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OCR for page 792
Wave Resistance Computations - A Comparison of Different Approaches
S. Gatchell, D Hafermamn, G. Jensen, J. Marz M Vogt
(HambuTgische Schiffbau Versuchsanstalt GmbH, Germany)
Abstract
Steady state fiee su face computations are still of
utmo t impo t mce to all model basms Among the
glorious computational approaches for bodh, bound-
ay element type as well as volume type methods
Hat have been presented over the past years, none
are f fly convincing in teams of stability md accu-
rmy for arbitrny ship hulls, being the'principle"
business of my model basin
HSVA is developmg free su face codes aiming at a
most vex atile Implication Three of these methods
are compared in file present pmer, showing exam-
ple computations for a contamer ship md a fast
monoLull
1. Introduction
Steady state fiee su face flow are till atop pnor-
ity issue wish my model basin As we do not ~-
pect developer of generalized flow codes to pro-
ide optimal solutions for this ve y pecial Naval
Archite tural problem, HSVA has dedicated sub-
t mtial effort End resources to file development of
pecialised methods suitable for practical mphca
tions in hip design md hull fonm evaluation as
well as optimization These developments follow
fEree principal lines:
I The iterative non-linear fiee su face potential
flow code SH LLO (J:nsen at al 1966),
which has long been used m hull fonm design
at HSVA md in several other installations, un-
d:went a major renewal, aimmg at a more ac-
curate predi tion of the wave making resist mce
of ships The major chmges to the method
were the introduction of a new p mel type
based on desingularised sources md using m
integral mass flux boundary condition on the
body instead of file usual Neum mu condition
implied on discrete collocation points used in
typical pmel codes Inhoducmg a continuous
reap meting of the hull up to the actual waned
so face, the new code w dks on arbihary grid
co figurations built from hia~gular md quad-
nlateral patches The results obtained wish fLis
code are encouraging
2. The ~ OF-Code is based on file Euler Equip
tions The method computes a smgle phase
flow md utilises a Volume-of Fluid ~~ OF) -
mproach to describe file fiee su face Although
it still neglects viscous effects m the flow held,
details like breaking waves in file vicinity of
file free su face are predicted Test cases indi-
cate signiEc mt improvements in file wave held
computed md m the numerical prediction of
file wave resi t mce The currant version of the
code is implemented in a multiblock mode it
is pamllelised using the message passmg pro-
digm md runs on shared md distributed mem-
o y computers
3 Additionally a commercial RANSE-solver -
Comet is applied This code also allow to
compute the fiee water smface The method is
simile to the one described under 2, but tw
phases are considered
4 b mother Unite volume solve' a level set
technique inhoduced by Osher & Sethim, is
used to cmt re file free smface between tw
distinguished phases, water md air b file for-
mulation used here, the goven ing equations
are solved in bodh file water md file air do-
mains md the two phases are considered as
one A level set function, ¢, deEmed in both
phases is mitialised as file did mce, wish sign,
to file undi turbed fiee su face instead of
solving the tw cur nit tiw equations for den-
sity md viscosity, which w uld c mse numeri-
cal difficulties, the scalar function ¢, which is
continuous even under ch mges of topology, is
con ected by the velocity held Dependmg on
file sign of ¢, the density md the viscosity are
given the values of water md air, respectively
Compared to fiont hackmg medhods to com-
pute free su face flow, no regadding is neces-
sary md no boundary conditions are mplied at
file free su face Further, file position of the
fiee so face need not be explicitly evaluated
during file computation, but is canted out m the
po t-processing The steep dersih gradients at
file tree su face necessitate the mtemolation of
file physical prope ties owr a few cells around
file tree su face However, the inte face itse f
remams sham Unfortunately, no stable com-
putational results for file sele ted test cases
were available at the submission deadline for
flus paper Hence, the method had to be ex-
cluded
Impor mt details of the fEree different Pph ache.,
mcludmg the mathematical formulation of the fiee
so face conditions used are show in the following
OCR for page 793
chapter Tw different te t cases, namely a smgle
screw displacement vessel (Kriso containeLhip
Gothenbmg 2000) md a semi-displacement hull
fomm with sub tantial trmsom submergence
(Athena), have been used as test cases G id re-
hnement studies show the sensitivity of the results
for each medhod Finally, a comparison of the
methods show the relative merits of the different
methods
2. Potential Flow Computations
Description of Method
Potential Flow computations how below were
pe tom ed using HSVA's new nonlinea teady
tate potential flow code v Sal LLO The code is
based on the prmcipals for IL tubing the nonlinear
fiee so face bommdxy condition iteLmtiwly in a
collocation method as described by (Jensen at al
1 9S5 I combined with file patch method for heating
file body boundary condition md pressure integ
tion described by (Boding 1993)
The flow is described by a potential f nction in
pace generated from the supe position of the par-
allel flow md a dishibution of Rmkine pomt
sources
~ = Ax + >,m,—
b this equation m,denotes the shengfh of each
pomt source md r is the di tance between the
pomt solace md the location where the potential is
computed Velocities md accelerations c m be
computed m file usual m mner as file derivatives of
file potential
(2 1)
v = Vq
(2 2)
b d is method the pomt sources are located outside
file flow regime to avoid smgula~ities in the emma-
tions Sources are distributed mside the wetted part
of the ship hull md above file tree su face in m
iteLmtive procedure, file flow code detemmmes the
mmknow solace shengfEs, the equilibrium floating
condition (h im md si kage), the wetted part of the
hip su face Ind the location of the fi ee so face
Computations are pe fommed following the struct re
how m the flow ch at below
The so face of the body is discretised using trim-
gmlar md re t mgular patches (Fig 2 2) in the Or t
tep in file itemtiun loop, fLis grid is cut at file ap-
proximated fiee su face Fig 2 3) mitially at the
mmdist bed water so face Thus, hi- md quxLilat-
eral pmels are distributed owr the wetted part of
file body only To avoid p mels wish m unfavour-
able
Am=
=~
| Cut p mel me h at wet- |
I tedbomdxy l
| Generate grid tm w ter |
1 ~U.I~ O.UU..U..U.. 1
| Inte polate flow fiom |
I Devious sten I
| Co efficients for body | | Coeffclents for free |
| boundary condition | | surface boundary |
| Solve linear equations |
I forsourceshength I
I Compute pressure I I Compute velocites md I
| md forces on body | | wave heights l
| Estimate chmge in | | Calcuiate enorinnon- |
| tam mdsmkage | | linear conditions |
aspect ratio near file watts line, some comer points
are rifler moved or omitted A point solace is lo-
cated near the contra of each p mel md shi ted m-
side file body depending on si e md shape of the
p mel There are no p mels on the h .Itrll; they are
simply led open
A mesh of collocation points is distributed on file
fiee su face around the hull The total length md
width of the grid, as well as the spacing, are deters
mined automatically based on file Fronds Number
Also, file lateral did mce of file innemmost row of
collocation points is pre-set, based on the Froude-
Number For submerged h msoms or ve y blunt
water lines at the stem, additional row of collocate
OCR for page 794
t=n ~~ ~ ~~ - ~ the Inns tn ~e
I - ' an und~ ~ ~ is mums.
For each In Bunt on ~ ~ s:~,
flow quotes t~ ve~e~;, and ac
in ~e 0e space Hungary mnd~-~on ~
':~erpol~md ~ the ~~us—. ~~ ~ ~+
clan Cons by mums p - ~~! flew with ~e ship
vow..
Is ~e Inch 0~e ~h =
pace An ~ ~e s~ m~h. The ~ ~d ~
a deduce Net on ~e long 5~ of
~e undt~r~d ~e surface. To ~~ ~e 0
t~ In ~ is ~o ~~ source 0w
mom upstream -~on Bind in ~b tow. In-
$~~ ~~ Is ~ ~ wI~t wur" do~
Mom each row of In po'n~ (ok. 2.~.
Th~ a system of I~ ~ - ons ts ~p Egg
~e sighs of ~e - trot w~= ~ ~ Ems.
T6~= ~ t~ ~~$ AILS:
each coll~n got on ~e ~e ~~r ~e
e -I k~e and ~~e ~ m~e
boundary Ins ~~ in tenon, et at. 1986'
I~ - ~-~ ~ ~prox~ wIudon ~ ~e
saw I~.~n ~ 0,0w pace Is
V~~~ - ) * vOY¢]
2 V~2 got
[2 ]?
-
2[ (' ~ ~ ~ ] ~
· ,- . .. --: i _ ~
g - V~Y~Z
On ~ posh on ~e wk~ed body, an -~on
IS ~~ ~~.-~g the ~ n~W "~ ~e pa~h tO
be zem (cam Iw3~.
Thus, ~ tone Deem of An why ~ ~~! ~-
c~t mix =d AL ~~ Durham} a; de-
~ ~e unknown mume sag 8,
solver comb~n~'ng elms - ~= and -~on steps ~s
urn.
The ~~ =d ~~ d=~ =e ~~n Lily
dete~'m:~ - on cash c~n Bent and - ~]
corner mom A.. Using ~e patio =d tt:s
nv~lYe on ~ p=h c~' the pang ~~s mm-
p~1 to Carmine ~e pm~m AFRO. 4~-~ ~C
hy4~£~c ~~ In i's eg0mn Is consI6-
em~ In Me ~ss~ '~on. In add~ He
~~ ot the vellum on ~e may Is In to
compute an appr=Ima~ ~ ~ man ~ ~G-
~-
k- ~ Vi ~
Betted
T-~:~s ~ ~~r Bunts ~ ~e change ~n went
s~ as ~~l ~ ~r ~e I~s V.
d~. It should ~ not t~ ~ must nor
£0nfi3 - Web ~ ~= 00t 6~6 ~ the
z~ Fmude^umber approx~m~n ~m ex~i-
men~.
Tum =d sink.—~ Amid ~ ~ ~e ven;-~-
cal ~~ am Be body ~~ is m - ~ I.
The ~ el~n ~ ~ =~on points ~
comp~ Firm B~:~s ~on. ~e ways
Amen ~~ ~e hull ~~s ~~ - by ~~:~ng
e Ash; mew of Con points o~ ~e
hull Bung ~e I~} sI~ of ~e ~ ~~ Thus
I~=ine~h y
gnd Or ~ new ~on. Fig. (~.~) s:~s the d:+
Ye~nem of ~e ~ ~d ~~ several An
Ace.
E~E ~~.~.s
Con~ons ~ ~en performe~l ~ `:o well
known ~ cams. ~) the ~~ ~~n~h,~p
id ~r ~e ~ c~ ~Q~mb~ ~~p
(~=bllrg 20) =d ~~) ~e ~~a hull p~Y~-
o~y Fed tn a nu~nber of e - amend =d com-
~Q=[ ~ - ~3 (~^ Add:.
6m ~ ~ ~ p=~! mesh b~ Den ~ner-
0 O'er ~ paw, - ~ ~ o
enburg ~vor~sh~ (~^ 2~) u5
lag. 2~ "he - P=e] ma fm ~~:] Bow Imps
_ ~m ~~~
Fig. 2.3: ' - t;= same ma, ~ in - Mso
Con
~ -_
Fig. 2.~: "I 5~ ~5, en-d o:~m - ~~m
.
:~: ~ ::
OCR for page 795
t~ mew ger~era - . ~ may m
21~27 ~~* For ~e ~~r my ~ ~d m
stay Is ~ ~ ~ng Mar ~~= (~y
d~h mesh (V2) ~d ~ ~" ~ (~3~. ~e
-I ~d ~ ~~ Id Band per her
~ . The ~~ me~s am ~~ in Fig. 2. 5.
ment ~ mom Lemma (~ - EFD)
mom our compu~3n (~= CED).
4.~=
3.~
id:
2.
1.
O.
, ~ . 1 :
, .
.~ tom
_=_ _. 1
l 11
1
I.
.- 1~ 1= ~ ~ ~
—. Imposts
3~
F~ 2.~. '~d Perky sky - ~so ~n~ne:rsh~pt'
FIg.~.~. "~d m6~t Em_ ~" And,
v-~0LLO rew~ o~i~ on Me Off -
she me~s ~ ~~ ~n ~e ~~;ng ~fig~
to ~ t.~. ~e Co~itIms Used b~ ~ (~] - Hi:
4 ~~' Fly ~ 0.2$W, ~0.8 m. In order ~ co
p~ wI~ ~ ex~ - data ~~ ~ =~
we:=—~~ed ~ ~1 As. ~ ~~ng
figure I.6 0ws Cash c=~cien~ (~ - c~ and
cT) ~ ~ mm~i~ to ~e expertm=~l- coda The
~ upper :~= ~~w ~ :=al ~03= c~-
F'~ ~ 8-: "aware I, up ~ eve but:} - K} To Akin - up',
F~g 2*? 0' ~ wow pattern o0~ed o~n ~~-
mesh ~03 ~—~ ~ ~~ mush (:b<~om i. It
c~ ~ In t~ ~e fine m~ sbows ~ smooth*
Make Oft rasters ~ sea* MAYO e1~-
hons ~ ~ ~ ash. Computing -oh to
Arise Container Chip, G;o~lk~bu rig Test class, I: kin, t~. ~ O~ ~~m (e>~$3
Fig. 2.7: " Peso ~~p - campus ~:w ~ ~r ~e boe me ~ =d ~ t~ copse mesh I"
:: ~ ~ ~ ~~: ~ ~~:~ ~ : :::::
OCR for page 796
Isle p~ in (Go~
t~ t~ Mar mew is c~ ~ experiment ~
For ~e Id teal ~, ~ Hem t~7 a pow
mesh ~ Ink ~ on ~ ~~g NAPA
m - ~~' ~~ N~A's new ~! M~r
~3. T5~8 ~s Awry ~ ~a~
Input ~,qne~ ~ ~e v-S~o code
~ _
~ _
: - _:
Ego 2.9 ~~ ~ - Acme ~'
A study of ~ ~s'dv~w of :~ ~ ~e ~~-
=~= ~~e:hull w~ - ~~
T~ d~'fferen1; bull m - ~s :~e ~: Cited, ~e
nr~ ~e having ~——el~ ~ stud ~~ W~
2~ ~~. ~ veer :~¢ ~~ bun - -
~m $" ~ I=~2 - : My ~ 2426p - ~ Figs
2.9 Mows ~e two ~~ - ~! mesh-= on we
TO -on ~d ~r Ace Hems wed
v-~0k~,9~=B-.73,1= I.Sm~Iseale
~ r
The ~e Bern o-~d on ~e one Ed on He
m~ mew (wow -s~) am shown In fig. 2.~.
H~ - ~n mn~= of ~e previous exerted -
~LC - F mew shows sty higher wave
elusions' Ails ~n tum Ding mom - chic the ~e
- at. cc wave ~ O~ ~ ~e
c~r mesh.
S~= newts ~ ~r the pmv~s c~ ~ pl
~nilg.~.11.
3.~ -
2~= ~ /
2 .~£ - A ' - I> . . .:'C' . ' . :.'
O.03
.~ ~ ~ . — j 3.
~ ~ - '1
show j ~ - : ~ ~ On
3~ - ~ 1 ~ ~ - ' 0.~0
_ _ ~ ~ ~ o ?
--=~ == ~—~ - Din
~ ' t
! - -- - i 1 ~.~
__
;
- ~ On
.. ~
sm 1~ ime zoo 2500
0. 0~" ~~
~ ~ ~ ~ I: `~ doped =~ - At
~~. 2~: ,,~= - Ins -e pan:: Brie ~ - y, He m~ - Em "
:: :: If:
i:
~ i..
Ail.
:: 3
OCR for page 797
3. Volume of Fluid Euler Method
During file past years, methods for solvmg the
Navier-Stokes-Equations have been developed
which describe file tee smface by admtmg the
mesh boundaries These methods, howeve' only
apply to moodh fiee su faces Here the develop-
ment md mplication of a Finite-Volume-Code
using file Volume of Fluid V OF) medhod for the
simulation of inviscid, unsteady fiee su face flow
will be described This medhod deicrbes file posi-
tion of file fi ee so face by file void fi action in each
computational cell Tw mplications will be
how
The trmsient flow of m inviscid md mcompressi-
ble fluid is considered it is de icnbed by the con-
se~vation equations for mass md momentum, for-
mulated in m inert Ca~tesim coordinate system
The moment m equations are w itten as
atilPY +IPY((Y Y6)it)dS=
rim s~hOnao ~ m com i.et m
(3 1)
| pi tdS + | p igdQ
s ~
pm~mfefome Em Enforce
where y = (up, y,w)7 denotes the velocity ve tor
with its components in x, y md z duection, p
file pressure, p the density md ig the gravity vec-
tor Fu ther variables se the conhol w lume Q.
file velocity of file control Flume
Yb (ub,Yb,Wb), the so face area S md the
nommal vector of the control volume su face it
The pressure p is the sum of the dynamic md the
hyd ostatic pressure
P=P+Pig' (32)
The ve tor if doff me. the position of the tree sm-
face, the gra ity vector ig is nommal to file undis-
t bed fiee so face For a completely hlled control
w lume the conservation equation for mass is
a | pdQ +| p(y y6)iidS = 0 (3 3)
To describe the fi ee so face, a fun tion f is mh o-
duced with a value of eifLer I denoting liquid or a
Cane of 0 denoting gas The f nction f is a dis-
continuous function The fiee su face is the bound-
aly Ire where f ch mges from 0 to I Fluid palti-
cles above file fi ee su face will always have a value
f of 0 md particles below a value of I This
yields a conservation equation for f which is mde-
pend:~t of file position of the control volume
a | pidQ +| pf ( y vb )ii3dS = 0 (3 4)
Below file tree su face, this leads to a mass conser-
vation equation The cell All ratio F is file ratio of
file cell volume hlled by file liquid to the total cell
volume
|fdQ
F= 3 (35)
|dQ
By definition this ratio has values between 0
(empty) md I (full) At the fiee so face ambient
pressure is assumed: p = p~=const (dynamic
boundary condition)
Fig 3 1: The Flow hat of file algorifEm
43
l c~cui~e P l
~1
| Sol e mom nUlm en |
| pressure correction |
| extrapolate p l
The figure above show the algorithmic scheme At
file beginnmg of eve y physical time tep, the VOF-
f nction F is calculated
OCR for page 798
T~ ~~= Integral ~ ~r the EY ~~:~ -
IS - EXIT USES ~e p0.~t of ~ nuX =d
the o~n Ce~:] s~ 00e ~e o~ =~! s
~£' Oe ~ -I Sl~C ~ IS dank ~ Chows
. ~
. ~
~ f(v ~~ of & = {~ (be)
~ i~
S~n-~;e ~e cell hi!—o :E is ~ d~£~i~ ~~-
t~on' ~e cel~! $~C =~D Ins ~ ~ - by
~~ =d mm ~ ~~M I~YCi>.
This leas to ~ do ~ ~e ~ of. The
ve~:ineS c~ to me ~ ~ ~ ~~
uStog ~e =~ng -I ARerwa~s, ~e
SIMPLE Al~nthm ~s a:~ ~ wIve ~ ~ v~
I~-~= ~ ~e ~~.: ~.i~ why ~ ~~-
m~ wIut~ ~r ~e pressure, ~e I~d ma
m~m ins ~ mIved. To - $6 the ante
nulls In ~e pm~ am ~e Yei=~s
c~ by - ~~g the w - ~~d ~~ cor
r - of. The ~ steps ~ ~~ - At. ~e m-
qui~ =~< ~s peachy. In M:~n ~ ~e ~-
n~e Weary Boon ~ ~e ~ so, ~;~-
e~ ~= Hoary c=~tions mum ~—And:
I. At the Into ~e velour ~s 6: - and the p=~-
~ ts ~ra~;la~
2. ~ ~e o~^ ~e =~ Is ~~ - ad ~e ve~-
'ty Is ex~ola~
3. ~ the ~~ panes, 0~= ~ =t
=d ~e =~ 's mirrors,
;~:~:~ :
~~ ~~ Ale.
The ~~= ~ one fin deacon ~ ~~W by
apply'~ an =~ ~~ which dep - s en the
ve;~W comb w=d ~e Aside ~m the
shop.
it.
E~E BATES
Comp~s have ~ pi. ~ the 0~e
my ~~$O tarp =d henna bull.
T~e cond~: ns u=d am ~e ~e ~ In the =,Fac
comb. ~ mob =e genies m
H:~VA One - mesh =~.
For the K~ ~ ~ ~ meshes with ~x.
470~ (~' I - ~ id 38~D cells (~)
m Ignited. The molest mew Is Sawn In
n~m 3.~.
j
Flu. 3.~. Co~ G~ ~r the ~18~} Oh.
The to~ bin fame ~s 2~ seconds. The Bow
~s a=~d ~m- ~ ~ ~ ~0 during the fit 40
=~.~a FI~ 3.3 shows ~e resists c=~ -
cw oYer ~ simulation fame. The finest mesh yards
a io~r Ant cw wiue of 0.~. l6e Fiats mesh
In ai~ p0~s smoker In.
-
~~ f
i ~
Off.
o ~
.; . . )
,-~
.,. ... . ...... . ................... . i . . .. .... . ~
50 We t
~ [I:]
fig. ... ~~= c - ~~t cw Her time -
K~-~ con~nemb~p
The ~~e p~ ~ ~ = 20 ~r Be KCS t=t
wn in fibs 3.4 ~r ~ ~st ~ the
fined ~d. Bo~ £mnpu~tions show ~e same ov~-
! waYe pattern ~e Knew ~~ however, gales
s~tly hn~ mmIut~n of Ike wave Cacti.
F~ 3.5 mm~ ~e wake din of the
mm =d ~e s~mul~-~on on the Anew ~d.
The admit ~s Yew good, High the edit of
the =~ being be on be costly =~n
throw dark.
The ~~ di - ~~= cp far the fine Kind
gad Is shown In fiche 3.~.
::::
.
:: ~ : : :
:: :: ~~ i: : aft: ::~
: :: :: ::
OCR for page 799
Em: 3~- M~ gem =d ~~ (~)
~e d~ - =~w ~~
ma. 3.~. Com0~ ~e parers ~ ~e - ~~O
£~n~h~p Cop: co~ ~~' Stan; Bend;
F~m 3.6 - USA d~n up on ~e ward
hull - -I conu~ne~tp (~ne Add.
The ~~d for the Athena t=t me ~~ of ap-
pro~ma~y 25~ Ads. The tom} muon dime
is SO wands. ~ computed me dir - ~~n its
she ~n togae 3.~. ~e operation at ~e ~~m Ad
the development of the waves con be =en.
::::;
:::
Fig. 3.7 Compote wave pa:~-m - Arena te~
Aid. 3.8 Pressure Con cp on the wetted
hull -Ala test c~
OCR for page 800
4. RhN~SO~er Com~;
D~ or Mat
Coma w1~s ~e ~S Ins us'~ a my:!
end bare Yost mend [id. `~e
P=~tct~m ~ ~~d mI~ me ~ .
-math.
Th~s my =~:~= ~ kind of ~ phase magi.
The phys'm! Ales (~'w p =d v`~s~W
~ ~ ot ~e ~~e 0~d depend
Hem of Nest 0~s (~.g. 0~d ~ ~ Omd ~ ~
=d ~ - = ~~= ~~ Hewn ~ volume
n C=, Carding ~ the ~~:~mg ~p~essu~:
Cpi +~l _~
~ ~] +~] -Cal (4 2)
Wee= ~ ~~ ~ =d ~ d~m ~ tWO =~-
sht~ Hu'Js (~-.g,. Car aM m0. ~e Ion ~ is
d~h Swan ~ different acids. A
value of one Nay the pie of hu'd ~ md
0 Y8~-~¢ 0t ~ ~~s ~ And 0. Vogue
n val~s ~~ ~~ t~ t~ Andre
Amp.
The volume Gabon ~ md ~e may - ~~:n ~ of
Hmd ~ ~ I~d by ~e em
~ = C PI . (4 3)
The In of ~ 's governed by
~ *~)=0
..
of ~ ~ I. The h~gh-r~n See canting
- ~ I) '~s ~sigr~ed to Become thme
- Hems ~ m: Abel accurately the ~~ - of
sharp ~ .~.
At the oudet ~ =~e Unwary is defined. The
e She ~ ~ Away ~~ due the hy-
dms=~e c~s cawed by ~~;e of the cash
Ion.
Con~at~s have ~ =~d ~ Be K~-
C~p ~~ ~e ~e co~s ~ ~e.
The Bed ~d w'th Ace. 450.~0 =~s
was general ~ ding {CEM<~D ~~d general.
The eo~adons wem Armed on ~ ~~ter
Dish ~ ~ in. The ~e pattem ~e sho~ ~n
5~ 5.2 ~ ~ ~~:~ng cb~r. The ~ment
w,th ~ m=$~t ~s ~ in the neighs
of ~e Ace. TO wan ~~t ~ ~e ship ~s showy in
no....
(do)
It ~s Awed ~ ~r the Ion of ~e Button
domain whew £ ~ ~ In ~ ~ 0' ~~
Hu~s sh~ ~e ~e Yellow ~ In. In ~~s
' ads Subsurface capturing mom - ~s ~
mode:: of muld-~s D~ 0~m Hu~W ~ ~s
Id; ~ s—~~= =d bird ~ ~ Wok—~d 0~.
The method ~s m1~y simple on ~~= ~ds'
but I~t l.S dI~t ~ Isle Em.
The ~~ c~ - ng Unshod is ~ on
It ted of ~ ~~ q~W which
New ~e presence of one of ~e Herds ~nvolY~
in ~e—-~e Dow. T~ ~ or physics ink;>
s sharp ~d ~ ~ ~~d ~ In ~e numenc
sin.
The u" ~ ~e UD scheme cams wry Bong
snowing of ~ Id. The CO p~= ~e
shad of He ~~e ~t ~ ~ same time ~}~-
trMu=s non-phys~:t -ens ~~nd ~e inter
~~e =d p - ~~s vows of the Ague -on
which am - - ~ prosily meanings Adds
F~ 4. ~ W=r s~e ele - on al~ 85~P
O Con~mh~p (
Calcu~;~?
The pM~ ~~: An (ep) ~s sho~ ~n
ng. 4.2
Fig. 4.~ ~~M p~e ~stnbut1~n -~met IBM"
::
~ ::::
:: ~~ i:
: :: ~~ ~ aft: ::
~ 5 ~
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OCR for page 801
S. Ma of Is
Fig. 5.~: ~i~ o:~OF-~r ms~ (above)
~ :~ ~ mSul~ (~ -
To Compaq ~e d~fii¢rcnt Is ~ ~~r
~ computed ~e pawing ~ pressure di~bu-
dm ~ ~~e mmp - d ms~s~¢ ~m Huh m~-
~ ~ ~ Afire aid used ~ ~e Container Ve
~~' ~ ~ A~a Id. it.
. -
a,5
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~ -5
~ ?0
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_~.O
_~.5
H~ 5 ~ ~~partsQn of ~~e porn- ~ C - ~t - ~~ solution (
Imp d - Imp'
Whop PATTERNS
fear Me KRIS£} mn~'n=~p ~s£ ~ crimp=-:
tom wem perched ~r ~e mMe] ~~ ~n him
i: i: i::
~~:
::: i:: : :~:
: ~~ :~::~::~::
:::: : ::: : if:
=d s:~kage, ~ ~n ~e me~:~ements. The wave
pa' concept w~h p-$~O cIc~y stows
divot In wave pane- - oh. in the VOF"
E~le~l~;~n ~~¢ ~~s d~i~= ~ ~me d-~e
f;ton~ Me Cumuli. Th'~s ~s d'ue ~ ~e =~al ~mp~
me ~~}~ed ~~ve The ~w w~e ~s mom
M ~n the V~ Amp. This ~s expected
.~3
9~,.,'~
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e the ~~} D~ caleu.~n en w-
~'iYt By ~p ~Y:~. Al~ ~e Down
her ~w = - is dee~r in ~e I solu-
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If-! e~ due ~ ~e hod some that is £~-
OCR for page 802
tised The details of file stun waves are comDletelv
different
b the VOF-R NS solution local bow wave as well
as the wave h ough at the fmwaTd shoulder se even
more pronounced thm in the previous cases The
f T held however show only limited similarity wish
file expected Kelvin wave p Stem
For file Athena test case file differences are much
more signiEc mt The ~ OF code gives steeper md
more pronounced waves The orientation of the
main wave bough is different The ~ OF code also
predicts the complicated struct res typically shad of
file trmsom edge of semi displacement hulls
PRESS RR DISTR 3UTION
N A 2 R 5 TAN
The overall pressme patted on the Containerwessel
hull is comp Sable except for file higher pressure
md local wave height ne T the tem
The residual resistmce coetlicienr fiom file One t
gads for file considered Froude- Number of 0 2599
are:
1000 CR
Potential Flow Computation 0 47
VOF-Euler Computation 1 25
VOFRANSE Computation 1 45
Measured at KRISO 0 73
In case of file Athena semi displacement hull at
Froude-Number 0 729 the results for file resistmce
as compared to measurements Be as follow:
l 1000 CR I
Potential Flow Computation | 1 45 l
VOF-Euler Computation | 0 92 l
Measure at HSVA | 2 1 l
This show that the qu mtitative accuracy is still not
satisfacto y
6. Practical Considerations
The fiee su face potential flow code V -SHALLO
pro ides results which des Tibe the global wave
p rem md pressure dish ibution well Although file
computed wave resi tmce values are much more
realistic than fiom e Therversions ofthe code, file
qumtitative accuracy is still not sufficient Never-
fLeless it is m efficient tool for hull fonm develop-
ment, becmse grid generation takes typically less
film one how md file computation, even for file
One t grid is finished in less film tw homs on a
Pentium PC in file practical hull fonm development
cycle, much more time is needed to modify file hull
fonm m the CA system
For simple geometries the grid generation for file
VOF-Euler code is also rather Pa t md shaight
fmwaTd For more complex hull ton s it is however
iffy' time consuming to generate grids wish suff-
cient quality Although the method obviously cm
reproduce details of file physical flow much better
ah m the potential flow code, there is no adv mtage
m accuracy for file resist mce m the considered
examples The shong dependency of the results on
gad resolution indicates Hat much timer grids se
needed However the computation time for the
One t gad was already 30 hours on a smgle
Pentium PC
For the fLi d case, file VOF-RANSE computations
file time required to produce the computational g id
is ce tamly the highest in the present comparison
Today's practice using ICEM/CF as grid generator
allow for approx I day for grid generation The
gad si e used for this exercise was 450 fLousmd
cells, file computation was pe ton ed using S nodes
of a parallel machine (based on Pmnmn 600), last-
mg apple ox 25 hour for 12000 iterations
K = 120 A)
The results presented in fLis article are promising
This holds less for the accuracy of global results as
for the resist mce of a ship but con ainly for the flow
held phenomena such as the wave patted or pres-
sure dishibutions it is ob ious Hat for practical
applications potential flow computations are not yet
so passed Newnheless, the held type methods
solving either Euler or R NS equations are more
promising for file futme Today's design process
relies heavily on file use of potential flow codes for
design optimization The present mvestigation
how that more reEmed results especially in teams
of details predicted m the flow held cm be ex-
pected fiom ~ OF or lewl set methods As compu-
tation time is still a major concern for these predic-
tions, considerable effort is presently pend on
pamllelising codes md running fLem on PC clus-
8. References
G. Jensen, Z. -X Mi md H Soding, 1966: Rarkre
Methods for the Solution of the Steady Wave Re-
sistmce Problem, Si teenth Symposium on Naval
Hyd odynamics, 1966
H Sodmg 1993: A Method for Accurate Force
Calculation in Potential Flow, Schip Technology
Rese Tch, Volume 40, 1993:
G that ha g 2000: hrp:Ow w iih'uiowaedu/ godh-
enbmg2000 /
OCR for page 803
sleistungsprognose, HSVA Bencht 1567, 1994 (in
Ge m m)
conhibu i NAPA user meetmg 2000' vario
C Schuma~m, 1999: Berechmung von reibungsfieien
Schiffsumshomungen unter Verwendung einer
,,Volume of Fluid"-Methode zur Beschreibung
de freien Wasserobe flk he, Ph. D Thesis, Ham-
bu g 1999
C Schummn, 1996: Berechnung von Schiffs-
m t m gen mit brechenden Wellen, HSVA
1, Dimud ic; AD Go m m, R. I Isa, M Peric
(1967): A calculation procedure for t rbulent flow
m comple geomehies, Computers & Fluids, 15,
E Schreck, M Peric: Computation of fluid flow
wfh a pamllel multigad solved' Int J. Numer
Medhods m Fluids, 16, 303-327 (1993)
OCR for page 804
DISCUSSION
H Bingham
Tech xcl University of Demmark, Denm uk
I cm sumrised that you are Cole to conclude that
Euler codes are not worth pursuing based on un-
converged results Would 't you expect m Euler
solution to converge using signffic Fitly fewer
grid elements f m c RANS solver?
AUTHOR'S REPLY
I ogre Nat my conclusion maybe premature it
is how ver based on the experience that no
subst mticl savings in computational effort or
grid generation have been observed Therefme, I
believe that development work should be
concentrated on R NSE applications
DISCUSSION
M R. ji
University of Tokyo, Jcp m
This papery Rmkine Source Method used
uniform flow et first value es base flow of fiee
su face But recently, double model flow or
exact flow is used to R Mine Source Method es
base flow How cutout do you thi k for base
flow?
AUTHOR'S REPLY
According to our experience you save et most
one iteration tep ff you use c double model
solution es the start up This does not seem to
make the extra complexity of She code
worthwhile I do not underst Ed what you me m
with the term "exact flow" in the coot :xt of the
start up of c panel method
DISCUSSION
L Rahejc
Indi m Petit te of Techmology, b din
You have mentioned that in your first code, you
used desmgulari ed panel medhod in pk e of
con- emmn~l panel method I would like to
k ow, how much cd mtage you gain by using
this method over the con- emigre one bee mse
sometimes you require to make adjustments in
the did mce fi om the wall where the source is
placed
AUTHOR'S REPLY
G Jensen
In using desmgulari ed panel medhod w used
the boundary condition in terms of no-flux
across the panel Ed w did not find my problem
with this Ed we have been using it for lo t ten
years We even use it for fiee surface boundary
The computation is very fast bee mse of no
singularity being present
Representative terms from entire chapter:
hull fonm
