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OCR for page 46
Forces, Moment and Wave Pattern for Naval Combatant
in Regular Head Waves
L. Gui, J. Longo, B. Metcalf, J. Shao, and F. Stern
Iowa nstitute of Hydraulic Research (I OR), The University of Iowa
Iowa City, A 52242, USA
ABSTRACT
A model-scale naval surface combatant, DTMB
5512, is studied experimentally in steady forward speed
ad regular head waves with the Iowa institute of
HydLalic Research BOHR) towing tank facilities
Un teady resista e, heave force, pitch moment ad
free-surfae elevations ape investigated with different
measurement syst ms for a fanly wide rage of te t
conditions Test data is procured for validation of RANS
CFD codes ad for mderstading the physics of
msteady ship hydkody amics Uncertainty assessments
are completed following She A AA Standard The
remits ad discussions for She forces ad moment cover
the time mea values, added resista e ad linear ad
non-linear responses Results of free surfa elevation
te ts include reconstructed msteady wave patterns,
diffraction wave patterns, ad free surface turbulence
dishibutions
1. INTRODUCTION
Rapid advert ements m computational fluid
dy amics m Cl have entitled solution of mcreasmgly
comply ship hydkody amics simulations (A abshahi et
al 1998, Wilson et al 1998, Ladkini et al 1999,
Alessadkini ad D Ihommea 1999) For development
ad validation of CFD codes, much more detailed
model-scale, surface ship experiment data is required
(Stem et al 1998, ITTC 1999) To keep pace with the
CFD simulations, the experimental fluid dy amics
FD) comm mity is expected to design ad execute
experiments that consider more real-world flow
conditions ad addkess a variety of physics of mtere t
with advert ed measurement techniques
Flowfield measurements ape commonly used for
CFD validation ad flow-physics st dy on ship
hydkody amics Hoeksha ad Ligtelijn 1991, Bertram
et al 1994, Ogiwara 1994, Suzuki et al 1998, Van et al
1998) Toda et al (1992) ad Longo ad Stern (1996)
aplied haditional 5-hole pitot probes to measure the
time mea velocities Laser-Doppler velocimeby LDV
or LDA) was used in towing tanks for reducing probe
distmba e effects ad measuring mea velocities ad
R y olds tresses Knaak 1992, Longo et al 1998a)
An optical ad large-field measurement tech iq~x,
particle image ~ el ~ an et y PPV), has also been aplied
for high spatial resolution ad relatively fast mea
velocity ad Rey olds tress measurement in towing
tanks Dong et al 1997, Gui et al 1999, Rodh et al
1999) For msteady free-smfae flows, experiments a
more complex to design ad minute ad, Therefore,
limited in m mber ad scope A phase-averaged
measurement of msteady f ee-surfae flows m a
open chumel was conducted by Mead (1995) with a
twocomponent LDA >! rem ad water-wave gages
Son et al (1999) used a cinematog Ethic PIV ystem
for msteady turbulent flow measurements in a wave
flume
In addition to flow field measurements in towing
ranks, experimental determination of f ee-smfae
elevations ad measurements of forces ad moments
are also of g eat interest, ad Hey are ve y important
aspects for CFD code development ad validation m
msteady free-smfae flows Journee (1992) ad Rhee
ad Stern (1998) conducted, respectively, experimental
investigations ad CFD simulations of m teady forces
ad moment for Wigley hulfforms For measurmg She
msteady free-smfae elevations aro md a ship model
Ohkusu (1990) described two methods, i e with wave
probes installed on the towing can iage for aquirmg
data pomt-by-point ad with wave probes fixed in She
young rank for Ime-by-line measurements The
measurement results were used to predict She added
resista e Kaai (1985) described a g id-projction
medhod for a whole tield measurement of the
instate ous waw tield A other optical method was
used by Nishio et al (1998) for mapmg the wave
height distributions aro md a ship hull m regular
waves
The goal of present work is to support the CFD
code development for m teady ship hydkody amics
th ough towing rank experiments for forward peed
diff action problem, i e ship model advert mg m
regular head waves, but reshained from motions
Currently, She forwad peed dfffr action problem plays
a impo tat role in engineering aproaches, which
use linear, potential flow, strip Theo y for ship ad
OCR for page 47
platform motions, and the exciting forces for motions
are solution of the forward speed diffraction problem.
This model problem can be considered first step in
merging of separate fields of resistance and propulsion,
seakeeping, and maneuvering. The specific physical
problem of interest is a 1:46.6 scale model of a modern
naval combatant, DTMB 5512, advancing in regular
head waves. The experiments include the measurement
of unsteady resistance, heave force and pitch moment
for a wide range of incident waves for identification of
the effects of the Froude number, wavelength and wave
steepness. In addition, a detailed mapping of unsteady
free-surface elevations is conducted for a selected test
condition. In comparison to previous works, the present
study provides much more detailed data with rigorous
uncertainty assessment for CFD validation and
systematic analyses of the flow physics in ship
hydrodynamics covering non-linear responses of forces
and moment and distributions of free surface turbulence.
Fr=
Fig. 1: Photos of DTMB model 5512.
2. TEST DESIGN
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 for housing the
carriage controls, computer (PC), and data-acquisition
instrumentation and a 3.7-m trailer which is used as a
platform for instrumentation and a point of attachment
for models. The carriage/trailer are cable driven across
level rails by a 15-horsepower motor and can reach
speeds of 3 m/s. The carriage speed (Uc) is monitored
with an IIHR designed and constructed speed circuit.
The details of the carriage speed measurement system
and uncertainty assessment are provided in Longo and
Stern (19984. A plunger-type wave-maker at the north
end of the tank is utilized for generation of regular
head waves. The wave-maker is powered by a
hydraulic system and controlled through a shore-based
PC and National Instruments Labview VI software and
MTS controller, and it is capable of generating regular
head waves with wavelengths of 0.5~6.0 m and wave
steepnesses 0.025~0.3 (Longo et al. 1998b). An
automated, moveable sidewall wave-damper system is
used in the towing-tank for wave absorption, which
enables twenty-minute intervals between carriage runs
for steady- and unsteady-flow tests.
DTMB model 5512 is selected for the tests
(Fig. 14. It has a length of L=3.048 m and was
manufactured at DTMB from molded fiber-reinforced
Plexiglas and equipped with appendages (brass shafts
and struts and wooden rudders) and stainless-steel,
twin propellers, although the present tests are for the
bare-hull condition. The model is fitted with studs at
x=0.05 to initiate transition to turbulent flow. The
studs are cylindrical with 1.6 mm height, 3.2 mm
diameter, and 10.0 mm spacing and located at x=0.05.
The model is rigidly fixed to the carriage using a
single-point mount and towed at the dynamic sunk and
trimmed condition, which is determined in calm water
condition (without wave) for each Froude number.
Two right-handed Cartesian coordinate systems
are used in the towing tank. The model coordinate
system (x, y, z) is attached to the test model with the
origin at the intersection of the undisturbed free-
surface and forward perpendicular (FP) of the model.
The tank coordinate system (X, Y. Z) is fixed in the
towing tank. The axes of the coordinate systems are
normalized with model length and directed
downstream, transverse, and upward, respectively.
The unsteady test conditions are determined with
Froude number (Fr), wavelength (~) and wave
steepnesses (Ak). Fr and Ak are defined as
(1)
Ak 2pA
(2)
where g is the local gravity acceleration, and A is the
amplitude of the incident wave. As shown in Table 1,
forces and moment data are procured for a fairly 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 varies from low (0.8 Hz) to high
(2.5 Hz). For seakeeping, the corresponding H/\ covers
very small (1/125), small (1/60), median (1/40) and
2
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mid-large (1/30) values Since some combinations could
not be conducted due to ge Oration of exheme wave
amplit des at the bow, the total m mber of test cases is
42 The test case for media Fr, small media Ak ad
media ~ (Fr=0 28, Ak=0 05, ad \=3 1148m) is chosen
for procuring precision limits ad assessing total
uncertainties, a d the results should be representative of
mo t test cases After observation ad analysis of the
fomes ad moment results, a test case of media Fr
(0 28), long ~ (4 572m) ad low Ak (0 025) is selected
for the m read f ee-surfae elevations, because This
condition produces She most maageale linear
response, especially, in the farfield region For all Fr,
tests are also conducted without waves, i e teady cases
When the test case (i e Fr, ~ ad Ak) is selected, the
carriage speed U. is determined with Fr Eq (1)), ad
the frequency of She regular head wave f ad the
frequency of the enco mter wave f are determined with
Has
fw=:
fe=fw+
(3)
(4)
The enco mter frequency f is the dominant f equency of
the msteady re ponses The incident wave amplitude A
is detemmined with AL ad ~ Eq (2))
Fr
019
028
034
041
Table 1: Unsteady test conditions
Re[106]
3153
4 647
5642
. 6 804
Ak
0025,005,0075,
01
0025,005,0075,
01
0025,005,0075
0025,005,0075,
01
0025,005,0075,
01
0025,005,0075
0025,005,0075,
0025,005,0075,
01
0025,005,0075
0025,005,0075,
01
0025,005,0075
0025,005
i(m)
1 524
3 048
4 572
1 524
3 048
4 572
1 524
3 048
4 572
1 524
3 048
4 572
f~k r)
1 693
I 056
0811
2 016
1 218
O 919
2231
1 325
O 991
2 482
1451
I 074
The measurement of free-smfae elevations is
conducted m She a a of -0 25< x ! ch oni:md with
the wave maker, a time (or phase) reference is needed
wish the Required time histories, i e She incident wave
atx=O,ie
~ (t)= l cos(2~t+y )
The amplitude of the reference wave is k ow, but She
initial phase Yr is determined th ough analysis of She
incident wave time histo y in She tests She incident
wave records a measured up tre m (BOO) of the
model in regions where the waveform is clean with a
tak-fixed wave probe (forces ad moment, torts id
elevations) or a trailer mo mted wave probe . neurtield
elevations) Thus, a phase shift is necessary to
determine the reference phase
Unsteady time histories are reconvey red with FS
When the phase of the reference wave, i e the incident
(5)
(6)
(7)
(8)
3
(9)
12 15/00
OCR for page 49
wave at x=O, is set to zero, the FS for time history X
(X= CT, CH, CM, (T) is determined as follows:
XF (t) =—+ 2, X n cos(2~fet + i\9n ) ( 10)
2 n=i
i\9n gn g!
Xn = i/an + bn
g t -~(bn )
an
the incident wave for determining the reference phase
A. A pair of photoelectric switches is used to
synchronize data-acquisition start times for the
carriage-based and shore-based measurement systems.
The load cell is mounted at the mid-ship of the model
(x=O, y=0.5, and the towing height is z=0.06414. A
sketch of the measurement system is given in Fig. 2.
(12) ~ I_
(13)
~ T
an = T Jx(t)cOs(2~fet)dt forn=0,1,2,3, (14)
o
Tbe = -—JX (t)Sin(2,~fet) At for n=1,2,3, (15)
o
wherein XF is the reconstructed time history; Xn is the
nth order harmonic amplitude; In is the corresponding
phase; N is the order of the FS and chosen high enough
to include all important frequency components. i\~/n is
the harmonic phase adjusted with the reference wave,
and for forces and moment it is the phase lead relative
to the reference wave. Time interval T' is a multiple of
the encounter wave period T (=l/fe).
Further processing of the test data includes
determination of the streaming component of unsteady
resistance, i.e. the added resistance CT,a`, and the
unsteady perturbation response of unsteady free-surface
elevation, i.e. the diffraction wave (D, and they are
defined as
CT ad CT CT'S~ 2
~ (16)
ZT,1 COS(~MGt + /\9 )— ~ COST 2}C{et—2,~ )
where CT (=CT,O/2) is the time mean of unsteady
resistance, CTS~ is the steady resistance, AT is the time
mean of the unsteady free-surface elevation. Note that in
Eq. (17) (T iS replaced with its first-order FS-
reconstruction.
3. MEASUREMENT SYSTEMS
3.1. Forces and moment
The measurement system for the forces and
moment consists of a four-channel (two force, two
moment) strain-gage loadcell and signal conditioner
and a carriage-based PC with 12-bit AD card. A shore-
based capacitance-wire probe and PC are used to sample
(18)
~ OR~VE
___ ~ (~f · ~ _ X Z
Y _
--it DA TRIGGERING CAPAG~TANGE
S\IVITCH WIRE PROBE
Fig. 2: Experimental setup for forces and moment
The signals are sampled from the loadcell and the
wave probe, amplified and filtered in the signal
conditioners, digitized through AD conversion in the
carriage and shore-based PC's, and finally converted to
time histories of forces and moment (CT(t), CH(t),
CM(t)) and incident wave It. Each time history
consists of 2048 samples producing acquisition times
of 30, 10, 15, and 10 seconds for Fr=0.19, 0.28, 0.34,
and 0.41 respectively.
The phase of the incident wave at the position of
the capacitance-wire probe is determined with the first-
order FS harmonic phase of time history zesty, i.e. A,.
When the data acquisition is started (t=O), the wave
<17y probe is in advance of the FP of the model by a
distance D (=11.99m). Therefore, a delay of COLD/\ is
required to determine the reference phase:
>( - E ,,
v = 0.082
jOATR%GGERING SHORE~BASED ~
Fig. 3: Experimental setup for farfield free surface
4
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OCR for page 50
3.2. Farfield free surface elevations
A longit dinal wave cut method with two wave
probes is used to measure the msteady Afield
freesurfae elevations As show in Fig 3, the
measurement syst m consists of a sidewall mo mted
boom, servo-type wave probe probe 1) ad signal
conditioner, acou tic-t pe wave probe probe 2) ad
signal conditioner, 2D automated traverse system,
shorebased PC with 12-bit AD card, carriage-based PC
with 12bit AD card, ad a pair of photoelectric
switches for external d la acquisition triggering
TO
i'0 ~~
,0 ~
.~-
.O .
AAAA,
Fog 4: Sample time history of Afield free-smfae
elevation at y 0 082
Fig. 5: Spatial dish~butions of Afield free-surfae
elevations t y 0 082
OO..
OOD
Omit 3\ .
O~ \ ~
Om. ~
=
Fig. 6: Dishibution of the free-smfae elev lion on
the initial phase at one pomt m aycut
The measurement of The farfield region is
completed with 32 longit dinal (constat-y) cuts, paced
at fly O 01 between the maxim m beam of The model
ad the sidewall damper The data acquisition is
triggered with photoelectric switches 9 seconds prior to
the model FP passmg The wave probes ad ended when
the measurement region is completely scatted The
total time interval for data acquisition is 13 3 seconds,
ad 2700 samples are recorded in every carriage r m
15-25 carriage r ms are pe formed at each constat-y
cut to ensure a satisfactory di tr~bution of incident
wave phases at The bedimming of the raw time histories
As a example, one of The raw time histories (z, y, t l I
taken at y 0 082 is show in Fig 4 Note That The
incident wave is record d in The initial 9 seconds, ad
this i fommation is used to detemmine the initial phase
(Y)
In the model coordinate system (x, y, /), the data
acquisition at each y-cut is started at x=-D L, ad The
wave probe moves in the positive x-direction with
constant can i me speed U. As such the x-position of
the measurement is dependent on the sample time (t)
Therefore, the measured raw time hi tories a
converted to spatial dishibutions of the free-smfae
elevations with
if, (a, I) = '(Y' with I= '
(19)
Fig 5 shows The spatial dishibutions of free-smfae
elevation obtained in 14 r ms at y 0 082 Based on a
g oup of spatial dishibutions of the msteady
tree ^ aortae elevations at a certain y cut, a dish ibution
of free-surfae elevation on the mitial phase is obtained
for eve y x-position As a example, symbols in Fig 6
show the dish~bution of f ee-surfa elevation on the
initial phase at x=0 169 m The cut of y 0 082 After the
dispersed distribution is fitted with a continuous
poly omial curve, see the curve m Fig 6, FS
coetlimem3 are detemmined with
on = I 1~(r)cos(nr)4r
be= Il;~(r)sin(ny)dy
(20)
(21)
wh rem (My) is the poly omial fit of The dispersed
dishibution of (<,, Y), ad it depends on position (x, y)
According to Eqs (12), (13), (20) ad (21) the FS
harmonic amplitude ad phase can be computed For
each y-cut, the first point xo (xo=-D L, D 14 45m) is
upstream ad far from the model Therefore, the first-
order FS harmonic phase (Ye) at xo represent The phase
of the local incident wave A phase delay of AD/\ is
considered for the incident wave at x=0 in addition,
because The data is obt ined at different time for
different x-positions in each y-cut, a time shift of
fit (x-xo)L U. should be taken into acco mt, ad The
corresponding phase shift is 2rde fit Finally, The
reference phase is determined with
~ U.
Note that Eq (22) is valid only for con tat y
s
(22)
12 15/00
OCR for page 51
Fig. 7: Experimental setup for nearfield free surface
3.3. Nearfield free surface elevations
The nearfield measurement system consists of the
same equipment as for the farfield measurement system
but arranged differently. The two wave-probes are
attached to the moving carriage. As shown in Fig. 7,
probe 2 is installed forward of the model on the trailer
for acquiring the incident wave, and probe 1 is installed
on a trailer-mounted automated traverse for measuring
the unsteady free-surface elevations. The measurement
area is mapped with 22 and 26 variably-spaced (in the
x-coordinate) transverse cuts at the bow and stern,
respectively. The measurement location spacing in the
y-coordinate is variable but mostly i\y=0.005. Two
points are measured in each carriage run with a probe-
movement. At each measurement point 3000 samples
are acquired in a 9-second time interval. In the data
acquisition procedure, time histories for the unsteady
free-surface (z~x,y,t)) and incident wave (z~(t)) are
obtained. In the post-processing procedure, the reference
phase is determined according to the time history of the
incident wave, and the FS harmonic amplitudes and
phases are computed for unsteady free-surface
elevations. The phase of the incident wave at probe 2 is
determined with the first harmonic phase of the sampled
wave elevation A,. Since wave probe 2 is installed at
x=-D/L (D=1.905m), a phase delay of CHID/\ is
considered to determine the reference phase:
Go = gz ~ - 2p /
4. UNCERTAINTY ASSESSMENT
Uncertainty assessments are completed for the
results on three levels: Raw time histories, FS
harmonics and the FS-reconstructed time histories.
Following the AIAA Standard (S-017A-1999), the
uncertainty of a measurement variable is defined as the
root-sum-square (RSS) of the bias limit and precision
limit for a 95% confidence level. For a raw time history
the bias limit is estimated according to the
data-reduction equation and elementary bias limits, and
the precision limit is estimated with repeated end-to-
end data-acquisition and reduction cycles. The bias
limits of the FS harmonics are determined either with
the time mean values of the raw-time-history bias
limits or with the bias gradient limits. The precision
limits of the FS harmonics are determined using the
same procedure as for the raw time histories. Finally,
the bias limit and precision limit of the FS-
reconstructed time history are computed with the bias
and precision limits of the FS harmonics according to
the RSS method. Detailed descriptions follow.
4.1. Raw time histories
Bias limit: For convenience we assume that the
measured value X is determined at time t with
independent variables Vi for i=1,2, ,M. The data-
reduction equation of time history X(t) is represented
as:
X(t) = X(V1,V2, ,VM it)
The bias limit for X(t) is determined with
(24)
B2 = ~(~iBVi )2 + (qtBt )2 (25)
i=!
where the sensitivity coefficients are determined with
OX OX
qVi aVi ' At at
(26)
and BVi and Bt are the elementary bias limits.
Respectively for the forces and moment coefficients
(CT, CH and CM) and the near and farfield free-surface
elevations ((FF & (NF) the data reduction equations are
as follows:
CT (t) = CT (FX'r,UC,S,t)
(27)
CH (t) = CH (FZ, r,Uc,S't) (28)
CM (t) = CM (My, r,Uc,S,L,t) (29)
OFF (X,y,t) = ZFF (y,Z,t,UC,D,L)
ZNF(X'Y't) =ZNF(x,y,z,L,t) (31)
The elementary bias limits BFX, BFZ, BMY and BZ are
estimated in end-to-end calibration procedures, and BP,
BUC, BS, BL are taken from historical uncertainty
assessment efforts (Longo and Stern 19984. Bt is
provided by manufacturer specifications, and bias
limits related to the probe position BX, BY and BD are
estimated during the setup of the measurement
systems. Note that the total bias limit BX is a function
of time in the unsteady cases.
6
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Precision limit: The precision limit is estimated
with multiple end-to-end dota-acqmsition ad reduction
cycles According to She A AA Stadard, the precision
limit for a single test of variable X is detffmmed by
P = Kt (32)
where K is the coverage factor ad equals 2 for a 95%
co fidence level The standard deviation ~ is defmed as
t =~
where N is the m mber of multiple tests, ad X is the
mea value of the multiple tests When X is used as 6hr
fmal remit, the precision limit is Then
p=Kt
In msteady cases the standard deviation ad precision
limit are computed at each phase
Total uneertrduty: The total uncertamty Ux is
obtained with She RSS method as
Ux =~
4.2. FS harmordes
In order to determine the bias limits for the FS
harmonic amplit de. ad phases, it is ass med Chat the
measured value X deviates f om the real value X' with a
bias error d When the random error is not considered,
the real ad measured value are related with
X = X'+ 3 (36)
The bias error d is not a constant, ad it is usually a
function of the measurement value For simplification,
we ass me She relation is linear, i e
3 = Y, + TV' (37)
where v is She bias g adient, ad do is the constant pa
of the bias error The FS harmonic amplitudes ad
phases (n=O) for She biased ad mbiased cases are
related as follows:
0~ = T' | (I + t )X (t)co~(2mrfl) At + , | Y, cos(2mrfl) At
= (I + t ) To | X (t)cos(2);rfl) At + 0 = (I + t )o~
be = (I+t )K
X~ =~=p+t)X~
y~ = t m ( ~ ) = t m ( · ) = 7/7=·m
(I +t No or
Wherein a', b', 15, ad ,' are for She mbiased case
The bias errors for She FS harmonic amplitudes ad
phases can Then be detemmined as
3~ = X~ X~ = X~
(33) A, = rim rim = 0
The above deductions indicate that the bias error of the
FS harmonic amplitude does not directly depend on the
bias error, but on She bias g adient of the measured
variable Also, She bias error of the FS harmonic phase
is independent of the bias error of the measured
(34) variable X According to Eq (42) The bias limits of the
FS harmonic amplit des can be determined as
B.., = , X~ for n ~ O (44)
I+t
where Ire is the limit (maximal magnitude) of the bias
g adient, which can be calculated with the data
reduction equation ad elementary bias limits The
bias limit of the perch FS harmonic amplitude is
determined as
2 ~
BE = , | Bent = 2Bx
According to Eq (43) the bias limits of the FS
harmonic phases equal zero, i e P =0 The bias limits
of She adjusted phases 3_s) a then determined with
Eq (11) ad equations for determining the reference
phase Yr For example, the bias limits of the adjusted
harmonic phases for She forces ad moment a
determined wish Eqs (11) ad (18) as
~ , By, . = By, ,., = 0DBD = 2~ ID (46)
The precision limit ad the total uncertainty for the FS
harmonics are detemmined with She same procedures as
for the time histories
(41)
(42)
(43)
(4s)
4.3. FS-reconstrueted time hdstones
The d.ra red i non equation for a FS-rt onnni red
time history Ott be represented as
(38) XF(,)=XF(X,.X,.X~. .X~.Ay,.Ay~. .Ay~.t)(47)
where N is order of the FS For the rt onnni red time
(39) histo y, time t is a given value, so it has neither bias
nor precision errors According to the dat3-reduction
equation the bias limit ad precision limit a
(40) determined with
7
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OCR for page 53
( ~oB~° ) + hi (0X' By' ) + Zi (OAK BAK ) (48)
~ 1|( x0 x0) ~i( is' is' ) +2i(O~KP~) (49
The sensitivity coefficients a
art = ..= 0~, = ax, 0~ = axe
(so)
The total uncertainty Uxl, is obtained with the RSS value
of B 5adPxs
5 RESULTS AND DISCUSSIONS
5.1. Incident wave
For all m dead tests, time histories of the incident
head wave (zip are f mdamentally impo tat references
for all ocher measured variables ~ Fig 8a, a sample
time history is preset ted for She media test case, i e
Fr=0 28, Ak=0 05, ~ =3 048 m, where the incident head
wave frequency is f =07155Hz ad the encomter
frequency f is 1 2175 H Ahhonfh 6 is case was
chosen for She detailed uncfftamty assessment,
experiff ce has shown that the ocher incident waves are
similarly repediale m terms of amplitude ad frequency
ad possess low uncetamty for these two parameters
Longo et al 1998) Note that the incident wave
elevation in the figure represents a nearly perfect first
harmonic signal during She initial 8 seconds of She time
hi tory but is somewhat distorted m the foal 2 seconds
due to the closing distance between wave probe ad ship
model The :osroth-harmonic amplitude is less than 1%
of the fi st-hamonic amplitude ad the uncertdinty in
wave f equency f ad wave amplitude A is 0 7% ad
2 65%, respectively, which is based on multiple tests
N=ll) ad estimates of the bias limits Also based on
multiple tests, She uncertamty of She enco mter
frequency f is determined with time histories of CM
Fig 8d 1 as 0 4% for She media test case which ensures
acuray m the time domain of the measurements Note
that f is determined with low r uncertamty th m f,
because CM includes more wave periods than Zb i e
f f The once tointy of f, A, ad f for the waze-
eievations tests is expected to be at le ff as good as for
the media test case
5.2. Median test ease for forces and moment
Basic results for the forces ad moment tests are
time histories of resista e (C ), heave force IC=I, ad
pitch moment (CM) for the 42 test cases Fig g -d
includes the raw data ad She fi st-order FS
reconfine non for the media te t case Note that the
discussions for His case can generally be aplied to
most ocher test cases The output signals, i e, CT, Cd,
(d)
CM e hibit . tong first harmonic responses at £, except
for some mb-frequency responses for CT ad Cd
Fig g -c) CT ad Cd contain limited high-frequency
signals at She peaks ad troughs, which are associated
with carriage Vibration transmitted to the smgle-point
mo mt ad load ell This noise is absent for CM due to
the large inertia of She model for pitching motion Note
that, in Fig 8, CT, Cd, a d CM are not m phase with zip,
which will be explained later in this section
t [s]
Fig. 8: Raw ad FS-reconstructed time histories for
the media test case
Fo ther investigation of She harmonic content for
the forces ad moment is show m Fig 9, which
includes the :osrodh, halt, ad first th ~ fffth-order FS
harmonic amplitudes ad the adjusted phases AY The
error t ends in He timbre are the precision limits
8
12 15/00
OCR for page 54
(P=Ko) obtained with multiple tests (N=ll). (Here the
bias limits are not provided because they are relatively
small and not essential for the discussion). The figures
show that the zeroth and first harmonic amplitudes and
the first harmonic phases, which are the main focus of
the discussions, can be determined with very low
uncertainties. Since the corresponding harmonic
amplitudes are too small in the median test case, the
uncertainties for determining the higher harmonic
phases are very high. However, in the case of high-Fr
when the higher harmonics have significant amplitudes,
see Fig. 16, the phase can also be determined at low
uncertainty. Because of the limited recording time
(~lOs), the uncertainties for determining phases of the
half FS harmonics are very large.
~ a.
-o ~ , .................................
-1 0 1 2 3 4 5 6
(a) n
ro~34L
1 :,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...1
1 0 1 2 3 4 5 6
(c) n
o.: 11~1....1....1....1....
-o ~ :, .................................
-1 0 1 2 3 4 5 6
(e) n
(0.0044), and the difference, i.e. the added resistance
CT,a,, will be shown more clearly in Fig. 12. Phase
differences between the incident wave (~ and the
unsteady responses of CT, CH, and CM can be
investigated clearly in the figures, Note that the
incident wave signal is determined at x=0 and the
wavelength equals the model length in this case. The
resistance (CT) and pitch moment (CM) reach maximal
values when the peak of the incident wave hit the
forebody of the model ship at t/T=0.3 and t/T=0.35,
respectively. The heave force becomes maximal when
the peak of the wave hit the midbody (t/T=0.54.
-0.5
-1
0.015
0.01 .
- 0.005
(b)
0
-1
-2
~ 3
~ 5
-6
-7
-8
, ~ -9
~!
1
0.5
' O
\
,~: Unsteady |
/ ~
,, 1,,,, I,,,, I,,,, I,,,, I,,,, I,,,, I,,,,
~ A ~
— Unsteady |
-- Steady I
-0 005
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
(b) t/T
-0.01
-0.02
-0.03
-0.04
-0.05
-n nn
| Unsteady |
~ ~~ 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
(C) t/T
0.015 .
0.01
0.005
O
-0.005
-0.01
-0.015, .
~ ~ --------- Steady
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
u 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
(d) t/T
Fig. 10: Reconstructed time histories with adjusted
' -1 0 i 2n3 4""5""6 stars phases in the median test case
Fig. 9: Amplitudes, phases and precision limits for the
median test case unsteady forces and moment
Using the first-order FS harmonics for the median
case, the time histories are reconstructed and presented
in Fig. 10. The results of the steady test are also plotted
in the figure for comparison. Slight differences between
the steady results and the mean of the unsteady results
for CT, CH, and CM can be observed in Fig. 10. The
mean of the unsteady resistance coefficient CT (0~0049)
is larger than the steady resistance coefficient CT S~
Uncertainty assessment results for the FS-
reconstructed time histories are plotted in Fig. 10 as
uncertainty bands. An analysis of the uncertainty
assessment results is given in Table 2. The precision
limit (85-98%) is the main uncertainty source for the
forces and moment coefficients, and the elementary
precision limit for i\y is the main precision error source
(61%-95%~. CH has a much larger precision error for
determining i\y than CT and CM, SO that its relative
uncertainty (9.76%) is much higher than those of CT
(4.23%) and CM (2.93%~. Uncertainty assessment
9
12/15/00
OCR for page 55
rest its of the FS harmonics for C, Cr. CM are provided
in Tale 3 with rel live contributions of bias ad
precision compel nts ad total cncertamties no mahzed
either with She first harmonic amplitt des for She zerorh
ad terra harmonic ad 2rr for She phase Again, the
mam conhibt tion to She Once tainty in She FS
harmonics is the pi cision limits The rest its of the
uncertainty assessment for She FS harmonics of CT, Ct.
CM are also illt strated in Fig 11, 13, 14 as uncertainty
bands ad will be disct ssed later
Table 2: Ut e tainty assessment for time histories
Term _ _
Px,oUx,o _
PA 9 x,
Pi 9
B
Ux -
(+ Norman .,
5 46%
157%
78 8%
113%
88 7%
4 23%
Ad with X
t
4 80%
0 73%
94 5%
14 1%
85 9%
9 76%
CM
20 2%
189%
60 9%
212%
97 9%
293%
Table 3: Ut ertamty assessment
Term _
Boo
Pro
Uxo
But
Pat
Uxt
Bmr
P=,
Utiyt
Cl
382%
618%
1 08%*
155%
84 5%
3 83%
0 45%
99 5%
362% **
T c, 1
11 7%
88 3%
123%*
18 1%
81 9%
318%*
0 26%
99 7%
6 24% **
for FS harmonics
M
2 21%
978%
2 80%
141%
859%
4 25%
0 70%
993%
232% **
5.3. Linear response for forces and moment
Sit e the regmlar head waves get rated by the IIBR
wave maker a typical fi st-order harmonic waves, She
et otmtet d waves by She ship hi 11 with a constant
forward speed are also fi st-order harmonics When
likening the ship hi 11 md the ff otmter wave ystem to
a dy comic (oscillating) system, She ot tpt t signals
(measured vaiales C, Cr. CM can be considered as
Imear responses, if they are also first-order harmonics
The Unsteady t spouses in the media te t case are
10
Imear because the measured variables a dominated by
fi st-order FS harmonics in cases of non-lit al
responses, She first-order FS harmonics represent She
lit ar portion of She total unsteady t spouses in She
followmg the Imear po lions of She unsteady re ponses,
i e She :mroth ad term harmonic amplit des ad She
first harmonic phases, a disct ssed for all test cases
Fig. 11 Zerodh ad first FS harmonic amplit de ad
the first FS harmonic phase for C
The zerorh ad fi st FS harmonics of C are shown
in Fig 11 For comparison, She zerorh FS harmonic
amplitt de of C for the steady (withot t wave) case is
also plotted in Fig l la The Broth FS amplitt de C ,o
initially dect ases with it reasmg Fr ad then
it reases with it reading Fr beyond Fr=0 28
Fig l la) Not surprisingly, CT o aproahes She steady
case for decreasing Ak Fig lla) in addition, CTO
it reases with it reasmg Ak Fig lla, d) or ~
Fig lldt The fist FS amplit de CT~ dect ases
nonlit arty with nor acing Fr, with the steepest
descents for mcreasing Fr at She highest Ak Fig l lb)
With it reading Ak or X, CT ~ it t ases rabidly
Fig llb, e) The phase lead of CT, AYCr ~ is mostly
constant verst s Fr ad Ak, bt t mcreases with
it reading ~ Fig llc, f ~ Fig lla, obviot s
differ t e betw en She tm ready ad steady C I, i e
dot ble of the added resists e, is it stigated,
especiallyforlowFradhighAk Asshow inFig 12
the added resists e C,.,~ decreases with it reasmg Fr
bt t it reases with mcreasmg Ak or ~
12 15/00
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Representative terms from entire chapter:
free surface
to ohs
to
3 I oo4
V 0002
(b,
~ Ak=0 025
F.' For,,
pgVL;i,
F.,
Pgaper,
' Pglt;,
where V is the vol me of displacement, A is She water-
pla area, IL is the longitudinal moment of inertia of
water-pla area about y :rcis, (rot, For, Fz,~ ad M, I are
the fi st FS harmonic amplit des for incident wave,
heave force ad pitch moment, respectively According
to previous st dies She non-dimensional exiting forces
depend mamly on She wave length, ad their amplitudes
Reproaches I when L/\ equals Pro, i e when ~ is
mlimited large
ad by Gerrit ma ad Beukekma (1967) for a ship
(51) model The dependents of the non-dimensional
exciting force amplit des on the relative wavelength
are similar for She f ee models, ad She observed
(52) dif rences may result from the model geomet y
(53)
u
20
Fig. 15: Exciting force amplitudes for th ee ship mo dels
The non-dimensional exciting force amplitudes F a.
F'z ad M>y a computed for DTMB 5512 at f ee Fr
mmbers ad presented in Fig 15 together with data
takenby Journee (1992
2) for a Wigley model t F - O 30
12
n
wit
Coo ~ ~ 5, , . 0
0C032, .,,, ' '" ' "'-' ''
(d) f [it]
Fig. 16: Time hi tories ad FT results of msteady
pitch moment for two t pical cases
5.4. Nomlinear response for forces and moment
In above discussions She fi st-order harmonic
responses m She present ship hull ad wave y rem a
considered as linear responses That implies that all the
sub- ad super harmonics in She test results a
referred to non-linear responses According to She
analysis in subsection 5 2, the msteady responses of
CT, Ce are CM are mostly Imear m She media test case
because She harmonics a considered to be noises
ad She super harmonics can be neglected ~
consideration of other test cases, the time histories ad
the corresponding FT results of CM are given in Fig 16
12 15/00
for a long-wave/low-Fr case Fr=0 19, Ak=0 025,
=4 572 m) Ind a short-wavehigh-Fr case Fr=0 34,
Ak=0075, \=1524m) Bodh the time history in
Fig 16a mdF reseltinFig 16bsuggetnearlyperfect
fi st harmonic msteady response for the former test
case Although a strong fi st harmonic msteady
re ponse is also observed for The bitter short-wave case,
a s per-harmonic response at Of is also present in
Fig 16d Similar tendencies in the harmonics are also
observed for CT md Cb but not shown here Amongst
the tests, The seper-harmonic responses are only
investigated m the short-wave cases, i e for \=1 524 m
Fig. 17: FS harm onic amplitudes for a sho t was eleng h
(~=1 524 m) verses Fr md AL
Detailed inve tigation of msteady responses for the
sho t-wave case 6 ouch malysis of the Ig, 2~3 md 3-d
FS harmonic amplitudes for C md Cb verses Fr md
Ak is provided in Fig 17 The FS harmonic amplitudes
for n=l, 2, 3 generally increase with increasing Ak, md
they are roughly Imear functions of Ak except for cases
at F - O 41 which mpear to be par:~olic The super
13
harmonics mpear to have signitlcmt magnitudes for
F - O 34 md 0 41 The tendencies in the FS harmonics
noted ibm H are similar for CM but not show here The
conclusions from Figs 16 md 17 point to non-linear
msteady responses m The forces md moment
coefficients but mly for combinations of sho t ~ md
mid-high md high Fr Further inve tigation of The
super harmonics are shown in Fig 18, m which The
dependencies of the FS harmonic amplit des on Fr for
Ak=0 I md \=1 524 are given For C, Cb md CM, the
first harmonic amplitudes decrease with increasing Fr,
md the thi d harmonic amplit de. are relatively ve y
small Interestmgly, for all th ee vari:3} lies The second
harmonic amplitude has a maxim m near Fr=0 34
eU,,[IO1 5 :~[101
\ ~ [rl 4 5 \ ~ [r
\~_.,2 : '\k
j e,,,[101 zo;
\ ~ trl 18f
Wri 12
5 \ 10
~ ~ B~
05 ~ 0~zoz5 o~ 035 O . Z015 03035 O
(s) Fr (b) Fr (o) Fr
Fig. 18: Dependencies of FS harmonic amplit des on
Fr for \=1 524 m md Ak=0 1
for Fr=0 34, \=1 524m md Ak=0 1
7he raw md reconstructed time hi tories of 6he
pitch moment coefficient CM are given in Fig 19 for
the most non-lmear case, i e Fr=0 34, \=1 524m md
Ak=0 1 7he reconshucted time history mcledes 6he
second-order FS md reflects a t pical non-linear
response in Fig 19, the raw time histo y is different m
12 15/00
different encounter periods due to some sub-frequency
content. Because of the limited data-acquisition time
(10~15s), the sub-frequency content cannot be
determined correctly with the current data.
-0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
n
In
n
n
In
n
n
In
n
Fig. 20: The oth (a) and 1St (b) harmonic amplitude and
the 1St harmonic phase (c) for the unsteady
free-surface elevation
5.5. Free surface elevations
The free-surface elevation data provided for CFD
validation includes the FS-reconstructed unsteady free-
surface elevations and uncertainty assessment results.
Detailed analysis of time histories at select locations in
the wavefield have verified that the unsteady wavefield
exhibits a strong first-harmonic response and, therefore,
can be represented with a first-order FS. The zeroth and
first FS harmonic amplitudes and the first FS harmonic
phase are computed in both far- and nearfield regions
and shown in Fig. 20. The zeroth harmonic amplitude
(Fig. 20a) of the wavefield displays the typical wave
pattern characteristics of a fine hull form advancing in
calm water, including diverging and transverse waves
and a dominant fore-shoulder wave. The zeroth
harmonic amplitude is, in fact, two times of the mean
unsteady free surface elevation. According to the test
results the difference between the mean unsteady free
surface elevation and the steady free surface elevation is
within the uncertainty band. The amplitude of the
incident wave (0.006) is 43% of the dynamic range of
the steady free surface elevation (0.0144. Fig. 20b
includes contours of the first FS harmonic amplitude in
the wavefield. Note that the contours are contained in a
wedge-shaped region with semiangle of 24.5°. A
dominant crestline is observed swept backward from
the forebody shoulder, and a weaker troughline
emanates from the transom corner. The maximum of
the first harmonic amplitude (0.01) is 1.7 times of the
incident wave amplitude. Fig. 20c shows contours of
the first FS harmonic phase. Interestingly, the two
regions where the contour lines are most affected seem
to be associated with the crest and troughlines of the
first FS harmonic amplitude. In comparison to the
uniform phase distribution of the incident wave (-
2~xL/~), phase leads and lags are present at the
forebody shoulder and transom corner, respectively,
and the dynamic range is about ~/3. Distributions of
the zeroth and first FS harmonic amplitude and the
first harmonic phase are used to reconstruct the
unsteady wave patterns. Examples are shown in Fig. 21
at four instants in the encounter period (t/T=O, 0.25,
-0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012
a. -
0.3
0.2
0.1
0.0
x -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
0.4
0 3
02
n 1
On ~.--.- - ~ - ~ - ~ - ~ ~ ~ ~ ~ ~ ~ ~
b) -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0 5 X 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
u . -
0.3
0.2
0.1
0.0
(C) -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0 5 X 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
On _. I,_
(d) -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0 5 X 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Fig. 21: Unsteady wave patterns at t/T=O, 1/4, 1/2, 3/4
The unsteady perturbation response of the free-
surface elevation, i.e. the diffraction wave, is computed
with the reconstructed unsteady free-surface elevation
and the incident wave pattern (Eq. (1744. Since the
unsteady free-surface elevation is reconstructed with
the first-order FS, the diffraction wave contains only
first-order FS harmonics. The distributions of the
harmonic amplitude and phase are shown in Fig. 22.
14
12/15/00
The contour patterns of the diffraction wave amplitude
(Fig. 22a) look similar to that of the first-order FS
amplitude of the unsteady free-surface elevation
(Fig. 20b). Two maximums of the diffraction wave
amplitude initiate at the forebody shoulder and transom
corner and diverge from the model at 24.5° with respect
to the centerplane. The maximal amplitude of the
diffraction wave (0.004) is about 40% of that of the
unsteady free surface elevations. There are two peaks in
the phase distribution of the diffraction wave (Fig. 22b):
one is near the forebody shoulder (x=0.354; the other is
inboard of the diverging stern wave crest (x=l.O94. This
implies that the diffraction waves originate, in principle,
from the forebody and stern regions of the model. This
can also be seen in the time history of the diffraction
wave (Fig. 234. Note that in Fig. 22b large errors exist
for the phase in regions of very low amplitude.
. .
^0.2
o.]
~o~
0.4
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
(a) x ~ 0~
A summary of the uncertainty assessments for the
farfield free-surface elevations is provided in Table 4 at
y=0.082 and y=0.232 for the steady and unsteady case,
respectively. For the unsteady case precision limits are
determined at six phases and averaged. For both the
steady and unsteady cases, the values are spatially
averaged in the region of x=O~1 and also time
averaged for the unsteady case. Table 4 shows that the
bias and precision limits are nearly the same order for
both the steady and unsteady case. In the steady case
the bias limit is larger than the precision limit, but
switched for the unsteady case. For both the steady and
unsteady cases the main bias error source is from Uc.
The uncertainty levels (1.5% and 3.3%) are reasonable.
-0.1 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.9 1 1.1 1.2 1.3
x
An,
~-
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3
(b) x
Fig. 22: Amplitude (a) and phase (b) distributions of
the diffraction wave
Table 4: Uncertainty for farfield free-surface
Term
B uct3uc
BE
BD~
Bye
BE
B.:
Pa
Us 1 -. . . .
(a: Normalized with maximal (T,I)
Steady, y=0.082
Magnitude (%)
3.0806X10-4 (79.3)
1.4364X10-7 (0.04)
2.2898X10-5 (5.89)
2.4636X10-5 (6.34)
3.2808X10-5 (8.44)
3.12X10-4 (59.0)
2.17X10-4 (41.0)
3.80x10-4 (1.50)*
b) :0.2 -0.1 o 0.1
(C)
it................
0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.9 1 1.1 1.2 1.3
x
,, ~ ~~,~.~ , , ,~
).2 -0.1 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.9 1 1.1 1.2 1.3
x
o. p.
~ or
Unsteady, y=0.232
Magnitude (%)
4.9762X10-4 (84.0)
2.3203X10-7 (0.04)
3.6988X10-5 (6.24)
2.5024X10-5 (4.22)
3.2808X10-5 (5.54)
5.01X10-4 (43.3)
6.55X10-4 (56.7)
8.24X10-4 (3.251*
................ ........ it i i i i i i i i i i i i i .................................... .
-0.1 o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 o.9 1 1.1 1.2 1.3
x
Fig. 23: Diffraction wave patterns ((D) at four instants
Uncertainty assessment results for the nearfield
free-surface elevation measurements are conducted at
two points in the wavefield corresponding to high
(x=1.075, y=O; HTR) and low (x=0.05, y=0.07; LTR)
free-surface turbulence regions and summarized in
Table 5. Note that for the unsteady cases uncertainty
assessments are completed for the FS-reconstructed
time histories, and the results are time-averaged. For
both steady and unsteady cases, precision limits are
obtained with multiple tests (N=104. Results for all
cases demonstrate reasonable uncertainty levels of 1.1-
4.2%. For the LTR, bias and precision limit
contributions are equally weighted for the steady case
15
12/15/00
but for She msteady case, She uncertainty value is
dominated by precision limit (84%) For She HTR ad
both steady ad msteady cases, the uncertainty values
are dominated by precision limit, 75% ad 87%,
respectively
Table 5: Uncertainty for negrfield free-smfae
Steady (Fr=0 28)
Term :=0 05, y 0 07 :=1 075, y 0
Mggmt de (a) Megnitude (a)
Bt 3 2808x10'(52 6) 3 2808x10'(25 2)
Pt 2 9600X10S (47 4) 9 7200X10s (74 8)
ut 44187X10S(l 10) 1 0259X104(1 90)
Unst sedy (Fed 28, t=4 572 m, At 0 025)
Term x=005,y 007 . of. A
Mggmt de (a)
PtDdtD 1 5754x10 ~(65 7)
Pt.~dt.~ 5 2452xl 0 s (21 9)
P~,~6~.~ 9945X] 0 ~ (] 2 4)
IT 32808XtOs(163)
Pt 1 6872x104(837)
ut 17188X104(286)'
(+ Normalized with local (Tat)
:=1 075,y 0
Megnitude (a)
1 5520X] 0 ~(40 1 )
1 1498x104(297)
1 1704xl 0 ~ (30 2)
3 2808xl 0 s (12 7)
2 2584xl 0 ~ (87 3 )
22821X104(423)'
Wifh data from the negrfield f ee-smfae test, the
harmonic content ad f ee-smfae turbulence are
investigated to detemmine She characteristics of the
msteady we field Eight measurement pomts located
in regions of high (x=1 0148, y 0~0 03) ad low
(x=1 0148, y 0 05~0 08) free-surfae turbulence are
selected for the d tailed investigations FT results of the
time histories at each location are presented in Fig 24
On ad near the centerpla Fig 24a d), the FT record
contains a pit e at f ad ahmdmt sub- ad super-
harmonic frequency content associated with the
naturally turbulent topog achy of the transom we field
Moving further from the centemla transversely
Fig 24 -h), She FT records abruptly become very clean
in the higher-f equency region, leg mg a dominat
spike at f surro mded by a small local region of FT
content prot at Iy associated with She coarse resolution of
the FT for She limited data requisition time (-9 i)
Fig 23 indicates chat the myority of She we field
e hibits a strong frst-hamonic (linear) response ad
provides support for representation of She un teady
we fieldwifhafrt-orderFS
The free-smfae turbulence level in the steady case
is usually described with She RMS value of f ee-surfae
fluct ations go ad the mea value Similarly, the
msteady free-smfae turbulence level is here defined
with the RMS value of the free-smfae fluctuations
pro ad the reconstructed f ee-smfae elevations (fi st-
order FS) Fig 25 shows She comparisons of mea ad
RMS flat ation of fre-smfae elevatims for teady
ad msteady cases at the stern of the model The
steady free-surfa elevation (<,,) ad the mea of
msteady f ee-surfae elevation (
regular head waves. Unsteady resistance, heave force,
and pitch moment are procured at a fairly wide range of
test conditions of interest. Unsteady free-surface
elevations are mapped in a case of median Froude
number, long wavelength and low wave steepness. The
test uncertainties assessed following the AIAA Standard
(1999) are in reasonable levels.
The mean of the unsteady resistance coefficient is
larger than the steady resistance coefficient, especially
at low Froude number and high wave steepness, and the
difference, i.e. the added resistance coefficient,
decreases with increasing Froude number but increases
with increasing wavelength or wave steepness. The
mean of the unsteady heave force coefficient is almost
the same as the steady heave force coefficient, and it
decreases linearly with increasing Froude number
without dependencies on the wave steepness and
wavelength. The mean of the unsteady pitch moment
coefficient is nearly the same as the steady pitch
moment coefficient, but it is slightly larger at low
Froude numbers.
Test results for unsteady forces and moment
demonstrate mostly linear responses in cases of median
and long wavelength, which agree with the previous
experiments and analyses basing on the traditional strip
theory for ship motions. For the linear responses, the
amplitudes of the exciting forces (or the first harmonics)
increase linearly with increasing wave steepness at the
same Froude number and wavelength. However, non-
linear responses are investigated in cases of short
wavelength and high Froude number. The non-linear
responses contain significant second-order harmonics,
and their amplitudes increase non-linearly with
increasing wave amplitude. Generally, the first order
harmonic amplitudes of the forces and moment
coefficients increase with increasing wavelength or
wave steepness and decrease with increasing Froude
number. Relative to the incident wave at the forward
perpendicular of the model, phase lags exist and only
depend on the wavelengths.
The unsteady response of the free-surface elevation
is linear in the case of median Froude number and long
wavelength, except for a small area near the ship hull at
the stern in the transom wave field. The mean of the
unsteady free surface elevation shows the same patterns -(0b)095
as the diverging and transverse waves in the steady case.
The reconstructed unsteady free surface elevation has
maximal amplitude of 1.7 times of the incident wave
amplitude. Relative to the incident wave patterns, phase
leads and lags are present in the range of ~/3 at the
forebody shoulder and transom corner, respectively. The
free-surface turbulence levels of the steady and unsteady
cases are nearly the same in the high-turbulence region
at the wake center, but in the low-turbulence region off
the wake center the turbulence level of the unsteady case
is higher. The maximal amplitude of the diffraction
17
wave is about 40% of that of the unsteady free surface
elevation. The phase distribution indicates that the
diffraction waves originate from the forebody and stern
regions of the model.
Results of uncertainty assessments indicate that
the main uncertainty source for the forces, moment,
and nearfield free-surface elevation measurements is
the precision error. The precision error can be reduced
in the future by improving the stability of the
measurement systems and by increasing the recording
time for unsteady signals. For the farfield free-surface
measurement the bias limit is as significant as the
precision limit, and the main bias error results from the
carriage speed. Therefore, the speed of the carriage
should be controlled better for future unsteady tests.
The test data and the uncertainty results is being
used for CFD validation in the IIHR, and it will be
archived at "I" for
general dissemination. For future tests, phase-averaged
PIV measurements of the unsteady flowfield are being
conducted in the IIHR towing tank using the same test
condition as for the unsteady free-surface tests, and the
results will appear soon.
0.09
0.06
n no
~ 0
-0.03
-0.06
0 09 1.05 1.1
(a)
n no
0
-0.03
-0.06
unsteady
~5
,,1,,,,1,,,,1,,,,1,,,,1,,,,1,,
1.05 1.1 1.15 1.2 1.25 1.3
x
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
O
-0.001
-0.002
-0.003
0.0012
0.0011
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
O
Fig. 25: Nearfield free-surface elevation at the stern:
(a) Steady and mean of unsteady, (b) RMS
ACKNOWLEDGMENTS
This research was sponsored by Office of Naval
Research under Grant N00014-96-1-0018 under the
administration of Dr. E.P. Rood. The generous loan of
the servo-type and acoustic wave probes by Prof.
Yasuyuki Toda, Department of Global Engineering,
12/15/00
The University of Osaka, Osaka, J ma is g usefully
ack owledged
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DISCUSSION
R. Beck
University of Michigan, USA
You monhoned that the diffractia wave
field was 200% of the incident wave.
Since the diffracted waves aga ust a wall
is double the incident wave height
(100%), can you explau why you found
such large diffractia waves?
AUTHOR'S REPLY
The diffraction waves are 67% of the
incident wave height, i.e., (0.004/0.006)
DISCUSSION
H. Bingham
Tech ica University of Denmark,
Denmark
What theory are you using to generate
your non inear incident waves? Have
you checked that you can indeed
produce a steady non inear wave?
AUTHOR'S REPLY
The incident waves are f rst-ha monic
inear waves.
DISCUSSION
R. Pe Ha
Inshtuto Naziona e per Studi ed
spenenze di Architettura Nava e, Ita y
In order to study the u steady flow in the
wake produced by the waves, I wou d
ike to know if you've schedu ed
experiments using PIV in a ta k.
AUTHOR'S REPLY
Yes. Cu rent efforts in the IIHR towing
are concermed with the expemmenta
setup and measurement by PIV of the
unsteady flowfield at He era conil ml -x
stations of the 5512 model.
Measurements vi I begin at x=0.935
(propeller plane) and then proceed to
forebody and wake stations.
