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OCR for page 330
Pressure Fluctuation on Finite Flat Plate
above Wing in Sinusoidal Gust
K Nakatake, K Ohashi, J. Ando
( Kyushu University, Japan )
ABSTRACT
It is generals said that the amplitude of pressure
tract ation induced by a sphere varying ow volume
wish time is propo tional to file second derivative of the
volume variation Pressme fluctuation induced by a
c witatmg wing is a similar es srnpl e
b 6 is panel as a modeled cavitation phenomenon,
we treat the pressme flu tuation on a unite flat plate
Educed by a wing advmcing m unifo m flow with a
sinusoidal gust md varymg its Ihmt new wish time The
wing is represented by a simple smface pmel method
" SQCM" which c m h eat the unsteady motion
b calculation for a Unite flat plate, we use four
kin d. of calculation methods: file btw one uses a min or
image method, file second one does the solid boundary
factor medhod, the fLi d one does file source dish ibution
method md the last one does QCM Comparing these
four kinds of results for 2-D md 3-D cases, we discuss
file availability of the fom methods md inw tigate the
relation between the amplitude of messme fluctuation
md the second derivative of file wing volume
1. LNTRODUCTION
Pressure fluctuation on a hull so face induced by a
propeller c m es hip hull vibration Pressure on the hull
so face tract ates largely becmse the propeller is
w king in the hull wake f ca itation occms, the
amplitude of pressure tract ation becomes large' M my
researchers, such as Huse (196S), Vorus (1974), Ho hino
(19S0), Wmg (19SI), Breslin et al (19S2), kehata &
Funaki 1985 Kehr et al (1996) etc st died pressure
flu tuation Educed by a propelle'
As a modeled cavitation phenomenon, we heat the
pressure fluctuation on a unite flat plate induced by a
wing add- rang in unifo m flow wish a smusoidal gust
md varying thickness with time in calculating pressure
tract ation, we need to model a propeller md a ship hull
There are a lot of t dies on propeller chanrten tics md
we c m obtain the highly accurate results (ITTC, 1993)
As to modeling of ship tem, there are a few t dies
using p mel medhod, but ship steni is usually treated as
al infinite flat plate, md a solid boundary factor (2 0) is
used to express file effect of the flat plate (Huse, 1968)
b order to represent hyd dynamically the unite flat
plate above a wmg, we adopt four kinds of methods: the
but one is file minor image medhod, the second one is
file so called solidbommdaryfactormethod, Method one
is file source distribution medhod (SDM) md the to th
one is QCM (Quasi-Continuous vo -. 1 De Method,
Lan 1974) SDM heats the flat plate as a mere solid
boundary md Q CM does it as a wing By using a simple
so face p mel method "SQCM" (Ando et al, 1998 I we
calculate the chamctenstics of al un teady wing varying
its w lume in a smusoidal gust md pressure fluctuation
on file flat plate above a 2-D wing md a 3-D wing m a
sinusoidal gust
By comparing the obtained results, we discuss the
mailability of the solid boundary factor method, the
minor image method, SDM md QCM md investigate
file relation between the amplitude of pressure fluc-
t ation md file second derivative of the wing w lume
with respe t to time
2 CALCULATION METHODS FOR PRESSURE
FLUCTUATION
Let us consider the problem of pressme fluctuation
acting on a unite flat plate, induced by a wing advancing
m unifo m flow with a sinusoidal gust The unsteady
wing is well represented by a simple surface pmel
method "SQCM" md its to mutations are described in
file reference (A do et al, 1998) Therefore we outline
file main equations m this pape' Fig I show the
schematic diagrams to represent file 2-D Mite flat plate
by QCM md by file mime image method when a wing
is adv mcmg in unifo m flow wish a sinusoidal gust md
ch mging its thickness with time We take the coordinate
system Axed to the wing md adopt four kinds of
OCR for page 331
~ -
v
vo tax sheet
(QCM)
~ Finite Flat Plate
source panel bound ~
,iL_ _ /votex Id
~~ ~ —
~tw(t) vRetdex
Mirror Image
~ v
9=~— d
_ d
_~_~,~ _
At)
Fig I Coordin se Sy hem md Schem tic Diagram for Wing md Fl t Pi he
calcul Lion methods to repn sent file Unite fl t pi he The
hut one is the minor image medhod md the second one
is file solid boundary factor medhod, which me Us to
multiply the pressure induced by the unsteady mono-
wing by the factor 2.0 The third one is the source
dishibution medhod (SDM) md the fou th one is
QCM(L m, 1974) Hen we describe the fonmul Lions for
SDM e d QCM, since other methods are mcluded partly
m these fommul Lions
Pi stly, file Educed velocity V due to the bound
vo ten on the camber su face md the shed vo -. x t time
t is expressed as follow
V7=zirUg~,t )(u VW[)A<+i (VW. VW.~)r(t ,)
where,
At =—sin 2V x
2N~ 2N~
N.: mmmber of divisions of camber so face
L number of shed w tices
(1)
b Eq (1), I . md l r are the Educed velocities due
to the bound vo tex md the bed vo -.x with unit
srenglh, re pectively, md F(t, ) is a circul Lion
around the wing t time t cd y~g~,t~) is the
trength of the bound vo tex on each p mel
Ne t the induced velocity Vet due to the source
p mel on file wing su face is expressed as
~ ON
Vo = inj(tz)Vo
where,
(2)
No: number of divisions of one side of the wing
b Eq (2), van expresses file induced velocity due to a
line soune wish unit tlrenglh. md n (t. I does the
source sh engfh on each p mel t time t SDM uses the
simile equ Lion with stnngth no to represent the
Unite pi he
Adding these velocity componems to the rel tiw
Chow velocity Vu, we have for a mono-wmg
V=Vi+V7+Vo
(3)
e d file boundary condition to be s dished on file wing
e d camber strife es is the solid boundary condition,
V.n. = 0, V.n~ = 0
where,
n ., n ~ unit nonmal vector t en h p mel
(4)
e d the unsteady Kutta condition (A do et al, 1 99S)
Ne t QCM to as file Unite pi he as a thm wing md
gPves file followmg e pression for the induced velocity
Her ~
where,
Atp = N sin N x
Vat= ~7~g~, tz)(v~ ~)~E~v
+ ~(v~ )r(tz ,) (5)
OCR for page 332
Ir : lengfh of pi te
N~r : number of divisions of pi te
b Eq (5), vpv md v~. ae fLe induced velocities
due to fLe bound vo tex on the fl t pi te md fLe shed
vo tex with unit shength, respectively, md l;(t~) is a
cacul tion aound fLe fl t pi te md y,> g^, t~) is the
trength of bound vo tex on each p mel on fLe fl t pi te
As to di isions of the fmite fl t pi te, we divide it
mto three pats i e fLe fiont pat, the wmg pat md the
afl pat, md adopt cosine divisions for each pat
Summmg up all velocity components, we hwe total
velocity V in Cff e of presence of fLe fmite pi te ff
V= Vi+ Vl+Vo+ Vlr
(6)
The bounday conditions on fLe fl t pi te ae also
fLe solid bounday condition a d fLe mm teady Kutta
condition The unknow strengths ae 7 ff ad y~
or ffr, but we solw the bounday conditions for the
wing md fLose for fLe fl t pi te, iter tively in fLis Cff e,
we need Usumiy sevffal times for enough conve gence
Lfftly, fLe unsteady pressure p(t) is expressed in
fLe wmg-hxed coordin te system ff follow
p(t) p0 = I p( V V 2) p i
where,
V,= Vi
(7)
b Eq (7), p, p, md ~ ae w ter density, the
ambiff t pressure md the velocity potential m the
wing-hxed coordmte sytem, repectively ~ cm be
obtained malytically md i¢/it is evaluted by
two-points up tream difference scheme We deEne the
unsteady pressure coeffcient Cr ff
Cp = (p(t) po)/—pV,
3. RESULTS OF 2 D PROBLEM
(g)
Let us consid~ fLe cffe whffe a wmg wifh NACA0012
se tion is set mmdff afmte h t plae mmmifomm flow V, wifh
asmusoidffgmtofvedicffwtocity v(:r,t)=vOe=( ~/V')
We t kc fLe vfftbm d6 mce d = 0.5c, (c: ch d leng h),
6he agle of aksck co = 0', fLe red ced heqpff y
k(= m / 2V~) = 1.0, fLe amplit de v0 = 0.1V~ md
6he time mcremfft At=xc/72V, m emresses fLe
circuk~rhequff y offLe gm t a ddhefmitefl tpl tehff leng h
1~ of 5c or lOc addhecfftffoffLepk~issetsoffk
comcide wi6h fLe mid h d of fLe wi g b fLis CffV, we
CffCUi te fLe p~ e fluctu tion on fLe fl t pk~ md ced by
6he wmg m mm fomm fl w wifh a smusoidm gm t by fLe fom
medhods
Fi tly we cmcuiae it by QCM a d SDM ~eSff tmg fLe
fl t pEte a d fhff compae fLese results wifh 6hose by fLe
mimx image medhod a d fLe soLd bommday fff k r medhod
Nmmbff of pa cl d6 isions of dhewmg mfff e is 60 along
6he pffimetff a d m mbff of dEscrete w dices on dhe cambff is
29 a d 6hose of 6he fla plae ae 49 (29 for wmg pa 10 for
fore md fl pats)for QCM mdnmmbff of so :~e pmek is 10
pff ch d leng h c for SDM
3.1 Prff sure Buetu ~d~m due to wing k' n gm~t
Fg 2 hows6hemiataeousp~ edEshbubon(tme
tep 2S0) cmcak~d by QCM a d SDM on dhe fla plae of
tw length 5c md lOc md Fig 3 show vo tex
dEshibution y ~ adso:~edEs~ibubon ffr adhesametime
tep Fmm Fig 2 we fmd dh t QCM giws nealy dhe same
messure dishibution for lp=5c, lOc, while SDM d es
dffe~ent dEshibutions for two kmds of 1~ dhough ffr is
nealysame y~ dEshbutionofQCM how ali61edfffffft
dEshbutions betwff 5c md lOc, but y~ saishes dhe
mm teady Kuba condbtion m ffkEtion to 6he solid b mday
condbtion a d how a kile nse nea dhe leadi g edge ff a
usual thm wmg Fig 4 how a c mpaison of,messure
dEshibutionsobtamedfor 1~ = 5c at time teps245,2S0
by QCM ad SDM ad Fig 5 hows dhe cone pondmg y~
a d ffr dishibutions From 6hese Fig es, we notice dh t
QCM results give more stale ad reffonmie pressme
dEs~ibubons dha SDM results eva~ if ffr hows smodhff
dEs~ibubon Thi seffms to be d e k dhe slable flowprod ced
by6heunsb dyKutacondbtion Fig 6 howsac mpaisonof
amplit de of ,mess :e fluctuaion AC~ betw ff QCM md
SDM We hnd QCM md SDM giw fairly different
dEshibutions of AC~ excffpt dhe cfftrd pat Epecimiy
SDM gi es lager AC~ dh m QCM m dhe fore pat a d does
loWff AC~ mflff6hecentffpat6hmQCM,addhff giws
k~rge AC~ nem dhe t aLmg edge F m 6hese results, we
dEmk dhff QCM giws more tale ad remitic pressure
fluctuffion f or 2-D m b Iffm 6h m SDM Fig 7 a d Fig S h w
6he contribubons of dhe mm teffiy componfft i ¢/it a d 6he
wlocity componfft to dhe kffm ACp mcffe of QCM ad
SDM, re pe tiw k We mm t notice dhff dhese c :ves ae not
ffkEtiw si cc effh ,mess :e fluctuffion hff phffe dffffff cc
F m dhese Figmres, we mmdfftad 6hm QCM giws more
~effona le beha iornem dhe ieffmg edge of dhe fff piffe 6ha
OCR for page 333
cp
o 1
_n
i] n p=5c(QCM)
y + p=10c(QCM)
+ p=5c(SDM)
Time Step 280 a p=1Oc(SDM)
-U
O Xk 5
Fig 2 Pres Ure Di tribution on Flat Plate
~ . r r , .
Ip=5C(QCM)
~ Ip=10c(QCM)
0 01 Ttme Step 280 ~L -
T lA Ji-
c Ip=Sc(SDM) y ~ ~
-O 01 e Ip=10c(5DM) ~J -
cp .. ,
Fig 3 SingmiarityD shibutiononFlatPlate
Cp
-o
-o
: - :
p=5c(SDMT me Step 245) -
p=5c(SDMT meStep280)
-2 0 2 Xk
Fig 4 Pressure Distabution on Flat Plate
ACp
02
01
O' + QCM TmeSteP245 t -
7p ~ QCM TmeStep280 ~ ~ -
_o ~.~
: r
00 ~,
-001 e SDM T me Step 2
+ SDM T meSt~p280 ' - ~
-2 0 2 Xk
Fig 5 Singularity D ish ibution on Flat Plate
. . .
+ QCM
+ SDM
_~
u
-2 0 2 Xk
Fig 6 mplitude of Pres Ure Fluctuation on
Flat Plate
r ~ . . ~ .
+ Tolal
_ Unsleady Componenl
n Velocily Componenl
QCM ~ \
~r . . .
-2 0 2 Xk
Fig 7 Component of mplit de of Pressure
Fluct ation on flat Plate
OCR for page 334
ACp +Total r , . r . , ACp ~Tota
~Unsteady Component —F at P ate Component
~ VelocityComponent ~ Y ngComponent
0 2 1~ ~ nteracton Component
O] S~-\~ O] ~\
-2 0 2 xk 2 0 2 xk
Fig 8 Component of mplitude of Pressure Fig 11 Component of mplitude of Pressure
Flu tuation on flat Plate Flu tuation on flat Plate
Cp ' ' ~ ' ' ' Ct ~ ' ' ' ' ' ' '
. )~\ i5 .
O ,~- O ~ ~
+QCM ~1
~ n Mirror image
-0 2 +QCM ~ Cp
n M rror mage
n 2Cp Time Step 280
- Time Step 280 -
04
-2 0 2 xk O xk 1
Fig 9 Pressure Di tribution on Fiat Plate Fig 12 Comparison of Pressm e D ish ibution
of 2-D Wing
C ~ - T 7 '
P +QCM CL . +QCM n 2Cp
n Mlrror image n n M mor mage
O.] J: _ :~
Fig 10 mplitudeofPressmeFiuctuationon O 100 200 tepNum300
Fiat Plate Fig 13 Tim e Histmy of Lifl Coeffcient
OCR for page 335
S b
1~_~_
+ QCM
n Mirror image
x=n se
1 Z ~ dk 4
Fig 14 Comparison of Solid Boundary Factor
O1L,
yk
—O 1
max
- I~
O xk 1
Fig 15 Vari tion of Wing Section
uas Steady
X=0 5e
Fig 16EffectsofFrequency k~ on mplit de
of Pressure Fluctu tion
o
ACp
01
......... ,1
O 05 th 0 1
Fig 17Effects of th on mplit de ofPressure
Fluct tion . I
ACp
01
X=0 5e
+QCM
n M~rror image
a 2Cp(Mono-Wing)
Leadl Lag
-~ 2 0 ~ 2 t (rad)~
Fig 13 Effects of Phase Ddffer:me y on
mplitude of Pressme Fluctu tion
_~
~ +~=00
$=7r 2
:~ :
-2 0 2 x/c
Fig 19EffectsofPhaseDifference y on
mDhtude of Pressure Fluctu tion
OCR for page 336
SDM We dEmk dhat 8he Kutta condition sta 3i es dhe fl w
OVa 8heflatplate
Ne t we c mpae QCM n sulk inh dhose of 8he min
image medhod a d dhe solid bounday fa tor medhod Fig 9
hows a compaison of pnss :e dishibutions at time sbp 280
on dhe flat plate obt med by dhe 8uee medhod he min
image medhod giws nealy dhe s me nsults a 2C, but
d ffffff t dis~ibubon f m QCM n suit nea 8he fl pat of dhe
plate Fig 10 hows a c mpaison of mplit de AC~ ad
Fig 11 d es c mponenk of AC~ c mposed of 8he flat plate,
dhe w~ng a ddhe mtfffftion c mponffts Fn m dhese Fig es,
we undff ta d dhat 8he dffffff cc betw ff QCM a d odhff
t medhod is c msed by dhe flat plate c mponent d e to dhe
fmite Iff gh effe t Ne t we i w tigate dhe effe t of dhe flat
plate on 8he lifl of 2-D mg a d check aso 8he ~kd bounday
fator2.0 We h wnhe,mess:e dishibutions on dhe mg
surihce mFig 12, mddhe Ifl coeffcifft Co mFig 13, ad
dhe soLd b mday fa tor Ss at dhe Cff tff of dhe flat pk~ m
Fig 14 We mmdff ta d dhat dhe fmite flat pEte of Co giws
simila effe t on dhe mg chaa tffi tics to dhe min image,
beca se QCM n suits ae amo t s me a dhose of dhe min
image medhod A to dhe solidb mday fa k ~ dhe w~ue of dhe
min image medhod convffges to 2.0 inh mcrea e of dhe
di tace d, hde dhe w~lue of QCM hows a difffffft
tff dff cy a d seems to convffge to 1.0 Acco dmgly we
dhi k 8hat dhe soLd bommday fator 20 is not away
applica le to 8h e fmik flat plate
3.2 Prff sure Buan~don due to fIdd~nff +wo ymg wmg tn
n gm~t
Let us considff dhe ca e hffe a dhickmes~wnymg mg
is m mmif m fl w i8h a smusoida gust We a me dhat dhe
mg fLickmess t.(t) wvies winh tme by dhe fokowmg
expresnon,
t, (t) = to + th sin(~t y)
(9)
b Eq (9), to is dhe igma wmg dhickmess, th dhe
ampEt de of dhickmess wviaion, m~ dhe circula flequen y
of dhickme~ wviaion a d y dhe pha e d ffffence f m dhe
si usoida gm t hff the second dffi tiw of wmg w Imme
winEn pettotime V(t) becomes a
V(t) = c~thm~ sin(m~t y)
(10)
b Eq (10), c~ is a contat kmown f m dhe e~ession of
NACA wmg sechon hff dhe amplit de of V(t) of dhe
wlmmewviaionbeCOmeS C[th~!
At fmt, we considff dhe cae whffe dhe wi g is i
mmif m fl w a d is aymg only umpff nrice (see Fig 15)
bhod cmg k~(=m~c/2V~) mtead of m~, we h w m
Fig 16 dhe nlaions betwff dhe amplit de of ,mess:e
fluctuaion AC~ tnhecfftffofnheflapk~ad k~,whff
k~ chmges f m 0.5 to 3.0 md f m 0.001 to O.05
WefmdbyQueemedhod dha AC~ chagesamotlmealy
Winh k~ for k~=1.0~3.0 ad AC~ does quite
dfffffffly for k~<0.05 For ma8 k~, dhe kmt of AC~
will be dhe w~ue of 8he qua i teady ca e Ne t we h w some
n sulk of AC~ whff dhe wi g is i a gu t a d is cha gmg
8he dhickmess winh pha e d ffffff cc flom 8he smusoida gm t b
caes of k~=1.0, y=0 ad th= 0.01to,0.05to,0.1to,
we how8henlaionof AC~ ad th mFig 17adgetnhe
kmea n laion betw ff AC~ a d th By se ti g dhe pha e
dffffffce y a - ~/2~/4~/2~ betwff dhick-
ness wviaion a d dhe gm t, we how dhe n laion betw ff
AC~ ad y m Fig 18 7he phae lead of 8hickness
wviaion ( y = n/4 ) giws a ma imum w~ue of AC~,
beca se ma immm I fl a d ma immm 8hickmess w dk togedhff
for ma immm AC~ Fig 19 hows 8he effeck of phae
dffffffceon ACp 7hffeforeweundfftaddhaoccu~ence
of cwlaion winh phae dffffff cc may affe t dhe amplit de of
8he ,messun fluctuaion on dhe hulL
4. RESULTS OF 3 D PROBLKM
Conesponding to the 2-D problem, we pe fonm
caculaions for dhe 3-D m blem Let us considff a ca e whffe
a3-Dwmgwinha pm s=3c adNACA0012setionisset
i un fomm fl w winh a si usoida gm t a d a fmik fla plae
winh a bnaddh 2s ad a Iffgh 5c is set a a vfftica
distmce d=0.5c abow dhe wmg (see Fig 20) We
takel~=5c, 6c, k= 1.0, v0 = 0.1V~, md the same
condtions for dhe gu t a d dhickmess vaiation t. (t) md
pha e diffffff cc y F g 21 h ows m ta ta e ous pn ss :e
dEshibutions obtamedby QCM s dSDM on 8he mid pa Ime
(y=0.0)ondheflaplaeatmesbpl48 mdFig 22d es
8he,mess:e dEshbutions ondhemid h d kme (:s=0.5c) a
8he same time tep These dEshbubons seem k be pla sible
a mmd dhe fore ad wmg pats Though SDM giws s me
edge effect to C~, but degree of the effect is not k~rge
c mpacd winh 2-D ca e Figs 23 a d 24 how a c mpaimn
of C~ obtained by the four methods m both :s,y
due tions it is mtffe mg to notice dhff 8he fom medhod giw
imik~r dEshbutions ~Cffpt dhe mfl pat md SDM ca giw
~effona le C~ a ow dhe wmg We dEmk dhff dhis may be
d e to dhe wemkff edge effe t c mpacd winh 2-D fl t piffe
We h w a compaimn of dhe ampEt de dishibution of dhe
,mess :e fl et aion AC~ mFig 25 a dFig 26 A mmddhe
wmg pat, ffl medhod giw nemiy dhe same wffues, but d
dfffffft tffdffcies m dhe mfl pat ff dhe 2-D cffe Fig 27
hows dhe niffions betw en AC~ a d k~ m cffe of dhe
8hickness-wnymg wmg We fmd agam Imeaity betw ff dhffm
i dhe n~nge of k~=1.0~3.0 Thff we h w i Fg 28 a
c mpaimn of dhe ~kd b mday ffftom ff dhe Cff tff of dhe
plae obtamed by QCM a d dhe min imffge medhod a d
fmmiy mFig 29 ac mpaison of dhe phffe dffffff cc effe ts
OCR for page 337
for Wing and Flat Plate
Cp ~
o
- o
_n
Cp ~
O
-02
-04
::
it st y=0 0
IY Time Step 148 -
y x p=5c(QCM)
+ p=5c(QCM)
~ ~ + p=5c(SDM)
X=OSC a p=5c(SDM) -
. . , .
2 0 2 Xk 4
Fig 21 Pressure Dish ibution on Flat Plate
X=0 5C
Time Step 148 ~c
~'~ o
+ p=5c(QCM) + p=5c(SDM) -
+ p=5c(QCM) + p5c(SDM)
-2 0 2 yk
Fig 22 Pressure Di tabution on Flat Plate
—0 4
_~
- +QCM
y=0 0 ~ SDM
TimeStep148 ~ ~ = Mrrorlmage ~
' x=0 5c P
-0 4 . 2 xk
Fig 23 Pressure Di tabution on Flat Plate
Cl
—02
+ QCM
+ SDM
_. x Mirror Imaue ._~~
~ :
X=0 5C
Time Step 148
.
-2 0 2 yk
Fig 24 Pressure Dish ibution on Flat Plate
y=OO
+ QCM
~ SDM
-2 0 2 xk
Fig 25 Amplitude of Pressure Fluctuation on
Flat Plate
OCR for page 338
Acp
o1
+ QCM
SDM
n Mirrorlmage
~ 2Cp
-2 0 2 yk
Fig 26 Amplit de of Pressure Fluct ation on
Flat Plate
0 03,
5 .M
Fig 27 Effects of Frequency ~, on Amplit de
of Pressure Flu tuation
Sb _
1 ~
O r
AC ~
o
_~ -~ 2 0 ~ 2 ¢(rad)~
Fig 29 Effects of Phff e Difference y on
Amplitude of Pressure Fluctuation
X=0 5C
y=OO
~:
SDM
~ M~rror image
o 2Cp(Mono-Wing
Leadl Lag
on AC~ by fLe four medhods Fmm 6hese results we
mmdff ta d fhat fLe solid bommday factor medhod is not ffwaw
applica le to fLe fmite flatpLte a d SDM is ffSO applica le t
e imation of ,mess :e fluct ation on 6he flat plate nffo fLe
wmg Smce fLese results ae obt med only by mmfficm
cmculations, we mu t ew~uate fLem by cone pondmg
e pffimffts 7hesecmcuLdionmedhod aceffilye tffdedto
6he Cff e of a pitchmg or hea~mg wmg m mmifomm flmu
5. CONCLUSION
'\ +QCM
~ n Mirror image
~ \
X=0 5C
y=OO
1 2 3 dk 4
Fig 23 Compa ison of Solid Bounda y Factor
We appbed QCM SDM, fLe mimn image medhod md
6he solid bommday faclor medhod t fLe m blem of mplit de
of,messure fluctuation mduced on 6he fmite flat pLte set a ow
a wmg i mmif m flow wif h a smusoidm gm t
F m fLe obt med results, we conchde ff follows
. 7he mimn image medhod fLe solid bommday factor
medhod, QCM giw nealy 6he s me mplit de of ,mess :e
fluctu dion on a finite flat plate m fLe upshe m md Uppff
regions of 6he wmg i 2-D a d 3-D problem SDM is
simiLar only m 3-D m blem
. CnlyQcMseemstogiwreff nale mplit dedEshbution
on a fin te flat plate m leng hwise direchon
. 7he mplit de of ,mess :e fluctuation w~ies ii ea y wi6h
6he second d wati e of wi g w lume w h re pe t t t me
i acffffsn~ngeofci~ulafleq ffcyofgmt
Aff~nowledgement
7he adhom w id ii e to deffply fhad M YffUiCo
Yamff a i for hff t pmg of fLis mamscript
OCR for page 339
REFERENCES
J. A d, S. Malta, K N kat kc, "A New Smface Papel
Medhod to Predict Steady apd Unsb dy Chafftffi tics of
Mame P pell¢'P c of 22 d ONR Svmposi m pp Naval
Hvd dumics,Wffhi top,1998
J. P. B'esim, R. J. Vap Houtep, J. E Kff m apd C -A Johmsson,
' hepretical apd E pffimeptai P pelLs -b duced H 11
Press:es A ismg f m b tffmiteptBIade CaviLtipp Loadmg
apd Thickness," T~ps SNAL5E, Vol. 90, mp 111-151,1982
T. Ho hmo, "Press:e Fuo atipp b d ced by a Sphfficai
Bubble Mo mg ifh Vffymg Radi~g" T~ps of fLe
We t-Japap Socieh of Naval Architeo ~ Vol. 5g mp 221-234,
1979
T. Ho hi o, "E timatipp of Unsbady Cavitatipp pp P pelLs
Blades as a Base fp Pred6o mg P ppelLs b d ced Press :e
Fuo atipps," Jp mal of fLe Socieh of Naval Archikos of
3apm,Voll4S,mp3344,19SO
E Huse, ' he Mal,mit de md Dishbutipp of P pellff
b d ced SmEace Fp es pp a Si gle Spew Ship Model,
" Np~wegiap Ship Model E pffimept Tpk Publication,
No 100, 1968
M kkehata & H Fmm ki "A alytical Chafftffi tics of
Oscdlati g Press :e Dishibutipp above aP ppells," Jommal of
fLe Socieh of Naval Archik P s of Japap, Vol. 159, pp 71 dl,
1986
2 th TC P pulsp Committee Repo t, 1993
Y-Z Keh, C -Y H m apd Y C Smm, "Calpplatipps of
Press:e Fuo atipps on fLe Ship H 11 b duced by
b tffmitteptLy Cavitffmg P pella;" P pc of 21 t ONR
S mposimm ppNavalHvd d p mics,pp 8g2 d97, 1996
C E Lap, "A O asi-V t~-L ttice Medhod m T m Wmg
The y," Jp mal of Ai~d, Vol. 1 1, No 9, pp 518-527,1974
WS Vpms, "A Medhod fp A alyzmg fLe P ppelLs -b d ced
Vihut y Fp es AP mg pp 8h e Smf ace of a Ship Stem," Tpms
SNAL5E,Vol82,pplS6-210,1974
G. Wang, ' he bafhence of Solid Bpmdffies apd Free
SmEace pp P pelLs b duced Press:e Fluo ations,"
Nmwegiap Mffit me Resem~h, No 2, pp 34 46,1981
OCR for page 340
DISCUSSION
T. Hoshino
Mitsubishi Hen y industries, Ltd.
Jcp m
The mthors should be con rcml.ned for their efforts
to make clear the solid boundary effect of c Unite flat
plate on the pressure fluctuation induced by c wing I
have the following questions
(1) Fig 6 sh ws fnat there is se y large difference of
amplitude of plessme fluctuation between QCM
Ed SDM, especially in She aft part of the plat
This difference would be due to the consideration
of trcilmg vo tices shedding from She nailing edge
of the put in QCM Does f is difference bee me
smell, ffthe aft part of She flat plat was lengthened?
(2)1n the calculation of She pressure fluctuation
induced by c propeller, She pressme Duct ction is
calculated m She pate fi ed in space, not moving
with propeller On the other h Ed, She pressure
Duct ction on th plat moving with She wing is
calculated m She present paper in this case, the
pressure Duct ction due to the Hick ess effect
c m't be considered Ed only She loading effect i
considered I Hi k that this would be He reason
why Here is large difference between QCM Ed
SDM
AUTHOR'S RtiPLY
Thmk you for your rcismg questions
(1) We thi k that f is difference is due to both the
shedding vortex (QCM) Ed the unstable flow
(SDM near th hailing edge In case of 2-D
problem, lengthening of only aft plate does not
improve the difference near the leading edge of
the plate L ngthenmg of plates forward Ed
fterward improves She difference in the fore Ed
upper parts of the pate (See Fig 2), but still it c m
not improve fnat m the aft part of She plate k
case of 3-D problem, how ver, the effects of
shedding vortex Ed the unstable flow seem to be
smell for the fore Ed upper parts of She plate (see
Fig 21)
(2) in f is calculation, only the loading effect is
considered in the sense that the relative position
of the flat plate to She wing is unch mged We
think fnat large difference betw en QCM Ed
SDM is due to She unstable flow (SDM et the
t~aili g edge Especially this effect is sensiri- e in
She 2-D problem
DISCUSSION
K Kim
Ntsvl Su face W tootle C nter, USA
Cavitation-induced hull pressme ht. been c
continuing subject for m my researchers in this field
The mthors h led different m mericcl sch me. to
predict induced pressme on c flat plate clove c
pulsating wing in c sinusoidal gust I have some
questions
(1) it is not clear where the boundary condition
expressed m Equation (4) was mplt d; on
camber surface, on She wing surface or on
both camber Ed She wing su face?
(2) it appears that Fig 9 pressure d~ttr~ on et
time step 230) Ed Fig 10 (cmplit de of
pressme fluct ction) are identical I cm
wondering if Fig I O should be replace by
Cp figure
(3) For Fig 7, the ~ hors stated fnat total Cp
was not the sum of She cmplit de of the
components due to the phase Ogle
dtlerence InFig II,however,total Cp
appears to be sum of the components \\ 9.
phase Ogle considered here or not?
(4) For 3 -D case, the ~ hors applied unsteady
Kuttc condition et downsheam edge of the
flat pate How did She mfhors treat the side
e dge s m term s of b oun dary c ondit i on?
(a Figs 16 md27, Cpisexpectedtobe
sensitive to She time- tep size for different
reduced frequencies Did the authors use
differe t time tep size in these figures?
(6 Judging from the large Prep e. in
predicted pressure dish ibution by QCM Ed
SDM, it appears fnat the validity of She SDM
is questionable I would like to suggest that
the mthors revisit the formulation Ed or
mmmericcl sch mes to identify possible
c mses of the discrep mcy
OCR for page 341
A171HOR'S RttPLY
We fharDc the discusser fp his minute
discussions md reply es follows:
(1) The boundary condition (4) was applied to on
both the camber md the wing surfaces
(2) We considered always She phase difference m
our calculation We show the pressure
Duct ctipms of components with time et x/c=3 0 in
Fig A-1 in case of Fig 7, md gnat m Fig A-2 in
case of Fig 11 From these Figures, w
under t md that in case of Fig 7 the phase
difference between unsteady md velocity 0 1
components is so large that two components
cancel to each other, on the other h md, in case
of Figll, She phase dfffe~ences among thee
components are smell, then She total amplit de is
nearly equal to sum of th ee components
(3) We did not apply my boundary condition et the
side edges, bee mse its effect seems to be smell
(4) We tested several time-step si es m the
calculation md co firmed the used one is
sufficient fp She given r mge of reduced
frequency Therefore w used the same time- tep
size
I 5) We fhirJc gnat the validity of SDM is not line
behind the un teddy wing especially in She 2-D
case The main c mse is that SDM c m not satisfy
the Kuttc condition et She hailing edge of the flat
plate This condition assures the smooch flow
do..- wards et the trailing edge md w fhirJc gnat
th flow field near md do..- sheam the hailing
edge is not expressed by SDM in principle
C
O
02
Total
Unsteady Compone t
~ Velocity Component
0 100 200 step Num300
Fig A-l Component of F'essure Fluctuation on
Flat Plate et x/c=3 0
01
O _
O1
02
Total
Flat Plate Component
s Wing Component
~ I teraction Component
0 100 200 stepNum300
Fig A-2 Component of F'essure Fluctuation on
Flat Plate et x/c=3 0
Representative terms from entire chapter:
image medhod
