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OCR for page 441
Free Surface Viscous Flow Computation
Around A Transom Stern Ship By Chimera
Overlapping Scheme
CW Lin, S. Percival
(Naval Surface Warfare Center, Carderock Division, USA)
ABSTRACT
The focus of this p Her is to investigate the
c mm ility of a numerical scheme Hat inco porates a
free so face bommdffy treatment md a smkage/tam
calculation into a viscous flow computation mound a
su face ship Utilizmg d is scheme computations me
pe to med on two selected h msom tern ships The
ff ility to compute file wet, partially wet, or d y
t msom is developed, including a new g id topology
for h msom .-. - 3 Computational results on two
t msom-stff ships are consistent with available
model experimental data The sh me of the wave
profile along the hull is generally predicted well,
while the magnitude of wave elevation still needs to
be improved The wave pattern is also well
copulated, except that wave cre ts md troughs me
not ff Shop ff the model measurements The
computed total resister ce is in good con elation wish
model measured values Aldhough two different types
of grid pacing md di tribution techniques me
investigated, a father tudy is needed to dete mule a
more effective gad system for free su face viscous
flow computations
INTRODUCTION
Computing file flow around a so face ship
moving steadily in calm water hff beff a challengmg
research task for yews The complexity of file flow
physics ff und a smface hip hff generally required
tw sepmate numerical approaches, one to compute
the wwe elevation on the fi ee smfff e md a second to
compute file viscous boundary layer mound ship hull
The basehne equation to compute file fiee so face
elevation is usually based on potential flow Leo y
The numerical scheme c m use either a complicated
Green fmmction or use file p mel method with simple
Rmkme sources The governing equations to
compute file viscous bommdffy layer on a ship hull
su face me based on the Nwie~Stokes equations
The mlm en cat medhods to compute viscous flow h we
been developed fiom a simpli led boundary iayff
mprox im at ion to a vat i ety of different lo mu l at i ons
of N wier-Stokes equations in this p me' a combmed
numerical techmique based on computing the free
su face viscous flow ff und a realistic ship hull is
developed it is based on sol ing the Reynolds
Averaged Navier-Stokes (R NS) equations using a
computational scheme that also calculates file water
su face elevation generated by a moving hip hull on
the fi ee su face boundary
A other challengmg task is to be ff le to
compute flow mound a su face ship wish mucous
types of ship geomet y in addition to the necessary
appendages required to operate a hip, designers have
developed a variety of hull h Yes to meet file
fmmctional requirements of a ship, eifLer for
commercial benefits or miEtffy advff tages Trot som
.-. -I ships me the focus of flus paper T msom .-.-
ships have beff used for ! ems, especially for high-
speed ship designs The hyd odynamic pfffommmce
of this type of hip hff beff investigated m ruious
model test facilities However, the flow ff und file
t msom ten is ve y complicated md di hcult to
compute due the discontinuity of file hull geomet y
It is e pecially challengmg to compute file
free so face elevation mommd file trmsom ten The
issue of wet d yh msom condition is amajorconcem
for a h msom-stenh ship design in flus paper, a
numerical technique is developed to hff die this
complicated flow phff amend The numerical
technique mcludes a new gad topology for t msom
.-. -I flow calculations in this way the wet d y
t msom condition c m be computed
A special topic of tree so face flow
computation is to calculate file Linkage md tl im of the
vessel The qu mtities of sinkas e md trim depend on
the sh me of underwater geomet y md the ship peed
Model test results have how a difference m
measured resist mce between hoed models md free to
sink/trim models Since file si kage md tam d Ha me
not know in advance, file free su face flow
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Representative terms from entire chapter:
surface viscous
computaion ha to caculae them a pat of the flow
solutions The nmm~sica scheme in fLis paper
includes this capability
The vaidaion discussed m fLis paper is the
compaison of computaiona results wifh a set of
expenmenta model dma For fiee su fa e viscous
flow caculaions, two series of experim:~ta
meaurements a~e chosen, DTMB Model 5365 (R
Ath:~a) md 5415 (a su fa e comba mt hull selected
by ONR for CFD w~lidaion) The compaisons
include tota resistmce coeffcients, smkage/tam,
wave prohles, md wave paten~ m the fiee su fa e
The numerica treaments for computmg fi ee smfa e
elevaion md smkage/tam a~e discussed m detail
The computaiona g id topology used to hmdle
t msom tem geomet y is descabed, a well a gad
spa mg, grid di tabution, md computaiona grid
domain A limited grid st dy on flow computaions is
briefly discussed
NUMERICAL SCHEME
Nmmerica caculaion of viscous flow
aound a su fa e hip mu t mclude tw major
physica mechmisms: computaion of the water
elevaion a the fiee su fa e md computaion of fLe
viscous bounday layer a und fLe ship hull Until
tly, fLe fiee su fa e wave elevaion generaed by
a moving ship ha been h mdled by the potentia flow
approximaion, which asumes no iscosity The
caculaion of fLe iscous bounday layer is
pe fo med by fLe doublebody approximaion, which
igmores fLe effect of the fiee su fa e Ba ed on this
kmd of decoupled nmm~sica treament, the free
su fa e viscous flow a ommd a moving hip c m be
affordably solved The interation between viscous
bounday lay~s a d fiee su fa e wavemaking is
a sumed to be minima As for pra tica :~gineering
ca cula ions, this a sumption rem ains va id to suppo t
ship design effo ts However, due to recent advmces
in CFD numenca schemes md computer CPU
power, fLis decouplmg of the mmmerica medhodology
may not be necessay One cm compute the iscous
bounday layer md the free smfae wave elevaion
together in m affordable ma ner This is a hieved by
solving the R NS equa ions wifh ca ef I trea ment of
free su fa e bommda y
The fundam:~ta RANS equaions in fLe free
su fa e flow computaions remain the same a those
used for caculaions of doublebody flow, with fLe
exception of the pressure te m which ha to mclude
staic head fiom fiee su fa e bounday The
numerica heament of double-body RANS
computaions cm be gen~saly adopted in fLe free
sufae R NS caculaions wifLout my
modiEcaions The mmmerica scheme for fLis double-
body R NS computaion in FREE9S ha been m
developm:~t for yea a d will not be discussed m
this paper Lin et a 1995, Lm et a 2000) The mam
numenca effo t h~se is to h mdle the movement of
the fi ee su fa e bounda y Sev~sa numenca methods
have been developed to compute this hee su fa e
bounday, md they cm generaly be clasibed m
th ee ways: su fa e htting, su fa e t~ckmg, md
su fa e capt rmg The effo ts of al these methods a~e
to compute fiee su fa e elevaion by saisfymg bodh
kmemaic md dynamic bounday conditions required
in the free su fa e The kinemaic bounday condition
forces water paticles on the fiee su fa e to remam m
the bommday su fa e al the time The dynamic
condition sai hes constmt amosphenc pressure on
the fiee su fa e bounday F EE9S ha adopted fLe
su fa e htting medhod developed by Famer (Fam~s
et a 1993) A volume gad comprismg fLe
computaiona domam is developed simila to fha for
a double body caculaion, with the difference tha it
extends abow fLe still wat~slme The Imes of this
initia g id fha a~e no ma to the fiee su fa e a~e
htted wifh B- plme cmves, which will be used to
t~ck the fiee su fa e elevaion durmg computaions
At fLe beginnmg of fLe computaion, the grid is
moved to the still water line by redi tributmg the grid
points aong the B-splme cm es The RANS
equaions a~e fLen solved for this cunent g id Ba ed
on fLe new computed flow w~riables, the wat~s
su fa e elevaions in the free su fa e bounday ae
updaed to saisfy both fLe kinemaic md fLe dynamic
bounday conditions For fLe fully nonlinea
condition, the fiee su fa e must move with the flow
bounday md fLe bounday conditions must be
applied on fLis disto ted fiee su fa e The water
elevaion on the free su fa e is computed by
integmtmg fLe fiee su fa e kinemaic equaion, which
is denved by treamg the fiee su fa e a a maena
su fa e requned by fiee su fa e kinemaic bounday
condition Through fLe interior of fLe fiee sufae
computaiona domam, al d~sivaiws a~e computed
usmg the second order cenha differ:me On fLe
bounday a second order centra stencil is used aong
the bounday tmgent md a fust order one-sided
diff
ff possible it hff beff found Hat nmmfficai
dissipation m file free so face computation hff
signi ~cmt effect on file do per On of file wwe
system Excessive dissipation may have better
numerical conve gence, but gives a w ong phase
mgle of the wave system Once the tree so face
update is completed, the pressure is adjusted on file
free su face The updated fiee su face serves ff new
boundary values for file bulk R NS flow
computations The coupling is ester li bed by
computing a bulk flow solution md Glen using file
bulk flow ff a boundary condition for the fi ee nxtfn e
computation The tree su face elevation is updated
md its present values are used ff a boundary
condition for the pressure on file bulk flow This
therefore completes a numerical iteration of free
su face RANS flow calculation
SINKAGE AND TRIM COMPUTATION
A nxtsce ship moving at a con tant peed
will End equilibrium m si kage md trim due to file
balm ce of dy amic forces generated by the motion
Model tests me pe to med in the same m mner; file
model is fiee to sink md tam, md file values of
smkage md tam me measured at different speeds
The si kage md him chmges the underwater hme
of the hull and the resulting hyd odynamic
pe to mmce it is therefore impo tmt to include file
smkage md h im in file computations
The smkage md him cm be computed
simultmeously wish the fiee so face R NS flow
computations At each iteration, the forces md
moments acting on the underwater geomet y me used
to compute file ch retie in si kage md him th ough a
simple hyd tatic calculation based on the hip's
wate piece geomet y Using the mitial watffpime
instead of calculating file cannot watemlme swes a
sub tmtial amount of computations The assumption
is the watemlme mea will not chmge sub tmtially
due to si kage md trim md therefore this imposes a
limitation
The smkage md him is implemented by
moving the hull (md the local grid) relative to file
global gad, other ah m t ying to move the me m free
su face reference All the fi ee nxtfx e elevations then
need to be recalculated to fulfill both kinematic md
dyn m ic b ommdffy conditions m the new fi ee surface
locations The cm ent venion of F EELS c m
activate the calculation of smkage md trim at file
begmning or =.- a ce tam number of fiee so face
RANS computations The results show in fLis paper
me obtained by activating file smkage md tam fiom
the bedimming of the computation md pe fomming one
smkage md him calculation for es fix 10 iterations of
free su face RANS computations
HULLFORM GEOMETRY
The tw hul fomms in this p Off were chosen
for pled t msom .-.- sh me md file availed ility of
model te t data Model 5365 R/V Athena) is a high-
speed, h msom .'. -I dispiacemfft ship Model 5415
is a so face combat mt hull selected by OUR for CFD
validation Dimensions for file hullfomms me show m
table I md bodyplm plots of tenons 0 to 20 se
show in figures I md 2 The only appendages
included in either file compm.rons or file model tests
me show in figures I md 2 Model 5365 hff a
centerline skeg md model 5415 hff m integrated
skeg md sonar dome
Figmre I DTMB Model 5365
Table 1. Hullform dimensions
1 5365 1 5415
Length (m) 5.960 5.724
Beam (m) 0.836 0.764
Draft (m) 0.183 0.248
CHIMERA OVERLAPPING GRID
Grid Topology
Free surface viscous flow computations
involve two major physical parameters, Reynolds
number and Froude number. To accurately compute
viscous flow phenomena due to the effect of
Reynolds number, fine grid resolution is needed in
the boundary layer. Conversely, to resolve the free
surface wave systems due to Froude number effect
requires relatively fine grid resolution outside the
boundary layer. The chimera approach has the
capability to handle the necessary grid refinement to
I've,.
~~:~\'~' of/' 'A ;
/
meet both requirements without using an
impractically large number of points. The
computational domain is divided into free surface and
double body grid components, which are connected to
each other with an interpolation interface. By
decoupling the topology of the two grids, enough
flexibility is gained to generate a suitable grid for a
viscous free surface calculation.
In addition, free surface flow computation
around a transom stern is a challenge. Very large
pressure and velocity gradients exist at the transom,
requiring fine grid resolution and high grid quality.
Furthermore, the free surface elevation moves up-
and-down with the transition from wet to dry transom.
Getting the computational grid to move with the free
surface around the discontinuous edge of the transom
is a topological challenge. The decoupling of the two
grid components enables a suitable grid block
topology to be developed.
'aft; ~ ~~] ~
Figure 3. Perspective view of overall grid topology
.\ i.< \.. y
\. /
· \. \, ~
.. . /
~ /
,
,
,
,
A reverse "~" 1opology, ~ co~in~bon of ~n ~llo~nce ~ be m~de 10 provide room ~r 1be tree
"H" 1opology ~11be bo~ ~nd ~n "~" 1opology ~11be sur~ce grid 10 redi~ribute ~self ~s ~ moves ~ ~nd
stern, ~s used ~r 1be grid ~1 1be tree sur~ce do~ 1be ~1L In order 10 si~li~ 1be do~le bo~
bound~. Tbe "H" 1opology si~liEes seHing 1be grid, 1be son~r dome on model 5415 ~ modeled ~ilb
-~re~m bound~ condition ~nd 1be "~" 1opology ~ ~ 1b~d grid system. A 1r~nsverse cu1 of ~11 1bree grids
e~cien1 ~nd provides ~r ~ rel~bvely uni~rm, ~1 s1~ion 1 ~ sbo~ in Egure 4.
rec1~ngul~r grid ~round 1be stern ~ere grid qu~li~ is
Tbe mos1 co_on ~pro~cb 10 "ridding
mos1 crhic~L In 1be 1r~nsverse pl~ne 1be grid s~eeps
R~nsom ~ern ship b~s been 10 ex1ode ~ block hom
do~ hom 1be tree sur~ce ~round 10 1be pl~ne of
. . 1be b~nsom ~ce ~R 10 1be outer bound. Amongs1 1be
s~e1~ 1n "~" ~shlon. Fo~d of 1be stern 1be
. . . . , m~ 1r~de-o~ of 1bls ~pro~cb, 1bere ~re ~o m~or
CO-u1~08~1 dOm~lD 1S spl~ equ~lly be~een 1ne
. d~dv~n1~ges ~r ttee sur~ce co~u1~bons.
tree sur~ce ~nd do~le bo~ grid co~onents ~long
. Conb~ing 1be bound~ l~er sp~cing ~R o~ 1be
45-degree line. In 1be ~R region 1bls dlvldlug 45- . . .
. . . . 1r~nsom results 1n extreme v~rl~1lons 1n cell sl~e ~nd
degree bue 1S ro1~1ed ~ou1 ~ vedlc~1 Q\1S Q1 1be stem
. dls~lbutlon. Tbe second m~or dls~dv~n1~ge 1S
n order 10 ~0~ 1bC "~" 10pOlOgy. A perspective
. . . 1be b~nsom block b~s no~ere 10 move 1n 1be c~se of
vle~ of 1be over~H 1opology ~ sbo~ 1n Egure 3. In
1r~nsom Tbe "~" 1opology in co~unction ~ilb
bis ~nd succeeding grid Egures only eve~ 2nd poin1
. . . chimer~ grids solves botb of 1bese problem~ Tbe cell
sbo~ ~r cl~n~. Abboupb 1b~ Egure depicts 1be
. sl~es ~re ~lrly unl~rm ~nd 1be dlstrlbutlons ~re
and ~r model 5415 ~ 20 ~o~ 1be 1opology ~r ~1
. . . . ' smootb. Flgure 5 1S ~ blo~-- of 1be stern ~re~ in
1be grids 1n 1bls p~er 1S ldOD11C~l.
Figure 3~ sbo~ing jus1 1be tree sur~ce block. Tbe
grid hnes 1b~1 move norm~110 1be tree sur~ce R~vel
do~ 1be 1r~nsom ~nd ~rd under 1be ~lt 1~s
~ ~ ~ ~e ^e ~ ~ ~ s~ ~ ~d
2~/ ~/ ~ / ~ - ~ - - ~ - - - - ~ - - - - - -!- - beneE1 of 1bis 1opology is 1b~1, bec~se of its rel~1ive
~,~ ~ ~ ~ ~ ~S,~,~:
B~ ~ ~^~^~
~ ~ ~ \~ ~ ~ ~ ~ ~ ~/ ~ ( [~1eatofDom~la ~ad Crid D1stribu110a, S1ze
Figure 4. A 1r~nsverse cu1 of 1be grids ~1 S1~1ion 1
To co~ute ~ccur~1ely 1be ~ve system
gener~1ed ~round ~ moving ship, especi~Ny 1be
. . . diverging ~ve system requires ~ sui1~le dom~in
Tbe grid on 1be ~11 sur~ce 1S Spll1 be~een '
. . ~nd grid reEnemen1 in 1be tree sur~ce. ~orm~lly in
1be ~o grid systems ~1 ~pro~lm~1ely b~lf 1be ~e11ed '
. . do~le bo~ ~S 1be di~nce 101be outer bound
g~1b lengib Ide~lly 1be do~le bo~ grid ~ould '
of 1be co~u1~bon~l dom~in is b~sed on 1be ~11
enco-~ss mos1 of 1be ~H sur~ce. Ho~ever, some
length For fiee so face computations, lager Froude
numbers me m longed wavelengths m the wave
system, which requite lager computational domains
to cover several wave components of file generated
wave system it wa decided to set the dist mce to file
outed bound at 2 chaacteri tic wavelengths Lw =
2vFr: L) in m attempt to define the grid resolution it
wa decided to set the ma imum dimension of my
cell wifLin one wwelength of the hull to be no la tiff
thmLw/20 md as cell my here m be no la=er~hm
Lw /10 20 points hould be enough to satisfactorily
define a wave md 10 pomts hould give a rough
deEmition at the outer bound
The most difficult dimension to achieve flus
criterion is no mat to the hull, where the boundary
layer requires e tremely mall spacing Tw
approaches were tried using different dishibution
fmmctions for file fi ee smfa e block The hat gad for
Model 5365, hereafter retorted to a G id 1, used a
smgle tw -sided hyperbolic tmgent dishibution
(TANH) h om the hull to the outer bound The mitial
spacing no mat to file wal wa si ed to y+ value of
10 The growdh rate of the grid pacing wa a con t mt
10% for file Bust wavelength away fiom file hull md
then law, mptoticaly approaches 0% at file outer
bound, where the gad spacing is Lw /10 The effect of
this di tabution is to concentrate a large Faction of
the total the points inside file boundary layer
A single tw -sided Monotonic Rational
Quadratic Spline distribution fiom the hull to file
outer bound wa used for subsequent gads of Model
5365, refened to a G id 2, md for bodh 5415 grids
The initial spacing nommal to the wall wa sized to y+
value of I The mitial grow h rate of the grid off file
wall is exLemely large md this results in a more
unifo mly spaced g id, with fat fewer points Aside
the bounda y layer
For file double body blocks in all gads a
TANH distribution wa used no mat to the hull Gnd
I wa intended to be relatively con e a d file
dimension on file fiee so face nommal to file hull wa
chosen to be 61 The mproximate total number of
grid points wa 500,000 Grid 2 md bodh 5415 grids
were si ed to 111 pomts md reamed in file other
dimensions a well The mproximate total number of
grid points wa 1 3 million for each gad
EXPERIMENTAL DATA
Model 5365 wa tested m the bare hull
condition ~ ah the centerline skeg in place Model
tests were condu ted at tw different facilities, one at
David Taylor Model BE m (Jenkins 1964), md file
other at the National Maritime Instit te (Gadd md
Russell 1961) The model emeriments were
conducted m two modes: ~ ah file model fiee to sink
md trim, md with the model rigidly resh amed at file
static d afl Total resistmce of file model wa
mea wed with file floating girds Hat is attached to
the c or age The bow md stem Linkage of the model
were mea Red with two displacement transduced
that were mounted at the bow md -. n of the model
The wave elevation along file side of the model wa
reco ded mamally, using a grew e pencil to mark file
water height at 21 locations Subsequently, file
di tmce between the marked heights md file cam
water so face wa measured, taking into account file
Linkage md him of the model b addition, a set of
mea moments of the .-. -I wave elevations wa made
on Model 5365 in the hoed condition a a Froude
number of 0 46 The .-. -I wave heights were
obtamed using thm rods fha were ma ually adjusted
until then tips just touched the water smfa es, once
the model reached a steady stale condition The
accuracy of file mea red total resi tmce wa
repo ted to be +1 5% No sy tematic unce tamty
malysis wa done a file time of flus experiment
The experimental data for 5415 wa
collected during several tests pmning mmy yea
(Radcliffe 1999) The original bare hull resistmce
tests were done in 1962 Around 1990 mea rements
of the fiee smfae wwe heights aommd file model
were obtamed using tereophotoghvmmehic
techniques Tw Ha selblad met tic still camera were
mounted on a ceding mounted hat re above file
Carriage I bat in As the model wa towed doss file
bat m, sequences of photog mhs were taken,
sy chronized by trobe lights The water smfa e wa
"seeded" using computer punch cat d chips fha .: e
di tributed on file so face before each m A array
of calibraed target gad pomts pa endowed file free
su face m the fat held These grid points were also
imaged in the stereo pans a d served a control
points Ming the malysis of file photographs The
resultmt -. .o photog mhs wise subsequently
"measured" by the Naiona Ocem Sm e! over a
76 2 mm X 76 2 mm grid The da a w ff obtained a
model speeds of 4 01 md 6 02 kmots, cohespondrg
to Fh ude numbers of 0 26 md 0 41
Subrace wave height me inurements wed
made on the bow md .-. - waves r 1996-7 The
mea Hem wed obtamed on file ha e hull model
off d We berg towed r the Carriage 3 Towing Baler
For these mea rements, a dy amic wave height
probe called a "whisker probe" We used At each
da a collection point, x, !, md z Adzes were recorded
via a voltage readmg from the probe md traverse
encoded The him conditions for file tw peed
were repo tedly file same a the 1982 test
Wave profile mea moments Song file length
of the hull were obtamed on file bare hull model
during emeriments run in 1997 The model wa fiee
to sink md tam a en h peed The wave profile
truces were d a on file model md reco ded wifh
relerence to the diva waterlme The tam conditions
for file tw speeds were repo tedly the same a file
1982 te t
The whisker probe wave data wa combmed
wifh file stereophotogrmbic data by the whop to
obtam a more complete pict re of file wave patem
Due to male unkmow s file accmacv of flus data
c mnot be qu mtital ively established
RESULTS AND ANALYSIS
Model 5365
Flow computations using Grid I ale
pe to med for Fn = 0 35, 0 4g md 0 65 m hxed
condition it is obvious this Gnd I is too smal for Fn
= 0 65 a d magina for Fn = 0 48 Flg ire. 6-8 how
the wave patems using G id I for these th ee Froude
mlmbeh m a hxed condition These wave prlems
aso show file la held bounday condition is well
implemented a file Mar boundary of file
computations domain Computed wwe profiles
Song the hull for these fEree Froude numbers se
compa cd with expenmenta mea ured da a show m
Flg n e. 9-11
Flow computations ale pe to med on Gnd 2
for Fn = 0 '8 0 35, 0 4g md 0 65 in both hxed md
sink/trim modes Wave patems on these fEree grids
for fom Froude numbers a e show m Figures 12-15
for hxed condition md Figures 16-19 for smk/trim
condition Since no mea nemem is available, these
wave pa -. ~ e how to exam me then rela ionship
wifh a wide retie of different Froude mlmbeh
quaitaively Compamg with wave pat:ns fiom
Gnd I caculaions, only minor differences are found
except that file wave patem in G id I is trunca cd by
the outer bounda y Only m mor doff erences a e found
on the wave patems between hxed md sinktmm
conditions The computed wave profiles ale
compa cd wifh the expenmenta mea urements m
both hxed md silLWtrim modes, which ale how
re pectively in Figures 20-27 Generals the wave
profiles new bow area a e well predicted compa ing
wifh both sets of expenmenta data The bough of
wave profile a the mid ad po tion of the hull is
predicted consi tent with Gadd's expert enta data
md under predi ted compa mg with Jenkins's da a
A compa i on of the mea red md
computed .-. -I wave elevations in the hxed condition
a Fn = 0 48 is show m Flgn e. 28-29 The
computed elevations fiom Gnd 2 how better
conelaion with expenmenta data ah m G id I Since
the meatt ed data is archer limited, file comparison
here is only qu mtitaively -and ted
Forces md moments are calclllaed Song
wifh computations of flow va iables m the process of
flow computations They a e obtamed by integmting
the shed stress md pressure on file wa I smfa e The
total resist mce of a smfa e ship is flus computed a
the x-componem of total mtegraed force a ting on
the ship wetted hull su fa e Table 2 how file
computed total resista cc compa cd wifh available
mea ured da a for Model 5365 computation For file
hxed condition, bodh calclllalons on G id I a d Gnd
2 ale mostly over-predi ted compa Id with Jenkms's
measurements, while file result from G id 2
computation is closes to file model meatt ed data
However, the prediction treed is consi tent wifh
expenmenta t end b Table 3 file computed results
for sink tam condition conelae well wifh the model
test data with file exception of Fn = 0 65 in Tables 4
md 5, file computed Linkage md him forModel 5365
computation using Gnd 2 are listed Song wifh file
model measured data it is found that both sinkage
md trim cumputatiuts have consistent trends wifh
model experimental data An mcreaed positive tam
(bowup) is obtained trom Fn = 0 28 to 0 65, but file
magnitude is over-predicted The Linkage caculaions
are well conelaed in magnitude wifh experimental
data a low peed, but over-predict a both higher
Froude ma hers
Model 5415
For model 5415 caculaions, two
computaiona gads were generated for tw different
ship speeds, 20 md 30 knots Only the caculaion on
the hxed-a-fLe-mea ured-smk/trim condition is
pe to med. The computed wave prtems for both ship
speeds are show m Figmres 30-31 Song wifh file
meatt ed wave contours b genera, computed wwe
prtems a e consistent with the mea ured patems for
both bow md stem wwe wstems The pha e mgle of
both wave wstems is well conelaed The mamit de
of wave elevation is however under-predicted a d file
wave crests md troughs are not a sham a mea Ned
data This may he due to file problem of having not
enough grid Solution r those Alan of cre t/tmugh
tom awns The wave pmEles Song file hull ale
shown in Figures 32-33 for both speeds respectively.
They are well correlated with experimental data,
except being under-predicted in the bow wave
elevation. The trend of wave elevation profile is well
predicted. The total resistance for both ship speeds
are shown in Table 6 and correlate well with the
model measurements.
CONCLUSION
Computations of free surface viscous flow
around two transom stern ships are performed to
investigate the capability of a numeric scheme
developed for surface ship hydrodynamic
performance prediction. The inclusion of free surface
boundary treatment into the viscous flow computation
is first described. The technique to handle wet/dry
transom computation is developed, which includes a
new grid topology for transom stern flow
calculations. The capability to compute sinkage and
trim for a moving surface ship is important, which is
one of the focuses in the paper. Computational results
on two transom-stern ships are consistent with
available model experimental data. The shape of the
wave profile along the hull is generally predicted
well, while the magnitude of wave elevation still
needs to be improved. The wave pattern is also well
correlated, except that wave crests and troughs are
not as sharp as the model measurements. The
computed total resistance is in good correlation with
model-measured values. Although two different types
of grid spacing and distribution techniques are
investigated, a further study is needed to determine a
more effective grid system for free surface viscous
flow computations. In addition, more systematic
comparisons between numerical flow computations
and model experimental measurements are needed so
that the applications of numerical flow tools into ship
design effort can finally be accomplished.
REFERENCES
Lin, C.W., Percival, S., Gotimer, E.H., "Viscous
Drag Calculations for Ship Hull Geometry", Ninth
International Conference on Numerical Methods in
Laminar and Turbulent Flow, Atlanta, 1995.
Lin, C.W., Percival, S., Fisher, L., "Validation of
Computational Forces and Moments on an Appended
Body", International Maritime Association of
Mediterranean IX Congress, Italy, 2000.
Farmer, J., Martinelli, L., Jameson, A., "A Fast
Multigrid Method for solving the Nonlinear Ship
Wave Problem with a Free Surface," 6th International
Conference on Numerical Ship Hydrodynamics,
Iowa, 1993.
Jenkins, D.S., "Resistance Characteristics of the
High Speed Transom Stern Ship R/V Athena in the
Bare Hull Condition, Represented by DTNSRDC
Model 5365," DTNSRDC-84/024, June 1984, David
W. Taylor Naval Ship Research and Development
Center, Bethesda, MD.
Gadd, G.E., & Russell, M.J., "Measurements of the
Components of Resistance of a Model of R.V.
'Athena'," NMI R1 19, October 1981, National
Maritime Institute.
Ratcliffe, T.J., (1999) "Model 5415,"
i, (1 May 2000).
Table 2. Comparison of Resistance Coefficient for
Model 5365 at Fixed Condition
Froude #
0.28
0.35
0.48
0.65
Jenkins
4.774
4.239
4.437
4.219
CT X 1000
Grid 1
Grid 2
5.102
4.795
5.085
3.784
n/a
5.428
5.987
5.727
Table 3. Comparison of Resistance Coefficient for
Model 5365 at Sink/Trim Condition
Froude # CT X 1000
Jenkins | Grid2
0.28
0.35
0.48
0.65
5.531
5.030
5.774
4.924
5.432
5.020
5.516
3.962
Table 4. Comparison of Sinkage for Model 5365
Froude # ATm/L x 100
Jenkins | Grid2
0.28
0.35
0.48
0.65
0.105
0.200
0.245
0.095
0.135
0.209
0.389
0.25 1
Table 5. Comparison of Trim for Model 5365
Froude # | (ATf- ~Ta)/Lx 1OO
I Jenkins | Grid2
0.28
0.35
0.48
0.65
0.060
0.095
1.240
1.760
0.224
0.392
1.249
2.250
Table 6. Comparison of Resistance for Model 5415
Froude # CT X 1000
Ratcliffe Computed
0.28
0.41
4.14 4.541
7.01 7.218
Wave Height/(L*Fr2)
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07
1
~ ~> J
To 1 x/L 2
Fig 6. Wave Pattern for Fr # = 0.35
Wave Height/(L*Fr2)
-0.05 -0.03 -0.01 0.01 0.03 0.05
~ ~ \
1 1
1
1 X/L ~
Fig 7. Wave Pattern for Fr # = 0.48
Wave Height/(L*Fr2)
-0.04 -0.02 0.00 0.02 0.04
1
\
! ~
1
x/L
2
Fig 8. Wave Pattern for Fr # = 0.65
0.15 1
~ 0.1
LL
—0.05
. _
I O
>
~ -0.05
OR
1'-'
Fixed Condition
· Jenkins
------- Grid 1
—
~ —
~ , ~ ,
0 0.2 0.4 0.6 0.8
Distance from FP, x/L
Fig 9. Comparison of Wave Profile for Fr # = 0.35
0.15 1
~ 0.1
LL
—0.05
.=
I O
>
~ -0.05
Fixed Condition
· Jenkins
0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 10. Comparison of Wave Profile for Fr # = 0.48
0.15
~ 0.1
LL
—0.05
. _
I O
>
~ -0.05
Fixed Condition
· Jenkins
------- Grid 1
I_
0 0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 1 1. Comparison of Wave Profile for Fr # = 0.65
Wave Height/(L*Fr2)
0.15 1
-0 08 -0 04 0 00 0 04 0 08 ~ 0.1
LL
—0.05
I O
>
-0.05
Do 1 x/L 2
Fig 12. Wave Pattern for Fr # = 0.28
Wave Height/(L*Fr2)
\- · · ~
Fixed Condition
· Jenkins
Grid 2
1
0 0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 20. Comparison of Wave Profile for Fr # = 0.28
0.15 1
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 t~ 0.1
—0.05
. _
I O
>
-0.05
../ ~
O.
I` 1 x/L 2
Fig 13. Wave Pattern for Fr # = 0.35
Wave Height/~*Fr2)
21
-
1
-0.05 -0.03 -0.01 0.01 0.03 0.05
~ of\
,., ..... ...... ~
O. ~ 1 x/L 2
Fig 14. Wave Pattern for Fr # = 0.48
I'm- -
~ ~ ~ ~ ~ ~ I ~ ~ ~ I ~ ~ ~ I ~ ~ ~ I
0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 21. Comparison of Wave Profile for Fr # = 0.35
0.15
~ 0.1
LL
—0.05
. _
I O
>
~ -0.05
Fixed Condition
· Jenkins
— Grid2
· - - —
i... it.
Fixed Condition
· Jenkins
Grid 2
·,m,
1
0 0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 22. Comparison of Wave Profile for Fr # = 0.48
Wave Height/(L*Fr2)
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
2
o( ) 1 2 x/L 3 4 5
Fig 15. Wave Pattern for Fr # = 0.65
Wave Height/(L*Fr2)
0.15 1
~ 0.1
LL
—0.05
. _
I O
>
~ -0.05
Fixed Condition
· Jenkins
Grid 2
0 0.2 0.4 0.6 0.8
Distance from FP, x/L
Fig 23. Comparison of Wave Profile for Fr # = 0.65
0.15 1
-n nP -n n4 n nn n n4 n nP ~ 0.1
LL
—0.05
I O
>
~ -0.05
~ . . . .
,. 1 x/L 2
Fig 16. Wave Pattern for Fr # = 0.28
Wave Height/(L*Fr2)
-0.05 -0.03 -0.01 0.01 0.03 0.05 0.07
,:;~
x/L
Fig 17. Wave Pattern for Fr # = 0.35
.
Sink&Trim Condition
Jenkins
Gadd&Russell
— Grid2
~ .
\ . · · · -
. · ·-
,r' ~~ ·
.
~ —
0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 24. Comparison of Wave Profile for Fr # = 0.28
0.15
~ 0.1
LL
—0.05
. _
I O
>
~ -0.05
Sink&Trim Condition
Jenkins
~ Gadd&Russell
/) Grid2
I \
A\—
1 ~
.
l
0 0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 25. Comparison of Wave Profile for Fr # = 0.35
Wave Height/(L*Fr~)
0 1 AL 2 3
Fig 18. Wave Pattern for Fr # = 0.48
Wave Height/(L*Fr2)
0.15
0.1
LO
—0.05
. _
I O
>
~ -0.05
Sink&Trim Conditiol.
Jenkins
Gadd&Russell
Grid 2
.
_
-
~ .
\~ ·
:,__ ~
~~ i
0 0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 26. Comparison of Wave Profile for Fr # = 0.48
0.15 1
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 ~ 0.1
\- ~
~ 0.05
.=
I O
>
~ -0.05
n
0.06
I, O
0 03
Sink&Trim Condition
Jenkins
Gadd&Russell
— Grid2
.
~ ma_
·~ ~.
...... * ~ t ~ ~ · ~ ~
0 1 2 x/L 3 4 5
Fig 19. Wave Pattern for Fr # = 0.65
~ .
~ !·····-
_~
0.2 0.4 0.6 0.8 1
Distance from FP, x/L
Fig 27. Comparison of Wave Profile for Fr # = 0.65
L*FK)
~040
0.030
0.020
0.010
0.000
-0.010
-0.020
-0.030
-0.040
1 , ~ ., mu. 1 -0.050
1 1.05 C/L 1.1 1.15
Fig 28. Comparison of Wave Pattern for Fr # = 0.48
I, u
0 03
a'\ ' ' J
0 004
-0.004
1oo36
-0.044
0.067_ _ - ~~ >~> ~ -0.052
1 1.05 C/L 1.1 1.15
Fig 29. Comparison of Wave Pattern for Fr # = 0.48
0.6
0.04
0.00
-0.04
I:: ~
-0.6
0.6
n
-0.6
Wave Height
_ z/(L*Fr2)
0.12
0.08
~ Ratcliffe
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0.5 1 X/L 1.5
Fig 30. Comparison of Wave Pattern for Fr # = 0.28
Wave Height
_ z/(L*Fr2) ~ ComDuted
1 1
2
0.12 aim ~~ r---- ~ /~) Jut
~ .. ~ .... ~ .
~ O 00 ~ ~
. ~ .
Ratcliffe
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0.5 1 X/L 1.5
Fig 31. Comparison of Wave Pattern for Fr # = 0.41
1 1
2
03q
5415
Fate ffe 28
Computed
0 2- i\
0 1- \-
0 2 0 4 0 3 0 8 1
D stance from FP x/L
Fig 32 Comp of Wave Profile forFr#= 0 28
u \
01- ~
03~
5415
e Fate ffe41
— Computed
0 2-
0 1- W. . .
~ o ~ 1
0 1- . . =
0 02 04 03 08 1
D stance from FP x/L
Fig 33 Comp of Wave Profile forFr#= 0 41
DISCUSSION
Gzbor Kzrafizfh
Naval Surface Wzrfz~e C nter, Czrderock Div:, USA
I The mthors must be congratulated for devising
the ingenious griddmg medhod Fiat enables the
combmed free surface viscous flow computation
This methodology was also used by He mthors to
perfomm free surface viscous flow calculations to
study the flow behind z stern flap md help co fimm
the scale effect Fiat occurs between model size md
ship size barafiath et al 1999) in that particular
case, the use of the Chimera gridding was z great
asset with regard to the efhcient mmmerical geometry
definition of She stern tarp
2 in ener31, She cunent commercial practice
associated with z ship hull fomm development is to
use either the free su face potential flow computation
or the double body RANS calculation for viscous
flow The combined free surface viscous flow
calculation, either She one presented by the mthors or
one of the f w of her emerging he surface viscous
flow codes, is generally not used becmse of the
newness of She codes md he mse of the associated
extent co t of She calculation Could She mfhor's
comment on the turn around time, grid preparation
md calculation effo t that is reqmred for the
combined fiee surface viscous flow calculation?
3 Given that Here is z somewhat greater cost for
this new calculation method, what do we gain?
Could we see z comparison of the wave height
prediction relative to the equivalent tree surface
potential flow code prediction Ed also z comparison
of She boundary layer fhickmess rektive to the
prediction from She double body RANS code?
4 in Figure 30 md 31, we see z comparison of the
predicted fiee surface viscous wave field to the
model measurements using the whisker probes As
characteristic of mmy similar comparisons, the
predictions are very smooth in nature whereas the
model measurements have z great deal of high
frequency content that is not captured m the
prediction My observation of mmy model tests
conducted in very still calm water is that the flow
field around She model is in reality m unsteady flow
with z significmt temporal flow variation tendency
near She tr msom md that the high frequency content
in She wave field is real Could the mfhor's comment
on She resolution of this problem of z steady state
prediction for phffmmenz that has some temporal
variztmn?
Kzrafiath G. Cusanelli,D S. tnd Lm, C, W. "Stern
Wedges md Stern Flaps for mproving Powering
U. S. No y E perience" T msactions of the Society
of Naval A chitects md Mzrme E gineers, 1999,
Bzltimore,Mzrylmd
AUTHOR'S REPLY
DISCUSSION:
Y. Tzharz
Oskskz Frefectme University, Jzp m
(I ) As the mfhors mentioned in the paper, Most recent
high- peed fine ships as w 11 as Model 5415 have
t msom stem in order to obtain wide waterplane area to
secures fficient stability H wever,th widetrmsoms
tend to Increase disturbance on t msom wave fields, md
that results in increase of hull resistance The present
mfhors md of hers Kawasaki et al, 1996; Tzharz et al,
1997) had carried out investigation on tr m, m flow md
wave fields using computational md experimental
models in the work, it appeared that tr msom wave field
c m be classffied as the following 3 types: (A) wish dead
water zone right after stern end; B I with no dead water
zone, but wave Mel m g in near wake region; md (C)
with neither dead water zone nor wave breaking in near
wake region, i e, free surface is smooth y continuous
from She stern end in your paper, the above are simply
retorted to d ylwet conditions
My question is how accurately your mmmerical
method c m predict She above (A) th ough (C) for ship
models considered m your work
(2) For She zbove-mentioned type (A) tr msom wave
condition, She signffic mt bubble end Pi merit is usually
observed in the measmements The effects must be
included in tree-cm t Ice boundary conditions m order to
accurately predict the wave field Cunently, inclusion of
the effects may not be focused in your work; how ver, I
would like to Mow if you have prospect or suggestion for
feasible mmmerical treatment to include the effects
REFERENCES:
Iwasaki, Y. Tzharz, Y. Okuno, T. Himeno, Y. md
Yam mo, T. "Studies on Re ktionship between Water
Surface behind Stern md Stern E d Fomm of Fine
Ships," J. of Society of Nils Pi Architects of Jzpm,
Vol. 130,1996,pp 13-20[Jzpanese]
Taharc, Y. md Iwasaki, Y. "A St d. of Tr msom-
Stem Free-Su face Flows by 2-D Computatiom~l md
E perimentclModels,"J F.cnssi Society of Ncs-cl
A chitects, No 227, 1997, pp 7-19 [Jsp mew]; also,
Proceedings of She 2nd Co terence for New Ship &
Marine Techmology into 21 st C ntury, Hong Kong,
June 1995, pp 53-92 [E glish]
AUTHOR'S REPLY
None received
