with
particles before the start of a run.
a) Profile view
b) Close-up view.
it__
_ __
~ _
_ _
~ _
_ _
it:
~ _
~ ~
Figure 2: Dye injectors and boundary layer trip wire.
F]
L-----------------
-
i
>~ PITCH & YAW PIVOT POINT
1':::::::1~ - Jew
e—an,
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ _ _ _ __ 4_ _
WATER LINE
,
~==~ ~ ;-_
Figure 3: Sting-mounted submarine model for
Rotating Arm testing.
The captive model is attached to the carriage
using a sting-mounting fixture. A line drawing
showing the sting arrangement is shown in Figure 3.
The diameter of the sting is 0.17 m. (6.5 in.) except at
the model's tail cone where it narrows down to a
diameter of 0.10 m. (4 in.) for a distance of 0.23 m.
(9.25 ink. The inside diameter of the tail cone is 0.13
m. (5 in.) at the point where the hull ends. The model
was supported in an upright position (to allow easy
access to the interior by removing the top covers) by
two gimbals spaced 1.83 m. (6 ft.) apart. The
gimbals were, in turn, mounted to a box beam located
inside the model. With the cover removed from the
top half of the model, one can see in Figure 3 the
tapered channel (box beam) affixed to the end of the
sting. The sting was supported by an 0.2 m. (8 in.)
diameter vertical cylinder with a length of 3.38 m.
(11.094 ft.) between the pitch pivot and the hull
centerline. The centerline of the vertical cylinder was
6.46 m. (21.18 ft.) aft of the forward perpendicular
(FP). The model reference point, which corresponds
to the longitudinal location of the center of buoyancy,
was positioned on the hull centerline midway
between the two gimbals, 2.354 m. (7.7233 ft.) aft of
the forward perpendicular.
The longitudinal, normal, and lateral force
components with respect to the body axis were
measured by means of three block-gage assemblies
located at each gimbal. Pitching and yawing
moments about the reference point were computed
from the measured forces at each gimbal. The rolling
moment about the longitudinal axis was measured by
an additional gage located at the forward gimbal.
The yaw and pitch angle of the model could be
changed by yawing and pitching the entire sting
assembly via the rotating arm undercarriage
positioning equipment. The roll angle could be
adjusted by rotating the model about the sting axis
using roll positioning equipment built into the sting
assembly. The roll angle was measured via a
OCR for page 658
,- -
~— Ad- ~ ~ 1=
k-~ \- ~
sat ~~- ~
Figure 4: Sketch showing standard submarine
coordinate system and positive directions of angles,
velocities, forces and moments.
synchro-resolver located underwater inside the aft
portion of the sting. Accelerometers calibrated to
measure roll and pitch angle were installed in the
model to allow for accurate zero settings. The
nomenclature for the forces and moments is standard
and may be found in the SNAME bulletin (SNAME,
1950~; the positive directions for the forces and
moments and the orientation of the coordinate system
are given in Figure 4.
In order to balance the static pitching
moment of the sting assembly and model, the sting
assembly was mounted to the rotating arm
undercarriage in such a way that the model reference
point was 2.134 m. (7.000 ft.) forward of the
undercarriage pitch and yaw pivot point. As a result
the radius to the model reference point is altered as
the model is pitched or yawed. For example, the yaw
angle and radius at the model reference point is
different than that set at the pivot point, as can be
seen by the sketch in Figure 5. The relationship
between a yaw angle and radius at the undercarriage
yaw pivot point ~ firs and Rs, respectively), and yaw
angle and radius at the model reference point (him
and Rm, respectively), are as follows:
Is = Arm + sin~l L a COS \Vm 1 ( 1 )
',v = ¢~ - sink [ a cos lo, ~ (2)
Rm = 1. Rs + a - 2aRs sin As ~ 2 = R. cos US (3)
cos Am
Figure 5: Sketch showing relationships between yaw
angles and radii.
a = 1 1.094 sin ~ + 7.000 cos 0, (4)
where ~ is the model pitch angle.
Rotating Arm Basin
The test was performed in the Rotating Arm Basin at
NSWCCD. The Rotating Arm Basin is a circular
basin, 79.25 m. (260 ft.) in diameter and 6.1 m. (20
ft.) deep. The rotating arm (a rotating bridge-like
towing structure) pivots on a pedestal in the center of
the basin and has a span of 39.32 m. (129 ft.) and a
width of 6.1 m. (20 ft.) (see Figure 5~. It is capable
of towing a submarine or a surface-ship model in a
circular path through calm water at a maximum linear
speed of 15.4 m/s (30 knots) in half a revolution at a
radius of 36.58 m. (120 ft.~. On the underside of the
arm is an undercarriage, which is movable and may
be positioned radially to as many as 30 different
radii. The previously described sting-mounting
fixture is attached to this undercarriage. Viewed
from above, the arm rotates clockwise with steady
angular velocity, r, and for a model mounted in the
upright position, this implies that the model is
executing a turn to starboard. The steady non-
dimensional yawing angular velocity, r', is related
to the length of the model, L, and the linear velocity
U as follows:
, rL
U
(5)
The linear velocity is, in turn, related to the angular
velocity, r, and the towing radius, R. by
U =rR
(6)
Therefore, the non-dimensional angular velocity is
typically expressed as
L 1
r' = = _
R R'
(7)
OCR for page 659
Model Configuration
In the present application, the ONR Body-1 model
was mounted with a centerline depth of 2.03 m.
(6.67 ft.) below the free-surface. The radius to the
model reference point, (Rm in Figure 5) was 9.816
m. (32.206 ft.), and the dimensionless radius was
1.89 after dividing by the model length of 5.18 m.
(17.0 ft.) The angular velocity of the arm was r =
0.163 rad./sec. The linear speed at the model
reference point was U= 1.60 m./sec (5.26 ft./see) or
3.11 knots. Finally, the dimensionless angular
velocity of the arm was found by inverting the
dimensionless radius to get r' = 0.53 . The model
was oriented such that it was pitched at 2.0 deg. (bow
up), rolled 2.1 deg. (to starboard) and yawed 9.5 deg.
to starboard (~m in Figure S). The rudder was
maintained at a fixed angle of -20 deg. (for a
starboard turn), and the sternplanes were set to -
1.0 deg. (rise). These configuration values were
chosen as a result of conducting steady turning
maneuvers with a free-running, radio-controlled
model (RCM) configured as ONR Body-1. These
values are representative of average conditions
32 sec. after execution of the maneuvers during the
steady portion of the turn.
Fifty data acquisition runs were performed.
Each run consisted of the following sequence of
actions. The arm was accelerated from rest until the
desired angular velocity of r = 0.163 rad./sec was
reached, these conditions were maintained at steady
state for approximately half of a revolution. The arm
was, by that time, approximately 1/8 of a revolution
from the center of the submerged PIV equipment.
Force and moment data acquisition was then begun
for a period of 10 sec. (approximately 1/4 of a
revolution) at a rate of 100 Hz (for each channel of
data). PIV data acquisition was started just prior to
the bow of the model entering the field of view of the
imaging equipment by means of a photo-interrupt
trigger placed at a fixed location on the arm. PIV
data acquisition continued until the desired 20 images
taken at a rate of 4 Hz were obtained. The arm was
then decelerated to rest. A minimum of 15-
20 minutes was allowed to elapse between runs in
order to allow the wake produced by the sting to
subside.
_
JHU Submersible PIV System
The measurement of the cross-flow velocity field
around the ONR Body 1 model was performed using
the submersible PIV system from the Johns Hopkins
University (Bertuccioli et al, 1999~. Schematics of
6a) Overview
6b) Close-up
.. ~
Figure 6: Submerged PIV instrumentation deployed
in the Rotating Arm Basin.
the mechanical hardware, optics, and image
acquisition and laser systems are presented in
Figures 6 and 7. Two digital cameras, housed in their
submersible enclosures, were used to image two
adjacent areas (43cm x 43 cm each) in a plane of
measurement. Two sets of laser sheet optics in their
housings were installed on a single optical rail to
provide two possible measurement planes (although
only one is used at a time). Light from a flash lamp-
pumped dual-head dye laser, operating at an output of
120 mJ/pulse at 595 nm, was launched into a 400-
micron fiber and expanded into a sheet to provide the
required illumination. The camera housings and the
laser sheet housings were mounted on a motor-driven
turntable platform, which allowed adjustment of the
orientation of the measurement system. The whole
assembly then sat on top of a hydraulic scissorsjack,
which permitted adjustment in the vertical position.
OCR for page 660
500 MHt d - '
procea~r P111
258 SIB R"
~m,
staring
mirrors
.. ~ ~ 1 ~ ~ 1 ~ 1 a,,,,,,, Data.
ham Sandra
Laser
cor~o1
C _
S - amstor
mode 308
SO GB capacity
Facusi~ Ens
Dualized flash~mp
pumped dy* laser
Presicsion3-axis
the - Boon *sage
Figure 7: PIV instrumentation: image acquisition and
laser systems.
The complete unit was lifted and placed within the
Rotating Arm Basin. Fine adjustments in orientation
and vertical position finally placed the cameras and
laser sheet optics in the desired positions. Note that
the pale blue lines visible in Figure6 represent a
chain drive and rail assembly mounted on the floor of
the basin.
Each of the two image acquisition systems
utilizes a scientific grade digital camera with a pixel
resolution of 2K x 2K (model 4m4, Silicon Mountain
Design, Inch. The camera contains a high-
performance 28.7mm x 28.7mm COD array and is
capable of capturing 12-bit images at a frame rate of
4 Ups. The camera, thus, has a maximum output of 24
Mb/s in RS422 data format. One inherent limitation
of the RS422 data format is that the data integrity
degrades significantly for cable lengths of more than
30 m. To overcome this limitation, the data is first
converted into MECL (Motorola emitter-coupled
logic) format before it is transmitted through the
required 75m. cable length necessary for the
experiment. At the other end, the data is then
converted back to RS422 before being recorded by
the host computer. To manage such a large data rate
(24 Mb/s) the data stream was recorded in real time
onto an array of hard disks controlled by a Boulder
Instruments, Inc. (model Streamstor PCI-306) disk
array controller. This "real-time disk" system allows
the image acquisition system to capture as much as
80 GB of images continuously at the full frame rate
of the camera.
A schematic of the image-forming lens
system is shown in Figure 8. The desired wide
coverage (43cm x 43cm) dictates the usage of a wide-
angle lens in order to minimize the subject to
lens distance.
:
.,
Virtual , ~
~ . ~ ~ _
meal point ~ 28mm
~ lens
Enclosure
Dome _,- ~~' '^~' ~ .
:~' '+2 diopte _
'1
_ Camera
Figure 8: Camera lens optics and submersible
enclosure.
Reducing the amount of water between the
subject and the lens results in sharper detail and
increased contrast. To compensate for the distortions
introduced by the refraction at the water/optical-
window/air interface at the front of the housing, a
concentric spherical dome port is used instead of a
flat optical window. When a dome port is used
between water and air, it acts as a diverging
(negative) lens. The optics of the diverging lens
results in a virtual image being formed a short
distance in front of the dome port. To make it
possible to focus on the virtual image, the 28mm
photographic lens is fitted with a multi-element,+2
diopter, close-up lens. For wide-angle underwater
application, the image-forming lens system results in
extremely flat-field imaging, yielding only a 2%
maximum distortion around the edges.
Raw images of double-exposed particles
were processed into velocity data using a PIV
analysis software package from LaVision, Inc. The
DaVis software package utilizes advanced
algorithms, including local adaptive cell shift and
second-order correlation, to enhance accuracy and
improve data integrity. A benchmarking test was
carried out to measure the stability and accuracy of
the software package against a set of"standard"
images provided by the PIV-STD project. The PIV-
STD project was developed to provide standards and
guide tools for the PIV community (the project
website can be found at http://vsj.orjp/piv/). One
useful product of this project was a set of computer-
generated standard PIV images that a PIV
practitioner can use to benchmark his or her analysis
algorithms. The benchmarking test showed that the
DaVis software package compares very well with
other state-of-the-art analysis software packages,
providing a high degree of stability, accuracy, and
user-friendliness.
One of the critical issues in utilizing PIV is
the importance of providing a uniform distribution of
PIV particles in the image plane. For this test, this
issue was a particular concern due to the large
volume of fluid that needs to be seeded. The model
~ ~ rig ~
OCR for page 661
itself was used as the seeding device by utilizing
injector ports on the nose of the model.
Approximately 110 liters of dilute mixture
(1500 ppm) of 15-micron hollow glass spheres and
water was pumped to the injectors through a plenum
and a network of Tygon tubing. This process not
only guaranteed that there were enough seed particles
around the model but also that the particles were
placed at the correct depth. Seeding of the flow field
was done initially at the start of each day. Re-
seeding after every third run was found to be
necessary due to dispersion of the particles
throughout the tank.
FORCE & MOMENT MEASUREMENTS
A forward and an aft set of block gages were used to
measure the longitudinal, lateral and vertical force
components with respect to the body axes, denoted X,
Y and Z. respectively. The forward and the aft set of
block gages was attached to a tapered channel inside
the model through two gimbals. The longitudinal
distance between the centerline of the two gimbals
was 1.83 m. (6 ft.~. The origin of the body coordinate
system or reference point was located 2.35 m. (7.723
ft.) aft of the forward perpendicular along the
centerline of the hull. The pitching and yawing
moments about the reference point, M and N. were
determined from the difference in the measured
reaction forces at each gimbal, multiplied by one-half
the spacing between the two gimbals. The roll
moment, K, was measured by a strain gage unit
located at the forward strut.
Before a run is made, small nonzero forces
and moments present at each gage (electrical zeros)
are measured and recorded so that they can be
removed from the underway force and moment data.
The underway force and moment data were then non-
dimensionalized. Representative equations for
vertical force, ZT, and pitching moment, MT, are
shown in Equations 8 and 9, respectively, and similar
equations apply for the remaining quantities,
z = (I + z2) (I + z2)o `8'
—pU2L2
2
and
M, = L(z2 Zl ) (Z2 Z1 )0 J Lh (9)
2pU L
where Zag and z2 are the vertical force
measurements from the forward and aft block gages,
respectively. The subscript"0" indicates the values
of the electrical zeros, and the prime symbol denotes
dimensionless values. The density value that was
used in the normalization was 999.33 kg/m3
(1.9367 slugs/ft3 ).
During a run, the measurements of each
force and moment include both a contribution due to
the hydrodynamic force distributions over the hull
and appendages and a contribution due to the
acceleration of the mass of the model. The latter
contribution was removed from the measurements to
determine the hydrodynamic forces and moments by
using the procedures and equations given in Fu et al.
(2001~. The notation for the dimensionless linear
velocities: u',v' and w', and the dimensionless
angular velocities: p',q'andr', is standard and is
defined in the SNAME reference (SNAME, 1950~.
Each of the instantaneous values in the time
series for each of the force and moment variables had
tares removed and was rendered dimensionless in the
manner described above. The data were then
averaged over the 10.0 sec. sampling period of the
measurements for each run. The mean values for
each run were then averaged over the 50 runs. These
data are shown in Table 2. Also shown are standard
deviations of the mean values computed across the 50
runs. Sample means and standard deviations were
computed using the standard formulas:
— 1 N
N ~ i (10)
i=}
1
SX =LNI-1 ~ (Xi X)25 (11)
where N is the number of runs.
Following Coleman and Steele (1989), a
precision index for a variable X and for its mean
value X may be computed using
PX=tSx and Px =tSx= Aid, (12)
where t is a value drawn from Student's t-distribution
for N-1 degrees of freedom and a specified
confidence level. Note that the normalized variable
(X - ,u)/Sx, where ,u is the true mean value of the
OCR for page 662
Table 2a: Dimensionless Force Measurements
X'X 103 Y'x 103 Z'x 103
Mean -1.10 5.29 -0.15
Std. Dev. 0.04 0.14 0.07
F' ]> -1.11 5.25 -0.17
F'+ by, -1.09 5.33 -0.13
Table 2b: Dimensionless Moment Measurements
N'x 105
Mean 3.80 -0.50 -14.95
Std. Dev. 0.37 1.76 1.03
F'- PF' 3.69 -1.00 -15.24
F'+PF' 3.91 0.00 -14.65
parent distribution from which only a sample of N
measurements was drawn, is not normally
distributed but instead is distributed according to
Student's t-distribution and is the reason for its use in
Equation 11. The l-value for N-1=49and for a
confidence level of 0.95 is 2.010 After computing
the precision indices, we can then determine 95%
confidence intervals for the true mean value of the
parent distribution as described by
Prob (X-PX < ~ < X+Px)= 0 95
(13)
The 95% confidence bounds X-PX and X+PX
are also supplied in Table 2.
Before proceeding further, some comments
are in order to describe how one should apply
Equation 12 to compute precision indices. Assume
for the moment that only a single run was available
for the computation of mean values of the forces and
moments. A total of 1000 measurements, 100 per
second for 10 sec., were acquired for each of the
forces and moments during the run. Should N equal
1000 for the computation of PX? Implicit in the
definition of Equation 12 is the fact that the N
instantaneous values must be independent
measurements of X. Therefore, one must determine
the smallest timescale over which the variable X can
change. Successive measurements of X that are
separated by a time less than this inherent timescale
are not independent measurements. To determine
this timescale, one may compute a power spectrum of
X and determine the largest frequency at which there
is any noticeable power (that is not due to noise) in
the signal. The data would suggest that this cutoff is
somewhere in the 6-10 Hz range. A conservative
estimate would therefore be 5 Hz. Therefore, only 5
samples per second are independent, and N= 50 for
the 10 sec. sample period. If only one run existed,
then using this value of N would be justified and
would provide a more realistic estimate of the
precision index of the mean than by using N = 1000.
Now, return to the fact that we have 50 runs.
Assume that an additional source of precision
uncertainty is present - random errors that arise run-
to-run. If only one run were available, then the
precision index computed as described in the
previous paragraph would contain no information
about run-to-run uncertainty, yet it would be the best
that we could do. The fact that we have multiple
runs, however, gives us an opportunity to compute a
more realistic estimate of the precision index of the
mean that includes run-to-run uncertainty. This
means that even though a mean value computed for
each run is the result of many independent,
instantaneous measurements, these multiple
measurements within a given run give us no
information about any run-to-run variation in the
data. Thus, we use the mean value for each run to
form a mean value for each configuration, and we
assess the precision error using N= 50.
The procedure, then, was as follows. A
simple mean value for each of the forces and
moments was computed (using Equation 10) from the
instantaneous measurements from each run using N=
1000. A set of 50 mean values was then obtained for
each variable. Then, a final mean value and standard
deviation was computed for each variable using N=
50. The precision index of the mean was then
computed using Equation 12.
Examining Table 2 one can see that the fluid
exerts on the model a steady non-dimensional drag of
1.10, a force to starboard (into the turn) of 5.29 and a
very small upward force of 0.15. The latter value is
not unreasonable given the 2 deg. bow-up pitch of the
model. The drag and spanwise forces are steady with
standard deviations less than 4%. The model
experiences a rolling moment to starboard of 3.80
which results from the fact that the fluid exerts a
force component on the sail, which is asymmetric
about the centerline. The fluid appears to exert a
small pitch-down moment on the model of 0.50, but
this is statistically insignificant due to the large
standard deviation. Finally, with a yaw angle of
9.5 deg. to starboard, the model experiences small
drift angles at the bow and much larger drift angles at
the stern during clockwise rotation with angular
OCR for page 663
velocity r. As a result, the fluid exerts a steady
moment of 14.95 in the counter-clockwise direction.
RESULTS & DISCUSSION
The maneuvering characteristics of a submarine
depend on the hydrodynamic forces and moments
that are developed on the hull, appendages, and
propeller. In a turning maneuver the lift that is
developed on the deflected rudder causes the
submarine to develop yawing angular velocity and an
angle of drift, ,8 (defined in Figure 4), resulting in the
submarine pointing into the turn. The combination of
the yawing angular velocity and forward motion of
the vehicle produces a variation of the angle of drift
over the entire length of the submarine. At a point
just ahead of the sail, the local angle of drift is zero.
From that point aft, the angle of drift increases so that
at the rudder, the local angle of drift is quite large.
As lift is developed from the sail, a strong vortex is
shed from near the tip, and is convected downstream
with the ahead speed of the submarine. The lift on
the sail also causes a large transient rolling angular
velocity and large roll angle. This snap roll is the
initial peak in the roll angle response, and it is usually
much larger than the steady roll angle. The data
presented in this paper is for ONR Body-1 in a steady
turn, pitched at 2.0 deg. (bow up), rolled 2.1 deg. (to
starboard), and yawed 9.5 deg. (to starboard). The
rudder was maintained at a fixed angle of -20 deg.
(for a starboard turn), and the sternplanes were set to
-1.0 deg. (rise). These configuration values were
chosen as a result of conducting steady turning
maneuvers with a free-running, radio-controlled
model (RCM), configured as ONR Body-1. These
values are representative of average conditions
32 sec. after execution of the maneuvers during the
steady portion of the turn.
Figure 9 shows an example of the velocity
(represented by vectors) and vorticity fields
(represented by contours) in several cross manes
downstream of the sail, looking aft. The planes of
measurement are the seventh to tenth planes from the
nose of the model as shown in Figure 1. The thick-
lined curve represents the location on the submarine
body where the laser sheet hits the model. The area
between the thick-lined curve and the thin-lined
curve (in gray) represents the area contaminated by
the bright diffuse reflection off the body, rendering
data in that region unreliable. From Table 2 the
average vertical force, Z. has a value of-0.15
(upward) and the average pitching moment, M, a
value of ~.50 (pitch down).
Evident in the measured flow field and vorticity
contours is a prominent trailing vortex (near y = 0.2
m. (0.66 ft.) and z = -0.33 m. (-1.1 ft.) in Figure 9a),
.
which originated from the tip of the sail of the model
undergoing a steady turn. This vortex can be seen in
the successive data planes as it moves downstream. It
should also be noted that the vortex moves laterally
away from the body, y = 0.2 m. (0.66 ft.) at plane #7
end y = 0.36 m. (1.2 ft.) at plane #10. At the instance
of measurement, the model heading is approximately
out of the page, with the sail mounted on top.
Because the model is undergoing a mildly severe turn
with r' = 0.53 and is pitched up slightly and yawed
to starboard, the local angle of drift and cross flow
velocity geometrically dictates that a region of flow
separation is expected on the leeward side of the
body, slightly towards the deck. The velocity and
vorticity fields in Figure 9 show a region of negative
vorticity, most easily seen in Figure 9d around y =
0.33 m. (1.1 ft.) and z = 0.06 m. (-0.2 ft.), being shed
in the starboard area, and a region of positive
vorticity (CCW, partially out of view) on the deck of
the model (z=-0.24 m. (0-0.79 ft)~. These two
regions represent points of flow separation
commonly observed around a bluff body in a cross
flow; however, they appear to be rotated clockwise
from what is normally expected, judging from the
direction of local angle of drift and cross flow
velocity alone. The region between the two
separation points is normally a region of low
vorticity, as observed in Figure 9.
An argument is presented here that the sail
tip vortex, due to its strength and proximity to the
body, will tend to delay the starboard separation and
enhance the deck separation by effectively imposing
a negative circulation (COO) around the body. In
other words, the interaction of the sail trailing vortex
with the body will generate a negative vorticity flux
across the body such that the separation points will
rotate clockwise, as observed in Figure 9. Because
the separation zone is an area of low pressure (with a
corresponding area of high pressure on the opposite
side of the hull), the aforementioned mechanism
which causes the low-pressure region to rotate
towards the deck, contributes to an upward force on
the hull aft of the sail. Since the trailing vortex
originates around the tip of the sail and the CG on the
ONP Body-1 model is situated close to (0.145L aft)
the trailing edge of the sail, the interaction of the sail
tip vortex with the hull exerts most of the influence
aft of the CG. An upward force, which acts primarily
aft of the CG, will result in a net downward pitching
moment, consistent with the measured results. It is
important to note that the mechanisms leading to the
downward pitching moment discussed above are
limited to situations in which cross-flow separation is
dominant, i.e., a submarine in a turn with large r'.
In fact, a submarine with a similar body/sail
configuration has been observed to pitch up in a mild
OCR for page 664
-0.3 Hi~§
~! ~ ~ ~
-0.1 ~ ~
O ~ 1 1
a)Plane#7
b) Plane #8
I I 1 1 1 1 1 1 ~ I 1 1 1 _
0.3 0.2 0.1 0 -0.1
y (m)
-0.4
-0.3
7~G
~3
am,
1.6 m/s
~: I.?
0.3 0.2 0.1 0
Y (m)
Figure 9: Cross-cut velocity and vorticity fields, for planes 7, 8, 9, and 10 as shown in Figure 1
OCR for page 665
1.6 m/s
-0.4 14~15
-0.3
-0.1
c) Plane #9
d) Plane #10
-0.4
-
-
N
-0.2
-0.1
_ ~
~ . ~
0.4 0.3
Y(m)
C3X (HIS)
30
26
22
18
14
10
1.6 m/s
. 1 1 1 1 1 1 1 1
0.2 0.1
y (m)
Figure 9: Continued
C0x (1/s)
OCR for page 666
turn. As discussed in a previous section, the various
parameters defining the orientation of the vehicle for
captive model testing were taken from conditions
developed on a free-running, radio-controlled model
(RCM). Specifically, the RCM conducted a series of
turning maneuvers, and the configuration parameters
are representative of average conditions 32 see after
execution of the maneuvers during the steady portion
of the turn. This captive model experiment provides
insight into the hydrodynamic conditions that prevail
during that steady turning phase. However, during a
free-running maneuver, the submarine transitions
from steady forward motion to the steady fuming
phase in a period of time dominated by unsteady
effects.
This unsteady phase of the free-running
maneuver begins with the rudder deflection initiating
the turn and extends until the yawing moment
generated by the distribution of forces acting on the
hull and sail is balanced by the moment created by
the lifting rudder. Note that this argument is ignoring
the complicating factor of out-of-plane forcing for
simplicity. The horizontal orientation of the vehicle,
measured by the angle of drift ,l], is determined
during this unsteady phase as the orientation, which
leads to a force distribution that balances the lifting
rudder. The steady drift angle that is ultimately
determined during the course of the unsteady phase is
critical to the resulting distribution of out of plane
forces acting on the vehicle and therefore to the entire
turning maneuver.
CONCLUSIONS
Particle Image Velocimetry (PIV), a quantitative flow
visualization technique, was utilized to characterize
the flow field around a sting-mounted captive model
in a steady turn. The submarine model (ONR Body-
1) was also instrumented with block gages, yielding
force and moment data in tandem with the detailed
map of the cross-flow velocity field. The results
indicated that in a mildly severe turn ~ r' = 0.53), the
interaction of the sail trailing vortex with the hull
separated flow results in a net circulation around the
body in such a way that the separation zone is rotated
toward the deck of the model. Since the separation
zone is an area of low pressure and a corresponding
area of high pressure exists on the opposite side of
the hull, this mechanism contributes to a net upward
force on the hull aft of the sail. Because the area aft
of the sail is for the most part aft of the CG, this net
upward force results in a net downward pitching
moment, consistent with observations.
The proposed mechanism that leads to the
generation of out-of-plane forcing on the hull could
be further substantiated and verified with additional
experimentation. This test concentrated on a single
steady turn condition and relied on PIV
measurements combined with total force and moment
data. Of particular interest in a future experiment
would be to supplement the above measurements
with the simultaneous acquisition of surface
pressures at locations defined by a regularly spaced
grid on the hull. Pressure measurements on the
submarine's surface would provide an additional
means to accurately describe regions of flow
separation and provide information on the
distribution of forces acting on the hull. The
experiment should be extended to include a series of
fuming conditions (variation of turning radii,
orientation and speed), and the experimental data
should be compared with calculations from a
Reynolds-Averaged Navier-Stokes (RANS) computer
code. Distributed force information would also
provide guidance on grid spacing issues required to
correctly resolve submarine pitching and yawing
moments with CFD codes. Comparison of CFD
calculations with field measurements of velocity and
surface pressures would serve to direct future code
development and may also illuminate additional areas
on which to focus experimental study.
Future experiments, on model submarines
and in other naval applications, would also benefit
from improvements to the PIV instrumentation.
Ongoing efforts will allow PIV measurements on a
much larger scale, making possible testing on larger-
scale models such as the LSV1, LSV2 and even full-
scale vehicles. Stereoscopic PIV, which would allow
measurements of all three components of velocity in
a plane, is also being actively developed. For the
current problem of cross-flow separation around a
turning submarine,
the coupling of PIV
measurements with the acquisition of surface
pressures consideration of additional turning
conditions, comparison with RAN S calculations and
improvements to the PIV configuration will provide
additional fundamental insight into the complex
mechanisms advanced in this paper.
The implementation of PIV in a large-scale
Navy facility as an optical diagnostic to probe the
highly complex, three-dimensional flow field near the
hull of a maneuvering submarine has been successful.
Instantaneous maps of velocity components at many
points in a plane have permitted the computation of
derivative quantities such as vorticity to provide
physical insight into the origin of the out-of-plane
forces acting on the vehicle. These detailed
measurements of the flow field also provide valuable
OCR for page 667
validation data for CFD codes and serve to stimulate
future submarine designs. This experiment has
demonstrated the tremendous potential of PIV and
has shown that it has matured to the point where it
can become a routine diagnostic for future naval
applications.
ACKNOWLEDGEMENT
The work described in this report could not have been
done without the hard work and dedication of Dr.
David Fry, Ms. Deborah Furey and Mr. David
Mackintosh. Their effort and expertise are much
appreciated. The authors would also like to thank:
Dr. Joe Katz, of Johns Hopkins University, for use of
his submersible PIV system, Dr. Jerome Feldman of
NSWC for sharing his insights into submarine
maneuvering, and Dr. In-Young Koh, of NSWC, Dr.
Thomas T. Huang and Mr. Wade Miner of Newport
News Shipbuilding for their support of this project.
REFERENCES
Adrian, R.J., "Particle-imaging Techniques for
Experimental Fluid Mechanics," Annual Review of
Fluid Mechanics, Vol. 23, 1991, pp. 261-304.
Bertuccioli, L., G.I. Roth, J. Katz, and T.R. Osborn,
"Turbulence Measurements In The Bottom Boundary
Layer Using Particle Image Velocimetry," Journal of
Atmospheric and Oceanographic Technology, Vol.
16,No.11, Part 1, 1999, pp. 1635-1646.
Coleman, Hugh W. and W. Glenn Steele,
Experimentation and Uncertainty Analysis for
Engineers. John Wiley and Sons, New York, 1989, p
275.
Fu, T. C., Atsavapranee, P., and Hess, D. E.," PIV
Measurements of the Cross-Flow Velocity Field
Around a Turning Submarine Model (ONR Body-
1)," NSWCCD-50-TR-2001/036 July 2001,
Carderock Division, Naval Surface Warfare Center,
Hydromechanics Directorate Research &
Development Report.
Grant, I., "Particle Image Velocimetry: A Review,"
Journal of Mechanical Engineering Sciences, Vol.
211, No. 1, 1997, pp.55-76.
Liu, H. L. and T. Fu, "PIV Measurement of Vortical
Structures in the DTMB Rotating Arm Facility,"
CRDKNSWC/HD-1416-02, 1994, Carderock
Division, Naval Surface Warfare Center,
Hydromechanics Directorate Research &
Development Report.
"Nomenclature for Treating the Motion of a
Submerged Body Through a Fluid," Report of the
American Towing Tank Conference prepared by the
Hydromechanics Subcommittee of the Technical and
Research Committee of the Society of Naval
Architects and Marine Engineers, Technical and
Research Bulletin No. 1-5, Apr 1950.
Sinha, M. and J. Katz, "Quantitative Visualization of
The Flow in A Centrifugal Pump with Diffuser
Vanes, Part A: On Flow Structure and Turbulence,"
Journal of Fluids Engineering, Vol. 122, No. 1,
2000, pp. 97-107.
OCR for page 668
DISCUSSION
Craig Merrill
Naval Sea Systems Command, USA
During the course of the experimental runs that
were performed, did you notice any significant
run-to-run unsteadiness? If so, were you able to
quantify it or identify its source?
Did you note any discernable time-dependent
relationship between forces and vortex position?
How stable were the separation lines?
Similarly, were you able to trace the time-
dependent path of the sail vortex and, if so, did it
give you any insight into typical radio controlled
model vehicle responses during a turning
maneuver?
AUTHORS' REPLY
There is a moderate level of run-to-run variation
on the forces and moments on the submarine
hull. For example, the standard deviation on
both the hull vertical force and pitching moment
is roughly 10%. This variation in forces and
moments is possibly due to run-to-run variation
in the position and strength of the sail tip vortex,
even though these cannot be statistically
characterized due to the limited amount of PIV
data available for each ensemble. Qualitatively,
the variation on the position and strength of the
sail tip vortex appears small when compared
among the 4 to 5 experimental runs for each PIV
configuration.
The PIV images were taken with a stationary
submersible PIV system as the submarine model
passed by. Each successive image pair
represents data at different cross sections along
the model. Therefore, there is no time-
dependent data fixed to the frame of reference of
the submarine hull to correlate with time-
dependent hull forces.
A steady trajectory of the vortex along the hull
was constructed and shown in the figure below:
Vo~x lrajec~y
m~VG
art;
-0.4
-
N
~Q3
_a 8
0 ~
~ .1.
. ~
DOWNSTREAM
.
~ 15 1 05
Y(m)
However, it is difficult to extrapolate the results
to the behavior of a radio-controlled model
maneuver since a RCM maneuver is inherently
unsteady. The vortex trajectory shown above is
for a rotating-arm model performing the steady
portion of a time-dependent RCM model turn.
Representative terms from entire chapter:
flow field
