Phase-Averaged Towed PIV Measurements for Regular Head Waves in a Model Ship Towing Tank
J. Longo, J. Shao, M. Irvine, L. Gui, and F. Stern
Iowa Institute of Hydraulic Research
The University of Iowa, Iowa City, IA, USA
PIV and Modeling Water Wave Phenomena
Cambridge, UK
17-19 April 2002
unsteady forces and moments, wavefield, and flowfield for
model 5512 in regular head waves [Gui et al., 2001c; Gui et
al., 2002; Wilson and Stern (2002)] of which the EFD work
was part of an international collaborative project between
IIHR, INSEAN, and DTMB on EFD/CFD and uncertainty
assessment for DTMB model 5415 (Stern et al., 2000). The
remaining EFD task is procurement of the unsteady
flowfield and UA for model 5512 at the nominal wake
plane. The present study is precursory for this task and will
provide documentation of the unsteady data-acquisition and
reduction procedures along with detailed data of the incident
headwave flowfield and comparisons with 2D progressivewave theory for evaluation of the results herein.
Abstract. Phase-averaged towed PIV measurements are
made for regular head waves in a model-ship towing tank
using both fixed and towed PIV systems in preparation for
tests with model ships. Data reduction and uncertainty
assessment software are developed and tested for both calm
water and long wave, low steepness conditions used in
previous tests with surface combatant. The results are
validated through comparisons with progressive wave
theory.
1
Introduction
Focus of engineering fluid dynamics research is moving into
unsteady flows in support of computational fluid dynamics
(CFD) code development for simulation-based design with
numerous natural and forced unsteady flow applications for
aerospace, turbo machinery, and marine and ship
hydrodynamics industries. Meeting this challenge requires
significant advances in both CFD and experimental fluid
dynamics (EFD).
Present interest is in unsteady viscous ship
hydrodynamics in support of unsteady Reynolds-averaged
Navier Stokes (RANS) code development. Authors have
identified forward-speed diffraction problem, i.e., restrained
body advancing in regular headwaves, as building block
problem towards ultimate goal of physical understanding
and simulation of viscous nonlinear seakeeping and 6DOF
maneuvering. Approach is complementary CFD, EFD, and
uncertainty assessment (UA). CFD is used to guide EFD,
EFD is used for validation and model development, and
lastly CFD is validated and fills in sparse data for complete
documentation and diagnostics of flow. Initial CFD study
was conducted by Rhee and Stern (1998) and validated
using Wigley hullform EFD data from Journee (1992) for
investigation of unsteady forces and moments. A
concurrent EFD study involving detailed measurement (Gui
et al., 2001b) and UA (Gui et al., 2001a) of the turbulent
nominal wake boundary layer of naval combatant DTMB
model 5415 geosym (model 5512) was completed for
development and commissioning of a towed, particle image
velocimetry (PIV) measurement system for the Iowa
Institute of Hydraulic Research (IIHR) towing tank. Both
CFD and EFD efforts were then initiated to investigate
2
Test design
2.1
Facility
The tests are conducted in the IIHR towing tank, which is
100 m long and 3.048 m wide and deep. The tank is
equipped with a drive carriage, plunger-type wavemaker,
and moveable wave dampener system. The drive carriage
houses a computer (PC) and data-acquisition
instrumentation, and pushes a 5.5-m trailer which is used as
a platform for the PIV system and point of attachment for
models. The wavemaker is hydraulically driven and
controlled with an MTS controller and LabView software.
It is capable of producing a wide range of wavelengths
(λ=0.5-6.0 m) and wave steepnesses (Ak=0.025-0.3) and
can also generate irregular waves. The wave dampeners are
raised and lowered from the carriage before and after runs
and enable twelve- and twenty-minute intervals for steady
and unsteady tests, respectively.
A right-handed Cartesian coordinate system (x, y, z) is
used for the tests (Fig. 1). The origin is at the intersection
of the calm free surface and the leading edge of the PIV
measurement area (MA). The x, y, z axes are directed
downstream, into the page, and upward, respectively. The
coordinate system moves with the speed of the carriage,
trailer, and PIV system Uc. PIV data is transformed into a
wave-based coordinate system after defining the phase angle
associated with each vector map.
1
2.2
Data-reduction equations
Measured variables are the incident wave flowfield (U,V,W)
and elevation (z). The data-reduction equations for discrete
PIV measurements, vector map phase angle, and wave
elevation are expressed
Lobj S k ,i
C k ,i =
for k = 1, 2, 3; i = 1, 2,L , M
(1)
Limg ∆tU c
γ i = −γ I −
D
∆t
2π −
2π ; i = 1,..., M
Te
λ
(2)
z
(3)
L
where Lobj is the width of the camera view in the object
plane, Limg is the width of the digital image, Sk,i is the
component of the particle image displacement, ∆t is the time
between PIV images, D is the distance between a wavemeasuring servo probe and the PIV MA, and L is the tank
depth (L=3.048 m). k equals 1, 2, 3 for the coordinates x, y,
z, respectively. Mean and turbulent flowfield can be
computed from a population of M discrete measurements.
Incident wave-elevation data (z) is normalized with the
towing tank depth.
z
MEASUREMENT
AREA
x
DETAIL 1
(COORDINATE SYSTEM)
PIV
Uc = 1.53m/s
SERVO-WAVE
PROBE
WAVEMAKER
zma
INCIDENT
WAVE
SEE
DETAIL 1
Ak = 0.025
λ = 4.572m
MEASUREMENT
AREA
Fig. 1. Experimental setup showing wavemaker, PIV
system, servo wave probe, model trailer, and
incident head wave (λ=4.572 m, Ak=0.025).
Post-processed variables include encounter
frequency (fe) and Nth-order Fourier series (FS) coefficients
for PIV and wave elevation data. fe is computed with a
standard fast-Fourier transform (FFT) of the ζI(t) time
history. Next, a FS analysis is conducted on ζ I(t) to
determine the phase of the incident wave at t=0 sec. The
generalized Nth-order FS for given variable X (X=ζ, U, V,
W) is expressed
X F (t ) =
X0 N
+ ∑ X n cos (2πnf e t + ∆γ n )
2 n=1
(4)
∆γ n = γ n − γ I
(5)
X n = an2 + bn2
(6)
b
γ n = tan −1  n
 an
(7)



(8)
bn =
2 T′
∫ X(t)sin(2πnf et )dt for n = 0, 1, 2,K
T 0
(9)
2.3
Measurement systems
The towed DANTEC PIV system combines hardware and
software that are integrated into a single measurement
system illustrated in Fig. 1. The PIV hardware components
(hydrodynamic strut, laser, light-guiding arm, light-sheet
optics, digital camera) are assembled with a massive 2D,
computer-controlled traversing system capable of automated
movement along the transverse (y) and vertical (z) axes.
Movement in the x-coordinate is done manually. The strut
is pressurized, partly submerged, and contains a 20 mJ, dual
cavity Nd:Yag laser and light-guide arm for steering 532 nm
beams through the light-sheet optics, which are housed in a
submerged, streamlined torpedo. The digital camera is a
1K×1K (1008×1018 pixels) cross-correlation camera fitted
with a f/1.4 50 mm lens that views the light sheet from a
distance of 50 cm through a 90° mirror. The maximum
object-plane size or MA is 7.5×7.5 cm2, however, smaller
areas can be utilized to increase processor throughput. The
camera is housed in a separate submerged, streamlined
torpedo. Light-sheet and camera torpedoes are joined with a
rigid, streamlined mini-strut such that the light sheet is
orthogonal to the viewing axis of the camera. Fig. 1 shows
the system configured to measure the vertical (xz) plane
wherein mean (U,W) and turbulent (uu,ww,uw) variables
are acquired. Counter-clockwise rotation downward
through 90° of the torpedoes and mini-strut about the light
sheet torpedo longitudinal axis enables measurements in
horizontal (xy) planes wherein mean (U,V) and turbulent
(uu,vv,uv) variables are acquired. Synchronization of the
laser and camera, image processing, and acquisition of
towing carriage speed are performed with the DANTEC
PIV 2000 processor which is equipped with a four-channel,
12-bit analog-to-digital (AD) card. Data acquisition and
parameter settings are facilitated with an IBM-compatible,
Windows NT PC equipped with a National Instruments
GPIB card and DANTEC v.3.11 Flowmanager software.
Results in the form of vector maps are displayed virtually in
real-time at a rate of 7.5 Hz. Unsteady data is phase-locked
by connection of a servo wave probe to the PIV AD board.
The probe monitors the incident wave either directly above
the MA or from some distance D upstream of the MA. The
PC
PIV
2000
PROCESSOR
2 T′
∫ X(t)cos(2πnf et )dt for n = 0, 1, 2,K
T 0
wherein XF is the reconstructed time history; Xn is the nthorder harmonic amplitude; γn is the corresponding phase; N
is the order of the FS and chosen high enough to include all
important frequency components. ∆γn is the harmonic phase
adjusted with the incident wave. Time interval T’ is a
multiple of the encounter wave period Te (=1/fe).
ζI =
y
an =
2
second and fourth elevations provide 50% overlap with the
first and third and third and fifth elevations, respectively,
and the values are taken from the calm free surface to the
top of the MA. Incident wave amplitude is 18.0 mm which
means shallowest elevation places top of MA 7.0 mm
beneath wave troughs. For the xy configuration data is
taken at z=-62.5 and -137.5 mm. For NMA, z=-25.0, 53.34, and –110.45 mm where the second elevation provides
roughly 66 and 33% overlap with the first and third
elevations, respectively. For the unsteady cases, incident
wave data is taken directly over the center of the
measurement area (WMA) and 4.42 m upstream of the
measurement area midpoint (NMA).
servo probe is a ±5 cm, pre-calibrated Kenek wave probe
with a resolution of 0.1 mm and maximum probe velocity of
700 mm/s.
Silver-coated hollow glass spheres with a density of
1600 kg/m3 and an average diameter of 15 µm are used as
seed particles. These particles have demonstrated very good
light-reflectance for PIV image capture and adequate
suspension capability. Additionally, the particles are
capable of following sinusoidal motions with frequencies up
to 1375 Hz.
The second measurement system is composed of a DOS
PC and the IIHR speed circuit. This measurement system is
used for monitoring and measuring the carriage speed for
each data-acquisition run. The DOS PC also monitors the
output from the servo wave probe.
2.5
Data acquisition (DA) setup and procedures
For WMA, the full measurement area is used with 32x32
pixel interrogation areas, no overlap, 8 pixels of offset in the
axial direction to account for strong axial component, and
no window function. For NMA, a subset of WMA is used
which is 412 pixels wide, full height, centered on WMA,
and 18% total area of WMA. Interrogation areas are 32x32
pixels, 50% overlap in both coordinates, 8 pixels of offset in
the axial coordinate, and a Gaussian window function is
used in the correlations. Above parameters yielded highest
quality data. The final vector numbers are 31x31 and 11x62
for WMA and NWA, respectively. PIV image pairs are
taken at 133 ms intervals, i.e., 7.5 Hz data rate and time
between images is ∆t=490µs and 16170µs, for cases with
and without forward speed, respectively. DOS data is
sampled for 10 seconds over two analog channels at a rate
of 410 Hz.
For unsteady DA, first reference voltages for the servo
probe and speed circuit are measured, then sidewall
dampeners are raised, and the wavemaker is started and
allowed to push a fully developed train of waves across the
length of the tank The carriage is started and reaches a
steady speed after which PIV acquisition is initiated from
the PC keyboard. The laser goes into a free-running, 15 Hz
mode. For each double image, the PIV processor makes one
sweep across the analog inputs which includes the output
from the servo wave probe (ζI) and correlates the digital
images. The DOS computer runs in parallel with PIV
windows machine, acquiring carriage speed and incident
wave data. Vector maps are stockpiled over several carriage
runs at a rate of 100-200 maps per carriage run.
Convergence time histories (Fig. 2) reveal that roughly 1200
and 2000 vector maps are required for steady and unsteady
tests, respectively, for converged mean and turbulence
variables and harmonics. For steady DA, same procedures
apply except the wavemaker remains stationary.
2.4
Conditions
Steady (without wave) and unsteady (with wave) tests are
performed with and without forward speed. For cases with
forward speed, Uc=1.53 m/s. For unsteady cases, the head
wave parameters including wavelength, frequency, and
steepness are λ=4.572 m, fw=0.584 Hz, and Ak=0.025,
respectively, where fw and Ak are defined in equations (10)
and (11), and A and g are wave amplitude and local gravity
acceleration (g=9.8031 m/s2), respectively.
g
fw =
(10)
2πλ
2πA
Ak =
(11)
λ
The wave parameters and non-zero forward speed cases
combine to produce an encounter frequency
U
g
fe =
+ c ≈ 0.922 Hz
(12)
2πλ
λ
which is the dominant frequency of the unsteady response in
the incident head wave flowfield. The above speed and
wave conditions are based on Gui et al. (2001b,c) and Gui et
al. (2002). Uc=1.53 m/s produces a Froude number
Fr = U c
gL pp = 0.28 for model-scale testing with the
Lpp=3.048 m model 5512 which is the cruise speed for fullscale version. The wave parameters were selected following
observation and analysis of unsteady forces and moment
results because these parameters produced the most
manageable linear response in the farfield of the ship model.
Measurements are performed with wide (WMA) and
narrow (NMA) measurement areas with vertical (WMA,
NWA) and horizontal (WMA) lightsheet orientations along
the centerline of the tank. WMA captures significantly
more area and data. NMA has 18% the area of WMA but
was used for study of Gui et al. (2001b), has higher data
throughput, and will later be shown to fortuitously crop
unwanted amplitude and phase errors in the unsteady data
with forward speed. For WMA and the xz configuration,
z=-25.0, -62.5, -100.0, -137.5, and -175.0 mm where the
2.6
Data reduction (DR) procedures
Data is post-processed with unsteady and steady FORTRAN
90 source codes written and executed from a Windows PC.
For unsteady DR, data is phase averaged by processing
3
systematic and random error sources and 95% confidence,
multiple-test approach. Previous development of PIV UA
procedures (Gui et al., 2001a,b) has yielded uncertainty
estimates for turbulent nominal wake plane and are listed in
Table 1. Ongoing UA of the current datasets and
development of UA procedures for unsteady PIV will be
provided in the full paper.
batches of carriage runs. Datasets (PIV and DOS speed
files) are grouped by elevation and read as input. fe is
computed from DANTEC-sampled ζI for each carriage run
and FS coefficients are then computed which yields firstharmonic phase at t=0 sec and wave amplitude. The
following procedures are completed at each grid point in the
MA. fe is then used in equation (2) to compute specific
phase angle of all vector maps in each carriage run. Data is
sorted on phase angle from 0-2π and then filtered with a
two-stage range filter and 2D-median filter to remove
spurious vectors. Rejected vectors are not replaced because
the phase-averaging technique does not require this step. A
5th-order least-squares curve is fit to the filtered data which
represents the average unsteady response through one
encounter period. Then, a 2nd-order FS is computed of the
least-squares curve fit to obtain the harmonic amplitudes
and phases of the response. Turbulence quantities are
computed for valid vectors by first taking differences
between raw vector and FS reconstruction. Then, RMS
values are obtained from statistics of these differences over
all phase angles (0-2π) or in eight phase groups equally
spaced in 0-2π to test for phase-dependence of turbulence.
Convergence time histories for 0th and 1st-harmonic
amplitude and 1st-harmonic phase are computed Mvalid-10
times at seven equally spaced locations on the center of the
MA from top to bottom.
3. Results and comparison theory
Results are presented as percent difference between theory
and experiment. Theory for steady cases are calm water
(UT,WT=0) and uniform flow (UT=1, WT=0). Theory for
unsteady data is 2D progressive-wave theory which
characterizes the external flowfield with following
equations
γU1,W1 (radians)
U 1, W 1
0.02
(a)
0
1000
M valid
2000
4.00
2.00
0.00
(b)
0
1000
WT = 2πf w Ae kz sin( kx − 2πf e t )
(14)
3.1
Steady (calm water) with and without forward speed
Steady-flow data is presented for without and with forward
speed conditions in Figs. 3 and 4a,b, respectively, and
averages over MA are summarized in Table 1 for WMA and
NMA. Steady UA results from Gui et al. (2001c) are also
included in Table 1 for comparison. The results include
mean (U,V,W) and turbulence (uu,vv,ww,uv,uw)
parameters. V,W data is not displayed in the figures. V
data is not included in Fig. 4a and Table 1 but will be
provided in the full paper.
For Uc=0 m/s, contours (UT-UE) display a random
pattern and magnitude is two orders less than axial velocity
uncertainty (UU). Turbulence levels are several order-ofmagnitude less than uncertainty values for ship flowfield.
6.00
(i,j)=(6,1); U 1
(i,j)=(6,60); U 1
(i,j)=(6,1); W1
(i,j)=(6,60); W 1
(13)
The perturbation for headwave flowfield is computed by
subtracting the non-dimensional advance speed of the
carriage (Uc=1) from equation (13).
0.04
0.03
U T = 1 + 2πf w Ae kz cos( kx − 2πf e t )
2000
M valid
Fig. 2. Convergence histories of 1st-harmonic amplitude
(a) and 1st-harmonic phase for U,W at two grid
points.
Z
For steady DR, data is also reduced by processing
batches of carriage runs. Data is read and spurious vectors
are removed with a two-stage range filter and a 3D median
filter where the third dimension is time. Mean and
turbulence results are computed with statistical analysis at
each grid point from the full population of valid vectors.
Convergence time histories for each variable are computed
Mvalid-1 times at seven equally spaced locations on the
center of the MA from top to bottom.
X
U T-U E (%)
Uc=0 m/s
-0.01
-0.02
z
-0.03
-0.10
0.00
y
Y
0.10
0.925
0.930
0.935
0.940
x
0.945
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Fig. 3. Comparison (theory-experiment) of mean axial
flow for Uc=0 m/s
2.7
Uncertainty assessment
The uncertainty assessment of the measurement results
follows the ASME Test Uncertainty (1998). The UA
procedures are based on separation and identification of
For Uc=1.53 m/s, WMA, contours (UT-UE) display
organized, repeatable patterns independent of z with cells of
decelerated flow at leading and trailing edge. Origin of
patterns are unknown but are thought to be consequence of
4
either optical distortion of digital images or induced flow
about PIV underwater torpedoes, or both. The former
theory was tested by imaging standard grids, but no
detectable distortion in the test images was observed.
Z
are very small but 2 orders-of-magnitude larger for the case
with forward speed.
3.2
Unsteady (waves) with and without forward speed
Unsteady-flow data is presented for without and with
forward speed conditions in Figs. 5 and 6, and 7,
respectively, and averages are summarized in Table 2
(WMA) and Table 3 (NMA). The results include 0th
harmonic (U0,V0,W0), 1st-harmonic amplitude and phase
(U1,V1,W1,γU1,γV1,γW1), and unsteady turbulence (uu0-2π,ww02π,uw0-2π).
Z
Uc
Y
X
X
U T-U E (%)
U c=1.53 m/s
U T-UE (%)
Uc=1.53 m/s
Uc
-0.02
-0.04
z
-0.06
z
1.75
1.58
1.40
1.23
1.05
0.88
0.70
0.53
0.35
0.17
0.00
-0.02
Y
-0.04
1.75
1.58
1.40
1.23
1.05
0.88
0.70
0.53
0.35
0.17
0.00
Z
X
z
y
0.93
0.94 x
(a)
0.40
0.20
0.16
0.12
0.08
0.04
0.00
-0.04
-0.08
-0.12
-0.16
-0.20
-0.02
-0.03
-0.06
0.20
U 0T-U 0E (%)
-0.01
-0.08
0.00
Y
0
y 0.005
-0.005
0.000
0.005
y
(b)
0.935
x
0.925
0.930
0.935
0.940
x
0.945
(a)
Z
Fig. 4. Comparison (theory-experiment) of mean axial
flow for Uc=1.53 m/s for five elevations (a: WMA)
and three elevations (b: NMA).
Table 1.
X
U 1T-U 1E (%)
-0.01
Summary of steady PIV results with and without
forward speed and z=-25 mm.
Y
1.30
1.22
1.14
1.06
0.98
0.90
0.82
0.74
0.66
0.58
0.50
-0.02
U
NMA
z
WMA
0 m/s
1.53 m/s
1.53 m/s
UA
0.05%
-1.0%
1.2%
UU=2.4%
-
-
-
UV=7.7%
W
0.0004%
0.5%
0.080%
UW =4.4%
uu
0.00003%
0.012%
0.006%
Uuu=4.7%
vv
-
-
-
Uvv=4.3%
ww
0.00002%
0.0070%
0.0066%
Uww=5.0%
uv
-
-
-
Uuv=4.1%
uw
0%
0.00032%
0.00028%
Uuw=5.8%
-0.005
0.000
0.005
y
0.925
0.930
0.935
0.940
x
0.945
(b)
Z
X
-0.02
-0.03
-0.005
0.000
0.005
y
Also of interest is that potential-flow calculations for the
PIV underwater torpedoes in a uniform flow do not replicate
trends observed in Fig. 4a. For NMA, contour patterns (UTUE) have increased uniformity since focus area is a narrow
strip centered on WMA. Absolute value (UT-UE) roughly
same in comparison WMA and turbulence levels are same
order as for WMA but somewhat reduced. Uc=0 m/s and
1.53 m/s results set the mean and turbulence noise levels of
the fixed and towed PIV system, respectively. For the
former, mean-flow levels are roughly 0.05%,0.0005% for
U,W, respectively, and for the latter levels are roughly 1-2
order-of-magnitude larger. Turbulence levels for both cases
Y
γU1T-γU1E (%)
-0.01
z
V
-0.03
0.925
0.930
0.935
0.940
x
0.945
2.50
2.25
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
0.00
(c)
Fig. 5. Comparison (theory-experiment) of 0th and 1stharmonic amplitude and 1st-harmonic phase U for
Uc=0 m/s and one elevation.
V,W data is not displayed in Figs. 5 and 6 and V data and
unsteady turbulence are not included in Tables 2 and 3 but
will be provided in the full paper. Second-harmonic data is
computed but not shown.
For Uc=0 m/s, contours U0T-U0E, U1T-U1E, γU1T- γU1E
(Fig. 5a,b,c) display random patterns through WMA. γU1TγU1E is positive everywhere, thus making it a phase lead.
Magnitudes U0T-U0E, U1T-U1E, γU1T- γU1E are small
5
agreement theory is within a cross pattern centered on
WMA.
everywhere and regarded satisfactory, especially in
consideration of present orbital velocity magnitudes which
are about 5%Uc for the wave parameters and measurement
depth. Comparisons for W variables are similarly
satisfactory as shown in Table 2. Second harmonic
amplitudes are order of 1e-3 and 1e-4 for U2 and W2,
respectively, which is 1-2 orders magnitude smaller than
U1,W1 and indicates dominant 1st-harmonic response of the
flowfield to the incident wave. V1 (not shown or in Table 2)
is an order-of-magnitude smaller than U1,W1, which
confirms the 2D nature of the flowfield.
Z
Uc
X
Y
Z
-0.04
Y
z
0.925
0.930
0.935
0.940
x
0.945
0.935
x
Uc
(a)
X
z
0.925
0.930
0.935
0.940
x
0.945
-0.04
z
W 1T-W 1E (%)
1.50
1.35
1.20
1.05
0.90
0.75
0.60
0.45
0.30
0.15
0.00
-0.04
-0.06
0
y 0.005
Uc
Y
-0.06
0
y 0.005
0.935
x
0.935
x
Z
γU1T-γU1E (%)
z
-0.03
-0.005
0.000
0.005
y
0.925
0.930
0.935
0.940
x
0.945
Uc
X
Z
Y
Uc
γU1T-γU1E (%)
Fig. 6. Comparison (theory-experiment) of 0th and 1stharmonic amplitude and 1st-harmonic phase U for
Uc=1.53 m/s and one elevation.
-0.04
For Uc=1.53 m/s, contours U0T-U0E, U1T-U1E, γU1T- γU1E
(Fig. 6a,b,c) are changed and show organized, repeatable
patterns. 0th-harmonic trends are similar in shape and
magnitude with those observed in Fig. 4a, i.e., the uniformflow perturbation pattern is recovered. U1T-U1E mostly
uniform except for two circular cells downstream and
upstream of WMA leading and trailing edges, respectively,
where U1E is decreased. Phase comparison displays phase
lead everywhere and a quadrant pattern where best
-0.02
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
-0.04
-0.06
0
y 0.005
0.935
x
Y
γW1T-γW1E (%)
-0.02
(c)
X
z
-0.02
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
z
-0.01
Y
(b)
Z
X
X
-0.02
1.50
1.35
1.20
1.05
0.90
0.75
0.60
0.45
0.30
0.15
0.00
z
1.50
1.35
1.20
1.05
0.90
0.75
0.60
0.45
0.30
0.15
0.00
Uc
U 1T-U 1E (%)
Y
-0.02
Z
Y
U 1T-U 1E (%)
-0.01
0.935
x
Z
-0.02
X
-0.06
0
y 0.005
Z
-0.005
0.000
0.005
y
1.00
0.80
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
-0.04
-0.06
0
y 0.005
Uc
-0.03
W 0T-W 0E (%)
z
1.00
0.80
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
-0.02
-0.005
0.000
0.005
y
Y
U 0T-U 0E (%)
-0.01
-0.03
X
-0.02
1.75
1.58
1.40
1.22
1.05
0.88
0.70
0.52
0.35
0.17
0.00
Uc
X
Uc
U 0T-U 0E (%)
z
-0.02
Z
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
-0.06
0
y 0.005
0.935
x
Fig. 7. Comparison (theory-experiment) of 0th and 1stharmonic amplitude U,W for Uc=1.53 m/s and 1stharmonic phase U,W for three elevations.
6
harmonic amplitude and within 4-6% theory for 1stharmonic phase . As such, investigations of the unsteady
nominal wake flowfield for model 5512 can move forward
using the NMA and same DA/DR procedures documented
herein.
Average FS-amplitude differences are smaller than theory
but compare satisfactorily as deviation from theory is 1.0%.
Experimental phase leads theory by average of 4.2%.
Comparisons for W are similarly satisfactory as shown in
Table 2. As for case with zero-forward speed, second
harmonic amplitude U2,W2 are 1-2 orders magnitude
smaller than 1st-harmonic amplitudes U1,W1 confirming
dominant 1st-harmonic response of measured data with
moving carriage. Origin of the patterns in the unsteady data
are unknown but also could be consequence of either optical
distortion of digital images or an unsteady, induced flow
about PIV underwater torpedoes, or both. No CFD was
undertaken to determine if the observed patterns could be
simulated.
Patterns and trends in Fig. 6 indicate that best
comparison with theory occurs in a subregion (NMA)
centered on WMA. Results for this region are shown in Fig.
7 for both U,W and Table 3. Contours of comparisons 0thand 1st-harmonic amplitude and 1st-harmonic phase are
mostly uniform throughout NMA. Average 0th-harmonic
differences are very similar with those from uniform flow
test. Average 1st-harmonic differences are halved from case
with WMA. Average 1st-harmonic phase leads are 4-6% for
both U,W.
Table 2.
Table 3.
Summary of unsteady PIV results with and
without forward speed for WMA and z=-25 mm.
U0
Uc=0 m/s
Uc=1.53 m/s
-0.02%
0.40%
V0
-
-
W0
0.02%
0.43%
U1
1.0%
1.0%
V1
-
-
W1
0.8%
1.5%
U2
0.16%
0.15%
V2
-
-
W2
0.09%
0.18%
γU1
1.5%
4.2%
γV1
-
-
γW1
0.8%
-0.3%
uu0-2π
-
-
vv0-2π
-
-
ww0-2π
-
-
uv0-2π
-
-
uw0-2π
-
-
Summary of unsteady PIV results with forward
speed for NMA and three elevations.
z=-25.0
mm
z=-53.34
mm
z=-110.45
mm
U0
1.31%
1.23%
1.43%
W0
0.10%
0%
-0.22%
U1
0.7%
0.8%
0.6%
W1
0.7%
0.7%
0.7%
U2
0.13%
0.11%
0.17%
W2
0.07%
0.06%
0.08%
γU1
6.0%
6.2%
5.9%
γW1
4.3%
4.8%
4.5%
uu0-2π
-
-
-
ww0-2π
-
-
-
uw0-2π
-
-
-
4. Conclusions and future work
Phase-averaged towed PIV measurements are made for
regular head waves in a model-ship towing tank using both
fixed and towed PIV systems in preparation for tests with
model ships. Data reduction and uncertainty assessment
software are developed and tested for both calm water and
long wave, low steepness conditions used in previous tests
with surface combatant. The results are validated through
comparisons with progressive-wave theory.
Steady-flow results indicate random and organized
patterns for cases without and with forward speed,
respectively. Average comparisons with theory are roughly
within 0.05%,0.0005% for U,W for the former and
1.0%,0.1% for U,W for the latter. Turbulence values are
nearly negligible for both cases. All results are well within
previous steady-flow UA results. Unsteady-flow results
also display random and organized patterns in the FS
harmonic amplitudes and 1st-harmonic phase for cases
without and with forward speed, respectively. Best average
comparisons with 2D progressive-wave theory are roughly
within 1% for the 0th- and 1st-harmonic amplitude and 4-6%
for the 1st-harmonic phase and occur inside a narrow
window centered on the PIV object plane.
The origin of the patterns that emerge with forward
speed in the steady and unsteady flow are unknown. Efforts
to understand the source of the patterns included testing of
the digital images and potential-flow calculations of the
flow around the PIV torpedoes for the steady case but both
were inconclusive. The prevailing theory for these patterns
Based on the above data, Fig. 7 and Table 3
demonstrate good agreement with theory and are considered
benchmark performance levels for towed, unsteady PIV at
IIHR, i.e., approximately within 1% theory for 0th- and 1st-
7
is sub-pixel distortion in the digital images, induced flow by
the underwater PIV torpedoes, or a combination of both.
The final paper will include expanded discussion of the
DA and DR procedures including a figure summarizing the
DR processes, complete discussion of procedures and
results of the steady and unsteady UA, and complete
presentation of the three-dimensional steady and unsteady
measurements including figures for xy-plane data and
updates of tables for V results and unsteady turbulence.
Future work includes steady and unsteady PIV
measurements and full UA of the nominal wake plane of
model 5512 for same long wavelength, low wave steepness
incident wave presented herein. Documentation of the test
program and results are ongoing (Longo et al., 2002). The
data and UA will be archived at
www.iihr.uiowa.edu~towtank.
Wave Field,” Int. J. Num. Meth. Fluids, Vol. 37, pp.
445-478.
R. Wilson and F. Stern, (2002), "Forward Speed Diffraction
Problem for a Naval Surface Combatant using an
Unsteady RANS Method," 24th Symposium on Naval
Hydrodynamics, Fukuoka, Japan (in preparation).
Stern F, Longo J, Penna R, Oliviera A, Ratcliffe T,
Coleman H (2000), International Collaboration on
Benchmark CFD Validation Data for Naval Surface
Combatant. 23rd ONR Symposium on Naval
Hydrodynamics, Val de Reuil, France, 17-22 September.
Acknowledgements
This research was sponsored by Office of Naval
Research under Grants N00014-96-1-0018 under the
administration of Dr. E.P. Rood and N00014-01-1-0073
under the administration of Dr. Pat Purtell whose support is
greatly appreciated.
References
ASME, (1998), “Test Uncertainty,” ASME PTC 19.1-1998,
The American Society of Mechanical Engineers, 112
pp.
Gui, L., Longo, J., and Stern, F., (2001a), “Biases of PIV
Measurement of Turbulent Flow and the Masked
Correlation-Based Interrogation,” Experiments in
Fluids, Vol. 30, Issue 1, pp. 27-35.
Gui, L., Longo, J., and Stern, F., (2001b), “Towing Tank
PIV Measurement System, Data and Uncertainty
Assessment for DTMB Model 5512,” Experiments in
Fluids, Vol. 31, pp. 336-346.
Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F.,
(2001c), “Forces, Moment, and Wave Pattern for
Surface Combatant in Regular Head Waves-Part 1:
Measurement Systems and Uncertainty Analysis,”
Experiments in Fluids, Vol. 31, Issue 6, pp. 674-680.
Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F.,
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8