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OCR for page 527
Simulation of Incompressible Viscous Flow Around a Ducted
Propeller Using a RANS Equation Solver
A. Sanchez-Caja, (VTT Manufacturing Technology, Finland)
P. Rautaheimo, T. Siikonen (Helsinki University of Technology, Finland)
ABSTRACT
Th mc ompre s sib le vise on. -l ow ar o Ed c mar me
ducted propeller is simulated by solving th RANS
equttiorr with the kid turbulence model The
FPNFLO solver developed et Helsinki Umversity of
Techmology is used in She calculation F NF O is c
mult~block cellcentered fmitewol me computer code
with sliding mesh mm tag g id Ed fre-surice
cm~oilities in f is paper, the flow over c lie series
propeller Ed NSMR nozzle 19A is analyzed Th
concocted flow patterns doss tream of th propeller
Ed duct are illustrated Ed compared with
experiments for one advance n mber Calculated
f ~ t Ed torque are also provided for several
advance n mbers Good correction with experiments
is obtained in terms of force coefficients Ed velocity
distributions
INTRODUCTION
Ducted propulsors are k ow to offer sigmflc mt
cdvmtages for particular marine applications Since
1931, they hive been fi st mstalled m t 3., push-
bocts, tTtsslers, Ed Inter m research vessels, d illing
platforms, submersibles, etc There are some
mstalktions in commercial ships, Ike lard ttnl.erS
Ed buk carriers, Ed warships like mmal destroyers
Ed submarines Among She benefits of d t led
propulsors are remarkable incenses m efficiency for
high propeller loadi 3. with flow- ccelercti g ducts,
or citerrurtively smaller propeller size; reduction of
i flow velocity Ed, consequently, of cavitation Ed
noise with flow-decelercting ducts; better cone ol over
the i flow to the propeller; improvement of
mcnenwxability Ed position-keepmg civilities of
vessels; protection from damage to th propeller, etc
From c Theoretical t mdpomt, the hyd odynamic
inrertorion betw en duct Ed propeller produces c
twofold effect O the one h Ed, the presence of the
duct permits to h m fer the me m lif mg truce on the
propeller blade closer to She propeller tip, which in
tom efficiently deflects th truce to c direction near
that of She ship's motion On She other h Ed, the radial
cone action of She flow due to the propeller action
results in m cdditiorurl f ~ tmg truce on She duct,
which mcreses She total f lust of the propulsor mit
provided chat She loading is sufhciently high to
overcome the duct viscous d cg How ver, Here is m
upper limit also for the duct loadi g, which is
detemmined by the risk of flow separation, es w 11 es
for the propeller loading, which is detemmined by the
risk of cavitation et the propeller tip The design of c
d t red propeller is, the~efme, c complicated process
in which She desig er of en has to make c comprom ise
benison co flictmg ~equi ements in such cases,
having access to i formation on She details of the
flos-.1ield m problematic areas is most valuable for c
successf I desig
Most of She nrLtlv is methods for d t red
propulsors have t en based on potential th ory, using
m actuator disk (Gibson Ed Lewis, 1973; Gibson,
1974; Ftlc.i3 de Ccmpos, 1983, etc 1, lifimg-line or
Iffting-smfce approaches lierss: et cl 1987;
H ghes & Kimus, 1991, etc) for modeling the
propeller Th more recent panel methods also belong
OCR for page 528
to fhis ckss of potentitlbtsed theories Hoshmo
1989, Ktwakitt 1992, etc) All these medhods
~epresent t g ett t dvance in mdttst mdi g the mt m
fett tes of the flow ttomd ducted propulsors
How ver, they tll htve the shortcoming of
mcorporati g viscous effects tttiflcitlly th o gh
empi ical correctiom extenud to fhe fheory in othtt
words, dett ils t s import mt to th desig t t t s fhe gt p
flow tt fhe tip of the propeller ctimot be properly
tmt Iyed with fhese methods Rt ently, some hybrid
models htve been developed ft~t combine viscous
md potentit I fheories mt mly for fhe desig problem,
for example, in Kerwm et t I (1994) More recently,
et Icoktiom of th flow t to md t ducted thuster htve
been mtde tt Postdtm Model Btsm for Schottel
Shipyt td GmbH usmg either hybrid or f lly iscous
models This work ht s ben outlmed m Abdel-
Maksoud (1999), but no validttion dtta w ~e
~elett d in fhe p~esent ptper. fhe RANS equatiom
are solved for t ducted propeller co flgmttion usmg
fhe FINFLO code inititlly developed tt fhe
Labort tory of At todynamics t t Helsi ki University of
Techmology (Siikonen, 1990) The flow ttomd t
ducted propeller of fhe NSMB (now MAllIN) Kt
t ries is simokted md compt ted to experimentt I dt ta
fiom fhe ct itttion tura~el of the Ntgasaki
E perimental Tmk Ktwakita, 1992) The
expttimental dtta ~eported by Ktwakitt tte among
fhe few twaibble in fhe open literttme for fhe
validt tion of ducted propellers
FINFLO is t multiblock t 11-cente~ed flnite-
vol me multig id-shuctmed computer code wifh
slidmg mesh, movmg-g id md fre-t tft e
ctpbilities The code hts been validtted for t
m mber of test et ses meludmg mt tme t ppliet tiom
For propeller flows, validt tion work wt s ct tried out
for conventiomd propeller geomeh ies such t s ft~t of
DTMB propeller 4119 (Smcht -Ctjt, 1998)
Rce tly,the mteldyflowltomdt ht torthruster
wls simullted usmg t slidmg mesh techmique md t
compttison of some tvailble expttime ttl dttt to
computed re mlts wt s p~esented (Stm hez-Ctjt, et t I
1999) The sliding mesh techmique was fo md robust
for the tmt Iy is of fhe time-depende t vit ous flow
The comp tttions w ~e performed in t quasi-steady
md time~cc ttte mtmnet The former ~educed fhe
CPU time to tbout 1/10 rektive to fhe ktter its mt m
merit consisted of demet smg fhe CPU time while
mt mtt mmg t f 11 rep~esentation of fhe propellf t
geomeby, ie without inhoducmg simplifled models
for simulati g fhe propellf t t tion, such t s t tuator
disk or body force models
~ the p~ese t study, the flow t to md t ducted
propeller mit is considered Ew~n though fhe mit
consists of t rotating pt tt (th propeller) tmd t
statior~ty pt tt (fhe duct), t tet dy-state flow ctm be
tst med provided thtt fhe i flow tmd duct tte
axisymmehic Cont quently, the~e is no need to use
specitl techmiques based on overltppmg or sliding
meshes
NUMEBICAL METHOD
Governing Equationt and Turbulence Cloture
The flow simult tion is bt t d on fhe solution of the
RANS equations Thet ctm be writt in the
followmg cont rvt tive form
OLl + O(F Ft ) + O(G Gt ) + O(H Ht ) Q (~y
at a~ ay az
where U is t vector of conservttive varilbles p, p,
P . P t, Pt pZ)T; F. G tmd H tue th invit id flwD:s;
F.,, G' tmd H., t te the viscous flw.es; u, v tmd w t te
the ttsolute velocity components; p is fhe density, k is
the t tbule t kmetic tmergy tmd z is the dissipt tion of
k The so tce tt tm ,Q ht s non+zero components only
for fhe t tbulence equations For fhe steldy-state
propeller tmt Iy is, fhe equations are solved in t co-
ordinate sy ttm ft~t rotates t to md th x axis with tm
tmg kt velocity fi in this case, ,Q ht s fhe t dditiomd
component (0, 0, pfiw, - p~v, O. O) For time~cc ttte
simulltions, fhe so tce terms for th t tbulence
equations are retained, but the~e are no somce terms
in fhe moment m equations
~ fhe low-R y olds mmber k~ model, the
sol tion is e tended to fhe wt 11 mstet d of usmg t
wtll-function tpprotch (Chien, 1982) The so tee
temm for Chien's model is given t s
P Pc 2E T
t = c~ k P c: Pk 2,u ~ e ' /2
(2)
~ Chien's model z is solved msteld of z The
varilble z is deflned so thtt it obttins t :D:ro value tt
OCR for page 529
6he wt 11 tmd 6he true dissipt tion ctm be exp~est d as
7be equations for k tmd z contain empirict I
coeffcients h this study, 6he followmg coefhcients
are tpplied,
cl = 1 44
c: = 1 92(1 0 22e ) t, ~ 1 3
c~=009(1 e °°~s' )
whtteth t tbulenceRey oldsn mberisdefnedts
pk:
R
~ ~
Pteudo-eomprettibility
7be FNFLO RANS solver utili:oss t tructmed
mult~block g id 7 he code wt s initit 11y developed for
compress~ble flows (Sikonen, 1990) tmd it hts been
extended to incomp~ ble flows using t pseudo-
compress~bility medhod (Chorin, 1967) in 6he
pst do-compressibility tpprotch th contimmity
equation V V=0 isrepit edby
~+V V=0
(4)
In the atual implementttion of 6he p~esent
medhod, all 6he dt tivttives dp/og t te repit cd by t
pst do-compressibility ft tor p ~ahmtm et t I .
1997) in 6his wt y, the cht tt teristic speeds reduce to
simple exp~essions of A~=u+p 7he flux
calcoktion is btt d on t simplifcttion of Roe's
medhod Roe, 1981) 7he implicit stage ut s tm
tppro imtte ft torization tmd t multig id method is
t pplied for the t ceiert tion of convergence
A fmite-vol me techmique is used for solving 6he
equatiom 7he dffferentitl equations tte mtegtted
over t computttional cell
where
V,—= ~ SF +V,t,
dt . ~.
(5)
F =ti(F F)+t,(G G)+t (E/ E/~) (6)
tmd the s mmttion is extended over the ft es of the
computttional cell in t rottting f~ame, ie for
propeller ct Iculltiom, 6he f mctional form of 6he flux
equations is simikt to 6he ctse without rotation 7he
diffe~ence is tht t m t rott ting frt me th motion of the
cell ft es is ttkt mto t court m 6he t~luation of
convective velocities (Siikonen tmd Ptm, 1992)
7he inviscid flux is ctit Itted with 6he help of t
rotttion mttri, which htmsforms 6he dept dent
varilbles to t loctl sytem of coordinates nommtl to
the cell s tface (Siikonen, 1994) 7he mtf tface values
t te evaluated by t M SCL-t pe formok
Solution Algorit m
For steldy-sttte flow simoktions, the dit reti:osd
equations tte integtted in time by tpplying the
DDADI ft torization Lombttd et tl 1983) 7his is
bt sed on splitting 6he Jaobitms of th flux terms 7 he
resulting tpproximttely ft tmed implicit scheme
consists of t btckwt td tmd t forwt td sw ep in t ry
coordinate di ection 7be sw eps are based on fi st-
order upwmd diffttencmg in order to t celertte
convergence, loctl time-stepping tmd t multig id
method are also impitmented in F NFLO (Si konen et
tl, 1990) in time-t ttte simoktions for msteldy
flows, th tbove mentioned pt udo-time mteg ttion is
performed im ide t phy ict I time-step (S mch z et t I .
1999) More detailed descriptions of F NFLO ctm be
fomd in Siikonen et tl (1990), Sikonen & Ptm
(1992) tmd Pi6 men & Siikonen (1995)
NUhdEtBICAL BEtSULTS
Gt~mttty, Mmh and Boundaty Conditiont
The case selected for tmtly is is 6he ducted
propeller pret nted m Kt wtkita (1992) The propeller
hts five bkdes, t ditmeter of 0221 m tmd t pitch
rttio of 0 9741 it belongs to th NSMR Kt series
The duct is NSMR nozzle no 19A The clet ttm tt
the propeller tip is 0 72% of 6he propeller ditmeter
LDV met smements w ~e reported t t t rt te of rott tion
of 25 rps conespondmg to tm t dvance coefhcient of
OCR for page 530
0.5. The thrust and torque were measured as well as
the velocities downstream of the propeller.
Computations were performed under the same
conditions. Two additional computations were
performed for advance coefficients of 0.35 and 0.65.
The axial inflow was varied keeping the propeller
rotational speed constant, as in the tests. Only thrust
and torque measurements were available for
comparison for these last computations.
Figure 1. Grid on the surface of the ducted propeller.
Detail of grid construction on the duct.
The grid used in the computations has over one
million cells, as shown in Table I. Special emphasis
was put on modeling the propeller blades and their
near-wakes accurately. The only noticeable difference
in geometry from the ducted propeller model was that
the hub of the computational grid was extended
downstream of the propeller, as is the practice of
MARIN, whereas the experimental model has it
extended upstream. Only the portion between two
contiguous blades has been used in the computations
due to the periodicity of the solution. Figure I
illustrates the grid shape on the duct and propeller
surfaces, and Figure 2 shows the topology.
Table I. Number of cells in the mesh
| Propeller l Duct T Rest | Total Grid |
1 562,688 1 154,112 T 440,832 l 1,157,632 1
/ BLADE ~ / /
Figure 2. Grid topology.
/
The topology was H-type around the propeller
blades with over a half-million cells inside the duct,
and O-type around the duct. The grid has the inlet
boundary modeled by a spherical sector located at
more than three diameters from the propeller center.
The outlet boundary is a plane located at an axial
location between 3 and 4 propeller diameters from the
propeller center. Fine grid spacings are used in the
vicinity of the leading and trailing edges of the
propeller blades in the chordwise direchon, and near
the blade and tip in the radial direction. The minimum
grid spacing in the circumferential direction for the
resolution of the boundary layer was such that the y+
parameter was found to be about 1-1.5 over most of
the blade, and I on the duct surface. A total of 19
blocks was used in order to distribute the computing
load between 8 processors.
OCR for page 531
n.o~t ~
-0.060 _
o
.0.044
-o.o~o _
.o.o..
-o.o`e
oosz 1
1 -0.0s2 _
4000 8000 12000 0
CYCLES
Figme 3 Cormergence histo y of fhe ove~all Ifft
coeffcient
Th hub 2md bkde surfaes of the propeller 2re
rotating solid w211s wifh bo md2 y conditions
e forcmg the velocity fleld to match fhe propeller
rotatiomd speed The velocities 2t fhe duct surfae 2re
set to :D:ro m order to sati fy fhe non-slip bo md2 Y
condition Th 12te~a1 surfaes adjaent to fhe
propeller bkdes 2md duct have cyclic or periodic
bo md2 y conditiom Th block bo mdaries where two
2diaent block surfaes 2 e comcident 2 e deflned 2s
com~ectivities A miform flow condition is aplied to
fhe inlet 2md periph rical smfa s Th st~eamwise
g 2dients of fhe flow variables 2re set to :D:ro 2t fhe
outlet
Convergence
Th computations w re performed on a SGI
Origin 2000 mahine Eight processors were used
The computation time was 13 seconds per iteration
cy le For the second g id level, fhe computation time
was 1/8 times fnat of the flrst g id level A satisfatory
cor~rgence was obtained with 2 Courat n mber of
O 5 usmg two multig id levels
Th corwergence histories of the ove~all lid 2md
d 2g coefficients 2 e prese ted m Figs 3 2md 4 After
3000 iterations, fhe over211 d 2g coefficient cormerged
withm 1% of fhe final value, 2md fhe over211 Ifft
coefficient withm 0 5% Figure 5 shows 2
magmflcation of the convergence history for fhe
cwv211 Ifft coefhcient
Figme 4 Cormergence histc--
coefficient
-O 0.ss:
~°'°488 I 111~ ~
-0.04s7
4000 sOOO t2000
CYCLES
~ry of the over211 d 2g
\~/~~
.o.o~ss~ ~
0 dooo sooo t2000
CYCLES
Figme 5 Cormergence history of the over211 lid
coefficient Mag ffication
Forces and Presares
The k~ tmbulence model gave 2 good conelation
of flow patterns 2md pe formance coefficients with
measmements T2ble 11 shows that th perform2 e
coefficients w ~e c21cu12ted for advance n mber 0 5
wifhin 4 5% of fhe measureme ts ~ p2 ticul2, the
thrust coefhcient for fhe propeller ~TR) was predicted
very acurately Th difference of 2bo t 4% from
measmements m fhe prediction of duct f ~ t (KTD)
OCR for page 532
made a total difference in the total thrust coefficient
(KT) of less than 1%. The torque coefficient (KQ) was
overpredicted by about 4.5%. For other advance
numbers, the differences in thrust were a little higher
but reasonable, although the torque was better
predicted. Figure 6 compares the experimental
performance coefficients to the calculations for three
advance numbers.
Table II. Experimental and calculated performance
coefficients for J=0.5
KTP
KTn
KT
Kid
Experiment
(~)
0.197
0.048
0.245
0.0345
1 st level
0.197
0.046
0.243
0.0361
Calcu~ rations |
2nd level
0.220
0.042
0.263
0.0418
(:k) as read from the test diagram in Kawakita (1992)
0.5
0.4
0.3
o
w
it.
~ I
0.2 mu<
0.1 arm
-0.1
Kt ED
Ktp en
Ktd en
~1 OKq exp.
Kt Cal.
Ktp Cal.
Ktd Cal.
1 OKq Cal.
0 0.2 0.4 J 0.6 0.8 1
Figure 6. Comparison of experimental and calculated
thrust and torque coefficients for several advance
numbers.
The calculated pressure distribution on the ducted
propeller surfaces is shown for the suction and the
pressure side of the propeller blades in Figures 7 and
8, respectively. A low-pressure area can be identified
in Figure 7 at the suction side of the propeller tip
extending to the duct surface.
Figure 8 shows a large area of moderate negative
pressures at the pressure side of the propeller blades.
The duct accelerates the inflow to the propeller, which
results in a large extent of low pressures on the
propeller blades compared with a corresponding open
propeller.
A.. In..
Pd~
above
-
4500
1500
-1500
4500
-7500
i/
-13500
-16500
below
Figure 7. Distribution of pressure difference or
suction side of ducted propeller NSMB l9A.
Pd~
above
4500
1500
-1500
4500
-7500
-I.
-10500
-13500
-16500
below .
Figure 8. Distribution of pressure difference on the
pressure side of ducted propeller NSMB l9A.
Velocities and Hydrodynamic Pitch
Figure 9 illustrates the circumferential variations of
the velocity components downstream of the propeller
plane at r/R=0.5, 0.9, 1.0 and 1.05, and at x/R=0.65
(just behind the duct) for both experiments and
calculations. The velocities are non-dimensionalized
with the axial inflow. The advance number is 0.5.
Each velocity fluctuates with the blade frequency. The
computations show the same trends as the
experiments reported in Figure 3 by Kawakita (19924.
OCR for page 533
3.O1
~ 2.0
. - o
' 1 0
._
an,
z
_ ~
-1 .0
3.0
2.0
0
._
4)
~ 0.0
z
-1 .0 -
3.O1
~ 2.0
.-
'1.0
=e 0.0
z
3.0
{6
0
i,, 1.0
.~
o o
z
-1 .0 -
Ducted prop. (x/R=0.65, r/R=O.9)
Angle (deg.)
Figure 9 Calculated circumferential variations of
velocity components downstream of the propeller at
x/R=0.65 and r/R=0.5, 0.9, 1.0, and 1.05.
Ducted prop. (x/R=0.65, r/R=1.05)
90 1 80
Angle (deg.)
270 360
Ducted prop. (x/R=0.65, r/R=1.00)
90 1 80 270
Angle (deg.)
.~
360
—V~V
—v~lv
—V~V
—VVV
VrlV
Figure lOa. Velocity contours downstream of the
ducted propeller (J=0.50, x/R=0.654. (Kawakita,
19924.
vx
above
2.1
1.9
L 1.7
.5
.3
1.1
of
0.7
below,
Figure lob. Calculated velocity contours downstream
of the ducted propeller (J=0.50, x/R=0.654.
Figures lOa and lOb provide a comparison of
experimental and calculated velocity contours at the
same axial location. The location and shape of the
calculated trailing vortex sheet is apparent from the
figures and coincides with that of the experiments.
The agreement is good. Figures 1 la and 1 lb compare
the experimental and calculated velocity vectors,
OCR for page 534
respectively. The agreement is good except for the
fact that the grid is not completely aligned with the
propeller trailing wake, which results in some lack of
circumferential grid resolution and consequently in a
prediction of tip vortex weaker than in the
experiments.
z
Figure 1 1 a. Tangential and radial velocity field
downstream of the ducted propeller (J=0.50,
x/R=0.654. (Kawakita, 19924.
rR
above
Figure 1 lb. Calculated tangential and radial velocity
field downstream of the ducted propeller (J=0.50,
x/R=0.654.
Figure 12a. Velocity contours downstream of the
ducted propeller (J=0.50, x/R=1.004. (Kawakita,
19924.
vx
above
2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
Below,
Figure 12b. Calculated velocity contours downstream
of the ducted propeller (J=0.50, x/R=1.004.
Figures 12a and 12b show the velocity contours at
x/R= 1.00. The agreement is not so good due to
numerical dissipation. It should be mentioned that a
third-order upwind was used in the radial and
circumferential directions and a second-order in the
axial one for the calculation of the convective fluxes.
Probably, the use of a third-order upwind in the axial
OCR for page 535
direction instead of a second-order discretization
would have improved the results.
1.4 1
1.2
1.0
0.8
-
0.6
° Uncorrected Pitch
~ Corrected Pitch
0.4 ~ Pw/D exp. 0
0.2
0.0
COO 0.25
o
T 1 T 1
P(r)/D 1.00 1.25
out
of
0
process can be repeated for the experimental results
presented in Figure 8 by Kawakita (19924. It can be
compared with Figure 14, where the computed
hydrodynamic pitch angle has been calculated with
and without the correction to the tangential velocity
sign. The agreement with experiments is also very
good. Only at the duct wake located at about r/R=1.05
did differences appear, i.e. the strength of the duct
wake is a little stronger in the calculations.
50
45
40
35
30
Figure 13. Comparison of calculated and experimental
distribution of hydrodynamic pitch in the trailing
vortex wake at x/R=0.65 for J=0.5.
15
10
Figures 8 and 9 in Kawakita (1992) show the
experimental radial distribution of hydrodynamic
pitch angle and of hydrodynamic pitch of the trailing
vortex wake at x/R=0.65 for J=0.5. In this reference,
the hydrodynamic pitch angle of the trailing vortex
wake of the ducted propeller was calculated in the
experiments using the averaged axial and tangential
velocities VX and vt as
flow = tan ~ ~ (7)
rQ + vie
It seems apparent that a small error was made
when the above formula was applied: the
circumferential mean tangential velocity was
introduced in the formula with a positive sign instead
of the correct negative one. The error resulted in a
low pitch and low pitch angle that is not easy to
notice. If we calculate the hydrodynamic pitch for the
computational results in the same way, i.e. giving a
positive sign to the vt, the curve labeled "uncorrected
pitch" in Figure 13 is obtained, which can be directly
compared to Figure 9 in Kawakita (19924. The
experimental data from this reference have been also
included in Figure 13. The agreement is very good.
On the other hand, the computed hydrodynamic pitch
with the correct negative sign is presented also in
Figure 13 with the label "corrected pitch." The same
5
A
IW
IW con
IW exp.
r 1
0.2 0.4
Betaw
Betaw con
· Betaw exp.
a
~~ .
0.6 0.8
rlR
Figure 14. Comparison of calculated and experimental
distribution of hydrodynamic pitch angle in the
trailing vortex wake at x/R=0.65 for J=0.5.
CONCLUSIONS
The incompressible viscous flow around a Ka
series propeller with NSMB nozzle l9A has been
simulated by solving the RANS equations with the k-£
turbulence model. The FINFLO code was used for the
calculations. The grid contained over one million
cells. Good correlation with experiments is obtained
in terms of force coefficients and velocity
distributions in the wake at locations not far away
from the duct. The thrust coefficient has been
calculated without noticeable error for the design
advance number; however, the torque coefficient
differs from measurements by 4.5%. For other
advance numbers, the differences in thrust were a
little higher but reasonable, although the torque was
better predicted. Important features of the flow, like
the hydrodynamic pitch angle of the propeller wake
and the propeller wake itself, were accurately
predicted. The calculation reveals areas of low
pressure at the propeller tip and duct. This
OCR for page 536
i fommation is pseful for improvmg c dupted propeller
desig from the st mdpoint of cavitation The results
of fhe computations show that RANS solv rs me
matme ep gh to provide valuable i formation to fhe
desig er
ACKNOU7LEDGEMENTS
T is work was fumded by th T phmology
D v lopment C nhe TEKES) of Finkmd The
computing time was pro ided by th Cc tre for
Scientiflc Comp tmg of Finkmd The cubhors wish to
fPmk D Jaskko Pykkanen for th valuable help
pro ided dp ing fhis ~esearch
BEFEBENCES
Abdel-Maksoud, M md Hei kc, H. -J. "Ip tigation
of Vi pops Flow A opmd Modern Proppision
Sy tems," CFD'99 Interpatiopal CFD Co ferep e, 5-7
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Chorm, A J. "A m mericcl method for solvmg
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D cted Propeller Perfommance m A i-symmetric
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Gibson, I S md L wis, Rl, "Dpcted Propeller
Apalysis by Sp face Vorticity md Actpator Disk
Theory," Procedings of the Symposipm on Dpeted
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Teddington, E ghmd, Mcy 1973
Gibson, I S. "Themeticcl Studies of Tip Clearance
md Rsdicl Variction of Bkde Loadmg on th
Operction of D cted F ms md Propellers," Jop pal of
M ph miccl E ~meerm~ Sciep e, Vol. 6, No 6,1974
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Propeller in Stecdy Flow Using c Sp face Pcnel
Method," The West-Jcn m Societv of Naval
A chitects, Vol. 166, D c 1989, pp 79-92
H ghes, M J. md Kim~s S A, "A Apalysis Method
for c D cted Propeller wifh Pre-Swirl Stator Blcdes,"
Proceedmgs of Propellers/Shaftmg '91 Symposipm,
Vi gmicBecch,USA,1991
Kcwakita, C, "A Sp face Panel Method for D cted
Propellers with New Wcke Model Bcsed on Velocity
Mecsurements," Jop pcl of fhe Societv of Naval
A chitects of JCP m Vol. 172, 1992
Kerwin, J. E, Kep m, D P. Bkck, S D, md Diggs,
J. G. "A Coppled Viscops Potential Flow Desig
Medhod for Wcke-Adapted Mpiti-Stag, D cted
Proppisors Using Gep rcli:D:d Geomeby," SNAME
Tpmsactions,Vol 102,1994,pp 23-56
Kerwin, J. E, Kim~s, S A, L e, J. T. md Shih, W. Z.
"A Smface Pcnel Medhod for the Hyd odynamic
Apaly is of D cted Propellers," SNAME
Tpmsactions 95, 1987 pp 93-122
L htimiLki, R. Lcme, S. Siikop n, T. Sckmmen, E,
Ncvier-Stokes Ccicpktions for c Complete Al craft,
20th ICAS Cong ess, Sonento, ICAS-92-4 2 1, 1996
Lombard, C, Bardipa, J. Vericatcpathy, E md
Olig r, J. "Mpiti-Dimensiopal Formpiction of CSCM
- A Upwind Flp Dffferep e Eigep ctor Split
Medhod for fhe Comp~ ble Ncvier-Stockes
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Dynamics Co ferep e, Darvers, ~ssachp etts),
1983
Rshmm, M, R~ptaheimo, P. md Sikop n, T.
"Npmericcl St dy of Tp bplent Hect Tpmsfer from
Co fmed mpingmg Jets Usmg c Psendo-
Comp~ bility Medhod," R port 99, Helsmki
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V ptors, md Differep e Sch mes " Jop pal of
Comn tatiopal Phvsics, 43:357-372, 1981
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1995
S mche~Ccjc, A, R~ptaheimo, P. Scimip n, E, md
Sikop n, T. "Comp tation of the Ippomp~ ble
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OCR for page 538
DISCUSSION
C Dci
NSWCCD
This paper is mother example of proliferation of
Reynolds Averaged Navier-Stokes Solvers
RANS) applications in crurlyzing propulsor
performances Today, RANS crurlysis of
propulsor design is part of c stmdard design
procedure m most d sign orgsruzstiom R NS
simulation gives the designers greeter co f dence
in Heir prediction it also enables She designers
to expand th ir d sign envelopes md or explore
new concepts that the designers may feel too
risky to do m the pest Furthermore, the
simulation results cm also serve es c guide for
experimentation This paper show d excellent
agreements on thrust coefficient Ed 4 5%
difference on torque coefficient betw en
computation md experiment data There are
se- end possible cmses, both mmmericcl md
experimental, for the discrepancy One potential
c mse is She difficulty associated with the
computation of integral functiomtl such es th ust
md torque Active research [1] is undergoing to
add ess She issues of accmacy improvement in
computing integral q mtities The flow field
computati ms w me mostly qualitative md it did
ccptme She geneeal pattem especially et near
field of x/R=0 65 in geneeal, the designers are
mterested m the details of flow field to c less
degree of accuracy es compared with thrust md
torque There are sit cti ms that the flow field
parameters me importmt m She overall propulsor
design Examples Include designs for multi-
blcde rows ducted propulsor, md management of
vorticcl flow structures near She tip gap region
Despite big strides have been made in R NS
lech olo t i: th re are still issues that designers
have to be aware of, when they use RANS codes
in then work in general, Here are th ee major
areas of concerns:
(1) Discreti ction schemes md Humeri al
algorithms for robu tness md accmacy:
There are c wide variety of tech lames
available Some of them have been
developed to c level for production use
while others are still undergoing
development Various r tdbotls betw en
speed md accuracy, ease of use md
robust ess et need to be assessed before it
c m be used m the production mode
(2) Turbulence models md their relevance to
the reel simulation:
RANS simulation makes use of
phenomenological models that had its origin
of Rey olds decomposition md Prmdlt
eddy diffusivity conjectures They rely on
the calibrations of experimental date in order
for She models to be effective A
appreciation of then limitation m temms of
regimes of applications is recurred in order
to conduct simulation credibly
(3) Grid struct res md Heir sensitivities
Propulsor is c complex geometric artifact
Blade surface modeling needs to be robust
md accurate Purthemmme, the grid
clu termg md spacing in order to obtain
prop r accuracy needs eye t m: e s md skills
of m experienced modeler
It must be said that verifications md validations
are c must before my use of RANS codes in the
propulsor design process I would I ke to
conclude by mentioning c number of topics that
may be useful for the f ture applications of
RANS to propulsor design md crurlysis
(1) Highfidelitydesignoptimi ction
The time seems mat re to consider
propulsor design optimization et RANS
level High pe formcnce computing
techniques for optimization using high
fidelity physicsbased models have
advanced th ough the rapid development of
cdjomt formulation The cdjoint approach
greatly reduces the mmmber of flow
simulations for computing sensitivities of
design variables in the optimization process
md makes the design optimizati m feasible
et the detailed design stage
(2) Ease of use md implementation
Seamless integration of date t msmission
betw en file desigogeomeby mdthe surface
represe tation for RANS simulation is
highly desuable A adaptive md versatile
grid ystem that cm offer users more
flexibility m grid layout is definitely need d
Unstructmed grid approach may seem to be
the way of griddmg for the futme
(3) High order physical mod long
Ability to predict flow h msition is of -rest
intere t, m particular, for the scaling
problem Approaches are also needed to
add ess chmge of flow nature from one part
of flow domain to mother For example,
from boundary layer adjacent to fihe blade
su face to fiee so tical flow inthe wake
Use of RANS m propulsor design md analysis
will continue to have a significmt role in the
fut re it will compliment experimentation
OCR for page 539
nicely Ed aid designers m exploring more
design options f ough optimizations
[1] Pierce, N. A Ed Giles, M B. "Adjomt
Recove y of Sup mmnm mat Functional from
PDE Approximations," SIAM EVIEW, Vol. 42,
No 2, 2000, pp 247-264
AU7 HORS REPLY
We would I ke to f mk Dr Dci for his valuable
comments on She present concerns Ed future
trends of RANS applications to propulsor design
Ed crurlysis We agree with his views Ed m my
of the topics he has quoted are subject to
contimmous research m our Institutions
He hr. mentioned th e major areas that should
be add essed when using RANS codes es part of
the design work With respect to grid generation
w would like to point out that care should be
taken for the definition of She grid shape She
designer should define the grid shape in such c
way Nat legions with trong gradients of flow
qu mtities are correctly ccptmed by core enn ctmg
enough mmmber of cells in such areas She grid
that w have used in the computations is
stmct red in such c way There is c high
concentration of cells in She propeller wake for
x/R<0 7, which explains She good correction of
flow patterns et x/R=0 65 On the other h Ed et
x/R=1 0 the correction is not so good since the
grid is not following the wake mymore et this
location, Ed She size of She cells is relatively
large A other topics that should be mentioned
are the criteria of convergence Ed the boundary
condition In this calculation w get relatively
fast c d op by thee orders of mcgnit de m
pressure residuals, but this does not guar mtee
the convergence of oveeall qu entities like th ust
Ed torque Boundary conditions Nat reproduce
in c mat Al way the physics underlying the
hyd odynamic problem are key to solving it m c
fast mdaccu~ateway
DISCUSSION
K Nakatake
Ky shu University, Up m
I cm impressed by your huge CFD calculations
In She region behind She propeller hub, Here is c
white region of velocity field Could you
cclcubte the propeller hub vortex by your CFD
scheme?
AU7 HORS' REEL Y
We have modeled The propeller shaft following
the practice et MARIN, i e the shaft is extended
do..- stream of the propeller/duct The
experiments et the Nagasaki experimental tank
w re performed with the shaft extended
upsheam of The prop Her For d is reason Here is
such white region in our results et axial locations
do..- .- or; ~ of The propeller For modeling The
hub so tex we only have to build the
computttiorLtl grid with the shaft pouting
do..- stream instead of upstream, which does not
me m my further complication in fact, we have
used grids for podded propulsors with 0-0
topology around the pod, which allows to
ccptme hub vortices (see 5 mchez-Ccjc et cl
1999) How ver, we have not investigated the
details of hub vortices
Representative terms from entire chapter:
hydrodynamic pitch
