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OCR for page 579
Large-Eddy Simulations of Turbulent Wake Flows
Shaoping Shi, Andrei Smirnov, lirrrai Celik
(West Virginia Umversity,USA)
ABSTRACT
A m meri cl medhod for solving f ee denenr offal.
time-dependent mcompress~ble Ncvier-Stokes equa-
tions using the large eddy simulation LES) is briefly
described A new r mdom flow generation technique
RFG) was used to provide She turbulent i -I w bo md-
ary con dit ions he c omb me d LES -RFG proce dare was
applied to simulate She wake of flat plate Ed c ship
model he simulations of flct-pkte wake w re vali-
dated cgamst the experimental date ~ She case of c
ship-wake (ship model 5415), recsorurble results were
obtained
1 INTRODUCTION
Most of the comprtthorLti fluid dynamics ego ts cp-
plied to -I w pa t ships are based on R ynolds-
Av raged Ncvier-Stokes tANS) equations utili ing
various turbulence models (Sotiropoulos Ed Pctel,
1995;Pctersonetcl,1996;Rctcliffe,1998) hecom-
monly used models include k—c, k—m Ed tlgebrtic
shess models tANS is often quite cd .pNe for me m
flow predictions, but pr Sides only limited i fommation
Croat turbulence characteristics Ed almost no details
onk ge-sccle mstecdyshuctmesofthefl wfleld LES
technique, on She other h Ed, was desig ed to simulate
the m teddy behavior of et least She large coherent tom -
bulent eddies here is hardly my study m She literctme
where LES is applied to -I w aro Ed ship-hulls mclud-
ing She wake he mom reason obviously lies on the
computer resource limitation which increases clmo t
exponentially wish the R y olds n mber ~ 5, the
energy conbinmg eddies of the flow are computed ex-
plicitly, while only She more univ sol (isotropic) smell
eddies me modeled hus v ry flme grids hav to be
applied m order to lesolv She bo mdary layer near the
wall where the turbulence length scales tend to Pro es
the the wall is aproahed However, m some cpplicc-
tions, like bubble dynamics modeling, it is still neces-
sary to ~esolv coherent -I w shuctmes - large turbulent
vortices Ed eddies in RANS simulations, e peciclly
those using two-equation models such es k—~ model,
these m teddy -I w fectmes me usually smeared out
he prediction of bubble population m She wake is im-
portat m controlling She signature of surface ships
Since it c m be computatiorurlly proh~bitiv to mchde
the ship hull ad the wake in LES, it would be desir-
ctle for She purposes of pure wake simulations to start
the computations somewhere m the near wake exchd-
ing the shipbody his technique, called by of her re-
searchers the Initial Deb Phne ,Ir)P) cpproah Hy-
m m, 1998; Peterson et cl, 1996; Dommermubh et cl,
1996) c m imtt oduce large errors es pointed out by Hy-
m m (1998) By applying His procedure She flow field
in the far wake m be cclcohted hen the wake com-
putation can tart form c pane m the near wake his
is similar to our aprotch in which we cell it i -I w
bo mdary instead of IDP ~ IDP method, She date re-
flects She me m flow, me m turbulence q entities Ed
the scaly ft id et 6 is plume in our cpproah, c R m-
domFl w Gererttion tFG)algorithm(Sminovetcl,
2000b; Shi et cl, 2000b) is applied to generate the in-
flow turbulence based on the i formation fiom exper-
iments or tANS cclcohtions he appropriate time
scale Ed leng h scale c m be specified for e tch point
et She i -I w bo mdary also by usmg She tANS results
In addition to that all si turbulent shear stress com-
ponents c m be giv n, thus providmg misoh opic Ed
i homo~eneor s turbulent inlet conditions he gener-
Ted v locity fluctuations satisfy in t Aqueous conti-
mmity equation, Ed the h rbr ler e statistics Hey olds
OCR for page 580
sh esses) pr scribed o prion fi om tANS or experimen-
tal re mlts Th 3s m some sense, cltho 3gh the LES starts
et c pkme behind the body, the body is still seems vi t 3-
clly to be 6here The fectmes of 6he ger mted flow-field
s3chcscontm3ity, misohopy mdi homoger itymrke
it clso w 11 s flted for settmg 6he initicl conditions for
LES The dev loping flow field is calc 3kted directly
both spaticlly md tempordlly wi6h cppropricte bo md-
aryconditions Inpartic3kr w cpply misohopic, m-
homoger o 3s, mstecdy DP condition md let 6he flow
develop according to the dyrrmics of Ncvier-Stok s
equations witho 3t for ing ~ 6his case our cpprocch
differs from that of Dommerm 36h et al (1996) in 6heir
cpprocch, 6he flow fleld was initiclized with f 11y de-
v loped isotropic, homogff~eo 3s tmb fler e HT) m-
perimposed on 6he mecsured (or cclc flcted vie RANS)
flow fleld A for ing function (or c sti rmg force) is cp- wher
plied to 6he m oment m equation to pr vide c pr scobed
turb flent dissipation rcte it seems to 3s that Dommer-
m 36h et cl's method relies too heavily on the miticliza-
tion 3sing tANS res flts Smce, in its tree sense, spaticl
development is not cclc 3kted b 3t ass med to be rekted
to tempordl developmff~t, the initicl tmb flent flow fleld
m 3 t plcy domi mt role m 6he s 3bsequent dev lopment
of 6he tmb fler e By imposing turbflent dissipation
rcte (es cclc 3kted from tANS) vie c forcmg function,
this medhod become even mor dependent on tANS
Moreov r, it is not clear ff the periodic bo mdary con-
ditions cpplied by Dommemm 36h et cl in the axial di-
rection where there is c sig ff mt fl w development is
cppropricte for fl ws in 6he r ar fleld of c ship wake
In what follows w fl st briefly describe the LES
scheme md 6he RFG clgori6hm Then we pr sent 6heir
cpplications to 6he wrke flow of c flct plate md c
ship-wrke The i fl w bo mdary of 6he wrke of flct
plate is cclc 3kted based on the experiment r s flts by
Rcmapri m, et cl (1981) Ship wake cclc fl3tions me
base d on 6he r s flts of 6he RAN S - so lv r C DSH P -
lOWA(Stern mdWilson,2000) Comparisonbetweff~
LES md experiments or tANS hav been mcde Con-
cl 3sions md r commendmg for f 3tme work are giv n
et the end
2 MATHEMATICAL / NUMERI-
CAL MODELS
2.1 Navier-Stokes Solver
tion of the gov rnmg equations md 6he SGS models
which are 3sed m 6his t 3dy The LES code we 3se was
origir~lly developedby Z mg et cl (1994) The spaticlly
flltered fl w conservation equations are I
aui =o
a~j
Ou~ _ a
at a~
ptj = q~qj _ p6~j -
T,j = U,uj —
TTj — 3 T t = —2VTSI;
o
(1)
(2)
- VaUt - T,j (3)
(4)
— Cr(lv — 3 l tJ ( )
In 6he ctove equations, uj is 6he fllter d v locity v c-
tor, p is pressure, v is the km matic viscosity md 6~; is
Kror cker delta in Eq 5 S~; is 6he resolv d rtrdin mte
tensor,
md lv is deflmed es
S l~3q~ _ au~'
'/ 2 O~j Ox
iv = utuJ — ~qJ
(6)
(7)
wher the val 3e of Cr is either O or I depending on the
type of s 3bg id-sccle(SGS) model bemg 3sed When
Cr = 0 , Eq 5 repr sent s the Smcgor insky m o de l W hff~
Cr = I it represents 6he dyrrmic ml ed model of Z mg
et cl (1993) The dyrrmic ml ed model is mor tc-
ble th m dyrrmic model Ithcs the ccpability to present
thebackscatterer rgy mdr arwallfectmes H wever,
iThe mplied smmm dbc r te mplies to repe ded indioes (i.; =
1,~,3)
OCR for page 581
it r quir s c very smell time step due to m merical m-
rtRbilit Mor over, fiom our experien e, 6his model
sh ws high dfff sion m c turbulent wake fl w when
used with r htively coarse g id
7 he originRI code hcs ccp~o ility of h mdling curvilin-
ear coordinRter but her w only use Cartesi m coordi-
nRter
As for m merics, C mk-Nicolson discretization
scheme is cpplied for diagonRI viscous md diffusive
temms for time-cdvancement while Adams-Bcshfo th
scheme was chosen for 6he other temms Spaticlly,
QUICK scheme J'onx d, 1979) or centrcl differ n -
ing(CD) scheme is cpplied to discr tize 6he cor ctive
terms C nbal differ n ing scheme is used for 6he odher
terms With QUiCK scheme, no subg id-sccle (SGS)
model is used while for centrcl dffferen mg scheme
Smogarinskymodel (Smcgormsky,1963) is mplied
Mor detciled mformation c m be fo md in Z mg, et
cl (1994; 1993) mdShietcl (2000c)
2.2 Random Flow Generation (RFG)
methodology
Here w provide c brief description of 6he medhod used
for gen rctmg 6he i flow bo mdary 7 he clgori6 m pro-
ceeds in 6he following sequen e
I Given m misohopic velocity corr htion t n-
sor(sayfrom c RANS)
r~j —U,
(8)
2 Gen rcte c trmsient flow-fleld in c th ee-
dimensional domcm jv~(x; t)}~j_l,,3 using the
modffed method of Krdich m (?)
v~(x t) = 5~[P, cos( jX; r )
—q~ sin~k; x;—mrt)] (1 l)
~j = li t = -,
\= _ j = kj~ (12)
pr = ~j ~ rlk 1 ql = c~jme jrlk I (13)
51 i I . tDr ~ N(O I ) K ~ N(O, 1/2).
where /, ~ are the length md time-scales of turbu-
lence, R~; t is the permutation tensor used in vector
product operction (Spcm, 1965), md N(M a) is c
normcldishibutionwithmemM md tmdardde-
viction a Symbo is kj. mr r present c sample of n
wa~m mber vectors md frequen ies of the mod-
eled turbulen e spech m
E(k) = 16( - )~2k4 expt—2k) (Id)
3 Apply c scaling md orthogonRI h msformations to
the flow-fleld v~ gen rcted m the pr vious step to
obtam c n w flow-fleld u~
of c turbulent fl w fleld JU~(Xj~t)},j_1..3, flmd m
or6hogonRltrm formationtensorovthatwoulddi- w~ = \~lv`~' (15)
cgonRli~ ; u~ = 0ttwt (16)
0mlarJ~t; = 3mr~ r'
0ttati = 3ti
(9)
(I O)
As c remit of this tep both o~; md kr become
k own f mctions of space
sf~ = ~ Repe ded t dexes mply smmm dbn, parectheses
arommd indexes prechde smmm dbc
7 he procedme described ctove hkes es m mput the
corr htion tensor nq of 6he originRI tmbulent flow-flied
i~(xj.tl md i formation on length- md time-scales of
turbuien e (/.~) 7 he output of 6he procedure is the
time dependent flow-fleld u~(xj.tl, which satisfles the
misotropy md i homogen ity of 6he originRI fl w-fleld
i~, i e 6he shear-str sses of the gen cted flow-fleld are
equal to nq md length- md time-sccles to / md ~ re-
spectively As was sh wn by (Smimov et cl ,2000b;
OCR for page 582
Shi et cl, 2000c), the new flow-field u~ is div rgence-
flee m case of c homogeneous tmbulence md to c high-
deg ee div rgence free for m i homogff~eous turbu-
lence By vi t e of Eq (11), paticl md t mporcl varic-
tions of u~ follow G mssi m distribution wi6h charater-
i tic length md time-sccles of / z, how v r, other dis-
tributions m be used to simulate dffferent tmbulence
spechc More details of this method cm be fo md m
Smi novet cl (2000b)
3 APPLICATIONS
he pseudo~mdom flow field genercted by the RFG
medhod is cdded to 6he mea flow to established 6he
bo mdary condition et the inlet pkme he ov cll pro-
cedme is cpplied to two sigmificmtly dffferent cases,
rumely flct plate wake md c ship model wake Since
w try to zvoid solving for the fl w aro md 6he bod-
ies, w tart the computatiorurl domcin from 6he i flow
bo mdary(initial date plane) located immedictely cfter
the bodies in 6he wake where there is no fl w~eversal
For 6he flct plate wake, we start the computational
domcmfrom 19 Smm (z/l= 0.01)behmdthe edge of
the pkte, which conesponds to c location where mec-
smements were a~ilable For the ship wake the do-
mcin starts from L = I OS ( L=l is the end of
the ship model) At these pkmes the tFG method de-
scribed ctov (Smirn v et cl, 2000c) is used in con-
junction wi6h the the RANS cclculations (Stem md
Wilson, 2000)
For b oth case s,6he i flow md outfl w b o mdary c on-
ditions are cpplied m x di ection For outfl w bo mdary
both convectiv md Ne marm (fiee g cdient) bo md-
ary conditions hav been cpplied A comparison (not
sh wn he~e) indicated that 6here is not much diffe~ence
between 6he results obtamed by cpplymg 6hese two con-
ditions
Symmet y conditions me used in y di ection a d pe-
riodic b o mdary conditions me used m the sp mwise (z)
di~ection At 6he free surfae slip in x md z directions is
cllow d but 6he v locity component normcl to 6he free
smfae is set to :mro As such 6he free surfae is cp-
proximated es c movmg flct plane
For flct pkte wake,6he domcm si:m is l.Om x 0.2m x
0.6m in x,y md z di~ection, ~espectiv Iy he g id sic
is 82 x SO x SO Non- miform g id is used in bodh x
md y directions wi6h shetching not exceedmg 3 per-
cent Note that, m our tudy, xrepresents sheamwise di-
rection, y represents v tical direction md z rep~esents
sp mwise direction, re pectiv Iy (see Fig I )
For the ship wake, 6he domcm si:m is l.S x 0.2 x 0.6
giv n m non-dimensiom~l mits in ship length) in x, y
md z-di ections, respectiv Iy he g id size is 162 x
SO x 66 Non~nfform g id is used m bodh x md y di-
rections
he leng h sccle md time sccle are selected es con-
stmt in this pcper For 6he flct pkte, the length sccle is
4mm which is chosen es l O% of the width of the wake,
md time scale is O OOl s For ship wake, the length sccle
is 0 02, dimensionless of ship leng h, a d 6he time sccle
is O 01
4 RESULTS
4.1 Flat Plate Wake
In Fig 2,6he v locity time histories are show et differ-
ent points m the wake From these pictures it is scn
that bodh the cmplit de md the flequency of 6he v loc-
ity decrecse (decaying turbulence) clong 6he sh eamwise
di~ection, which is consi tent with the behavior of c tur-
bulent wake 7he predicted misotropy is clso not wor-
thy
7he logari6 mic part of 6he mcm v locity clong
sheamwise di ectionct 6he center Ime cmbe expressed
Nakayamc mdLm,1990; Rcmaprim mdPctel, 1982;
Wyg mski et al, 1986; And eopoulos md Bradshaw,
1980) by
U+ = A¢/og~oz+)—B (17)
whe~e Uc is 6he st~eamwise mcm v locity et 6he cen-
ter line, u~ = 0.853m/s is the friction v locity of the
bo mdary Icyer et the hailing edge, z is 6he distmce
from the pkte edge, v is 6he kinetic viscosity md A
md B me constmts which me 4 65 md 0 7 re pectiv IY
(A d~eopoulos md Bradshaw, 1980) in the h msv rse
di~ection(direction normcl to the pkte), the logari6hmic
part(if 6here exi t one) of the me m v locity c m be ex-
pressed es Nakayamc md Liu, 1990)
OCR for page 583
U+ = —Iny+ - 5.2
where U+—U/ul mdy+—yuT/v v is the Von Kar-
mmconstmt mdequalto 0.41
Figures 3 md 4 show the comparisons of our sim-
uhtions with experimental resters ~hrmapri m md PA
tel. 1982) She predictions are in good cg em ant both
wish Experiments md the theoretical log-profiles She
m m v locity along x-dimection for our simulation has
c wave-like oscillation his phenomenon maybe due
to c w ok vortex shedding which could :xist bec mse
w only perfommed She tatistical crurlysis et one line
in teed of the whole center plume
Fig 5 shows She decay of turbulent Emetic energy
along the center I me of She wake We ills o dep ict She t r-
bulentkmetic energyclongav rticcl Ime et x= 381 mm
in Fig 6 Agam She predictions cg ee w 11 wish She ex-
periments All of She ctov results were obtained by us-
ing the Q iCK scheme without my SGS model 7 his
scheme has c built-in 4th order dissipation which seem s
to act like c SGS model Large eddy simulations with-
out SGS are possible es elucidated by Boris et cl (1992)
She p mwise v rticity contours are show m
Fig 7(c) C ntral difference (CD) with Smcgorinsky
m odel was applied m this calculation She results usmg
the Q iCK scheme w re much smoother in this Fig-
ure, large c herent tructmes are clearly visible 11 Eve
shuctmes are similar in appearance to i arm m vortex
sheet bec mse They seem to be comprised of vortices
of clterrurting sig of vorticity which me also visible
in She experiments of Wyg mski et cl (1986) As
explained by Wyg mski et cl, 'Neither the varicose
mode, which requi es Flat the vo ti es appear m pa s
di tribute d symm eh icclly cay out the center line , nor She
sinuous mode, which requires v hi es whose center co-
incides with She centerline, dominate 6 is -I w"
4.2 Ship Wake
The streamwise v rticity contours et different phones
are sh wn m Fig 8 md the contours of She v tick
component of vo ticity me show m Fig 9 Fig 8
sh ws that concentrated v rticity decreases with axial
di tance, md in the far wake vorticity is only concern
tinted near the flee surface Some of this mpid decay
may be partially due to the g id e. p mdmg t wards the
(18) outlet plate, while She sin: of the wake Increases in
axial direction of the flow As c result of this, m my
turbulence sh uctmes may hav died out prematurely in
simul ttions it is interesting to note the two distinctly
concenh Ted v rticity creaks away fi om the center line
of She wake Fig 9) The rretmwise v locity contours
et c phone near She flee m face are show m Fig 10
Due to She lack of experimental data for This wake, we
c m not make c q mtitativ judgment of The predictions
H wever, we phi k that these re mlts me recsorurble As
the width of the wake increases, turbulence decays in
the far wake only Urger turbulence tructmes c m hen
seen This may be due to two reasons: (c) coarser g ids
are applied in The far wake; .1 ) the mall turbulence
shuctmes contain sig ff Fitly less energy so Shut they
c m only lest for shorter time comparedto the krgertur-
bulence shuctmes
lo testtheeffects ofthe g id sin: onthefl wfleldres-
olution, we doubled the g id m mber in x (sheamwise)
dimection md m the simulations again in Fig I I more
detailed turbulence tructmes c m hen seen clot Iy es
compared to the coarser g id solution Fig 9) The ~e-
solv d turbulence Emetic energy Ti E) for different
schemes mddifferentg id sins is show mFig 12 The
tANS solution is 31 so show in This picture for compar-
ison The ~esolv d TKE from flme g id is higher th m
that of the coarse g id as expected C ntrcl dffferencmg
discretization with Smagormsky model giv s better re-
suits th m the ocher t hemes From this flame it also c m
be seen that there is not sig dic mt dffference in fihe re-
suits when the QUiCK sch me is used with or wifihout
SGS model hforeov r, fihe resolv d TKE is I wer th m
that of central dffferencmg wifih Smagorinsky model
It me ms Shut QUICK scheme giv s ev n higher mm-
merical diffusion fi m fihe Smagormsky model This
is mostly due to g id resolution For mme detailed in-
formation about fihe comparisons of m merical schemes
md subg id-scale m odels the reader is refened Shi et al
(2000a) One once tamty in computations is pret nted
by simmsoidal-l he dish caution of TKE in the near wake
It may be be mse of fihe :xi ting surface wave (not ac-
co mted di ectiv Iy here) When the wave descends to-
wards to fihe bottom of the domain, it seems to crette
a consh iction wifih flow passing fi ough a small area
Thus both the v locity md TKE are higher at fi is re-
OCR for page 584
gion We checked the wave profile of tANS cclculc-
tion mmd 6he peak region of k-profile does indeed cor-
re ponds to 6he de pending wave it is mtere dmg thmt
op cclculations clso provide c similm hend clthough
no smfcce wave profile wm cpplied m op LES his
indicates thmt some wave i formation may be present
imp I ic itly in the i fi pw b opmdm y3
In figmes 13-18 6he velocity vectors on diffe~ent
ve tical cross sectiopml pkmes m p~esented Clemly,
the Imge sccle tp bplent eddies ( prtices) m ccptmed,
which cmm plcy mm impo tmmt role m bubble dypmmics
he prediction of optwm d fiow p m free smfcce, mmd
the shemmwise evolption of 6he vortices me very en-
cop cgmg mdications of the mpcess of 6he present LES
cpprocch
Cmrently, c case st dy with fimer g ids on 6he both
ve tipml mmd spm wise di ection is in prog ess He~e, w
show the velocity vectors m c cross-sectiopml plm et
x/l=0.2 Fig,15) Compmisonwi6h6heremltsfrom
ccomser g id mFig 13 showsthmtmoretp bpleppeed-
dies m ccptmed he shemmwise vorticity contop s on
the mme plm me clso show inFig 20 in oderto make
the tp bplent eddies mme vis~ble
he vo ticity contop s on diffe~ent verticcl plm s
shown m Fig 19,Fig21 mmdFig22 m indicative of the
deg ee of resolption of 6he pmlcpktions hese drup
tpses me hm d to see m Figmes 13-18 dp to ~elatively
smell mcg itude of 6he velocity vectors However, to
demondr de 6he smell w dk tp bpleppe druptmes, like
those m Fig 16(c), w enlmged 6he velocity vectors
where the~e is tp bp leppe struptpse corre pondmg to 6he
vo ticity contop plot mmd depicted it in Fig 16(b) A
conesponding m cc m the prticity contop plot is clso
ippluded m Fig 22 for ~eferep he cross s ption is et
L= 1 2 Havingno interpolation, it seems6mt inthe
velocity vector plot the Weak vortices cmm not be seen
dp to pcle dfffereppe, wherecs the mtemolated con-
top s plots do show smell shuptpses Figmes 21 mmd 22
show cgam thmt mpch of 6he vo ticity is coppentmted
p m the free sp fcce mmd the~e m two Imge counter ro-
t dmg vortices on two sides of the wake
Ac tmdioc oi the hip wake how t also w ilable d
htp://cid.mae.wm.ed /ddpwshe
5 CONCLUSIONS AND FU-
TURE WORK
A combip d LES scheme mmd mm tFG cpprocch spit-
ctle for wake fiows is briefiy de pribed he Wdke
fiow of c fict pkte is psed es c mlidation case Both
the memm fipw mmd tp bpleppe intensities m compm d
with 6he experimenwl ~esplts A good cg cement hms
been obtamed R gmding ship wake simpktions it is
diffcult to d cw mmy defimite copplpsions et 6his pomt
in the cbsff~p of experimental daw How ver, 6he ~e-
spits me very ~ecsopmble mmd it memms op cpprocch is
c victle dpprocch m 6 mt it is capable of ccptm ing the
mo d ep rgetic pmstecdy, tp bplent vo tices mmd or cd-
dies p~esent in the Wdke his st dy shows 6h d with
recsopmble k ge g id nodes LES of ship waker hmr very
good pro pects Never6heless, f 11 sccle LES cclcpk-
tions of ship fiow me still imposs~ble b pmmse of the
limitation of computer resop p s mmd may requi~e mm-
other 10 or 20 yem s Lm sson et cl,1998)
Appording to Hymmm Hymmm, 1998), fiee-
sp fcce/tp bpleppe mtepiption is impo tmmt for the
p m-smfcce Ictercl wake g pw6h So, ippluding the
effects of fiee smfcce will be 6he focps of op futme
work Pm cllel computing (Osmmm et cl, 2000) is clso
mm importmmt fcctor sippe it cmm fcciliwte the p mge of
mpch fimer g id resolption m LES
ACKNOWLEDGEMENTS
his work hms been performed pmder c DOD EP-
SCoR project sponsored by the Offce of Na~ml R -
sewch (ONR), Grmmt No N00014-98-1 -0611 he pro-
g mm monitor is D Edwm P. Rood We 6 mk Prof
Fred Stern mmd D' Robe t Wilson of University of
IOWA for providing the RANS resplts for the ship
model Speciml 6 mks me dp to Prof R. Sheet of
Stm ford University for providmg p s wi6h 6he basic LES
code Prof V C Pctel prompt response with 6he repo t
thmt conwip d 6he experimenwl daw for 6he fict pkte
wake is clso cpprecimted
OCR for page 585
References
A d eopoulos, J. md Bradshaw, P. 1980, Measure-
ments of mte~aotmg tmbulent shear kysers m the
near wake of c flct pkte, JFluid Mech 100, 639
Boris, J. Grmstein, F. O m, E, md Koke, R. 1992,
New msights into large eddy simoktion, Fhid Dy
n mics Reseomh I 0,199
Dommemmubh, D, Gharib, M, Hu mg, H. mis, G.
Maheo, P. Nov kov, E, Talcott, J. md Wyastt, D
1996, Turbulff~t fre shear fl w s A c om pari son be -
tween m mer ical simulati ons md exper imentcl mec-
smements, m 21st Symp slum on Now I Hydmdy
n mics,pp200 215,Trondhiem,Norway
Hymm, M 1998, Computation of ship wake fl ws
wi6h free-surface/turbulence interaction, in 22nd
Symp slum on Now I Hydmdyn mics, pp I 1 32,
Wcshmgton,D C
Larsson, L, Regmstrom, B. Li, D, md Jmson, C
1998, Fcilures, fmtasies, md fects m the themet-
iccl/m mericcl p~ediction of ship pe formance, in
22nd Symp slum on Now I Hydmdyn mics, pp I I
32, Wcshington,D C
L onard, B. 1979, A table md accurcte convective
modelmg procedme based on qua d ctic upst~eam in-
terpolation, Comput Method Appl Mech Engx 19,
59
Nakayamc, A md Liu, B. 1990, The tmbulent near
wake of c flct pkte et low rey olds mmmber, JFluid
Mech 217, 93
Osm m, A, Ammar, H. Smimov, A, Shi, S. md C -
lik, 1 2000, Parcllel crurlysis md implement~
tion of krge eddy simulations of ship wakes, m
IEEEInt nnotionol Confe~mceon C/ust n Comput
ing ClUSTER 2000 Technuche Univensitt Ch m
nitz, Saxony,Germmy
Peterson, E, Hym m, M, Stem, F. P. C, Bonetto, F.
D w, D, md Lchey, R 1996, Near- md far-
fleld cM for c r~l combatmt including 6hermal-
shatiflcation md two-fluid modelmg, in 21st Sym
p slum on Nowl Hydmdyn mics, pp 102 117,
Trondheim, Norway
Rcmapri m, B. md Pctel, V 1982, The symmetric tm -
bulent wake of c flct pkte, A AA Jouxnol 20,1228
Rcmaprim, B. Pctel, V, md Scshy, M 1981, Tur
hslent w k developm mt behind st eomlined bod
ier, Techmiccl R po t IIHR R port No 231, lowc
Instit te of Hyd mlic Research, The University of
IOWA
Rctcliffe, T. 1998, Vclidation of free surface ~ey old's
averaged r~vier stokes md potenticl flow codes, in
22nd Symp slum on Now l Hydmdyn mics, pp 96L
980, Wcshmgton,D C
Shi, S. C I k, I, md Smirnov, A 2000c, Comparison
of diffe~ent m mericcl schemes md mb-g id sccle
models m krge~ddy simulation, m ASME Fhid
Engine ingDivulonSummerMeLng,No 11232
in F DSM2000, Boston,Mcssachusetts
Shi, S. Smi nov, A, md Celik, 1 2000b, An cp-
procchfor genemtmg time-dependent i flow bo md-
ary wi6h cpplication to krge~ddy simoktion of flct
p Icte wake, in lnternah onol Mechonc iol Engineer
ing Congness and Exp sition, Orl mdo, FL
Shi, S. Smirnov, A, md C lik,1 2000c, Large eddy
simulations of particle-kden tmbulent wakes using
c r mdom fl w genemtion techmique, m ONR 2000
Fnee Surfoce Turbulence and Bubbly Flow Wwk
shop, pp 13 1 13 7, Cclifornic lostitute of Techmol-
ogy, Pcsaderur, CA
Smcgormsky,J 1963, Generclci culationexperiments
with the prim itive equctions, part i the basic exper-
iment, Monthy Weo6herRex 91, 99
Smi nov, A, Shi, S. md C lik, 1 2000c, R ndom
Flow G menotion Technigue in la ge Eddy Simula
tions and Ponticle Dyn mics Modeling, submitted
to Jourm~l of Fluid E gineermg
Smi nov, A, Shi, S. md C lik, 1 2000b, Rm-
dom flow simoktions with c bubble dynamics
model, in ASME Fluids Engineening Divulon
Summen Meeting, No 11215 m F DSM2000,
Bo ton,Mcssachusetts
Soti opoulos, F. md Pctel, V 1995, Application of
rey olds- tress h msport models of stem md wake
flows, Journol of Ship Reseomh 39, 263
Spcin, B. 1965, Tenson Colcuh, Oliver md Boyd
Stem,F mdWilson,R 2000, RdNSRerult of Ship
Wok simulohons, Private comm mication
Wyg mski, I, Champagme, F. md Marcsli, B. 1986,
On fhe large-scale tructures in two-dimff~siom~l,
mall-deflcit, turbulent wakes, JFhid Mech 168,
Zmg, Y. St~eet, R. md Koseff, J. 1993, A dynamic
OCR for page 586
mixed subg id-sccle model md its cpplocation to
turbulent reci culatmg flows, Phys Fluids 5-12,
3186
Zcng, Y. Sheet, R. md lioiett, J.: 1994, A non-
staggered g id, fractional step method for time-
dependent income Ale r~vier-stokes equations
m curvilinear coordinates, Journal of Comp to
do. al Physics 114,18
OCR for page 587
1 Y
/
1 0
go
~ 1 0
. _
g
-5 _
,
5 i/
5L
of
I~IFLOW E3-
x
:~?~-~ ~...~f^.f.~,.'','T
=~~1,~,~,~,,,,c,~1,~
WAt(E
Figure 1: The schematic of the flat plate wake
x=O.
X=0.007
o
5
l l l l l l l
265000 270000
iterations
x=0.16
, ~ ' ' · ~ ~ .
': ~ ~ ~'/~ ~Il7~\tf-(l\'~i\~i i>~41.
'I 1 0
o
g
-51
1
-' 1 or ~ ~ ;1
l l l l l l
265000 270000
iterations
X=0.53
~~v 'I
u
v
-
\ ./',,44.,;~_\>,'~'.~-~> . ~ ~
1 1 1
1 1 265000 270000
265000 270000 iterations
iterations
Figure 2: Temporal history of the instantaneous velocity components at different points on the center line of the flat
plate wake (x = 0 is the inflow boundary)
OCR for page 588
1.2 r
21
20
19
18
17
16
14
13
/.?
~'~
/'/,/
_ ~
_,/~'
~: £:
1 1 1 1 1 1 1 1 1 1 1 1
103
C) Experiment Results
U /u = 4.65 1O u v + 0.7
C T 9~0( T )
Ed Present LES Results
11 04
X = U r]C/V
Figure 3: Centerline velocity in the flat plate wake
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
1 1
10
~ c ¢
`_ _,
1 1 1 1 1 1 1 1 1 1
102 103
y = U rylv
~ x~ = 1,484
0 x~ = 3,520
~ x~ = 13,038
<~ x~ = 39,862
U/UT = 1 /K In (UTY/V)+
Figure 4: U-component of the mean-velocity profile in
the wake of the flat plate The experimental results are
from Ramaprian, et al.(l98 1)
1.1
1
o.s
N 0.8
>` 0.7
~ 0.6
.~ 0.5
04
0.3
0.2
0.1
- Experiment (Ramaprian et al., 1981 )
----------------------- LES result
N
it,
-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0 0.1 0.2 0.3 0.4 0.5 0.6
x (m)
Figure 5: Kinetic energy profile along the center line in
the wake of flat plate
I
~/ /00
>' 200
175
150
125
50
- Experiment (Ramaprian et al., 1981 )
LES result
_ _ _
O - 1 1 1 1
j..
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.2 0.4
kinetic energy(k)
Figure 6: Kinetic energy profile at x = 381mm (x/L =
0.2) in the wake of the flat plate
0.6 0.8
OCR for page 589
(a) The spanwise vorticity contours at one my plane in thewake of the flat plate
271 5.51
2440.01
21 64.52
1 339.02
1613.53
1 333.03
1 062.54
787.044
511.549
236.055
-39.4396
-31 4.934
-590.429
-865.923
-1 1 41.42
-1 416.91
-1 692.41
-1967.9
(b) A photograph showing the large coherent structures in the flat plate wake (Wygnanski et al., 1986)
Figure 7: Comparison of the turbulence structures between LES and experiments
OCR for page 590
Figure 8: The streamwise vorticity Contours on
0~............................................................
ifferent y-z plane in the ship wake
~ O
Figure 9: The vorticity contours(coy) on a x-z plane parallel to *ee surface at y/L = - 0.01 in the ship wake
OCR for page 591
u
0.945'
0.927'
0.908'
0.890'
0.871 ~
0.853'
0.834(
0.816'
0.797
0.779
0.760
0.742~
0.723E
0.705
0.686E
0.668(
0.649'
0.631 (
0.612'
Figure 1O: The streamwise velocity contours on a x-z plane parallel to free surface at y/L =—O.01 in the ship wake
' ~- 0.2
n
~ O
0.4
~. u ~
0.1 -
0.2
. rY
A
Figure 11: The same as Fig.9 but double grid number in streamwise direction
My
.............. 85.2211
it.. 77.085
68.9488
60.8127
52.6765
44.5404
36.4043
28.2681
20.132
1 1.9958
3.8597
. -1 .41 553
at.. -5.90366
-1 4.0398
-22. 1 759
-30.31 21
-38.4482
-46.5844
-54.7205
-62.8566
. 1 -70 9928
OCR for page 592
0.007;
0.00'
0.006;
0.00E
0.005;
0.00r
0.004;
y 0.004
0.003;
O.OO2
0.002;
0.00d
0.001
0.001
0.000r
· ,^
f ?~
j? ?~
~ I
j 1~
· '[ ~ ~ Smagorinsky Model (CD)
i, ~ ~ Smagorinsky Model (QUICK)
~ -----~----- No SGS Model (QUICK)
· ? '\ ------~----- RANS Result with Wave
? ~ ~ Smag.Model(CD) forCoarseGrid
1
-0 01
--- - 1
-0.02 1
-n n.q L
. _
>-0.04
I
0 0.5 1 1.5
~L
Figure 12: Comparison of resolved turbulence kinetic
energy for different computing cases
-O.0
O 0.
-0.05 .
-0.06
-0.07 _
1
~ i, f ~ ~ f v; ~
; ~ ,, //f s, ? ', ~ Vs~, _ s
, ~ /f: f ' I ~ \\NN~ ~ _
f tl \N~ N \, ~ ~ .
. ? I~lf 1\ t~ . ~ 1 \ ~
Figure 13: The velocity vectors on y-z plane at x/L =
0.2 in the ship wake
-0.05
-0.06 _
-n nR ~ ~ , ~ , ~ ,
-0.05 0 0.05
Figure 14: The velocity vectors on y-z plane at x/L
0.6 in the ship wake
-0 02
-n nn
-
Figure 15: The velocity vectors of finer grid solution on
y-z plane at x/L = 0.2 in the ship wake
OCR for page 593
-nn1
-a n2
-0.
0.04 .
non
-0.06
-0.07 _
-0.08 _
A'
(a) The velocity vectors on y-z plane at x/L = 1.2 in the ship
wake
-0.
-0.043
-0.044
-0.045
-0.046
-0.047
-0.048
-0.049
-0.05
-0.051
-0.052
-0.053
-0.
-cross
0.06 0.07
\
l
z
/
(b) The enlarged view of area A in Fig. 16(a)
Figure 16: The velocity vectors and the enlargement of
area A on y-z plane at x/L = 1.2 in the ship wake
E
-0.03
,
>-0.04 .
T , .
-0.05 _
',
-0.06 _
-0.07 _
~ . /, I, ? i ~ i \ ~ \; ~ _ -
,,, ,, - ~ ~ f ? ? {. \; ~ ~ ~
'em/ f S,il l, ~ ~ ' S ', . '
. . ~ , //i's? ~ ~ \ \ \ .
, . .,, ,4 .~ s ' f ? ~ ~ ~
-n nR I I ~ I I I I ~ I I I I ~
-0.05 0 0.05
Figure 17: The velocity vectors on y-z plane at x/L
1.0 in the ship wake
-0.01
1
-0.
-0.
>-0.04 ,
,
-0.05
-0.06 _ .
-...
-0.07 _
-0.08 -o 05 0 0.05
Figure 18: The velocity vectors on y-z plane at x/L =
1.4 in the ship wake
OCR for page 594
u
n
nn1
non
In nd
-nn.E
-n no
-n n7
· -0.075 -0.05 -0.025 0
Figure 19: The vorticity contours (fox) on y-z plane at
x/L = 0.2 in the ship wake
.05
Figure 20: The vorticity contours (fox) on y-z plane at
x/L = 0.2 in the ship wake (finer grids are applied on
both y and z directions)
0.025 0.05 0.075
~~ 10.66a
9.6499
8.6396
7.6293
6.61 gal
5.6087
4.8005
3.7902
2.7799
1.9043
1.0287
0.4225
-0.01 56
-0.4625
-1 .1939
-1 .9348
-2.7430
-3.6859
-4.561 5
-5.4371
-6.31 27
-7.3230
-8.3333
-9.3436
-1 0.353
~ ~ PR4
Figure 21: The vorticity contours (fox) on y-z plane at
x/L = 0.6 in the ship wake
u
o
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07
· -0.075 -0.05 -0.025 0
0.025 0.05 0.075
~~ 1 0.660
............. 9.6499
· . 8.6396
7.6293
6.61 gal
5.6087
4.8005
3.7902
2.7799
...... 1 .9043
1.0287
0.4225
-0.01 56
-0.4625
-1 .1939
-1 .9348
-2.7430
-3.6859
-4.561 5
-5.4371
-6.31 27
-7.3230
-8.3333
-9.3436
~ -10.353
.1 -11 .364
~ -12.374
Figure 22: The vorticity contours (mx) on y-z plane at
x/L = 1.2 in the ship wake
OCR for page 595
DISCUSSION
M Hym m
Coastal Sy tems Station, USA
This pep r represents the next stage m m effo t
to obtain high resolution flow computations
around Ed downstream of c surface ship M my
parabolic algorithms exist to compute wake flow
Ed mme recently, Dommermuth(l 994) applied
LES to She wake of c ship That temporal
simulation could, sh ictly specking, begin some
dist mce do..- stream of the stern et c location
where She flow was decaying fairly slowly The
present work reports c patial simulation which
c m, in theory, be applied ve y near the stern Ed
extend es far do..- stream es c omput ttiorLtl
resources pemm it The method c m be initiated by
applying the mthors'r mdom flow generation
RFG) methodology The RFG allows one to
take RaNS simulation results Ed create c ve y
pi ms~ble estimate of She mst mtaneous turbulent
flow field Once this flow field is available, c
LES cclcubtion of the near wake c m be
undertaken The mthors show se- er tl
interesting results from applying then code to
compute the wake of c flat plate Ed of c surface
ship
While it is clear that this work is in its'early
stages, there are se- er tl issues That shm~ld be
considered in the course of future work The
near wake of c ship presumably contains c wide
r mge of length scales from flow off the hull
boundary Icyer, separated stern flow Ed
propulsor flow This complex flow is further
complicated by breaking stern .. 3 ~ e. et higher
Froude mmmbers I would like to ask the mthors
how they would propose to characteri e f is flow
by c single lengfh ~ ale, what f is length sccle
should be Ed how this length sccle should relate
to grid resolution for LES cclcubtions in
addition, I would like to ask ffthe mfhors'
experience with LES calculations using the
QUICK scheme ( Ed k k of SGS model) could
be rented to grid resolution
AUTHOR'S REPLY
We appreciate Dr Hym m's summit y Ed
comments on this paper Whet follows is c brief
response to his questions
QUESTIONS
Question 1: "I would I ke to ask the mfhors how
they would propose to characteri e this flow by c
single lengfh-sccle, what f is length-sccle should
be Ed how this lengfh-sccle should relate to grid
resolution for LES calcubtiom "
Though c con t mt was used in this study, in our
method it is not necessary to use c single length-
sccle In fact, m She cunent version the algorithm
is Greedy impl merited with the lengfh sccle
parameter es c f notion of space which c m be
computed fiom k Ed ~ or k Ed ~ it adds
practically no extra computttiorLtl burden to the
procedure There c m be c slight loss of accuracy
in satisfying the inst mtaneous contimmity
equation in c flow field generated with She RFG
procedure associated with using i homogeneous
turbulent length-sccle How ver, for She
purposes of inlet plane initialization c smell
violation of contimmity c m be tolerated since the
flow solver will mtomaticclly adjust the
velocities in She next plane such that the flow
field sati fies continuity The lengfh scale used m
the RFG procedure is cunently not related to
grid resolution This might be c good idea to
pursue m the future
Question 2: I would like to ask ff the mthors'
experience with LES cclcubtions using the
QUICK scheme land lack of SGS model) could
be rented to grid resolution
A swer:
From Fig 12 m the paper, it c m be seen Nat
there is no signffi mt difference in She results
when QU CIC scheme is used with or without
SGS model Moreover, She resolved turbulent
kinetic energy is lower th m that of central
differencing with Smcgorinsky mod I This
me ms that QU CIC scheme gives even higher
diff sion thm Smcgormsky mod I
Theoretically, the mmmericcl diffusion increases
with increasing grid si e, so She low r resolution
of sccle in the LES cclcubtions using the
QUICK scheme (Ed k k of SGS model) is most
proton ly related to grid resolution However, et
this point w could not make assertion with
regards to how strong the resolution depends on
the grid si e A new run with c finer grid
resolution is underway to Investigate this issue
OCR for page 596
DISCUSSION
L Davidson
Chalmers Univ of Tech olo :, 5den
The paper presents LES of compressible wake
flow The method is applied to the wake after c
flat pate md after c ship model The
computations are started do..- stream of the
bodies At the inlet plume, t rbulent inlet
boundary conditions are generated by specifying
c turbulent pectrum; the procedure is celled c
"Rmdom Flow Generation" RFG) tech lame
The mthors claim that the RFG technique is
new Are they aware of She medhod develop by
the group et ECL [ I ] used in Aeroacoustics?
How are the results presemed in F igs 3 -6
compared to what c m be achieved with RANS
(either eddy-viscosity m odels or second-moment
closure)? Maybe She mfhors c m Include some
comments?
On p 4, col 2, the mthors comment upon He
waviness of the velocity profile m Fig 3 They
saythat this isbec mse theyhave averaged only
clo g the centerline Instead of in the whole
plane This is probably correct, but the same
effect would of course be achieved if they
increased She time Integration
The reco h s show in Figs 3 -6 have been obtained
with the QUiCK scheme md no SGS model
The mthors say that they also have carried out
simulations with central dffferencmg md She
Smcgormsky model Whet about These results?
It ..-m~ld he interesting to see c comparison
A lot of contour plots are presented I don't
thi k this is very mterestmg I would prefer to
see m ore qu mtitative results Furthermore, I'm
surprised that in She wake flow behind She ship
model no comparison is mad wish experiments
Why? Doesn't it :xist my expenm ent tl date for
the ship model wake? If so, why was it chosen
in the fir t pk e?
I W. Becharc mdC Bcilly mdF Lcfon,
"Stochastic Approach to Noise Modelling
for Free Turbulent Flow", A AA J. volume
32, Number 3, pp 455-463, 1994
L Davidson
Chalmers Univ of Tech olo :, S.. den
2 Howaretheresultsp~esentedinFigs 3-6
compared to what c m be achieved with
RANS (either eddy-viscosity m odels or
see md-m merit closures)?
3 The results showninFigs 3-6havebeen
obtained wish the QUiCK scheme md no
SGSmodel The mfhorssaythattheyclso
have carried out simulations with central
differencing md the Smcgormsky model
Whet about these results? It ..-m~ld he
interesting to see c comparison
4 I'm sumrised that in the wake flow behind
the ship model, no comparison is mad with
experiments Why?
AUTHOR'S REPLY
We would I ke to point out that there must be c
r-.po-raphi 91 enor in the fast paragraph of
reviewer's comments This paper presents LES
of incompressible rasher thm compressible flow
We agree with She reviewer that one cm find
numerous applications of K Rich m's method
pertaining to dispersed phase modeling,
turbulence-genercted noise et Our RFG
technique is also based on the K Rich m
method How ver, She original method was
modified by us so es to handle the case of
misotropic turbulence while p~eservmg the
contimmity of the flow field A other novelty is
the way the tech lame is implemented in
conjunction with LES, md Lcgr mgim particle
dynamics routines, which enable m efficient md
flexible flow-field enersn on by matching all the
Rey olds stress components measured or
obtained fi om R NS (see for details Smimov, et
cl 2000) in this re pect w do not clam RFG to
be c new method, but rather c new technique
used to mgment the LES md particle dynamics
computations
The comment of She review r about averaging
may have resulted from some misunderstmding
Prot at h w did not make it clear enough in the
paper that the velocity prod le in Fig 3 was not c
result of pace averaging along the centerline,
but rather of time averaging in this context there
is no disagreement with the reviewer's statement
Answerto Question2: Ramaprian, et cl (1931)
perfommed RANS cclcubtions with the k-e
model Thea results agree fairly well with Heir
measurements How ver, no matter what the
OCR for page 597
outc me of this comparison may be, LES
technique provides extna i formation on
unsteady krge-sccle component of the flow-
field, Ed thereby provides c more consistent Ed
necessary approach for mod hng Lcgr mgi m
bubble dynamics m the wake which is the
ultimate goal of the present work his, in our
opinion, gives LES c definite cdv mtage over
RANS methods in this particular application
mea
Answer to Question 3: Fig I included h re
shows the treamwise velocity et the center line
calculated by using QU OK scheme without sub-
grid sale model Ed central dffferencmg with
Smcgorinsky mode As expect, the central
differencing scheme gives better results
compared to She QUICK scheme his is also
tme for the turbulent intensities (not show
~ere I
Answer to Question 4: Measurements of the
flow-field m She wake of No y ship model 5415
is m on-going work Ed the experimental results
are not available et this time he this respect our
ship wake results represent c prediction rather
than c post-diction Our results will be compared
win h exper imental date es they bee ome cvailab le
On the other hand our flct-plate computations
presented in this paper w re specfficclly done to
validate our model Ed provide justification for
extending its application to th ship-wake it
must be pointed out that the LES predictions
w re done for c shear tree flat wall in teed of
we y fiee surface he i tluence of waves on
turbulence is usually not negligible
OCR for page 598
: .:4i^.~ ~
: I
:~}
~:i
: it. ~
.~ ~~ ,,,,:.
by:
:~-
Fig. 1. Modified comparison of predicted
mean streamwise velocity at center line
with measurements.
Reference:
1. A. Smirnov, S. Shi, and I. Celik.
Random flow simulations with a bubble
dynamics model. ASME Fluids
Engineering Division Summer Meeting,
number 11215 in FEDSM200O, Boston,
Massachusetts, 2000.
Representative terms from entire chapter:
quick scheme
