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ANTI-ROLL TANK SIMULATIONS WITH A VOLUME
OF FLUID (VOF) BASED NAVIER-STOKES SOLVER
E.F.G. van Daaleni, K.M.T. Kleefsman2, J. GerTits2, H.R. Luther, A.E.P. Veldman2
('MAR N. P.O. Box 28, 6700 AA Wagenrngen, The Netherlands,
2University of Gronrngen, Depa tment of Mathematics,
P.O. Box 800, 9700 AV Groningen, The Netherlands)
ABSTRACT
Results of comp ter simulations of She water motion
in ship mti~oll t mks are compared with
experimental data The m meri cl computations are
done with c Vol me Of Fluid VOF) based Navier-
Stokes solver Both fiee-surface mti-roll tmks md
U-tube mti-roll tarns me considered Calculated md
measured results for She local wave heights, th sway
force md roll moment are presented for bodh leg lar
md i regular tank motions A simple but effective
simulation model for She active co trol of U-tube
me roll talk is i nod i ed Finally, She f 11y
nonlinear time-domcin coupling of the ship motion
md the t mk water motion is estate lished
INTRODUCTION
A ship subjected to wind md wave forces will
perfomm motions m six deg es of freedom, i e surge,
sway, he, roll, pitch md yaw The roll motion is
the most critical one bec mse it is lightly damped md
therefore prone to dynamic mcgmfication, in
particohr m th resonance fiequency 9 ge Ship-roll
stabilization hr3 Therefore Deceived considerable
attention; it till is c major subject of mterest to ship
designers md naval architects Among c wide variety
of roll-damping devices Vastc et al 1961), mti-roll
tmks me appreciated for their simplicity, low cost
md action et low or even zero speed The concept of
using fluid tmks for ship-roll reduction was fi st
conceived by Froude (1861) in She pa t, several
types of mti-roll t mks have been proposed md h led
in practice Two basically deferent desig s c m be
disting ished (see Fig 1) Fi stly, th flee-surface
mti-roll tank Watts 1883, 1885), having one urge
Ire surface md secondly, the U-tube mti-roll tank
Frahm 1911), which hr. two smeller fiee surfaces
Tl.eoreri al tudies on U-tube tmks are based on m
equivalent double pendul m theory (Stinter 1966):
the mass of the t mk fluid c m be regarded es c second
Fend HI m attached to the Fend HI m representing the
ship, over most of She roll fiequency r mge The
phy ical behavior in c flee-smface t mk is completely
different md must be classed in She g oup of shallow
water waves herhrgen & Vim Wijugsarden 1965)
Since She mom stioili ing action is created by c bore
trampling up md down th tmk's width, She fluid
flow is essentially nonlinear ( ho et al 1968) So, the
basic principle the two mti-roll tank t pes have in
common is the h msfer of fluid from starboard to port
side md ice verse, with c ce tam phase kg with
respect to the ship's rolling motion; thus, c
co interacting moment is provided Sometimes c
limited control is exe ted over She motion of the fluid
by installing resh lotions or baffles m She center of the
fre-surface t mk or m the duct md or wing t mks of
the Up mk Active cone ol is often applied to Up mks
by means of valves on top of She wing t inks or m c
com cting air duct Detailed descriptions of passive
md active mti~oll t mk are due to Bell & Walker
(1966) md Webster (1967) Mme recently, Lee &
Vcssclos (1996) investigated She stabilization effects
of mti~oll t mks
Wish th ongoing increase of comp ter resources md
the improvement of m meri al clgori6 ms,
experimental studies of fluid flow are more md more
accomp Died (or even rephcedl by computer
simulations Nevertheless, experiments remam
crucial for validation of Computational Fluid
Dynamics lo Dl codes md c better phase al
alder t mding of fl id motion m complex geomeh ies
Computer simulations of the fluid flow in mti-roll
tmks are scarce Zhong et al (1998) present results
from two dimensional simulations of c U-t be t mk
The discretised No ier-Stokes equations are solved
using She Gclerkin scheme, based on th finite
element medhod The roll motion is ass med to be
smell, slow md simmsoidal Fur6hermme, She flow is
less med to be kminar et all times in th n mericcl
model, the g id is kept fixed md the position of the
Ire surface is specified as part of th 1-3 mdary
conditions; the g id does not move with She free
surface Simulations with various duct heights md
wmg-tmk width are discost d Ytmiguch et al
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Representative terms from entire chapter:
fluid flow
(1995) simulate an impeller-activated U-tube tank.
The Navier-Stokes equations are discretised using the
SOLA-SURF scheme based on the finite difference
method. The impeller is modeled as a velocity jump.
The numerical simulations are done for a ship in
regular waves. Unfortunately, these numerical
models were not validated with experimental results.
The computer program ComFlo solves the Navier-
Stokes equations for unsteady incompressible fluid
flow in complex geometries. The method is based in
part on the Volume Of Fluid (VOF) method (Hirt &
Nichols 19814. ComFlo has found many applications
in a wide variety of flow problems, ranging from fuel
sloshing in space satellites (Gerrits et al 1999) to
green water loading on the fore deck of a ship
(Fekken et al 19994. The computational model has
proven to be robust and accurate. Recently, an
extensive validation program was set up and
systematic series of computer simulations were
performed for both free-surface type and U-tube type
anti-roll tanks in regular and irregular motion. A
selection from these results is presented here.
H
our
B
cc~ntrc,1 valves
~ ~ ~~~~— ~— ' ~~ - ' —~ ~
~ .
~ air ~ air ~
~ ~ ~ /
~ fluid
t
Figure 1: Definition of geometry and tank
dimensions: free-surface anti-roll tank (top) and U-
tube anti-roll tank (bottom).
~ wing
The outline of this article is as follows: First of all,
we briefly discuss the ComFlo program, in particular
the underlying mathematical model and numerical
method. Next, we focus on the tank fluid motion and
the corresponding forces and moments. To this end, a
series of computer simulations was carried out where
the tank is given a prescribed rolling motion. The
calculated results for the local wave heights and the
forces and moments are compared with experimental
data.
Next, the problem of active control for U-tanks is
addressed. In practice, a simple and effective way to
control the internal fluid motion is by closing and
opening air valves located on top of the wing tanks. It
is shown that by making use of the ideal gas law, the
damping effect of the air volume above the fluid
column can be taken into account. In this way, the
fluid flow is blocked and the tank's roll peak period
can be matched with the ship's natural period of roll.
Finally, the nonlinear coupling of the ship motion and
the tank fluid motion is solved with a time domain
method adopted from a numerical technique
developed for nonlinear fluid sloshing in spinning
containers (Gerrits & Veldman 20004.
COMFLO - MATHEMATICAL MODEL AND
NUMERICAL METHOD
The motion of a fluid can be described by a set of
partial differential equations expressing conservation
of mass, momentum and energy per unit volume of
the fluid. The Navier-Stokes equations for three-
dimensional incompressible fluid flow can be written
in conservation form as follows:
V v=0
a + v ~vv ~ =——vp +v
are imposed in (4), vet is the v locity component
perpendicular to She solid fixed bo mdary, ~ is the
t me ticl stress Ed vat is the tang nticl v locity
compone t
On the free surface the dynamic conditions hold, to
ensure that (i) She flee-surfa pressure equals the
atmospheric pressure Ed (ii) the pi does not exert
t me ticl forces on th fiee surface These
requi ements are expressed es
P-P°=V~---~, W+aVt)=0 (5)
P ~ P at ~
wh re pi is the atmospheric p~essme, ~ is the smfae
tension Ed ~ is She surface curvature Usually, the
fi st term on th right-h Ed side of (5) is neglected A
fixed Cartesi m ('ectilmear) g id is Icid ov r the fluid
domain The discretization is based on c taggeeed
g id: She pressure is calculated m th cell centers,
whereas the v locity is calculated m She center of
each cell face Using so-celled geometry Ed edge
3p t Yes (openi g f actions), fluid domains of
arbihary shape m be h mdled Each cell is assigned
c cell Abel to disti g ish betw en She fluid, the air,
the fluid~ir interfile Ed the fl id domain
bo mdaries Finally, v locity labels are attributed to
the cell faces to Taco mt for She various types of
bo mdary conditions
For mteg ctmg th time-dependent Ncvier-Stokes
equations, the fir t order explicit forward Euler
medhod was chosen A predictorcorrector medhod
was implemented m such c way that et all time lev is
the v locity field is div rgerce-tiee, m compliance
with (1) The diffusiv terms m 2) are discretived
centrally Ed for She convectiv terms en append
dismetization is used Th Poisson equation for the
pressure is solv d by Successiv Ov r-R lactation
Fimtlly, the fiee-surfae profile is updated using c
refined v rsion of the so-celled Donor-Acceptor
algorithm (Scbeur et at 1998)
For c detailed description of ComFlo w refer to
Gerrits (1996) Ed Loots (1997, 1998)
FREE SURFACE TANKS IN REGULAR
MOTION
E periments w re performed by V m den Bosch Ed
Vogts (1966) to collect i formation Croat the
performance of fiee-surfae mti-roll ticks A
rect mg lar tarn, partially filled with water, was
forced to execute sinusoidal oscillations Croat c fixed
axis while the moment due to the water motion was
amplitude AM cod phase male CM with re pect to the
forced rank rolling motion Aft) w re determined
Sy tematic measurements w re done for c wide r mge
of rank parameters (tick widthB, mean water depth
h) Ed motion parameters (roll amplitude A. Ed
frequency 03, height s of rotation pomt al TV tank
floor) The t mk length Ed height w re k pt const mt
et L=lm Ed H=0 Sm re p m- Iy The complete
series of e periments was simulated with the prog cm
ComFlo VmDaaleneto/1999)
When the water depth is large, the wave motion in
the rank is c simple ocilhtion of th fiee surface for
all fiequencies The f mdamentcl mode of 6 is
standing wave hr. c length \=2B For shallow water,
say for h B < 0 1, he picture is entinely differe t At
low frequencies the Jong) studding wave is present
Fig 2a), b t with Increasing frequency v y short
prom essiv waves appear Fig 2b) in She t msition
regime the short waves i terfere with the long ~ are
Af er these smell disturbances the bme rises rather
suddenly Fig 2c), while the phase kg betw en the
water h msfer Ed the imposed motion Increases (see
Fig fib); th quad azure component of the moment
increases rapidly Fig 3c) O er c k g fiequency
r mge She phenomenon does not ch ma sin fficatly,
c16hough th water motion becomes mme violent ad
lark vortices appear when the direction of wave
propagation is rev rsed Next, the bore passes into c
solitary wave Fig 2d), c singde steep wave rmmmg
from one side of She t mk to She other After the bore
hr. disappeared, She mome t exmted by She water
falls dow rapidly (see Fig 3a) Wish c smell further
increase in fiequency the water approximates the
"frozen" tate Fig 2e) ffthe tick bottom is situated
below She axis of rotation WE n the t mk is mo mted
al TV 6 is axis, the water motion becomes rather
chaotic in this high fiequency r mge th re is hardly
my water tr msfer
Figme 2 (lef col mn): Fre-surface tmk in ~eg lar
roll motion Sm~pshots tak n from computer
simulstions wifh ComFlo 111u tmtion of ws types
for dffferent f~equency regimes: (c) stmding ws;
(b) t mdmg ws md short t~avelling ws s; (c)
bme; (d) solitary ws ; (e) fi o:D:n tate
0015
_ ~ - ~'~
,^oolo ~ ~
OOD
oo 05 10
~/(~B) [ ]
150 1 1 ~ 1
~:o 1 1~i 1
~90 ~'
oo 05 10 15
~'(~B) [ ]
_ 0005
_ 0 ooo ~ ~
:= 0005 ~ ~ ~f
'~oolo ~ ~
oo 05 10
~1/~/~\ 1 1
,,~,~, ,,
Figme 3: F'ee-surface tmk in ~eg lar roll motioa
Moment smplitude (top), phase mgle (middle) md
quad ctme component (bottom) cs function of roll
frequency Parsmeters: s R=0 2, h R=0 08,
A,, 3 8deg Closed squares: experiments; pen
squares: ComFlo
In the Yoq~r41 we sh~ll discuss 6he influence of each of
the followmg tamk 6md motion p6 6meters sep6 6tely:
roll 6mplitude, meam w4ter depth, height of robtion
pomt 6bo o tamk bottom 6md tmk width in the
computer simoktions, 6he g id has typic611y 40 cells
in horim t61 din4ction 6md 20 cells in ortic61
directioa
Figme 4 pn4sents th nomdimensional moment
6mplitude AM/(pgB3L) 6md ph6Y4 6mgde cM 6s
function of the non-dimensiom~l roll fiequency
{~/ B)'~ for various values of 6he roll 6mplitude Ao
When the roll 6mplitude in xe6 ses, th treng h of the
bon4 6md 6hereby th moment 6mplitude inxeases
too This i duerw4s 6he phase 6mgles 6s well The
incn46se in moment 6mplit de 6t the 6heoretic61 tamk
resonance fn4quency is not lim46, but cam be
6pproximated by 6 square root expression Verhagen
& V6m Wijug6arden 1965, V6m D6~1en & Wes6huis
2000),6sshow inFig 5
rD/(g/B) [ ]
o/(g )1~ [ ]
Figme 4: Fn4e-Yurf6 o tamk in n4g 16 roll motioa
Moment 6mplitude (top) 6md ph~se 6mgde ~ottom) 6s
function of roll fn4quency P6 6meters: s B=0 0,
h B=0 06 Triamgles: Ao=1 9deg; Squares:
A,, 3 8deg; Cimles: A~=5 7deg CloYod symbols:
experiments; Open symbols: ComFlo
-0015 = = _ _ ~
<~0005 f ~ / _ _
0 ~ 4 6 8
Ao [deg]
Figme 5: Fn4e-Yurf6 o tamk in n4g 16 roll motioa
Moment 6mplitude 6t 6heoretical resonance fiequency
6s function of roll 6mplit de P6 6meters: sB=00;
h B=0 06 Lme: 6heory; solid squares: experime ts;
Opff~ squares: ComFlo
The meam w4ter dep6h h is 6 p6 ticul6 impo tamt
p6 6meter. becamM4 it is cie6 th~t for 6 cc tam tamk
width B the only possibility to chmge 6he m~tm61
period of 6he water t msfer, 6heoretically gi on by
To=2B/ h)'~,isbyvaryingh Itis61socle6 thatat
or r~o6 this m~tmal period the water hamsfer is 16 gest
6md cl c mstances 6 e most f6 orable for roll
d4mpmg The effect of mcreasing water depth is
twofold: ~ 6he fi st pkce the cur o of phase 6mgles
orsus roll fiequency is shifted to the higher
freq~roncy ramge, Y e Fig 6 (middle) Whff~ th ph6 se
6mgles Ye plotted orms {04)o, when4 030=(~/B) h)'~
is the tamk's fheoretical 4tur61 fiequency, then4 is
h6 dly Ymy noticem le dfffererwo except for fhe higher
freq~roncies (Ye Fig 6 (bottom)), that is for the
region in which the bon4 t msforms into 6 solit6 Y
w6 o in fhe second pl6 o the moment 6mplitude
incn46sesbecamse ofth krgeramo mt of water inthe
tarJc, Ye Fig 6 (top) Again, the incre6Y 6t tmk
resonance is not lim46, but cam be 6pproxima ted by 6
square root expression Verhagen & V6n
Wijngaarden 1965, V6m DYAIen & Wesfhuis 2000), 6s
show m Fig 7
00 05 10 15
. . .
Figme 6: Fn4e-surfs s tarDc in n4g lar roll motioa
Moment rmplit de (top) mdphase mgle (middle md
bottom) es f nction of roll fiequency Parrmeters:
s R=0 0; A,, 5 7deg Trimgles: h R=0 04; Squares:
hR=006; Circles: hR=008; Rhombs: hR=010
Closed symbols: experiments; Open symbols:
ComFlo
_oo~o = = _ _ _ l
'-ooio _ ~ ~ ~ _
<-0005 f = = = =
nnn nm nn4 nn~ nnn n o
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . ~
htB[ ]
Figme 7: Fn4e-surfs s tarDc in n4g lar roll motioa
Roll moment rmplitude et theon4ticcl resonance
freq~rsucy es function of me m water depth
Ps rmeters: s R=0 0; Ao=5 7deg Lme: theory; Solid
squares: experiments; Open squares: ComFlo
oo~o
0015 \'
~=ooio ~ ~ ~=~ ~ ]
040 o~o ooo o~o 040
s/B[ ]
~i50
=,i~o . ~
~ ~60 i e4 t—~
~
040 o~o ooo o~o 040
~B[ ]
Figme 8: Fn4e-surfs s tarDc in n4g lar roll motioa
Moment rmplit de (top) md phsx4 mgle ~ottom) et
resonance fiequency es function of rotation pomt
height with respect to tarDc bottom Parrmeters:
h R=0 06; Ao=5 7deg Closed squares: experime ts;
Open squares: ComFlo
The position of the t mk with respect to She axis of
rotation is moth r import mt design parameter When
the t mk is mo mted below the axis of rotation, the
centrif gel force adds to She g avity force When the
t mk is mo mted cl ale the rotation axis, the
centrif gel torce subtracts from th g avity force; the
transverse acceleration is reversed es w 11 When the
t mk is situated It c higher level, the moment
amplitude Increases considerably (see Fig 8 (top)),
ash rest the phase male decreases b t slightly (see
Fig 8 (bottom)) As c remit, the quad store
compone t becomes larger md covers c wider
frequency r mge, as show m Fig 9 (bottom)
.~ .
Figme 9: Free-surface t mk in red lar roll motion In-
phase (top) md quad ctme Bottom) component of
moment as f motion of roll frequency Parameters:
h Bull 06; AIRS 7deg thomt .: s Bull 4; Squares:
s B=0 2; Tri males: s B=0 0; Ci cles: s =9:1 2
Closed symbols: experiments; Open symbols:
ComFlo
It c m be expected that She moment exmted by the
t mk fluid is proportional to She fourth pow r of the
model scale Considering th moment per mit tank
length in c two-dimensiorul problem, this will be
proportional to the third pow r of the model scale,
which in turn is governed by She t mk width B. The
fact that physically the phenomenon in th fiee-
surface tank is c we problem implies At for
scaling p Froude's Isw of similit de applies; to
create c comparable flow pattern the t Inks ho Id be
filled according to th some value of hB When
plotted m c non camels Coal way, it appears that the
chic acted lesults fully co fi m These expectations,
see Fig 10
0015
^ oolo ~ ~~
_ ~ W:
= 0005 ==
0 Coo
00 05 10
/(tB) [ ]
5t = =
90
550
n ~ '~
00 05 10 15
~/(( BB) [ ]
Figme 10: F'ee-surface rank in red let roll motion
Moment amplitude (top) md phase made bottom) es
function of roll frequency Parameters: s B=0 2;
h Bull 08; AIRS 7deg Squares: B=1 00m; Ph mt .:
B=0 75m Closed symbols: experiments; Open
symbols: ComFlo
U-TUBE TANKS IN REGULAR MOTION
A systematic series of tests with U-tube anti-roll
tanks (see Fig. 11) in regular motion was conducted
by Field & Martin (19764. The results of these
experiments in terms of moment amplitude and phase
angle were used to validate the ComFlo program.
Three test cases with varying mean water depth were
selected. The numerical simulations are done on a
uniform grid with 100 cells in horizontal direction
and 44 cells in vertical direction. The test parameters
are given in Table 1:
Table 1: U-tank regular motion test parameters.
parameter value
L 5.334 m 1 17.5 ft
s 1.372 m 4.5 ft
bduct 7.315 m 24 ft
induct 0.305 m 1 ft
brim 2.743 m 9 ft
hwin~ 3.048 m 10 ft
hmean—case 1 0.914 m 3 ft
hmean—case 2 1.524 m 5 ft
hmean—case 3 2.134 m 7 ft
I,
lowing
Wing
bduct
l
,
~ 2 ~ hfluid
hducl i 41 . r
~ _ _ _
lowing
Figure 11: U-tube anti-roll tank (cross section).
Figures 12-14 show the moment amplitude and phase
angle as function of the roll frequency. For all three
test cases the calculated results are found to be in
good agreement with the experimental data.
80000
60000
Z 40000
¢
20000
o
~ 1 ~
0.0 0.2 0.4 0.6 0.8 1.0
t) [rad/s]
150
be 120
90
'0 60
30
o
~ ~ .
'1
1 l
1 .
· 1 .
0.0 0.2 0.4 0.6 0.8 1.0
t) [rad/s]
Figure 12: U-tank regular motion test. Case 1:
hmean=0.914m(=3ft). Moment amplitude (top) and
phase angle (bottom) as function of roll freauencv.
Closed symbols: experiments;
ComFlo.
80000
60000
Z 40000
20000
o
180
150
120
90
60
30
o
r
E~'-
0.0 0.2 0.4
1 J
Open symbols:
.
_ ~ ~ .
_ ~
_ c
0.0 0.2 0.4 0.6 0.8 1.0
t) [rad/s]
. 1 ~
~ 1
. rd4 1 1
1 1
1 1
t) [rad/s
1
0.6 0.8 1.0
Figure 13: U-tank regular motion test. Case 2:
hmean= 1.524m(=5ft). Moment amplitude (top) and
phase angle (bottom) as function of roll frequency.
Closed symbols: experiments; Open symbols:
ComFlo.
80000
$:;2(l~l(~} Aim=
0.0 0.2 0.4 0.6 0.8 1.0
t) [rad/s]
~b029om
30
0.0 0.2 0.4 0.6 0.8 1.0
t) [rad/s]
Figure 14: U-tank regular motion test. Case 3:
hmean=2.134m(=7ft). Moment amplitude (top) and
phase angle (bottom) as function of roll frequency.
Closed symbols: experiments; Open symbols:
ComFlo.
U-TUBE TANKS IN IRREGULAR MOTION
Recently, tests were done in MARIN's former
Seakeeping Basin with a ship model equipped with a
U-tube anti-roll tank (Lush 19994. The water heights
in both wing tanks and the sway force and roll
moment exerted by the tank on the ship were
measured during calm water roll decay tests and in
irregular wave conditions. In the computer
simulations, the measured sway, heave and roll
motions were imposed on the tank (Kleefsman 20004.
Figure 15 shows a cross-sectional view of the ship's
hull and the U-tank.
bduct
1
1..~
Figure 15: Ship with U-tank (cross section).
In the zero speed roll decay test, the ship is given an
initial heel angle and is then released. The computer
simulation is done with 200 cells in horizontal
direction and 88 cells in vertical direction. The test
parameters are given in Table 2:
Table 2: U-tank roll decay test parameters.
j j
L
s
parameter
VOuid
lowing
bduct
induct
Hogan
hpS(t=OS) - hogan
value
1.20 m
3.10 m
10.2 m3
1.95 m
5.40 m
0.25 m
1.692 m
0.955 m
hsB(t=0s) - hmean -0.993 m
Figure 16 shows the results in terms of the sway
force and roll moment and the water height in the
port-side wing tank. During the first three oscillations
the agreement between calculated and measured
results is good. When the amplitude of oscillation
decreases, the agreement becomes less good. This is
may be due to
.
.
the absence of boundary layers; since the free-
slip condition is applied at the wing tank and
duct boundaries, boundary layers are not
incorporated. Accurate modelling of the
boundary layer flow would require a significant
larger number of cells;
the absence of a turbulence model in ComFlo.
The observed discrepancies call for further research.
~'l~v71~-
~ ~ ~ - w 4w =w 4w
t[s]
Figme 16: U-tarDc decay test Sway force (top), roll
moment (middle) md water h ight (bottom) m port-
side wing tarDc es function of time Solid line:
experiments; Dcshed line: ComFlo
The computer simulation of th ineg lar wave te t is
done with 100 cells in horim hl di ection md 44
cells m verticcl di~ection Th te t parameters which
have ch mged with ~espect to th values m Tctle 2
are given in Tctle 3:
Tctle 3: U-tarDc i regmlar wave test p~meters
parameter value
V~,d ISlm
h~ 2 652 m
h~s(t=Os) - h,,~,, O 533 m
hs~(t=Os) - h,,~,, 0 527 m
Figme 17: U-tarDc ineg lar wave te t Snapshots
taken fi om simohtions wi6h ComFlo
Figme 17 shows two sm~pshots taken from these
simohtions wi6h 6he exLeme water vol mes m both
wmg tarDcs Figure 18 shows 6he mecsured md
cclcuhted results The cg eement for the sway force
is good, whe~ecs 6he water height m the po t-side
wmg tarDc md the roll mome t (which me related
q mtities) me over-predicted
30
20
0
z~ o
-10
-20
-30
t [S]
1.U
CQ 0.5
.~ o.o
Is
-0.5
-1.0
1000
~ 1
900 920 940 960 980 1000
t [S]
Figure 18: U-tank irregular wave test. Sway force
(top), roll moment (middle) and water height in port-
side wing tank (bottom) as function of time. Solid
line: experiments; Dashed line: ComFlo.
U-TANKS WITH ACTIVE CONTROL
A major disadvantage of anti-roll tanks is that the
free surface always reduces the metacentric height so
that roll stability will be reduced. As a consequence,
passive tanks amplify roll motions at low encounter
frequencies. In certain circumstances this
amplification may become a serious problem and it
may be necessary to immobilise the tank by draining
it or filling it completely. This will take a
considerable time and passive tanks are therefore not
suitable for ships, which are required to change,
course frequently (e.g. warships). A solution may be
found in the active control of the internal water
motion. This is shown schematically in Fig. 19 for a
U-tank.
port-side
valves
starboard
valves
t. closed
. ~
open _
, ~~ open _~
7 8 1
Figure 19: U-tank active control principle.
Stage 1 corresponds to the situation where the ship
has reached the maximum angle to port and starts to
right to starboard. At this stage the tank water is
flowing with maximum velocity from starboard to
port under the influence of gravity. When at stage 2
the tank water has obtained the maximum level in the
port-side wing tank, the port-side valves are closed
by the control. The ship continues to roll to starboard
and- due to the closed port-side valves - the tank
water is prevented from flowing into the low side
tank, thus creating the stabilizing moment acting
against the roll motion at stage 3. The water is kept
blocked in the port-side wing tank, due to the low
pressure created in the upper part of the wing tank,
from stage 2 until stage 4. At stage 4 the control
opens the port-side valves. This enables the water to
flow from port side into the starboard wing tank. At
stage 5 when the ship has obtained its maximum roll
angle to starboard, the tank water is flowing with
maximum velocity into the starboard wing tank.
After stage 5 the ship starts to right to port while the
tank water continues to flow to starboard to reach its
maximum level at stage 6. At stage 6 the starboard
valves are closed in order to prevent the tank water
from flowing back to port side. Between stages 6 and
8, the blocked water on the upwards moving ship's
side produces the stabilizing effect. At stage 8 the
control opens the starboard valves, the tank water
flows from starboard to port side and the cycle starts
once more.
In ComFlo, the active control is modeled on the basis
of the ideal gas law, which states that for a gas in a
closed container at constant temperature, the product
of pressure and the volume is constant. Suppose that
at stage 2, when the water has reached its maximum
level in the port-side wing tank, the pressure is given
by p0 and the volume of air above the water by V0.
Somewhat further in time, the air volume will have
changed (due to the water motion) to V=V0+AV and
the corresponding change in pressure Ap can be
obtained from
pa + p)(vo +Av) =povo
or, in first order approximation,
;' = ~P ° V
The ch mge m air pressure is then used in the
dynamic fre-smface condition to acco mt for the
effect of She closed valves in 6 is way, the water is
blocked for c certain delay time AT
. .
Figme 20: U-tmk marmcl control te t Moment
amplitude (top) md phase m ale (bottom) es f motion
of roll period Parameters: Ao=4 9deg Squares:
AT=0 Os; Rhombs: AT=0 Ss; Trimgles: ~T=I Os;
Crosses: AT=1 Ss; I: nclev AT=2 Os; Plusses:
AT=2 5s
Figme 20 shows the cclcokted moment amplitude es
function of roll frequency for various values of the
delay time AT The mNturcl flequency of the t mk is
~h=0 56rad/s, which corresponds to c m~tmcl period
To=11 2s A smusoidal rolling motion is imposed on
the U-tmk When the water reaches it maxim m
height in eifner one of the wing t mks, it was block d
by me ms of the clove procedure The delay time AT
was varied (marmclly) from O to 2 5 seconds with
inclement O Ss in f is way, the t mk's peck period
(i e She period et which th moment amplitude has its
(6) maxim m) c m be increased For mstance, ff the
ship's roll fiequency equals fiFO 40rad/s, She delay
time mu t be set to AT=2 Ss, accordi g to Fig 20
Indeed, the exact deny time is given by AT'=(2'V~
To) 2 which yields ~T*=2 3s
Figme 21 shows the velocity field md the fiee-
surface profile m c UP mk vifh active control The
snapshots are taken et the time takes where the
valves are closed md opened
Figme 21: U-tmk active conhol simulation
Sr~tpshols tak n fiom simulation with ComFlo
Velocity field md fiee-surface profile et time of
closmg (top) md opening (bottom) of She valves
From She clove it is clear that the deny time AT c m
be used to match the peck period of She water motion
to th ship's roll period To his end, AT is set to
AT = t overt —t Glove = 2(t v= v max t ~ s ) (8)
ah re tv=v= denotes She time tage et which the
wmg tank vol mes me exlremnl md t~=o denotes the
time stage et which the ship is in it's Bright position
Figme 22 shows the roll moment as finction of time
for She U-tmk in semi-i red lar motion (c
superposition of harmonic components) Clearly, the
moment cmplit de is effectively mcresed by the
control, as c direct consequence of She increased
maxim m water-height amplitudes in th wmg t mks
The deny intervals are decoy iced as hori ontcl
sections in th g cphs of She water vol me in the
po t-side wmg t mk md She duct flow rate
bottom: roll mgle, water voi me m pmt-slde wing
tarp, duct flow mte Ed moment versus time Dash d
Ime: no control; Solid Ime: active control
COUPLED SHIP AND TANK FLUID MOTION
~ c coupled >! tem of c ship equipped with m ~ -roll
tardy, She ship r acts to the forces of the waves Ed the
action of the tactic fluid The tactic fl id, m its ton, will
be i fluenced directly by She motion of the ship This
mterction is essentially nonlinear Ind must therefore
be solved in She time domain A similar approach was
follow d by A memo et cl (1996) for c ship with
particllyfilledbaffled Ed mtaffledtarDcs
The motion of the water m She U-tarDc is governed by
equations (1) Ed (2) The fiequency domcm equations
of motion for She coupled ship-tarDc system e press the
conservation of linear Ed mg lar moment m, i e
M + ilk + B x + C x = F e eG + F rad + F ~ (9)
where x is She 6-component vector with She ship's
h mshtions (surge, sway Ed h ave) Ed rotations (roll,
pitch Ed yaw), M is the (6x6)-mass matrix, A, B Ed
C me 6x6-mat ices with the fiequency-dependent
add d mass, damping Ed spring coefhcients, Tic is c
Component vector vifh the forces Ed moments due
to the mcommg Ed dfffi acted waves Ed Fad is the
co tobution fiom the radiated waves Th incoming
Ed dfffi acted wave conh~butions are calculated with
MARIN's ship th ory prod cm SH PMO (1998) The
madicted wave contributions me expressed es
convolution integ ills involving the so-called retardation
f motions Ed She time history of th ship's velocities:
Fled (t) =—A~x(t)—B~x(t)—J Kit—7)x(~)d~ (10)
The time-dependent retardation functions K(t) are
computed fiom the frequency-dependent damping
coeffcie ts B({3):
K(t)=J[B(~3)—BW]cos tdo
(I 1)
where Be is th (6x6) -matrix with th limiting values
of the damping coefficients for i finite frequency
The eq stiom of mot ~- /~irn~ ~A n~i-5 ~-
snsmged s~ follows:
M + Aw )x(t) = -B w x(t) - [K(t—~)x(~)d~
o
—Cx(t)+F=G(t)+Ft~'(t)
The fo ses smd moments due to th interrul wster
motion m 6he ta k s e obtained by integsting the
pressure smd shear shesses over 6he tsmkbo mds y S:
Fa~'=[J(pl—pVv)i)idS, i=1,43 (13)
Fa~ =[J((ix(pl—pVvt i)idS
s
i=4,5,6 (14)
where I is the (3x3) -ide tity mstri, 11 is the dy smic
fluid iscosity, i is 6he outws d pointing normal vector
onSsmd ;=x—XG isth positionvectorwi6h~espect
to the ship's center of g s ity G
The eq stiom of motion of the ship s e re-ssrsmg d
mch thst 6he "desd w ight" of the tsmk wster is shffted
to 6he left-hmd side of (12), wheress th moment m
co tobutions due to 6he interrurl dy smics remsin on
6he right-h md side in this way, s m merically stable
time integ stion sheme is obtained when, for e smple,
s fourth order Rmge-Kutta method is spplied (Gerrits
& Veldmam 2000)
Figme 23 shows the computed rollmg motion of s ship
with s n empty U-t mk smd s paltis 11y fllled U-t mk The
ship is e sited in rolling motion by th i soming ws s
st s fieque sy 5 = 0 60rsd s The natmal freque sy of
the U-tsmk is lDo = 056rsds Clessly, 6he U-tmk
dsmpens the ship's roll s mplit de by some 50% Figme
24 shows the moment conh~butions due to 6he ws
e sitation smd th U-tsmk
50 100 150
t [s]
Figme 23: Coupled ship-U-tmk simoktioa Roll smgle
versus time Solid Ime: ps tially fllled tsmk; Dssh d
Ime: emptytmk
180 185 190 195 ~oo
t [s]
Figme 24 Co pied ship U-tmk slmniatimm Roil
oment conh~bution: so id hn = wave itstmn,
ds shed line = U-tarDc
COUPLED SHIP AND TANK FLUID MOTION
\VITH ACTIVE CONTROL
Fim~lly, w present the results from s computer
simulstion where 6he coupling model smd the conhol
model s e combined Figure 25 shows the re mlts fi om s
simulstion for ~045rsds, ie off tmk reson~nce
Three co flgurstions w ~e sim 5sted: (1) ship with
empty tsmk; (2) ship with ps tislly fllled tmk without
co trol; (3) ship with ps tislly filled tsmk smd sctive
co trol it cam be observed 6~t the passive
(urrsontrolled) U-tsmk (co flgmstion 2) i s~esses the
roll smplitude by some 15% with respect to
co figmstion 1, wherecs th sstive (controlled) U-tsmk
(co figmstion 3) redDses th roll smplitude by some
10%
0 50 too
t 1~1
t50 ~oo
1 ..
Figme 25: Coupled ship-U-tsmk simoktioa Roll smgle
wxsus time Solid 6hick line: empty tsmk; Solid thin
line: ps tislly fllled tsmk, no conhol; Dsshed 6hick line:
ps tis 11y filled tsmk, s stive co trol
CONCLUSIONS
We hav presented results fiom the cpplication of the
computer prog cm ComFlo to th problem of water
sloshmg m fiee-surface cod U-tube mti-roll t mks The
mecsmed md cclculated results for the water heights,
6he sway fmce md roll-moment cmplit des md phcses
w ~e fo md to be m good cg cement
A simple simulation model for aotiv conhol was
mtroduced md fo md to be m effectiv mem for
t ming 6he t mk's peck period to 6he ship's roll behavior
Better co trol models will be implemented
R suits obtcined with c stable time mteg ction scheme
for the coupled equations of motion for the ship md the
tmk fluid w re prese ted ~ combim~tion wi6h the
cctiv conhol model, this sch me facilitates the
simulation of 6DOF ship motions m c seway with f lly
nonlinear acco mt of th mti-roll t mk fl id dynamics
~ 6he near futme the effect of coupled sway-roll
motions will be inve tigated, bodh mmmericclly md
e perimentally A odher step in 6he validation process
is th simulation of thee-dimff~siom~l fluid motion in
mti~oll tmks, taking mto acco mt mternal geometries
VmDaaleneto/2000)
RE}7ERENCES
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DISCUSSION
A Cariou
Institut de Recherche de la Construction Nacelle,
France
Here the tactic fluid motion simulation is fully
non-linear But She equctions used for the
coupling of the ship wish the tardy ( quctions (9)
th ough (12)) are She equctions of pme Imear
dynamics Could you plea me comment on that
point?
AUTHOR'S REPLY
The statement Nat the equctions used for the
coupling of th ship with She mti-roll tarlc are
purely linear is not correct The coupled
equctions of motion may se m to be linear with
respect to the ship motions, but Hey are not! The
forces exerted by the t : IL on the ship depend on
the ship motions in c nonlinear way, which
admit) hr. not been mad explicit in equctions 9-
12 Yet, this is exactly the point where the
nonlinearity comes into the time domain
equctions of motion
DISCUSSION
A Clement
Lctomtoue Mec mique de. Fluides, E ole
C Tale d Lyon, France
If I under t Ed well, the principle of your control
consists m ch Aging She namr al fiequency of the
tactic to make it fit the fiequency of the ship
motion This principle carmot be easily extended
to irregular motions, except ff you consider Nat
you know the near future of the excitation by c
suitable prediction of sophisticated control
process as w do with active wave absorbers for
wave basics Did you include such c predi tion
algorithm in your active cone ol?
AUTHOR'S R PLY
This is c very import mt observation which hr.
our cttff~tion We have not accounted for the
effects of inegular waves (L d motions) m our
conhol algorithm Undoubtedly, we will be
traced to include c prediction algorithm once we
start testing our method m Regular wave
conditions
DISCUSSION
M Hir mo
Mitsui Akishimc Laboratory, Up m
A trolling tactics me usually installed on c ship
as c part of ship structure he this sense, such
small structure members as stiffeners may be
fitted inside the tardy wall Question is whether
the effects of stiffeners on both roll moment
amplitude Ed phase Ogle c m be computed or
not in the computation?
AUTHOR'S REPLY
In principle f is is possible, although it would
require c very detailed grid Ed, consequently, c
very pow rful computer Up to now, w have not
m- e tigated the effects of local th ee-
dimensiom~l geometry variations
