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24th Symposium on Naval Hydrodynamics
Fukuoka, JAPAN, 8-13 July 2002
Phase-Averaged PIV for Surface Combatant in Regular
Head Waves
J. Longo, J. Shao, M. Irvine, and F. Stern
(Iowa Institute of Hydraulic Research,
The University of Iowa, Iowa City, lA, USA)
ABSTRACT
Results are presented from towing-tank tests of the
phase-averaged nominal wake velocities (U. V, W) and
~ . . .
Reynolds stresses ~ uu, vv, ww, up, uw ~ for a surface
combatant advancing in regular head waves, but
restrained from body motions, i.e., forward-speed
diffraction problem. The geometry is DTMB model
5512, which is an L=3.048 m, 1/46.6 scale geosym of
DTMB model 5415. The experiments are conducted in
a 3x3x100 m towing tank equipped with a plunger type
wave maker. The measurement systems include a
towed particle image velocimetry and servomechanism
wave probe. Uncertainty assessment following
standard procedures is used to evaluate the quality of
the data. Comparisons steady and unsteady data
indicate streaming effects in 0th-harmonic and phase-
averaged turbulence, which are primarily observed at
the location of a boundary layer bulge containing low-
momentum fluid. Unsteady data is analyzed separately
for its harmonic content and indicates clear trends in
IS'- and 2n4-harmonic amplitudes and 1 St-harmonic
phase patterns and phase leads and lags between
velocity components. Animation of the nominal wake
is achieved through Fourier-Series reconstruction of the
velocity components. Comparison with forces and
moment and wave elevation animations from previous
study for same conditions indicates boundary layer
contraction and expansion for local wave elevation
increases and decreases, respectively. Unsteady heave
force reaches maximum and minimum values when the
nominal wake contracts and expands to its limiting
values, respectively. The data will be used for
validation of Reynolds-averaged Navier Stokes
simulation of DTMB model 5512.
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 head
waves (or incident waves), 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 (2001) 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. 2001 b) and
UA (Gui et al. 2001a) of the turbulent nominal wake
boundary layer of naval combatant DTMB model 5415
geosym (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 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. 2001~.
The present study represents completion of the
remaining EFD task, which is procurement of the
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unsteady flowfield and UA for model 5512 at the
nominal wake plane. Precursory work (Longo et al.
2002) has been completed for towed PIV measurements
of a regular, two-dimensional (2D) progressive wave
flowfield in order to (1) develop necessary data
acquisition, reduction, and UA tools for conducting
unsteady PIV experiments with ship models; and (2)
evaluate the nature of the head wave flowfield which
will be used to excite the nominal wake of model 5512.
Progressive wave results have demonstrated
effectiveness of newly developed, phase-averaging
techniques for unsteady PIV. Results for wave
elevation and flowfield velocities show dominant 1St-
harmonic or linear response. Comparison of
experimental results with 2D progressive wave theory
for long wave, low-steepness waves indicate ~0.9% and
0.8-2.0% difference in 1 St-harmonic amplitude and
phase, respectively, for axial and vertical velocity
components. This paper provides detailed
documentation of the test design with ship model
including data-acquisition and reduction procedures,
UA methodology for unsteady PIV, steady and
unsteady results, and conclusions with future work.
2 TEST DESIGN
2.1 Facility and model
The tests are conducted in the IIHR towing tank.
The tank is 100 m long, 3.048 m wide and deep, and
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 (~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. 11. The origin is at the intersection of the
calm free surface and forward perpendicular (FP, x=O)
of the model. 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.
The geometry of interest is model 5512, a 1:46.6
scale, I'3.048 m, fiber-reinforced Plexiglas hull with
block coefficient, CB=0.506, Fig. 2. The model has a
forward-facing wedge-shaped bow above the waterline,
a sonar bow dome below the waterline, and a transom
stern. The model is unappended for the current tests,
i.e., not equipped with shafts, struts, propulsors, or
rudders. To initiate transition to turbulent flow, a row
of cylindrical studs of 1.6 mm height and 3.2 mm
diameter are fixed with 9.5 mm spacing on the model at
x=0.05. The size and spacing of the studs is in
accordance with standard practices. PIV measurements
are made on the port side of the model where the hull
surface is painted black for minimization of laser-sheet
reflection.
(a)
n Servo-wave
~~ ~-~
(b)
Fig. 1. Experimental setup: (a) wavemaker, PIV
system, servo wave probe, model trailer,
model 5512 and incident head wave (~4.572
m, Ak=0.0251; (b) coordinate system moving
with camera.
Fig. 2. Model 5512.
2.2 Data-reduction equations
Measured variables are the steady and unsteady
flowfield (U. V, W) and elevation (z). The data-
reduction equation for steady or unsteady,
instantaneous PIV measurements are expressed
C _ obj k.i. j
~ Bi Li~ng atUC
k=1,2,3; i=l' ,Nvm; j=l, tNcr (1)
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Representative terms from entire chapter:
nominal wake
where Lobe iS the width of the camera view in the object
plane, Limg iS the width of the digital image, Skid is the
component of the particle image displacement, and At is
the time between PIV images. The indices on C and S
designate (1) velocity component: k=1, 2, 3 for U. V,
W. respectively; (2) vector map number: i=1,...,NVm
where NVm is the total number of vector maps in a
single carriage run; and (3) carriage run number:
j= 1, . . . ,NCr where NCr is the total number of carriage runs
for a single position of the PIV measurement area. The
data-reduction equation for incident wave elevation is
Its zing
For unsteady PIV measurements, vector-map phase
angle is defined
Hi j =_ + D 271 _ ti 2~
where Gil is the 1St-hamonic phase angle of the jeh-
incident wave, D is the distance between the servo
wave gage and middle of the PIV measurement area,
is the wavelength of the incident wave, ti is the time
stamp of ith vector map, and Te is the encounter period.
Steady post-processed variables include mean
values, normal stresses, and shear stresses expressed
below in equations (4146), respectively.
ck =
4,, AtU N ~ Skij = ~ MU Sk (4)
| N. Aid 2
cock N ~ (Ck,ij Ck ) k = 1,2,3 My
CmCn = N ~ (C'n if Ck Xcn ij Ck )
n=1,2,3; mean (6)
NVa~ is the number of valid vectors at any given grid
point in the measurement area which remain after
applying one or more filters to NVm*Ncr data values.
Unsteady post-processed variables include
encounter frequency (fe), Nth-order Fourier series (FS)
coefficients for PIV and wave elevation data, and
phase-averaged turbulence. fe is computed with a
standard fast-Fourier transform (FFT) of the butt time
history. Next, FS analysis is performed on ~ bite to
determine the phase of the incident wave at t=0 sec.
The generalized N~-order FS for given variable X
(X=(, U. V, W) is expressed
X F (
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) Mane 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 to the incident wave
elevation 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 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 ,um 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.
2.4 Conditions
Steady (without wave) and unsteady (with wave)
tests are performed with forward speed, UC=1.S3 m/s.
Steady tests are repeated from previous study (Gui et al,
2001b) in order to map a larger region of the nominal
wake and facilitate comparisons between steady and
unsteady measurements. The model is rigidly fixed to
the carriage and towed at the dynamic sunk and
trimmed condition, which is determined in calm water
at Fr=0.28 (Longo and Stern 1999~. For unsteady
cases, the head wave parameters including wavelength,
frequency, and steepness are ~4.572 m, fW=0.584 Hz,
and Ak=0.025, respectively, where fw and Ak are
defined in equations (15) and (16), and A and g are
wave amplitude and local gravity acceleration
(g=9.8031 mls2), respectively.
fw =127~
21:A
(15)
(16)
The wave parameters and non-zero forward speed cases
combine to produce an encounter frequency
fe = ~ 2~. + ~,c ~ 0.922 Hz
(17)
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. (2001 b), Gui et al. (2001cy, and Gui et al. (20021.
UC=1.S3 m/s produces a Froude number
Fr=Uc/~=0.28 for testing with model 5512
which is the cruise speed for full-scale 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 farf~eld of the ship
model.
2.5 Data acquisition (DA) setup and procedures
Measurement area dimensions are 192x1018 pixels
(14.3x74.9 mm; Fig. 3d) or 18% of the total field of
view. Advantages of above area include previous use
by Gui et al. (2001 b), higher data throughput, and
reduction of amplitude and phase errors for the
unsteady tests (Longo et al. 20021. 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. With
above settings, the measurement grid is l lx62.
Measurements are performed in six zones with
vertical (zones A,B,C) and horizontal (zones D,E,F)
lightsheet orientations (Fig. 3 a,b,c). All zones are
centered on the nominal wake plane and cover the
region of interest in the yz-crossplane as predicted by a
RANS solution for the current test conditions, i.e.,
x=0.935; -0.06=y=~0,ys); -0.06=Z=~0,ZS) where Ys, Zs are
coordinates of the model for measurements bordering
the hull surface. Zones are arranged to provide
adequate overlap to check for measurement continuity
across zones. Overlap is variable between zones A,B
(28-80%), constant between zones B,C (28%), and
constant between zones D,E,F (32%~. Zone A sets the
nearest measurement locations to the model through
placement of the top interrogation area at x=0.935
adjacent to the hull surface.
Fig. 3. Measurement locations: (a) model 5512 and
nominal wake measurement region; (b) zones
for xz-measurements; (c) zones for xy
measurements; (d) typical measurement area
in zone B; (e) final measurement grid at
nominal wake.
0.04
nn2
. , . . , n
.~ 6.0C
.~ _
3- . ~ tt,4.0C
_0.03 ~ ~-. ,~
. ~ 2.0t
.,,,,,,,,,.
0.02 0.00 _
0 1000 2000
(a) Nv.ud (b)
. · · · .
~0~0.e.~41 -
,~s~*~*~`
-- -- - ’- -- -- - (iD=(6,1 ); u,
~ ----- (i.D=(6,60);u, -
~ +---- (`D=(6,1);w,
-- - - A- - -- (iD=(6,60); W. -
0 1000 2000
Nv.ud
Fig. 4. Typical convergence histories of 1 St-harmonic
amplitude (a) and 1St-harmonic phase for U. W
at two grid points.
This ensures a minimum distance of 1.2 mm between
the closest measurement and the hull surface. For the
unsteady cases, incident wave data is taken 4.42 m
upstream of the measurement area midpoint. PIV
image pairs are taken at 133 ms intervals, i.e., 7.5 Hz
data rate and time between images is /`t=490,us. 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
enters 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 (~) 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 200 maps per carriage run.
Convergence histories (Fig. 4) 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.
2.6 Data reduction (DR) procedures
Data is post-processed with unsteady and steady
FORTRAN 90 source codes written and executed from
a Windows PC. A flowchart (Fig. 5) illustrates the
major steps in processing the unsteady data. For
unsteady DR, data is phase averaged by processing
batches of carriage runs. Datasets (PIV and DOS speed
files) are grouped by elevation and read as input (Fig.
6a). Instantaneous PIV components are scaled up 1.2%
with a scale-factor derived from uniform flow (i.e., no
model condition) tests. fe is computed from DANTEC-
sampled ~ for each carriage run and FS coefficients are
then computed which yields first-harmonic phase at t=0
sec and wave amplitude. fe is then used in equation (3)
to compute specific phase angle of all vector maps in
each carriage run. The following procedures are
completed at each grid point in the MA. Data is sorted
on phase angle from 0-2~ (Fig. 6b) and then filtered
with a two-stage range filter and 2D-median filter to
remove spurious vectors (Fig. 6b,c). Rejected vectors
are not replaced because the phase-averaging technique
does not require this step. A 5'h-order least-squares
curve is fit to the filtered data which represents the
average unsteady response through one encounter
period.
, If all precision
! locations processed ~
! - comp. precision limits '~
\ - comp. total uncertainties /
~ ,
Linear interpolation for
xy/xz data in TECPLOT
to 1 50x150 standard grid
-0
Constant-y or-z data is then matched across zone
boundaries and five passes of a moving-average filter is
applied across the range of 'y' or 'z' values to remove
high-frequency content (Fig. 71. The three-dimensional
flowfield at the nominal wake plane is construct
through linear interpolation to a standard grid of the
final results from both xz and xy configurations.
Animations of U. V, W are then generated with the FS
harmonic content and equations (71-~121. 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 histories for each variable are
computed NVa~i~-1 times at seven equally spaced
locations on the center of the MA from top to bottom.
2.7 Uncertainty assessment
The uncertainty assessment of the measurement
results follows the ASME Test Uncertainty (19981.
The UA procedures are based on separation and
identification of systematic (bias) and random
(precision) error sources, and combination with a root-
sum-square (RSS) procedure to determine total
uncertainty. 95% confidence levels are maintained for
both bias and precision limits through judicious
selection of individual bias error sources and small-
sample (M=10) multiple test approach for precision
errors.
2.7.1 Background
Original development of UA procedures for steady
PIV measurements were undertaken to commission the
IIHR towed PIV system and document the quality of
nominal wake data (Gui et al. 2001b). This effort
produced a related study that assessed a technique for
reducing the PIV cross-correlation evaluation bias with
window functions (Gui et al. 2001a). UA for unsteady
forces and moments and wavefield were then developed
using same framework as for above PIV studies (Gui et
al. 2001c; Gui et al. 2002~. Present study requires
development of all-new software for unsteady PIV UA,
combining many of the ideas and concepts from above
three studies for completion. Since much of the bias
and precision limit code for unsteady PIV UA overlaps
with steady PIV UA, all-new subroutines were
developed for steady PIV UA. These were tested
satisfactorily on the previous steady PIV dataset to
evaluate new software for accuracy.
The steady UA is completed again on the current
PIV dataset and presented in the next section with
comparisons previous UA values from Gui et al. 2001b.
The unsteady UA is then outlined at two levels
including the FS harmonics and the FS-reconstructed
time histories and includes the equations and
methodology. The UA procedures for FS harmonics
and FS-reconstructed time histories will be discussed,
and a summary of results for current measurements is
provided.
2.7.2 Steady UA
Measurement uncertainties for the steady mean and
turbulence variables are provided in Table 1 including
previous values from Gui et al. (2001b). Bias and
precision limit contributions are applicable to current
results, only. Current results are considered satisfactory
and show 1-3% reduced uncertainties over previous
values for six of eight variables with ww and up
moderately higher in magnitude than previous values.
UA reductions are generally attributed to better
repeatability of measurements, i.e., lower precision
limits. For the mean quantities, more than half of the
uncertainty is attributed to the bias limits, whereas, the
precision limits are dominant in the Reynolds stress
uncertainties.
Table 1. UA summary for steady-flow results.
Term Bx Px Ux tUx
U 66.5% 33.5% 1 .6% 2.4%
V 78.8% 21.2% 3.8% 7.7%
W 94.5% 5.5% 3.2% 4.4%
uu 42.6% 57.4% 2.6% 4.7%
vv 35.3% 64.7% 3.1% 4.3%
ww 47.3% 52.7% 5.3% 5.0%
uv 25.3% 74.7% 5.9% 4.1 %
uw 20.0% 80.0% 2.6% 5.8%
t: results from Gui et al. 2001 b
2.7.3 Unsteady UA
ln order to determine the bias limits for the FS
harmonic amplitudes and phases, it is assumed that the
measured value X deviates from the real value X' with
a bias error p. When the random error is not considered,
the real and measured value are related with
X=X'+p
(18)
The bias error ~ is not a constant, and it is usually a
function of the measurement value. For simplification,
we assume the relation is linear, i.e.
F=fo+^
(19)
where K iS the bias gradient, and Q0 is the constant part
of the bias error. The FS harmonic amplitudes and
phases (n=O) for the biased and unbiased cases are
related as follows:
an = , ~ (~1 + K\JX (`t~Jcos(~2~nit~J dt + , ~ ~Bo cos(~2mnitiJdt
T 0 T 0
= (~1 + K) '; X (
harmonic amplitude uncertainties are judged
satisfactory in consideration of smaller dynamic ranges
for 1 St-harmonic quantities. Second harmonic
uncertainties are larger due to small dynamic range of
these quantities but later results will show repeatable
coherent patterns in second harmonics. First-harmonic
phase uncertainties are moderate but elevated for UP
due to high precision limits. Roughly 95% of the bias
limit for these variables is associated with the bias limit
in Te. Second-harmonic phase uncertainties are
increased as measured values are smaller and near
limiting resolution of PIV system. Precision limit
contributions for these uncertainties are nearly 100%.
Uncertainties for full-range, phase-averaged turbulence
are larger for 3 of 5 variables than for the steady case.
As with the steady case, precision limits are weighted
more heavily for the unsteady turbulence quantities.
Interestingly, many of the y-coordinate uncertainties are
elevated in comparison with the other coordinates. This
may result from conducting the multiple tests in a
region that has high natural unsteadiness. Additionally,
the 1St-harmonic amplitude and phase are very small in
this region and near the resolution of the PIV system
which makes accurate measurement more difficult.
Table 2. UA summary for FS harmonics.
Term Bx Px Ux
Uo 44.0% 56.0% 2.0%
Vo 30.9% 69.1 % 13.4%
Wo 94.3% 5.7% 3.2%
Hat 6.1 % 93.9% 4.4%
V1t 2.8% 97.2% 8.2%
W1t 3.9% 96.1 % 2.1 %
U2t 0.7% 99.3% 4.5%
V2t 0.4% 99.6% 4.4%
W2t 0.3% 99.7% 5.5%
JU1t 83.9% 16.1 % 6.2%
W1t 11.3% 88.7% 16.8%
Act 92.0% 8.0% 6.0%
U2t 61.2% 38.8% 13.7%
V2t 21.0% 79.0% 12.6%
N2t 67.2% 32.8% 19.9%
US FR 36.1 % 63.9% 4.1 %
VV FR 27.9% 72.1 % 5.1 %
WW FR 50.4% 49.6 3.6%
TV FR 3.2% 96.8% 8.7%
UW FR 2.8% 97.2% 2.3%
t normalized with X1; t: normalized with 2~
Measurement uncertainties for the FS-
reconstructed time histories are provided in Table 3.
These values combine influences of uncertainties in ash,
1St, 2n~ harmonic amplitudes and 1St, 2n~ harmonic
phases. All uncertainties are judged satisfactory with
highest accuracy in the axial coordinate as expected
since signal-to-noise ratios for this measurement are
consistently higher than for V,W. Precision limits are
weighted higher than bias limits for UF(t),VF(t) and visa
versa for WF(t).
Table 3. UA summary for reconstructed time histories
of U,V,W.
Term BXF PXF UXF
UF(t) 38.0% 62.0% ~ .7%
VF(t) 25.4% 74.6% 5.6%
W F(t) 90.7% 9.3% 4.7%
3. RESULTS AND DISCUSSION
Steady and unsteady PIV results are presented at
the nominal wake for Fr=0.28 and Fr=0.28, Ak=0.025,
~4.572, respectively. The results are organized with
initial discussions of the 5512 steady flow including
comparisons previous and current PIV results. Then,
the incident wave elevation and flowfield
measurements for Ak=0.025, ~4.572 m are discussed
to evaluate the nature of the inflow for unsteady PIV.
Previous unsteady forces and moment and wavefield
for current incident wave parameters are then
summarized to aid in later discussion of unsteady PIV
results. Finally, the unsteady flow is discussed with
regard to comparisons 0~-harmonic and steady, FS
harmonics, and FS-reconstructions of the flowfield.
3.1 Steady flow
The complete IIHR dataset for 5512 steady-flow
experiments at Fr=0.28 includes Longo and Stern
(1999~: resistance, sinkage and trim, wave profile,
nominal wake with five-hole pitot probe; Gui et al.
(2001b): nominal wake with PIV; and Gui et al. (2001 c)
and Gui et al. (20021: wave elevations. The current
steady PIV measurements replicate the data from Gui et
al. (2001b) in order to check the quality of present data
and facilitate comparisons of steady and unsteady
flowfield variables. Additionally, current PIV
measurements cover a larger area, which results
because unsteady effects in the flow are present further
from the hull centerplane and free surface for the
unsteady case. Fig. 8 is a sample comparison of
previous and current xy-configuration mean (U. V) and
turbulence ~ uu, vv, up ~ PIV data at z=-0.025.
Evaluation of new data-reduction software for steady
PIV is facilitated by plotting reprocessed data with new
code and published results from Gui et al. 2001b.
Current data represents processed results from zones D,
E, F prior to data-matching procedures illustrated in
Fig. 7 and allows evaluation of data overlap between
common areas in adjacent zones. Comparisons of
reprocessed data and published results show favorable
agreement but trends and magnitudes of the five
variables are not replicated everywhere which are likely
due to small differences in the range and 3D-median
filtering that was applied to the dataset. Tests have
shown modest levels of sensitivity in the mean and
turbulence variables for some data with different filter
settings and techniques. It was judged that most of the
data differences were within the noise of the data such
that the present steady PIV code performance was
satisfactory.
1.0C
O.9C
0.8C
0.7C
0.60
0.5C
0.4
nnn~
a' ' ' I ' ' ' .
~ - -
- ~ ~
- ~~ IF`'
: ~
"? Zone D
- 0 Zone E
o Zone F
Gui: zone A new processing
Gui: zone B new processing
Gui et al. 2001 b
0.2(
0.1'
0.1(
0.0!
n n'
0.00(
-0.06 -0.04 -0.02 0.00
y
-0.06 -0.04 -0.02 0.00
y
A AD
......
?
0 001 ' ' ' ~ ~ I
-0.06 -0.04 -0.02 0.00 i
? ~
Fig. 8. Comparison previous (Gui et al. 2001b) and
current xy-configuration data at z=-0.025. ?
Qualitative agreement between the previous and current
data in Fig. 8 appears very good, however, there are
some differences in uu and vv in high-gradient
regions that are significant. These differences may be
due to differences in model-roughness, laser intensity
and seeding density, camera focus, or Neat between
previous and current experiments. Finally, the
closeness of overlap between zones D and E and E and
F is generally good for U. V, uv but degraded
somewhat for uu and vv in the outer flow where
transition between high- and low-turbulence areas
occurs. This effect is currently unexplained but may be
caused by digital-image distortion or interaction
between the submerged part of the PIV system and the
free surface and or hull surface. Overlap regions in the
data are treated with a matching technique illustrated in
Fig. 7.
Summary of current steady mean and turbulent PIV
measurements is shown in Fig. 9 as contours U. V, W
a d VW vectors and Fig. 10 as contours ks,___
uu, vv, ww,uv,uw, respectively.
~3
~ Elf
:g =1
0. ~ . '.
~~t 2
'~0, ~ ;. .
~ REV
~:~,~ ,,, ,........
Fig. 9. Summary of current steady-flow mean
measurements.
1
6~j'
~'~2
o~ ..
O:~
DOE25
~Y=16 . y
=st 1 ~ |
Amp' A ~
=
~3
Q`~
~ Am:
~ ~:4
0.DOf2
D.~ Y .
~ ~ '
_ 0,it, .
.~:~j~: . ~ j i: ~
~ i. ~ ~
~.~1 3
Or - ' 2
bat!
Q bole .
t~ :
0.~
O.~ .
O.
0
0
q:~ t:
0~ i ~
~ - it :t .
'??'' : 'i ~ i: :. I, ,, j ,, ~ ~~ ? v?
~ eat
,. l ~ ~ <~?~ ~4 0,~
i ~a.~3~ At ~ 1~ 4~ G.
!I'4:~14 1, ~ ~ _- ~ 0,~
1111 5135:~3 I I ~ _ .1 1111 at
· ~ l' ~f~0 ~4 l ~ 1~ ~ ~ ~~?g °
f ~ l ~ ~ ~ .~` ? . l ~ I _ .? . ’.~ .,
I. ~~ ~~ ~~ i, , ,? ??~?~~9
Fig. 10. Summary of current steady-flow turbulence
measurements.
ks is the steady turbulent kinetic energy, uu, vv, ww are
the axial, transverse, and vertical normal stresses,
respectively, and up, uw are the measurable shear
stresses. Contours U show a low-velocity bulge
~ U ~ 65%Uc ~ near mid girth and relatively thin
boundary layer near the center plane. Cross plane
velocity vectors are generally upward with a region of
weak out board rotation in region of bulge and thin
boundary layer. Contours ks correlate with U contours,
but with largest values compressed in a narrow,
horizontal band closer to the hull (ail;: ~ 5%Uc ). The
normal Reynolds stresses show similar patterns as ks.
Values are not isotropic; since, axial stress is two to
tom times cros,~plane stresses ~ largest values
,,/uu ~ 6%Uc, Jvv ~ 4~oUc, and ,|ww ~ 4%Uc . The
Reynolds shear stress uv is negative in regions of
increasing au / by and positive in regions of decreasing
O~Dy with largest values where gradient is largest
(~/uv~3%Uc). uw is spar but correlates with
Ou/&z with largest value ,/uw ~ 3%Uc .
3.2 Incident wave elevation and flowfield
For the unsteady tests, time histories of the incident
head wave Czar are fundamentally important for
establishing the phase angle of each PIV vector map.
Fig. 11 shows a sample measured time history
presented for Fr=0.28, Ak=0.025, ~ =4.572 m, where
the incident wave frequency is fW=0.584 Hz and the
encounter frequency fe is 0.922 Hz.
2.54
~ 0.0 .
N .
-2.5
. \~ ~ 0,-
5.0 t (SeC)
Fig. 11. Typical incident wave elevation time history
for unsteady PIV tests.
In Fig. 11, incident wave elevation time history
represents a nearly perfect linear response. FS analysis
shows that the O'h-harmonic amplitude is less than 1%
of the 1 St-harmonic amplitude and the super harmonic
amplitudes are two-orders-of-magnitude smaller than
the 1 St-harmonic amplitude. The uncertainty in wave
frequency fw and wave amplitude Aw is 0.7% and 2.7%,
respectively, which is determined from multiple tests
(M=10) and estimates of the bias limits. Also, the
uncertainty of the encounter frequency ~ is determined
as 0.4%. More details on the incident wave elevation
and uncertainty are found in Longo et al. (1999) and
Gui et al. (20021.
Unsteady PIV measurements of the incident wave
flowfield with no model have been conducted and
documented in detail (Longo et al. 20021. Experimental
results were evaluated through comparison with 2D
progressive wave theory. Results using the same
measurement area size and data acquisition and
reduction processes as in present study yield
satisfactory comparisons of theory and experiment.
Fig. 12 shows differences theory and experiment of
harmonic amplitudes (uorUoE, worwoE; UIT-UIE,
W~rW~E) and the 1 St-harmonic phase (YUI~YUIE, Twos
]/WlE) for three elevations z=-25.0, -53.34, and -
110.45mm where the latter two elevations are
coincident with zones B and C in the test program with
ship model. Average departure from theory is
1.2%,0.10% for oth harmonic amplitude U. W. 0.9% for
1St harmonic amplitude U. W. and 0.8%,2.0% for 1St-
harmonic phase U. W._Full-range, phase-averaged
turbulence is 0.01% for UUFR,WWFR and negligible for
UWFR . Note that differences theory and experiment for
Oth-harmonic amplitude U is same as for uniform flow
tests in calm water and used as scale factor for
instantaneous PIV measurements previously mentioned
in section 2.6.
Wav:,
uc'
1 -0. 02 X I Y 1 - ~
U1T U1E (%)
·50
.04 1.20 ~
0.60 B
0.45 11
o,o ~
~ ~ o.o,
935 (h) Ann
Wave
luc'2' ~
]4.02 X4Y 1 1
8 | OT UOE (%)
311 I 1 50
J11 1~04 '2305
_ . .9 l
_ I 0.75 ;
I 0.60 i
·1 045 I
1 ~ ~ 015 ~
~ Do." ooo 1
_._ J- _1 ~ ~ 0.00
,pO.t _ 935 (a) ~O.Ot ~ --a V/ Hi--
Wav:,
'
ha
Z
.91 1
~ n n7 ~~`v
_ ~
-
811-0.02 X1v
Fig. 12. Comparison theory and experiment for ash and
1St harmonic amplitude U. W and 1St harmonic
phase U. W for case with no model.
3.3 Summary unsteady forces and moment and
wave field
Unsteady resistance, heave force, pitch moment,
and free surface elevations for 5512 at steady forward
speed and in regular head waves were investigated and
documented in Gui et al. (2001c) and Gui et al. (20021.
The test program included a wide range of conditions:
low (0.19), medium (0.28), mid-high (0.34), and high
(0.41) Froude numbers; small (0.025), small-median
(0.05, 0.075), and median (0.10) wave steepnesses; and
short (1.524m), median (3.048m), and long (4.572m)
wavelengths. The encounter frequency fe varied from
low (0.8 Hz) to high (2.5 Hz). For seakeeping, the
corresponding HIX covered very small (1/125), small
(1/60), median (1/40) and mid-large (1/30) values. The
total number of test cases was 42. After observation
and analysis of the forces and moment results, a test
case of median Fr (0.28), long ~ (4.572m) and low Ak
(0.025) was selected for the unsteady free-surface
elevations, because this condition produces the most
manageable linear response, especially, in the farfield
region. A summary of results for this specific case
follows.
Using the first-order FS harmonics for above case,
the time histories of incident wave, resistance
coefficient (CT), heave coefficient (CH), and pitch
moment coefficient (CM) are reconstructed and
presented in Fig. 13.
..00
0 50 flu ~=0° \ ~ SteadY7/~~
1.00
,....................
0.010
/ \ Unsteady
/ \ ~ Steady
0.000 \
-0.50 0.00 0.2\\`'/~.75
-1.00
day ooo 0.25 Cure 0~75
0.00
.02
nit
~_06
(C) 0.00 0.25 era
o.olt
O.OOt L
<,)~0.00C
~.005
Unsteady
----- Steady
-0.01C
~dy woo 0.25 OUT 075 1.00
Fig. 13. Reconstructed time histories of forces and
moments for Fr=0.28, Ak=0.025, ~4.572 m.
The steady results are also plotted in the figure for
comparison. At t~e=O, a wave crest is coincident with
the FP of the model. For CT, CT O/CT St and CT I/CT S' are
1.05 and 0.69, respectively. The added resistance
CT a~=CT D/2-CT s~=4~02e-04 which is about 9% of CT S[.
For CH, CHO/CHSt and CHI/CHS' are 1.05 and 0.69,
respectively. CM is nearly perfectly symmetric about
CM St. Interestingly, the exciting forces for surge, heave,
and pitch are the first harmonics of resistance, heave
force, and pitch moment, respectively, and the long
wavelength (~4.572 m) cases in the test program
produced the highest exciting force amplitudes. CT, CH,
and CM lead the incident wave phase by 70.0°, 140.0°,
and 60°, respectively. CH leads CT by 70° and CM lags
CT and CH by 10° and 80°, respectively. These phase
lags and leads will be shown important in explaining
the time-varying nature of the flowf~eld later.
Maximum values of CT, CH, and CM occur when an
incident wave crest reaches 0.30L, 0.57L, and 0.25L,
respectively. Although not shown, the local unsteady
wavefield at x=0.935 is decreasing, increasing,
increasing, and decreasing for t/Te=O, 1/4, 1/2, and 3/4,
respectively. These trends will also be important in
explaining the unsteady nominal wake behavior.
3.4 Unsteady flow
3.4.1 oth harmonic versus steady
Differences between oth harmonic and steady mean
and turbulence variables are facilitated through data
acquisition of steady and unsteady datasets at the same
locations. Percent-difference contours and data-
difference vectors are shown in Fig. 14. Contours of
UO-U reveal a sizeable curved region close to the hull
but off of the centerplane where the unsteady effect
accelerates flow by 3.0-3.5%. Smaller regions are also
visible for VO-V and WO-W where streaming effect is
evident but peak values are about 33% of UO-U peak
l
1.4
1
1
.;.-
at
4.,
42~ ~
44 -
.3 ~
.1.
Fig. 14. Differences in O'h-harmonic and steady mean
measurements.
Primary streaming effect is associated with the low-
momentum flow in the boundary layer bulge but
secondary cells for all three velocity components are
near the region of highest turbulent kinetic energy at the
hull/centerplane juncture. Difference vectors reveal
broad regions of increased upflow in the measurement
region whereas transverse flow increases and decreases
are more balanced.
Differences between the phase-averaged (unsteady)
turbulence and steady turbulence variables are shown in
Fig. 15 as data-difference contours, i.e., unsteady-
steady. Average turbulent kinetic energy increases by
11.5% from steady to unsteady cases. Largest increases
are confined to a small regions at the hull/centerplane
(primary) and hull/free surface (secondary) junctures.
Away from the hull outside the boundary layer, data
d fferences are very small or slightly negative. For
uv~2 - us, modest increases occur near the
hull/freesurface juncture. The broad positive and
negative regions that are side-by-side in up are
decreased and increased, respectively. UWFR - uw are
mostly positive everywhere with largest increases in a
small region close to hull/centerplane juncture.
3
I' 80~ L,] ~ ~~~
~ emit
S ' 0,~
_ a.r~:
_ ~4
_ ~~U
_ At
_ ~ :
_ : ~~=
_ -4:~:34
Fig. 15. Data differences in phase-averaged and steady
turbulence measurements.
3.4.2 FS harmonics
Contours of 1St- and 2nd-harmonic amplitude for U.
V, W are shown in Fig. 16. Ul shows distinct patterns
with highest values centered on the bulging portion of
the boundary layer. Peak value of Ul is 9% or roughly
6% higher than harmonic content of incident wave
flowfield with no model at this elevation. Two small
regions close to the hull/centerplane and
hulVfreesurface junctures have large Ul values. The
former is centered on the location of peak unsteady
turbulent kinetic energy and together with the largest
region of Us bracket a modest area where unsteady
effects are largely absent in Ul. In the outer flow, Ul
decreases with increasing depth and is constant for all y
at deepest elevations as per 2D progressive wave theory
prediction. Vl also shows distinct patterns, which are
similar to those for mean V (Fig. 9) and oth harmonic
VO. Vl is highest in a broad, curved region near the
hull/free surface juncture with peak values of about
3.5% which is a sole unsteady effect as Vl is O
everywhere for case with no model. Vat is O on the
centerplane as expected since V is asymmetric and
tends to O as y?O. Here again, Wl also shows distinct
patterns with highest values in a broad region beginning
near the hull/free surface juncture and extending
downward with decreasing values. Peak values of Wl
are present in this region and close to Vat peak values of
3.5%.
3 _
f
3 ~ ~
3
3
3
1 ~
3 Ire'
33 ~
2 1 -
Date
0..~.
O~ ~ .
Q~3
0 - 3
R3. '. · _
f~ 2'~,, ",: ~ ~: ~~ .'
1~;,>~<
Gaff
c Ales ~
O. Crl', A...
Q-
O.~ }
b~0 it.
O-,
:~:.~. ~~
~ .
Qua
0.~
a
0~4 .
dig
0
O~7
o~ :
0~
Ark .
amen ~ .
Fig. 16. Summary of 1St- and 2nd-harmonic amplitudes
of U,V,W.
This region is close to the outer flow which suggests
that most of Wl is from the head wave flowfield. Close
to the hull and centerplane, Wl effects are minimal
which suggests that the interaction of head wave
flowfield and hull boundary layer serves to dampen the
unsteady effects for W component. In the outer flow,
We decreases with increasing depth and is constant for
all y at deepest elevations as per 2D progressive wave
theory prediction.
Second-harmonic amplitude content in U. V, W is
generally insignificant in terms of magnitude but
exhibits interesting, repeatable trends, nonetheless.
Trends in U2 are dominated by two cells that bracket
the region of maximum Us. Average U2 values through
the measurement region are 0.4%, an order-of-
magnitude smaller than Us. Peak value is centered on
the dividing line between cells of maximum and
minimum Us. Smaller, secondary cells of U2 are also
present near the hull/centerplane and hull/free surface
junctures. IT is nearly zero in the outer flow. V2 has
one cell of interest coincident with largest U2 cell.
Average V2 values through the measurement region are
0.2%. Peak value is centered at the location of peak U2.
V2 is nearly zero in the outer flow. W2 has one cell of
interest near the hulVcenterplane juncture. Average W2
values through the measurement region are 0.2%. Peak
value is centered at the location of a secondary 1~ cell.
W2 is nearly zero in the outer flow.
First-harmonic phase angle and phase leads
and lags are presented in Fig. 17. Phase-angle contours
for U. V, W are presented with ranges of t7r,-~] except
for Owl which is presented for f~,-1.5~. Trends and
patterns within the boundary layer are unique for each
phase component.
Fig. 17. Summary of 1 St-harmonic phase angle and
phase leads and lags for U. V, W at the
nominal wake plane.
But includes two notable features including a wide cell
of 1.0~ close to the hull and free surface and a narrow
region close to the hull/centerplane juncture that
follows the boundary layer periphery where Cut
experiences a sharp, horizontal discontinuity and phase
sign change. As y,z? -8, but tends to the limiting value
(0~) for the external head wave flowfield. Eve also
exhibits a region close to the centerplane but starboard
of the boundary-layer bulge where a sharp, horizontal
discontinuity and phase sign change is present. As y? -
8, Eve tends to 2/3lrV but as z? -8, no trend in Eve is
evident. Apparently, the measurement region is not
large enough to observe Eve tend to its limiting value far
from the model. Owl is dominated by two, large regions
of negative phase angle, side-by-side beneath the
transom and offset toward the centerplane. A dividing
line between the cells is vertically oriented. As y,z? -
8, yew tends to the limiting value (-1.5~) for the
external head wave flowfield. Phase lags and leads are
also present in Fig. 17 as contours of Yu~-7v~, Yu~-yw~,
and ~v~-yw~. Positive and negative regions are
interpreted as second component phase lead and lag
over first component, respectively. Results show that
Tv~ leads but in a narrow, horizontal region centered on
the But phase discontinuity. The remainder of the
measurement area indicates that Eve lags Bun. In the
outer flow, Owl leads yu~ by roughly 1.5~ as per 2D
progressive wave theory prediction. Inside the
boundary layer Owl lags But in a region initiating on the
hull/centerplane juncture and moving diagonally away
from the hull and then downward. Finally, in the outer
flow, Owl leads Eve by roughly 2.5~, however, Awl lags
Eve in a narrow horizontal area centered on the Eve
phase discontinuity.
3.4.3 FS-reconstructed time histories
FS-reconstructed time histories are generated for
UF(t), VF(t), WF(t) using equations (7~-~12) and
presented in Fig. 18 at four instances in one encounter
period, i.e., t/Te=°, 1/4, 1/2, 3/4. FS reconstructions
include effects of oth-, lo-, 2n~-harmonic amplitudes and
1St- and 2n6-harmonic adjusted phase angle. Phase-
angle adjustments are made such that zero phase angle
(or t/Te=O) corresponds to an incident wave crest at the
FP. The phase delay from the FP to the nominal wake
plane is roughly 224°. Although only four instances are
shown, relative changes of contours reveal time-varying
behavior of the boundary layer. At t/Te=O, incident
wave trough is ~J4 upstream of the nominal wake plane,
i.e., the local free surface elevation at x=0.935 is
decreasing with time and the boundary layer is
undergoing expansion. Subplot for UF(t) at t/Te=0
indicates boundary layer thickening while VF(t) and
WF(t) indicate reduction in flow toward centerplane and
lax
a:: -
G~U
A.
0.~1
0
O~
~4
O.:~;
~1
0.~)
_ _
_ _
_UT=0.50~ ,,= ~
W91w''
~ .~
O.~.
_ b45i
0~'
....... _ _
_ ~
(a)
~ M. ,-~
n: an ,~ t~ ~
. ... ~ ~ .
. ~ ~
~0~54 1.a
0.
u
O
0.A~
O~
a:
046{
’~01
~ _
: _: :~ :: ~
`: anon ~ _ foci
:~m,:
~.~1
t..~t
~
I.
I
AGE
{~
~017
4.~t
'Am ~ '
'~11 ~
:~= <.
_
_
:
i.~1
2:='RS
ma.
6#:~.
my.:
waU
''2.~=
i,01'
Arty ~
_
_ _F
(b)
.~ _ ~ . ~d
A.. - i
a. - it?
.-~13.
I,.
airs
I.
:07
~33
.~H,
l=~ '.
^047 '.
~~ '
.
_i l'
~ ~ _
l ~ ~
l
. ~
11
V -~u
1 _
1 _~1
l ~
1 _
1 _1
1 _
__
am_
1 tm
1 ~.1
d:~’
1 g
I Q0~!
011
~C"
1 -}Lot!
i DA=1
W:
O.~
:~. -
0.~4
1 c~
o.=
1 ~~'
4~
1 decor;
1 ;~1
' 1 ~~
11_
~ An Gus r ,"
~ ~1=
~ ~ 11*
, ~1
t1, DOT
Pat!
f~P
' OUT
~3
b OC7
Q"
bO,0
-
_~_~s
_
_
_~
~~ ::~. ~
1_~.
_~ ~
_ .
em
81 J ~ ~ ~
rid
~1
0,1~
1tO
o.~m
For
~ lo',
dig=
it Ill,
t1, C8,T ~
Cur ~
I
_r ''
Fig. 18. FS reconstructions of the time-varying
nominal wake at four instances in one
encounter period: (a) UF(t); (b) VF(t); and (c)
WF(t).
At t/Te=1/4, CT and CM have recently passed maximum
values (Fig. 13) and incident wave trough has traveled
:,~'~' ~/4 downstream of the nominal wake plane, i.e., local
4~' free surface elevation at x=0.935 is increasing with time
and the boundary layer is starting to contract. At
~ O=' tlTe=1/2, CH has recently passed its maximum value
|~45$~ (Fig. 13). Incident wave trough has traveled ~/2
L. ~~ downstream of the nominal wake plane, i.e., local free
__
surface elevation at x=0.935 continues to increase with
t~ time and the boundary continues to contract. Note that
subplots for UF(t) at t/Te=1/4 and 1/2 indicate boundary
~ layer contraction, and VF(t) and WF(t) show evidence of
|| increased flow toward centerplane and model,
respectively, especially near the free surface and
centerplane, respectively. Apparently, the boundary
layer contraction and attending fluid flow toward the
model is associated with the heave force peak in Fig.
13. Finally, at t/Te=3/4, another incident wave trough is
approaching the nominal wake plane from ~/2
upstream. The local wave elevation is decreasing in
~ time as per t/Te=0 and the boundary layer is in
I expansion mode with rapid thickening occurring. VF(t)
shows increased strength near the free surface moving
fluid toward the centerplane, and WF(t) indicates global
reduction of upward flow.
l
4. CONCLUSIONS AND FUTURE WORK
Results are presented from towing-tank tests of the
phase-averaged nominal wake velocities (U. V, W) and
Reynolds stresses ~ uu, vv, ww, us, uw ) for a surface
combatant advancing in regular head waves, but
restrained from body motions, i.e., forward-speed
diffraction problem. The geometry is DTMB model
5512, which is an L=3.048 m, 1/46.6 scale geosym of
DTMB model 5415. The experiments are conducted in
a 3x3x100 m towing tank equipped with a plunger type
wave maker. The measurement systems include a
towed particle image velocimetry and servomechanism
wave probe. Uncertainty assessment following
standard procedures is used to evaluate the quality of
the data.
The incident head wave elevation and
flowfield (no model) have been measured and conform
closely with 2D progressive wave theory. Current
steady flow mean and turbulence results are within the
measurement uncertainties of previous steady PIV
measurements which validates current data acquisition
and data-reduction procedures where the latter were
developed specially for the current steady and unsteady
tests. Comparison of steady mean and 0th-harmonic
indicates small to moderate areas mostly near the low-
momentum, boundary layer bulge where streaming
occurs at the level of 3.5%, 0.7%, 1.5% for U. V, W.
respectively. Comparison of steady and phase-
averaged turbulence reveals 11.5% increase in unsteady
versus steady turbulence kinetic energy. Turbulence
increases for the unsteady case are mostly confined to
regions near the hull/centerplane or hull/free surface
junctures. First-harmonic amplitudes peak at 9%,
3.5%, 3.5% for U. V, W. respectively, inside the
boundary layer and tend to the 2D progressive wave
theory in the external flow. Second-harmonic
amplitudes are order-of-magnitude lower than first-
harmonic amplitudes and occur near locations of first-
harmonic amplitude peaks. First-harmonic phase
angles have sharp phase changes near the boundary
layer bulge and tend to head wave flowfield values in
the external flow. In general, Owl leads Eve and But
through most of measurement region and Eve lags But
through most of measurement region. FS-
reconstructions of U. V, W reveal expansions and
contractions of the boundary layer when the local wave
elevation is decreasing and increasing, respectively. In
general, boundary layer expansion is accompanied by
reductions in flow toward the centerplane and model
while boundary layer contraction is accompanied by
increased flow toward the centerplane and model.
Heave force maximums and minimums correlate with
limiting values of nominal wake contraction and
expansion, respectively. The steady and unsteady
uncertainties are presented and judged satisfactory such
that current test case can be used for CFD validation.
The final paper will include expanded discussion of
the FS harmonic amplitudes and phase angles through
subtraction of the incident head wave (no model)
flowfield. In addition, subregion turbulence for the
unsteady case will be presented in terms of its harmonic
content.
Future work includes roll-damping experiments for
model 5512 including motions testing, unsteady forces
and moments, unsteady wave elevations, and unsteady
flowfield measurements. For the unsteady
measurements, data acquisition will be phase-locked to
the roll-motion of the hull similarly as the current tests
are phase-locked to the incident wave elevation. The
data and UA from the current tests will be archived at
www.iihr.uiowa.edu/~towtank.
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. Special thanks are
extended to University of Iowa mechanical engineering
undergraduates Tanner Kuhl and Ben Orozco for their
efforts in data acquisition phases of this study.
REFERENCES
ASME, "Test Uncertainty," ASME PTC 19.1-1998,
The American Society of Mechanical Engineers,
1998,112pp.
Gui, L., Longo, J., and Stern, F., "Biases of PIV
Measurement of Turbulent Flow and the Masked
Correlation-Based Interrogation," Experiments in
Fluids, Vol. 30, 2001a, pp. 27-35.
Gui, L., Longo, J., and Stern, F., "Towing Tank PIV
Measurement System, Data and Uncertainty
Assessment for DTMB Model 5512," Experiments
in Fluids, Vol. 31, 2001 b, pp. 336-346.
Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F.,
"Forces, Moment, and Wave Pattern for Surface
Combatant in Regular Head Waves-Part 1:
Measurement Systems and Uncertainty
Assessment," Experiments in Fluids, Vol. 31,
2001c, pp. 674-680.
Gui., L., Longo, L., Metcalf, B., Shao, J., and Stern, F.,
"Forces, Moment, and Wave Pattern for Naval
Combatant in Regular Head waves-Part 2:
Measurement Results and Discussions,"
Experiments in Fluids, Vol. 32, 2002, pp. 27-36.
Journee, J.M.J., "Experiments and calculations on four
Wigley hullforms,". Report No. 909, Delft University
of Technology, Ship Hydromechanics Lab, The
Netherlands.
Longo, J., Rhee, S.-H., Kuhl, D., Metcalf, B., Rose, R.,
and Stern, F., "IIHR Towing-Tank Wavemaker,"
Proceedings of the 25th ATTC, Iowa City, Iowa,
1999.
Longo, J., Shao, J., Irvine, M., Gui, L., and Stem, F.,
"Phase-Averaged Towed PIV Measurements for
Regular Head Waves in a Model Ship Towing
Tank" Proceedings PIV and Modeling Water Wave
Phenomena, Cambridge, UK, 2002, (to appear).
Longo, J. and Stern, F., "Resistance, Sinkage and Trim,
Wave Profile, and Nominal Wake Tests and
Uncertainty Assessment for DTMB Model 5512,"
Proceedings of the 25th ATTC, Iowa City, Iowa,
1999.
Rhee, S.H. and Stern, F., "Unsteady RAN S Method For
Surface Ship Boundary Layer And Wake And
Wave Field," Int. J. Num. Meth. Fluids, Vol. 37,
2001, pp. 445-478.
Wilson, R. and Stern, F., "Unsteady RANS Simulation
of a Surface Combatant in Regular Head Waves,"
Journal of Fluid Mechanics, 2002, (in preparation).
Stern, F., Longo, J., Penna, R., Oliviera, A., Ratcliffe,
T., and Coleman, H., "International Collaboration on
Benchmark CFD Validation Data for Naval Surface
Combatant," Proceedings of the 23 ONR
Em on Naval Hydrodynamics. National
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DISCUSSION
Robert Beck
University of Michigan, USA
How did you translate the phase of the wave
from the wave probe ahead of the model to the
PIV measuring plane? Assuming you used linear
translation, what effect would the actual phase
translation have on your results?
AUTHORS' REPLY
Thank you for your question. The phase of the
incident wave at the PIV measuring plane is
computed with equation (3~. The wavelength
value (~) in the second term on the right-hand
side is measured at the halfway mark in the
towing tank with two servo wave gages. This
measured value (~=4.654 m) is underpredicted
(~=4.572 m) by 1.8% with the first-order
dispersion relation in equation (15~. We avoid
significant post-processing phase errors related
to this difference in ~ by using the measured
value in equation (3~.
The departure of ~ from linear theory may be a
consequence of nonlinearities arising from the
facility (plunger, tank sidewalls, or tank bottom)
or finite-amplitude effects. Nonlinearities in the
wave amplitudes appear to be insignificant based
on FS analysis, i.e., higher-harmonic amplitudes
are typically one- to two-orders of magnitude
smaller than for the 1 St-harmonic amplitude. The
dispersion relation relating wave frequency to
wavelength is valid to second order. A third-
order correction for wavelength is derived by
Borgman and Chappelear (1958) that is
qualitatively consistent with observed increases
in X, however, the correction has not been
evaluated quantitatively.
REFERENCE
Borgman, L. E. and Chappelear, J. E. , "The Use
of Stokes-Struik Approximation for Waves of
Finite Height," Proc. 6th Conf. Coastal Eng.,
ASCE, Council on Wave Research, Berkeley,
CA., 1958.
