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OCR for page 243
Flow- and Wave-Field Optimization of Surface Combatants
Using CFD-Based Optimization Methods
Y. Taharai, E.G. Paterson2, F. Stern2, anct Y. Himenoi
(iOsaka Prefecture University, Japan, 2University of Iowa, USA)
ABSTRACT
This paper concerns flow- and wave-field
optimization of surface combatants using CFD-based
optimization method. The main focus is placed on
development of a high performance optimization module
for application to Model 5415 hull form optimization,
which is capable in combination with CFDSHIP-IOWA
version 3.02, a RANS solver based on higher-order
upwind finite difference and a projection method for
velocity-pressure coupling. The optimization scheme is
based upon the work of part of the present authors wherein
tanker hull forms were optimized for minimum viscous
resistance. The module is general in formulation, and
basically independent from basic flow solver, e.g.,
different RANS solver or inviscid-panel method can be
used with arbitrary combination of constraints and
objective function to be minimized. In the following, an
overview is given of the present numerical method and
results are presented for flow- and wave field optimization
of surface combatant Model 5415 hull form.
NOMENCLATURE
p piezometric pressure
Hi, p2,etc. design parameter
mx axial vorticity
a,b parameters in modification function
. . .
b~J,g9, etc. geometric coefficients
B(x,z), etc. modification function,
B approximate Hessian matrix
CB block coefficient
pressure coefficient (=2 p /p Uoo2)
frictional resistance coefficient
pressure resistance coefficient
direction vector
benchmark data, drag
comparison error
objective function
Froude number (=U~/(gL)0 5)
g gravitational constant
G~,G2,etc equality constraint functions
Cp
cd(f)
Cd(P)
d
D
E
F
En
Hl,H2,etc. inequality constraint functions
L characteristic (ship) length, lift
P,Q,R grid clustering and stretching functions
r grid refinement
S simulation prediction
Rn Reynolds number (= Uo~LIv)
u,v,w fluctuating velocity components
Reynolds stresses
~ vi~ v}
U. V, W mean velocity components
Uv UD,etc. uncertainties
UOO characteristic (freestream) velocity
x, y, z Cartesian coordinates
v kinematic viscosity
p density
;~,:2,;3 body-fitted coordinates
INTRODUCTION
Naval surface ships in the 21St Century will be
radically different from those currently in the U.S.
Navy fleet (e.g., Webster and Mutnick, 1998). As such,
much of the current design database, which has been
developed over the past 50 years, is not directly
applicable, i.e., the new concepts are "out of the box."
Fig. 1 Naval Combatant (US Navy Photo)
Since it will be prohibitively expensive to quickly
expand the design database through model studies,
there is strong motivation to develop simulation-based
design tools.
OCR for page 244
Currently, CFD is used es m analysis tool to study
alternative designs Although e tr mely valuable, 6 is
cpproah s hers She limitation that it doesn't identify th
optim m desig This is She motivation for developing
CFDbased optimization tools wh rem automatic
determination of opt m m shape is part of th simulation
To develop c shape optimization tool, 5 components must
be built md are common among all the different
cpproah s Fi st, the optimization problem, which
consists of She objective f motion (e g, minim m d fig),
desig variables, md con tramts, must be formulated
Second, c geomeh y h mdler must provide c Imk betw en
th desig variables md c body shape defined by th
con tramts Third, c high-performance, genercl-purpose
CFD code is requited Forth the ystem must be able to
generate or mod h the comp tatiorurl g id es She shape
evolves Finally, c medhod is requited to solve the
nonlinear optimization problem formed by the objective
fixation mdcontramts
Some of She earliest work on CFDbased optimization
methods was in the serf pace comm mity md focused on
optimization of 2D foils for maxim m Ifft to d cg
performance (e g, Hicks et cl, 1974; Hicks md Hem,
1978) Until very recently, the principal obstacle m ihrFe
optimization was She large computational co t of
evaluating She sensiri ity of She objective faction to
variation of She desig pa3meters This is t pically done
though repeated cclcohtion of the flow Given th
development mbothCFDmethods mdhigh-pe formance
parallel computers, 6 is hr. oh tale ha been g ectly
reduced As such, CFDbased optimization methods have
sever rapid evolution in the zero pace comm mity
including f 11 co fgmations (Jcmeson et cl, 1998),
i tempt flow >! tems Perry et cl, 1998), m tructmed
CFD methods Elliot md Perspire, 1998), md geometry
h mdler algorithms based upon anetics md mech mics of
m~tmcl evol non (2hu md Ch m, l 998)
In the ship hyd odynamics comm mity, similar
development hr. taken pace However, due to geomeby
md phy ics (i e, free surface) which me more complex
thm Nat associated wish c wmg, development md
application ht. been slow r thm that in the arospa
comm mity Application to ships was initiated f ough the
use of solution to the Ne marm-Kelvm problem for
mimmization of wave making h sist n e More recently,
advancement of CFD ht. erLtbled th use of tANS
methods wish nonlinear prod cmmmg for minimization of
either viscous resistmce or nominal wake dished tion
leg, Larsson et cl, 1992; Hcmasaki et cl, 1996c;
Hcmasakietcl,1996b) Therecent3~3OsakcColloqui m
(i e, OC98) on Advanced CFD Applications to Ship Flow
md Hull Form Desigm Indicates that optim ization methods
are am ehy being developed in the ship hyd odynamics
comm mity Hino et cl, 1998; Suzuki md Mets moto,
2
1998; Taharc et cl, 1998) in general, OC98 show d
that optimization methods are cable of stern ihrFe
optimization for minimization of viscous nisi tance
However, k ge compuhtiorLtl co t is still c major
issue, but one that cm be overcome ff parallel
high-pe formance prod cmmmg technique is adopted
This paper concerns flow- md so t~e-lield
optimization of surface combatmts using CFDbased
optimization method Th mom focus is placed on
development of c high pe 1:3nnul e optimization
module for application to Model 5415 hull form
optimization, which is capable m comhirLtrion with
CFDSH P-IOWA (Stem et cl, 1996; Peterson et al,
1998; Wilson et tl ,1 99S I, c genercl-purpose parallel
multiblock RANS code based on hig)~er-order m pus md
Mite difference md c projection medhod for
vebcity-phssure co pli g T e optimization scheme
is bat d upon the work of pat of She present authors
(Tsars et al , 1 998; Tsars et al , 1 999; Tsars et al,
2000) wherem ttnl.er hull forms w re optimized for
minim m Viscous hsistace md delivered hors
pow r The module is general m formulation, md
basically independent fiom basic flow solver, eg,
different RANS solver or inviscid-pa I method em
be used with srbibsry combi ttion of con treats md
objective f motion to be minimi:D:d in the 1311 OWE g,
m overview is fig en of the present m merical medhod
md Insults ah pret nted for flow- md wave field
optimization of Mae combstmt Model 5415 hull
fomm
COMPUTATIONAL METHOD
tANS Equation Solver
The primary RANS equation solver in She prese t
st dy is CFDSH P-IOWA version 3 02 A overview
of She m merical medhod is given in the following T e
non-d imens tonal RAN S e quat ions for m teddy,
th ee-dimensionsl i oomph sable flow csq be w men
in Csrtesim tensor Station as
z au = 0
ace the U an, tip )t ap ~ v ~ =o
a ,~: ~ ale add ) a An
wish Vs = ~ a
,= az'az
(1)
(2)
When U.= UV V7 md U,=6U,hW) are the t: anew an
components of m m md fl qtustmg velocities,
re pectively, normalized by She refed he velocity U=,
Z =~xy.z) the dimensionless coordinates norm ah zed by
a characteristic length l, f She piezometric PhSSme
OCR for page 245
normali:D:d by pU~2, R = Ul/v R y olds n mber, md
,~ R y olds tresses normali:D:dby U~2 in fhis tudy,
R y olds tresses are gi p by psmg Bzldwinlomax
tp bplep e model vBaldwm md Lomax,1978) Eqpations
(1) md (2) are tr msfommed mto nonorfhogopal cp ilmear
coordipates such that th comp htiopal domam fomms z
simple rect mg kr parallel-piped wifh eqpal spamg 7 he
t msformation is partial op sip it mvolves the
coordipates only md p t the velocity compop nts 7he
h msformation is apomplished th o gh fhe expression for
th divergeppe md "ch~in rple" deflnitions of th g zdient
md Lzplai m operators which ~ehte the Cartesi m
coordipates Z=(Z.hZ) to fhe m merically gep rated
non-orthogopal coordipates ¢~=~i,i,;3) ~ fhis marmer,
th govermog eqpatiom (1) md v2) c m be w itt p m the
fomm of th contmpity md tr msport eqpations zs follows:
g~d ~(b!U,)=0
~,~=, d;td;~ 2~¢d;,=R,d +s~
(3)
(4)
optimization discpssed hter, smaller n mber of g ids
is prefened in order to avoid d zmatic mcrease of
computatiorul effort See Wilson et zl (1998) for
more details of fhe present computatiopal g id
Dp i g the optimization, the g id is pdated zt
eve y optimization cy le zs fhe hpil form is modffied
7bis is apomp lished by the pse of zigebp~ic sch me to
ip ease the computatiorul efficiency 7 he method is
described m fhe followi g After initial g id is
gep mted, th geometrical i fommation is computed
md stored in fhe memory, that is zs follows:
p = P(;',;~.~3)
Q = Q(;',;~.~3)
R = R (;, ~ . ~ )
(5)
whe~e P. Q. R are g id cipstermg md shetchi g
fp tion deflp d in (~i,¢3,;3) di ections, re pectively
Also, g id points are zLeady deflp d m computatiopal
coordipates, i e,
7he h m port eqpations (4) are reduped to zig braic form z =z(~ ~ ~ ;3)
though fhe p e of fhe higher-order ppwmd dffferep y=y(~ ;z ;3)
method 7be eqpations are solved p ing z projection z=z(~ ;z ;3)
method for velocity-p~esspre coppimg, md the medhod of
Imes For teady-flow zpplication, time serves zs z
conwxgep e parameter md the g id is ppdated zt eah
time tep to co fomm to both th body md free smfaes,
whe~e exat nonlipear kmematic md zpproximate z=z(;'1;3)
dypamic fiee-smfa bopmdary conditions are imposed Y=Y(; ,I,; )
See Pzterson et zl, (1998) md Wilson et zl (1998) for ~ 3
more details of 6he present RANS code z = z(; .1.; )
md hpil sp fae is expressed zs
Comp htiopal Grids
7he present body-fltted, sh petmed, mpitiblock g ids
are geperated psing commercial gid gep mtion code z=z(~i ;z ;3'
GR DGEN fiom Pomtwise, ~c For zpplicationto Model y =y(~ ~ ~ ;3,
5415, patched mpitiblock g ids md bopmdary conditions ~ ~ 3
arepsed Gidcipstermgcmbedop asforotherhpils, z=z(; ,~,,~.; )
e g, Series 60 or Wigley hpil, how ver, different topology
is req ired especially for tra som in 6his p~se, z separate
block is pla d in the trasom wake Fig 2 show partial
views of the present computatiopal g ids for Model 5415
Inthe p~esent st dy, Sblockg id sy tem is psed Npmbers
of 6he g ids me zs follows: for forebody ppper block,
104 25 21 (longit dipal, radial, md gi 6hwise di ections,
re pectively); for forebody low r block, 104 25x30; for
afterbody ppper block, 47 25 21; for zfterbody low r
block 47 25x30; mdtpmsomwakeblock,30 25 21;ie,
total number is 208,275 7bis g id is rektively coarse;
how wx, s fficient acuprcy in hends of sol tiom, eg,
resi tance, is zssp cd m th precp so y work ~ fat, for
3
(6)
(7)
On the odher h md, 6he o pter b opmdary i s gi p by
(8)
In the optimization procedp e, 6he hpil smfae is
modifled but oth r computatiorul bopmdaries, heppe
zilg idpomtsare~elocatedusmgP, Q. mdRwhendhe
sp fae is modffied Alhopfh 6his is dop by iterative
marmer, which p pally cop rges wi6hin 100 iteratiom,
the CPU time ~equi~ed is mpch less 6 m 6~t for
origipalg idgeperation Qpalityofg idisp arlyeqpal
to that of 6he origipal, md zppears to be zpplip~ble to
ch mg s m hpil sp fae occp s in th p~esent
optimizations
OCR for page 246
UncertamtvAsses ment
A16hough C D mmertainty ssses ment is not w 11
deflned for optimization method, i formstion for th
present RANS code must be pro ided C D unce tsmty
sssessme t consists of doc mentation, v rfficstion, md
validstion A ov vi w of v rfficstion md validstion for
th primary RANS code m the p~esent study is giv n in the
followmg
Simoktion uncertainty is divided i to two
components, one from m merics Uv md the odher fiom
modelmg USM The mmerical uncetsmty in th
simohtion m be sssessed usi g v rfficstion (Stern et sl,
1999) Therem Uv is estimsted for bodh pomt md
i teg sl q mtities md is based upon g id md parsmeh ic
st dies which determine g id USG, iterstiv Us~; md
time- tep Usy uncertsinties A root s m square ~SS)
spprosch is used to combine the compone ts md to
calcohte U~v, ie, UV=USG +Usr+Usr C D
validstion follows 6he method of Col m m md Stem
(1997), m which s new spprosch is dev loped whe~e
uncertsinties from both the simoktion (Us) md EFD
benchmark dsts (UD) me considered Th flrst tep is to
calcohte 6he comparison error E which is defmed ss the
difference betw en 6he dsts D (benchmark) md th
simohtion prediction wi6h S. i e, E=D S The validstion
uncertsinty Uy is deflned ss 6he comb instion of UD md th
portion of th uncertsinties in 6he C D simoktion thst are
due to m merics U v md which c m be estimsted 6 ough
v riflcstion srurly is, ie, Uy = UD +UV UY sets the
level st which the validstion cm be schiev d The
criterion for validstion is 6~t El must be less thm Uy
Note 6~t for m srurlytical benchmark, UD is vmo md Uy is
equal to Us', Vslidstion is critical for msking
improv ments md or comparisons of different models
smce U v is buried in Uy A detsiled example of th
v riflcstion procedure for computation of fiee-smface
flow is provided m thee md Stern (1998)
A16houghv rfficstion mdvalidstionresultsfor tesdy
DTM R 5415 simohtion hav not been fully completed for
C DSE P-IOWA v rsion 3 02, s status report for version
2 1 is prese ted md discussed in Psterson et sl, 1 998)
As m example for spplicstion to 6he practical hull fomm,
remits for Series60 Cs=0 6 hull are avaihtle for th
present tANS code in Wilson et sl, (1998), wh re g id
convergence wss st died by performing tesdy
simohtions using th ee computatiom~l g ids wi6h
reflnement, =47 m esch coordinate di ection Iterstiv
uncertsinty Us~ was ssse s se d 6 ough emm irurti on of th
iterstion ~ecord of mteg sl md point q mtities md wss
taken ss one-half th r mge of the q mtity of intere t once Subject to:
imtisl t msients had died out Th~t is 6he prefen cd meh ic
bee mse Usc c m be di~ectly evaluated Finslly, it is stated
in Wilson et sl (1998) th~t Uv for total ~esi tance
coefficie t is equal to Us~ Us~ +Usc) =
4
6052+652~°~= 65% for 6he gid whose dff~sity is
similar to 6~t of the p~esent study
Nonlinear Optimization Probl m
A general expression of 6he optimization problem
is as follows:
Mm: F( q)
Subject to:
G,(~) = 0 8,(~) ~ 0
G2(~)=0 1~(~)~0
G. (~) = 0 14(~) ~ O
(9)
(I O)
whe~e 5 =~b.~. pt) ~e desigm p~ameters, F
objectiv f mction to be mimmived, GbG~ Gp
equa lity con trsint functions, md H~,H:, H. mequa lity
conshamt f mctions
Th desigm parsmeters are used to express body
geomeby, i e, 6he solutions of the optimization
problem The objectiv fi:mtion giv s s value to be
minimi:D:d, e g, viscous resistmce Equality md
inequality conshamts limit 6he chmge of values. e g,
di placement or maxim m depth, etc ~ the p~ese t
st dy, desigm p~meters me used to defme
modiflcstion function, 6he objectiv fmction is
specffic value of flow or wa~ field, mddhe equality or
inequality comt~ai ts me imposed such thst th
di placement of modifledhull is equal to or larger 6 m
thst of th originsl Also, value of flow such ss lif or
d sg cm be used m equality or mequality con t~aint
Th present problem is nonlmear, since F, G, md H
are nonlinear fmctions of d Hence, s nonlinear
prog ammmg slgorithm must be inhoduced to solv
the p~esent problem
Nonlinear Prog ammmg Algori6 m
In the p~esent st dy, equations (9) md (10) are
solv d by successiv quad stic prog smming (SQP)
slgori6 m, in which th equations are spproximsted m
quad stic form such thst
Mm:
(I 1)
OCR for page 247
Gt(f3)+VGt(yd)71=0
(f = 1,L, p)
(f=1,L, 2)
(12)
when, 2 =(d,,,db df) is direction fctor, fmd B
z ppro imate Hessifm matri of th Lzg fmgifm in eah
optimization cy le (n), optim m 2 is obtzmed so zs to
mimmiyf F. fmd f3 pdated by fd~=f3~+ 2 in th
preYmt st dy, the derivati f terms in equations (11) ad
(12) fue evaluated by th Y>cond-order f mt~al fmite
diff` ence scheme
P:ut of fhe prese t athors compareyd fhe conwfrgence
chfuatf i tics of SQP with fo~t of the Y cessi f Imefu
prog z mm mg (SLP), which is based on extension of zfhne
scali g interior medhod fTzhY:~ fmd Himeno, 1998)
th work, the NACA00 12 wing section was optimi Y,d so
zs to maximiY, lif-to-dag ratio (=I/D, ie, I/D is
mimmiY>d) zt z fi cd incidence fmgie of 50, with th
con tramt mch that the cross-Y>ctiom~l fue of modffied
section is fme zs fo~t of th original The rffme RANS
equation sol u, geomet y modffication function, ad
comp rtational g id w ue efd Se Tahanr fmd Himf o
(1998) for mon, details Fig3 shows compfairon of
convergence history of objecti f f mction ( I/D), when
firstf conwfrgence for SQP is cle Iy indicated
In fhe precursory work (Taharz et zl 31998; Tahanr et
zl~l999;T~huzetal,2000),fheSQPtugorithmhtfdben
z pplied to mon~ pratical problem for ship desig ~ when~
tmker stern fomm wm; successf lly optimiY>d for
mimmi rtion of visco u resi tfm f fmd deli mfd horse
pow u ~ th work, how f u, it ziso z ppefued that I:ug
comp rtatiom~l cost is curre tly z major isrury Th~t is
mai fy due to z fat that, for f m optimization cy le. zt lest
2k+1 time comp rtations of F. i e ~ exec rtion of RANS
sol u, fue req ired for eval rtiom of terms in equations
(11) fmd (12), where tANS sol u was initirted wifh
diff` ent f3 ~ ie, f3~ =f f~+f~ f~, ff), f3: =
f b p. +f . f ), f3 f b~. ~+f f, f f f ~ f . ~. f ),
y3,.: f b~ f . f ), y3:, =f b~. ~ f ,, md f3: ~ =f f~.
ff),wheref isz-priorigi m foite-differf estep
In fhe prese t st fdy, con~futionai SQP zlgorif m
hz f bef modffied fmd e tended for pfufulel comp rting
in order to o ncome fhe isrury rehted to h ge CPU time
Fig4 ill rshates fhe differe~e of SQP tuchitectun,
betwyen the prese t pfm~llel fmd fhe conwyntiorurl serial
comp rtatiom For the fommer case, processor 0 conhols
o utul SQP procedun>,imd processors I th o gh m
(=2k+1) simfitmeorsly execrte CF f medhod, ie,
evaluationof,jf3)inthefgure Th pfuallelfuchitf tun,
offers zdvfmtage ow~r the serial fuchitecture for
consideraly higher comp htiork~l efhciency, ie,
comp rtatiom~l speed of the former is nefu Iy m times fzYer
th m 6~t of th ktter, since most of CPU time is e d
for CF f method, fmd comm mication o uh zd
betwen 6he processors is q 6te small Fmthemmon>,
comp rtmionai speed for SQP in pfm~llel fuchitectun
does not depend on n mber of desig pfuameters
In the present zpplication of SQP, 6he pfuallel
comp rtmion zigorithm was implemented zs fm
indepf dent mod rle, i e ~ 6he optimization method is
basically independent fiom basic flow solw~r, eg,
diffenmt RANS sol u or inviscid-pa fl method f m
be ued with fubiL:uy combi rtion of conxramts fmd
objecti f f mction to be minimiY>d, that h~s ben
demonshatedasshow inth presentremitsdescobed
hter
H fl Fomm Modifcation Function
Choice of h ril-fomm modifcation f mction is
import mt in optimization, becfmY the f mction m rst
hz f Yfhcient expressi meyss for derinfd h ril
modifcation in the preYnt st dy, z 6-pYzmetf
fi :mtion, which is de f loped m the pnfcurrory work by
Taharz et zl (1998) is ued Consider z ship fxryd m
the miform onset flow U~ zs depicted m Fig I TYke
the C:uterum coordinate sy tem with 6he origm on th
WZtf pifm f, Z fmdy fu~>r on 6he hori ontal pkme, fmd z
zxis din ted f tically rpwfud, where z=0 fmd I O
cornfspond to AP fmd FP, reYf ti fly Hence, for
e fmple~ t ms use modffication is defmedY follows
Y x.Z) = yO(~,Z)B(~,Z)
(1 3)
where, yo~z,z) is 6he original h ril Ynfae defnefd m
longitfdim~lfmdw~rticalcoordi rtes~z,z) Inthisform,
depthwise modffication of 6he flat bottom is not
considered B(zz) is 6he modffication function to
provide t msw~rse-dinfctiom~l expfmrion fmd
reduction rmtio for modif`~tion region in the rage of
Z72Z2Z, fmd Zf2Z2Z~, fmd 6~t is gi m by,
B(z,z) = ~ B, (z)sm(;r a3b3)}
|t (zg(d Zl~(~))/(zi: Zi )
lb=(Z Z~('))/(Zi(') Zi(d)
fB,(z)=f (z) fit tf~(Z)~
~B7(z)=f~(z)~it tf.(Z) ].
(14)
(1 s)
(1 6)
where, Bi~z) fmd B7(z) fue dep6hwiY fmd longit dim~l
modifcation functiom, f, ~ ~ ~ 6he desig
pfuffmeters, fmd fi, i,, f,, fn the Yime
s
OCR for page 248
i tepoktionfmctions B~(z) mdB:(z~aredeflnedmthez
coordinate md satisfy She following end conditions:
aB, PB: = 0 at ~z~ md z:
az az
(1 7)
The above m odffication fi Motion has co timmity m I st md
2nd longit dinal derivatives at th bo mdary of definition,
md She tw independe t 1-D f motions, defined m the
ve tical coordinate z, i e, B~(z) md B:(z), are capable to
provide co timmous t msverse-directiomzl exp msion md
reduction ratio varying in z z plane Note 6~t B,_B3
conhol cross sectional modification, md p6~.d6
lo fit dmnl mod It anon, e g, th longit dinal locations
of peak md bottom She Bit -) are moved forward or
backward Fig 6 shows distributions of She present 6
parameter mod It anon fixation for two combinations of
B~_B6 A cone pt of She pre ens mod It anon faction is
based on Ime modification designers do, mch that
desig ers t y to push m or pull out a control pomt of
each waterline without discontinuity of curvature at the
begm md end pm ts of modification The location of
cone ol pomts md limo mt of ch mge me miquely given by
selecting She values of if: Us
The prese t function c m essihy be applied to vertical
hull mod It anon by repkci g z by y, which is discussed
below for stern optimization, i e,
z(z'y) = zO(z'y)B(~, y)
B(z,y)=t B, y)9m(n~b )}
t2=(Z Al )/(zi Hi )
ib=(Z~'(Y) Zz'(Y))/(Zi' Pi )
JB, (Y ) = f (A )F, + + fit (Y )~
~B~(y)=f,~(y)d,~ + tf,(y)d,
(1 8)
(1 9)
(20)
(21)
where, Z6(Z.Y) is the original hull surface defmed m
lo fit dmnl md hansverse coordinates (by), B(z,y) -.
modification fmction to provide wxtical-directiorurl
exp msion md reduction ratio for mod It anon region m
th Se of z:2z2z~ md y: y -, B~(y) md B:(y)
t msverse md longit dinal modification fixations which
sati fy he following end conditions:
aB, PB:=0 at YE mdy:
By By
(22)
RESULTS
In the followi g, remits me presented for flow-
md wave field optimization of surface combat mt
Model 5415 hull form, wh re discussions are focused
on stern optimization, sonar dome optimization, md
bow optimization, all of which are related to practical
desig problem
Prior to application of th prese t method to
Model 5415 hull form optim ization, She comp tnhonal
efhciency of the present optimization module has i en
evaluated in comparison with results from th
precursory work (Tahara et al, 1998; Kitamura et al,
1997; Tahara et al, 1999), i e, Chose concern layout
optimization of 2-D t mdem hyd of oils mder flee
surface for minimization of wa~-makmg resi tance,
md stern optimization of t mker hull form for
minimization of iscous resistmce, in both of which
the conve tional serial SQP module was used The
comparison of computational speed Indicated that She
present parallel SQP module is nearly 13 times faster
thm She serial module The reset has appealed
consistent with She earlier discussion on adv midge of
the prese t method
Model 5415 Stern Optimization
Th Ist case is stern optimization for
minimization of disturbance on h msom wake field
Most rece t high- peed fme ships as w 11 as Model
5415 have transom tem m order to obtain wide
waterphne area to secure sufhcient stability The wide
t msoms tend to increase disturbance on h msom wave
field, md it remits m mcrease of hulMesistance
Th present authors md others ([wasaki et al, 1996;
Tahara et al, 1997) hod carried o t investigation on
t msom flow md wave fields using computatiom~l md
experimental models in the work, it appeared that
t msom wave field c m be clews tied as th following 3
types: (A) vifih dead water zone right after stern end;
3 I with no dead water zone, b t wave i Gel i g in near
wake region; md (C) with neith r dead water zone nor
wavebreakmginnesrwskeregion, ie,fiee surface is
smoothly contimmous from the stern end Also fihe
re mlts indicated final maller surface pressure g sdient
near fihe stern, which results in thi mer bo mdary layer
in the region, conektes wifih less disturbance on
t msom wave field h fihe present st d, averaged
surface pressme m n control area located near he stem
was used as fihe objective fi Motion to be minimi:D:d, so
that axial surLsce pressure g sdie t be Isrg r favorable
in fihe region This oh jective fimction has been show
capable for fihe present optimization problem as
discussed Inter, rasher fi m objective fimction di ectly
6
OCR for page 249
given by c value from mare field which of en oscillates
due to m teddy natme of transom flow fields, that occurs
especially for The at m e deli Ed type (A) condition
In th present optimization, the earlier discussed
parallel SQP module is used m combination wi6h c RANS
code, CFDSHIP-IOWA version 3 02 See Peterson et cl,
(1998) md Wilson et al (1998) for detailed evaluation of
accuracy in predict on of t msom flow md wave fields for
Model 5415, that had show sufhcient for application to
th prese t optimization Fig7 illustmtes the code
shuctme for the prese t problem D sigm parameters 3
modify hull surface in ve ticcl di ection by using
modiflcation fixation of equation (18) The surface
modiflcation also provides g ometriccl conshai ts as G
md H Then Did generator, RANS solver, md post
processor are exec ted to evaluate objective f motion F.
At present, only geometrical con tramts are considered in
G md H Computatiom~l conditions me as follows:
Rn=Sxl 06 md Fn=0 28; mod It anon region is given by
S S 0-2 (12 20 8) md 0 042y20; md the minim m
ve ticcl modffication ratio constraint is imposed, i e,
Bl.. :20 3
The optimi:D:d solution was obtained in 6
optimization cycles Figs 8 md 9 show comparison of
geomeby between for The original md optimi:D:d hull
fomms ~ The bodyplm show in Fig8, several S S
n mbers are indicated for reference Also in Fig 9, z
contours wi6h interval Az=0 01 me inchded for clearer
presentation of differences m tem forms Differences m
stern frame Imes are oh ions, in which maxim m
differences appear m th region between S S O 5 md I O
In the region, m i Election point, which does not exi t in
th original hull form, appears et each fmme line 7be
changes in ficme Ime curate concave surface, which is
clearly di phy d in Fig 9 for The optimi:D:d hull form
The clove mentioned ternmodiflcationshave di ect
i fluences on the flow field in the near-stern legion
Fig 10 shows comparison of surface pressure ICp)
contours in the flgure, the conhol men, where The
objective fixation is evaluated, is also indicated ~ th
area, low r pressme region is extended for the optimized
hull fomm, which is consiste t wi6h decrease of objective
f m t ion in ~ ddh i on, high pi e.. m e region appears aro md
z=0 934 near the ce ter line for the optimi:D:d hull form,
which results m larger favorable axial pressme g cdient
fiomthe~egiontowardshansom
Differences m surface pressme near the stern leads to
sigmfficmt difference in transom flow md wave fields
Fig I I shows comparison of axicl-velocity contours near
th stem et cente phone Dep6h of the tem-end corner
(denoted es "A" m the flgnre for origim~l hull fomm) is
slightly smeller for th optimized hull form For the
original hull fomm, larger extent of negsrhe contours (i e,
reversed flow region) is seen near The fiee surface
including The region right after The tern end
9~ t hors earner work, The wave field is chssifled es The
(A) type, i e, The fiee surface is highly disturbed wi6h
the reversed flow in the deed water zone beneath The
flee surface 0 th otherhmd,6heoptimizedtrmsom
wave field remains The (A) type; how ver, The reversed
flow region is almost cleared except m th region very
close to The t msom wall
Abe at me d~z oiled differences in center plane
stern flow field are cow i tent wi6h Those displayed m
t msomflowmdwavefleldsshow mFigsl2 md 13,
where wave contours md axicl-velocity contours me
compared, respectively For th optimized hull form,
wave elevation is g nervily reduced et the h ~ mm, md
extent of the reversed flow region on the fi ee surface is
almost all remmed it is oh ions Fist the optimized
hull form has much less disturbance on the tr msom
wave field fi m the original hull form Also, it is
not wonhz that maxim m wave elevation inner warm
is fihe k ger for optimi:D:d hull form
Lastly, Fig 14 shows comparison of objective
function (Obj ), wave elevation at fihe h msom wall
(Fst, defined as fihe difference in z coordinate betw en
the wave contact pomt at h msom wall centerline md
the on gm al stern~nd corner denoted as "A" m Fig I I ),
frictional resi tance coefficient Cd67, md p~e..me
resistmce coefficie t cd pa, all of which Sue for fihe
optimi:D:d hull form md show in % as compared to
thom values for fihe original hull fomm Objective
fixation md wave elevation at h msom wall Sue
reduced in aho t 30% md 60%, re pectively
Decrease in resistance coefficients Sue also men except
for fi ictionsl part, which is nearly equal to that for th
original hull form Th pres me resistance coefficient
is reduced in about 5%, md that is mainly rented to
reduction of reversed flow region m tr msom flow field
md less disturbance on wave field for th optimized
hull form The conflation betw off resistance md
t msom wave md flow fields coincides with that fo md
in z thors' earlier work 7waqki et al ,1996; Tstsrs et
91, 1997)
Model 5415 Sonar Dome Optimization
Th 2nd case is sonar dome optimization Flow
near he hull saner dome junction mvolves sigmffic mt
longitudinal vortices, which usually r mains even m
stern flow region at the operation peed in fihe present
st d, fihe afterbody of sonar dome is optimi:D:d so as
to minimize the vo ti es, wheee mad it de of averaged
axial vorticity (me) m Control area located at x=0 125
is used as fihe objective f men on to be minimi:D:d
At prese t, the optimization was done for Fn=0
condition, md fihe results w re verified for Fn=0 28
condition md used m the followi g discussion Note
7
OCR for page 250
th~t 6he overall hends m sol tiom have zppeared same
between for 6he two conditions, zlthough 6he magmt de of
~ is gep rally larger for Fn=0 28 condition
CF SE P-lowz version 3 02 was psed zs RANS solwx
7he code st petpre for 6he p~esent problem, in which 6he
parallel SQP module is mcinded, is basically same zs 6~t
for the pre iops case, i e, tem optimizatiop Eqpation
(13) is psed for sufae modffication, ie, only
modifcation m tpmswxse di ection is comide~ed 7be
modifcation ~egion covers mo t of afterbody md part of
forebody of sopar dome, md part of sopar-dome hpil
jp ption, i e, 0 12 20 01 md -0 042; ad
eqpal-or-larger volume comtp~int is imposed
Comp htiopal Rn based on ship le gth is Sxl 06
7he optimi:D:d solption was obtaip d in 5
optimizationcycles Figs 15 ad 16 showcomparison of
sopar dome geomeby betwen for the origipal ad
optimi:D:d forms, md Fig 17 comparison of smfae
pressp e (Cp) contop s md fiictional st~eamimes in
Fig 16, y co top s with i terval Ay 0 002 me ziso showp
in order to clearly prese t diffe~ep es in 6he g ometry
7he modffication of th dome is mamly seen m the
p ar-tail ~egion, in which the cross s ptiopal arez is
ippreased mostly for ppper hzff of th dome 7be
optimi:D:d sopar dome has slightly k ger volume 6 m the
origirul 7he shape modifcation cmses th larger low
pressp e arez on 6he dome aropmd z=0 9, which leads to
obviop differep es in the th ee-dimensiopal separation
patterm disphyed mfiictiorul sheamlip s
Figl8 provides comparison of `4 contop s zt th
conhol section betw p for 6he origipal md optimied
fomms 7he conhol arez to evalpate objective fp tion is
ziso indicated in 6he figp e ~ the present optimization
dop forFn=0 condition, 6he objective fp tion is redp d
aropmd 10%, whereas 6he valp evalpated for Fn=0 28
respits is reduped aropmd 35% it is showp in the figp e
th~t th vortices for optimi:D:d form are more diffpsed, a d
th maximum ~4 magmit de is clearly ~eduped it mpst be
noted 6~t wave profiles on the hpil are p arly same
betw en for 6he origipal md optimi:D:d forms, that maybe
dp to z fat 6~t g ometrical chmges occup ed m the
present optimization are rehtively small md th locations
are zt considembly k ge depth Altho gh the present
opt im iza ti on medho d ppce s fully re duped 6he j p pt ion
vortices, fmther extemion of the modifcation fp ption,
md mcipsion of wa~ effects in the optimization process
are of mte~est, both of which are issp s for f tp e work md
partly in prog ess
Model 5415 Bow Optimization
Finally, the 3rd case is bow optimization for
mimmization of bow wave For Model 5415 zt moderate
md high Fn, sigpatp e in wave field is remarkable
esp pially m the region p ar th bow, where wa~ rises
rapidly md shape of the mest is teep ~ the prese t
st dy, the parallel SQP module was aplied to
minimi:D: 6he bow wa~, m combipation wi6h 3-D
nonlip ar panel medhod developed by the zpthor
(Taharz, 1997; Taharz, 1998), 6hen the ~espits were
verffied by psmg z RANS solver, CFDSE P-lowz
version 3 02, m both of which Fn=0 28 condition was
considered Fig 19 shows the code t petpre for 6he
present optimization problem Desigm p~metersp
modifyhpil surfae m h msverse di ectionby eqpation
(13), where 6he modffication ~egion is S S 8-10
(O 22 20) md z2-0 35 Only z geometrical comtp~int
is imposed, i e, displaement of the optimized hpil is
eqpal to or larger th m 6~t of th origipal hpil
As showp in the zp6hor's earlier work Taharz,
1997; Taharz, 1998), which ippinded comparison of
Imear md nonlipear theories to predict bow wave, 6he
Imear theory gep p~lly pmder p~edicts 6he wave
elevation p ar th bow A nonlip ar panel medhod
developed in 6he work was showp capable for
prediction of 6he wa~ f eld aropmd bipmt pose body as
w 11 as comme pial ships opemted zt high Fn, 6~t had
been acomplish d by mtroduption of 6he O-type
f~ee-surfae panels md nonimear fre-sp fae
bopmdary conditions
A16hough CFDSE P-IOWA version 3 02 cm be
psed for prediction of bow wa~, the panel method was
psed in 6he present optimization, m which evalpation
of capability of 6he present optimization module was
somewhat more focp ed, md zt present lower
computatiorul effort was preferred Th ~espits w ~e
verffied by psmg CFDSE P-IOWA version 3 02, md
presented m 6he followmg discpssiop Npmbers of
panels psed in 6he comp tation are 1600 md 2000 for
hpil md flee surfaes, re pectively, 6~t had be p
fopmd optimum based on panelization dependep y
te ts
Figs20 md21 showcomputedwa~contop s md
profile for 6he origirul hull, re p ptively, by psmg 6he
present nonimear panel method In Fig21, th
experimental datz are ziso mcinded for comparison
Th p~esent ~espits mdicate considerably good
zg ement with 6he measurements especially for
elevation of bow wave crest, on which focps of th
present study is mainly plaed It mpst be noticed that
prediction of 6he tpmsom wave fleld is not satisfatory,
which is mainly dp to 6he limitation of th
in iscid-flow zpproah This leads to m impo tmt
cop Ipsion that, for optimization of h msom flow md
wave fields, RANS solver mp t be psed zs
demonshated m the present work ad discpssed in 6he
earlier sectiop O 6he odher hmd, the present panel
method has ben judged capable for 6he mitial
validation of p~esent optimization medhod zs far as
8
OCR for page 251
fixation F is taken to be maxim m elevation of The bow
wave crest in The computed wave prod le
The opnrmzed solution was obtained in 7
optimization cycles Figs 22 md 23 show comparison of
geomeh y between for the original md optimized bow ~
Fig23, x contours with interval A~=0 01 are show in
order to clarify differences m geometry Wave profile
evaluated by The present panel medhod for The optimized
bow is also included in Fig 21 Betw en for the two bows,
bore region, ie, maxim m elevation of The bow
wave me t is reduced aro md 20 % for The optimi:D:d bow
The mod to anon Sends in bow shape have been show
remarkable, e g, c ditch line is created m The mid-gi th
region, that may not commonly be predicted by th
conve tiom~l hull form desig
As The clove mentioned, the present optimized
remits w re verified by using RANS code, ie,
CF SO P-lowc version 3 02 for Fn=0 28 md Rn=Sxl 06
condition See Peterson et cl, (1998) md Wilson et cl
(1998) for accuracy of The RANS code m prediction of
bowwavefeldforth p~esentshipmodel Figs24 md25
show comparison of bow mare elevation, md wave
contours near th bow, respectively Altho gh maxim m
wave elevation for the original bow was somewhat alder
predicted due to The restively coarse distribution of th
present computational g id m radial di ection, The same
Sends of results es Those discussed clove are indicated,
i e, for optimized bow, elevation of th bow wan ore t is
reduced, which is clearly show in wave contours es w 11
es profiles The reduction of bow wave is somewhat
smeller 6 m that predicted by The prese t nonlinear panel
method, ie, Croat 15% m RANS solutions The RANS
remits indicated that, although not show m The fgme,
restively smell i duences of bow wave red i non are seen
on afterbody wave profile, that is also hue for the results
previously show in Fig 21
Lastly, Fig 26 show comparison of optimized
solutions mcludmg i tegal values, m The similar maimer
es those used for Fig 1 4, i e, percentag presentation es
compared to values for the original bow Except for
objective f motion (Obj ), val ues me for s eritl ed re mlts by
usingRANSsolver in the toggle, Fmax v is elevationof
bow wave crest, which hr. been reduced clout 15% es
mentioned ah me 0 th othrhmd,fiictional~esitance
coefficie t Cd67 hr. slightly Screwed, but that is less th m
1% Pressure resi tance coefhcient cd(p) hr. clearly
decreased, i e, that is clout 6 5%, which is consi tent with
th low r wave mcki g resist mce for low r bow mare
crest
The ctove-discussed results hose show that th
present method is very prom ~ Beg, md flasher verif cation
of the results 6 ough model tests is of g eat mte~est On
the oth r h Ed, it is also of i terest to replace The panel
method by CFDSH P-lowc version 3 02, since The
tANS solver is more comprehensive, m which viscous
Ed wave mslrmg effects me cow idered m The Theory,
Ed capable for accurate prediction of resi tance es
w 11 es flow e pecially for hull forms with tr msom
stern ~ addition, flasher mvestigstion mu t be done
on the medhod to modify The bow chap All of The
clove me issues for f tore work, Ed m part, curre fly
m prom ess
SUMMARY AND CONCLUSIONS
his paper concerns flow- Ed ss3se field
optimization of surface combat mts using CFDbased
optimization method 7be mom focus is placed on
development of c high pe fommance optimization
module for application to Model 5415 hull form
optimization, which is capable m combination with
CFDSH P-IOWA Version 3 02 She optimization
sch me is based upon fihe work of part of fihe present
authors wherein tsrD.er hull forms w me optimized for
fommulstion, md basically mdependent fiom basic
flow solver, e A, different RANS solver or
iniscid-panel method cm be used wish srbibsry
combination of con Faints md oh jective fi motion to be
minimi:md
In 6 is paper, m owxvi w is given for fihe prese t
primary RANS equation solver, computational g ids,
once tsmty awes me t for th RANS code, g neral
nonlmesr optimization problem, 9 high pe fommance
nonlinear pr on am m mg Vigor id m, md th 6 parameter
hull form modfficstion fimction he remits Sue
presented for flow- md wave field optimization of
surface combatmt Model 5415 hull form, where
discussions are made on tem optimization, sonar
dome optimization, md boss optimization, 911 of which
are related to practical desigm problem
Prior to application of th prese t method to
Model 5415 hull form, fihe computational efficiency of
the present optimization module hr. been evaluated m
comparison with resees from fihe precurso y work
Ibe resuRs show that the present parallel SQP
srchtecture offers sdvmtage over fihe conventional
serial SQP srchitectme for comiderstly higher
computational efficiency, i e, computational speed of
the former is nearly m (=2k+1: k is m mber of design
parameters) times faster thm final of fihe latter
Furfiherm ore, moth r sdv mtage of the pi e sent psral lel
SQP srchtectme is mch that fihe comp tuitional peed
does not depend on n mber of desigm parameters
First, resees for Model 5415 stern optimization
for mimmization of disturbance on h msom wave field
w re discussed he resees indicate that the prese t
9
OCR for page 252
method successfully reduced reversed flow region in
t msom flow field, which relates to less disturbance on
t msom wave field for optimi:D:d tem thm that for th
original A concave surface has cppemed in optimized
stern, which results m larger favorable axial surface
pressure g cdie t m She region Th ough evaluation of th
results, it hr. been show that She conektion of tem
modiflcation md flow es w 11 es i ted cl parameters
coincides with Nat fo md m the c thors' earlier work,
which concerns experimental md computational st dies
on t msom stern flow Ed wave fields
Next, R mlts for Model 5415 sonar dome
optimization were discussed, m which minimization of
hull/sonar-dome junction vortices was considered in the
present remits, mod It anon of She dome is mainly done
near the tail end, m which the cross sectional area Ed
vol me are increased mo fly for upper huff of the dome
Although modiflcation of She geomet y is restively mall
md father improvement on modti anon f motion may be
req ired, optimized sonar dome hr. clearly smeller
mcgmitude of longitudinal vorticity, which relates to
reduction of junction vortices
Finally, results for Model 5415 bow optimization
w re presented md discussed ~ She optimization,
mimmization of elevation of the bow wave ore t was
considered he differences m wave profile between for
th original md th present optimized bows me clearly
seen m the region near She bow, i e, th elevation of bow
wave Rest is oh iously decreased in She optimized results
he m od to anon Sends are notable, i e, c ditch line hr.
cppemed m She mid-gi ah legion, that may not commonly
be predicted by the conventional hull form desigm
In conclusion, the prese t method hr. cppemed very
promising, md will be practical design tool for flow md
wave-field optimization of surface combatants though
forth r improvement md evaluation of th metho d f ough
comparison of the re mlts with experiments mpo t mtly,
one of the major issues for former CFDbased
optimization methods hr3 been overcome by the present
high performance optimization module
In addition to issues Ed extension plums of mte~est
mentioned m She discussions, inclusion of propeller effects,
consideration of unsteady ship motion, md extensions of
CFD method for f 11-sccle Rn are also of mte~est, some of
which are Greedy in prod ess
ACKNOWLEDGEMENrS
his research was sponsored by the Office of Naval
R search g mt n mber N00014 99-1-0232 alder th
cdmimsh ation of D E P. Rood who se support is g ectly
appreciated Th Department of Defense
High-Perfommance Computing Modemization l Nice
HPCMO) md the Naval Dab mod cphic Office NAVO)
10
provided computing resources alder th mspices of
the DoD Challenge Prog cm
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"CFD-Aided Optimization of TarDcer Stem Form
(I st R port) - Mmimization of Viscous R sistmce
-," J. Kensei Society of Na~I Architects, No 231,
1999, pp 29-36 [Japanese]
Tahare, Y. Seitoh, Y. Met myame, H. md
Himeno, Y. "CFD-Aided Optimization of TarDcer
Stem Fomm (2nd R port) - Mimmization of
Delivered Horse Pow r -," J. Kensei Society of
Na~l A chitects, No 232, 1999, pp 9-17
[Jepenese]
Tahare, Y. Nishida, R. A do, J. md Himeno Y.
"CFD-Aided Optimization of TarDcer Stem Form
(3rd R port) - Mmimization of D live~ed Horse
Pow r Usmg Self-Propulsion Simulator -," to
eppear J. KmseiSocietyofNa~lAchitects, No
234,2000 [Jepenese]
Tahare, Y. md Himeno Y. "A St dy on Form
Optimization Problem Besed on CFD for
Two-Dimensiom~l Wmg Section," J. Kmsei
Society of Na~al A chitects, No 229, 1998, pp
27-35 [Jepenese]
Tahare, Y. Himeno, Y. md Ts~catera, T. "A
Application of Computatiom~l Fl id Dynamics to
Tarlcer Hull Fomm Optimization Problem,"
Proceedmgs 3~3 Osake Colloq i m on Advanced
CFD Applications to Ship Flow md Hull Form
Desigm, Osake, Jepm, Mey 25-27, 1998, pp
515-531
Tahare, Y. md Iwasaki, Y. "A Study of
T msom-Stern F'ee-Surfaee Flows by 2-D
Comp tatiorurl md E perimental Models," J.
K msei S ociety of Na~al Architects, No 227,1997,
pp 7-19 [Jepenese]; elso, Proceedi gs of 6he 2nd
Co fe~enee for New Ship & Marine Techmology
into 21 t C ntury, Hong Kong, June 1998,
pp 83-92 [E glish]
Tahare, Y. "A N mericel Approeeh for Steedy
Ship-Wa~e Problem Besed on Dewso~Type
RsrDcme-Somee Medhod wi6h Non-H-Type-
Topology F'ee-Smfaee Penels - I st R port: with
11
OCR for page 254
Mcm Emphcsis on Application of O-Type- Topology
-," J. Ksmsci Society of Ncval A chitects, No 228,
1997, pp 79-90 [hpcnese]
Taharc, Y. "A N mericcl Approah for Stecdy
Ship-Wave Problem Bcsed on Dcwson-Type
RsrDcme-S ource Medhod wifh Non-H-Type- Topology
Free-Surfae Pcnels - 2nd Repo t: Application to
Bl mt-Nose Body md Nonlinear Free-Surfae
Bo mdary Conditions -," J. Ksmsci Society of Naval
A chitects, No 230,1998, pp 147-152 [Jcpcnese]
Webster, J. md Mut ick, I, " Futme Surfae
Combatmt," Proceedmgs 25'6 ATTC Co ference,
lowc City, A, September, 1998
Wilson, R. Peterson, E, ad Stern, F. "IJn tecdy
RANS Simuhtion of Model 5415 m Waves,"
Proceedmgs of fhe 22nd Symposi m on Naval
Hydodynamics, Wcshmgton DC, Aug t 1998,
pp 532-549
Zhu, ZW, md Chm, YY, "A New Genetic
Algorif m for Aerodynamic Desig Bcsed on
Geometric Concept," A AA-98-2900,1998
12
OCR for page 255
Fig.2 Overview of body surface and computational
grid for Model 5415: rows, body surface, near the bow
view, and near the stern view, respectively.
22~
21 t
20g
19
13
1 7
it,,
,, ~
16 _ j
I:
~ L/D ~
SQP SLP
A.
Sol. converged
\
, ,,
\, /
10 20 30 40 50
Optimization cycle
Fig.3 Comparison of convergence history of objective
function between for SLP and SQP optimization
algorithms (Tahara and Himeno, 19984.
._
~ ( ~1 )
FEW
~E~
~ ~ ~ '_
IN PA ,
Con
Fig.4 Comparison of serial and parallel
computation architectures for SQP algorithm:
rows, serial architecture, and parallel architecture,
respectively.
Fig.5 Definition of coordinate system.
z 0~~ 0~7 0 75R1=_1 R2 - 0 R~3=1
n next 0.65 RA=1 RS=1 RA=1
z 0 ~1= - 1 R~2=0 Rag= 1
-0.05~ 0.65 ~R4=4 R5 - - 2 R~6=1
Fig.6 The present 6 parameter modification
function.
OCR for page 256
-
t Initial
SOP
1
~ ~ - Optimized ~
Fig.7 Illustration of code structure: Model 5415 stern
and sonar dome optimizations.
n no
Anne
-o.o~
n no
— ,, --
_ ,,, --
_ _ _
2 1.`
, ,.
_ _
_ _
_—
S.S.
1 0.-
iginal
Optimized
0.~_
Fig.8 Comparison of stern geometry between for the
original and optimized hull forms: Model 5415 stern
optimization (minimization of pressure rise at stern
end with displacement constraint).
NG]
G,0
Grid Generation
| CFDSHip-lOwA ~ ~^
Original
Optimized
Fig.9 Comparison of stern shape between for the
original and optimized hull forms: Model 5415
stern optimization.
., . _
- O
: it- ,/ ~
Control area
I ,/
~ Original
0.8 0.85
~1
, ~ ,, ,/ ~
lo
l
0.9 0.95 1
X
, ., ·, ,~
___-
·':
Control area
Optimized
0.8 0.85 0.9 0.95 1 X
Fig.10 Comparison of surface pressure (Cp)
contours near the stern between for the original
and optimized hull forms: Model 5415 stern
optimization.
OCR for page 257
Ln
c
0 (u) Original
~ c
N
N
,:~
Stern end / ~ 0.~ -
~ ~~ 0 _- ~~
0 6- - -----
0.99 0.995 x1 1.005 1.01
- (u) Original ~
_ -I— - 0.9----
_ .
=- ~~ ~-0.8
-I ~ I--- o 3 0 4 ----a
\ \ O I.
V\ '\\~ ''''"-\ ''''''''\
1i ' \
1 1.0X25 1.05
-
(u) Optimizaed
Stern end
c
0 _
0.99 0.995 x1 1.005 1.01
Fig. 11 Comparison of axial-velocity contours near the
stern at center plane between for the original and
optimized hull forms: Model 5415 stern optimization.
~ (Z) Original /
0 =
-
,.
1 025 1 05
,~
it,
(u) Optimized
-= = ~ it. ~ ~~ ~ /
I\ -A - hi=
I '' - :-:- ' '
~ - ~ - ---- o.4
~ ~ -
~ hi ; 0.1
0.8
O.S .
1 1.0X25 1.05
Fig. 13 Comparison of axial-velocity contours near
the stern on the free surface between for the
original and optimized hull forms: Model 5415
stern optimization.
- (z-) Optimized ~ / (
~ ~~ :~ ~~~
lo
O ~ ~ ! ~ ~ ~ ~ ~
1 1.025 1.05
x
Fig.12 Comparison of wave contours near the stern
between for the original and optimized hull forms:
Model 5415 stern optimization.
TO signal
0 20 40 60 80 100
I Fit
Cd~
Cd¢)
Fig.14 Objective function (Obj.), stern-end wave
elevation (Fst.), and frictional (Cd~f)) and pressure
(Cd~p)) resistance coefficients for optimized
results as compared to the original values: Model
5415 stern optimization.
OCR for page 258
o ~
-0 01
-0 02
-0 03
N
-0 04
~.~
-0 06
1L
10 c
A, 0 0 1 _
-nn1
-n no
n no
-n no
n no
-0 07—
, ~ ~
~ a:
Ori~nai
Optimized
Fig.15 Comparison of sonar dome geometry between
for the original and optimized hull forms: Model 5415
sonar dome optimization (minimization of averaged
at x=O. 125 section with displacement constraint).
Fig.16 Comparison of sonar dome shape between for
the original and optimized hull forms: Model 5415
sonar dome optimization.
0~
CM
a
a
O.
L
, , _,
0 005 X 0.1
Control
section
l
0.15
_ 4~ Control
~ = Optimized section
0 0 05 X 0.1 0.15
Fig.17 Comparison of surface pressure (Cp)
contours and frictional streamlines near the bow
between for the original and optimized hull forms:
Model 5415 sonar dome optimization.
Control area
/
Original
X=0.1 25
0.02 0~04y 0.06 0.08
~.~.~ = ---
Control area
of
c
Optimized
X=0.1 25
0 0.02 0~04y 0.06 0.08
Fig. 18 Comparison of ~ contours at control
section between for the original and optimized hull
forms: Model 5415 sonar dome optimization.
OCR for page 259
SOP
_ _
~ r
__
Surface Mode |
G,H
Panel Generation
3D Panel Method
(Cal. Free-surface Flow)
~ Post Processor
Fig.l9 Illustration of code structure: Model 5415 bow
optimization.
07s
05
02s
0.7 _
0.6 _
0.5 ~
.4 _
0.3 _
0.2
0.1
0
~ -1 -o 5 0 0 s 1 1 s 2 2 s 3
Fig.20 Panel arrangement and wave contours for the
original hull form (Fn=0.2804.
0.03
1
0.02 _
,,,,\
~ | A
N 0.01 ~
~ I
,,,--
O _
-0.01
Call-Original
Call-Optimized
. 3 EXP.-Original
,~}~~
0 0.25 0.5 0.75
X
Fig.21 Comparison of wave profiles (Fn=0.284.
O
-0.01
-0.02
N ~0 03 ~
-0.04
-0.05
-0.06
10
N 0.01 _
O tar
-0.01 _
-0.02 _
-0.03 _
-0.04 _
-0.05 _
-0.06 _
-0.07 A
-0.06
/
~::
, ,\,
,~\,
Original
Optimize _
1 1
.02
d
Fig.22 Comparison of bow geometry between for
the original and optimized hull forms: Model 5415
bow optimization (minimization of maximum
bow-wave crest with displacement constraint).
OCR for page 260
Opti mized
I ~
I !
of i ' ':
do
Fig.25 Comparison of wave contours near the bow
between for the original and optimized hull forms
(RANS solutions for verification): Model 5415
bow optimization.
Ooti mized
Fig.23 Comparison of bow shape between for the
original and optimized hull forms: Model 5415 bow
optimization.
O
O
I Original
Optimized
)
, \
,! \\
\'
I I - t I I
-0.1 0 0.1 x 0.2 0.3 0.4
Fig.24 Comparison of bow wave elevation between
for the original and optimized hull forms (RANS
solutions for verification): Model 5415 bow
optimization.
%0 r Final
0 20 40 60 80 100
Em ax
Cd~
Cd63)
Fig.26 Objective function (Obj.), maximum
bow-wave elevation (Fmax.-v.), and frictional
(Cliff)) and pressure (Cd~p)) resistance
coefficients for optimized results as compared to
the original values (Fmax.-v., Cuff), and Crisp) are
RANS solutions for verification): Model 5415
bow optimization.
OCR for page 261
DISCUSSION
H Chun
Pus m Nctiorul University, Korea
1) Which computer did you use? How long did
it take to fmish one case of optimum, for
example, the bow optimization case?
2) Usually, She hull form for bow optimization
would give m undulation (or oscillatory) water
lines shape However, your case does not
Couldyouexplcintherecson?
AUTHOR'S REPLY
1) All computations w me p rformed on c SGI
Origin 2000 sy tem, which is co figured with
256 cffthal processing units, 64 GB of
dishibuted shared memory, md 600 GB of disk
space he bow optimization case was
completed in cutout 6 hours
2) Unlike conventional commercial ships, for
which m ost previous optim i ction work ht. been
done, Mod 15415 has c very characteristic flmed
bow form with large sonar dome located near the
keel in addition, nonlinear fiee-surface effects
are signffic mt for She conditions considered
herefcre, optimization trends may be different
th m that shown in previous investigations O
the ocher hand, the present bow modification
appeared m restively limited region, i e,
midgirth region, where c ditch line had been
created As such, further investigation of the
present modification f notion is currently in
progress Firnlh, it should be emphcsi ed that
CFDbased optimization presents challenges to
the verification md validation process md that
there is c need for optimization validation data
Representative terms from entire chapter:
optimized hull
