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OCR for page 968
Flow Around Ships Sailing in Shallow Water
- Experimental and Numerical Results
X.-N. Chen, A. Gronarz, S. List
(Versuchsarlsitalt fur Bir enschiffbau e V. Duisburg)
N. Stuntz
(Gerhard-Mercator-Universitat Duisburg)
ABSTRACT
In this paper the results of the inve tigation of The
flow aro md the models of two ships in shallow water
without propeller, rudder md appendices are p~e-
sented he mtention is - based on reliable experi-
mentcl data - to compare computatiomcl results from
different method, obtained on different g ids, md see
how th se methods perfomm Ibe experimental
mouser merits comprise the velocity field et several
stations, the he smfae deformation, the hull pres-
sme dishibution md (not presented in 6 is conhi-
bution) The bottom p~essme Three different compu-
tatiorurl methods w re applied: A t mdard RANSE-
solver on two different g ids (one block-shuctmed
hexched cl, one mstructmed tehahed cl), c RANSE-
solver using c fictitious compel bility md Thus c
flux-dffference- plitting technique md c pole ticl
theoretic medhod devised for The h mscritical regime
Isolnons'l, where the hull is described merely by its
cross-sectiomnl area
INTRODUCTION
In 6 is paper The sp cial characteristics of the flow
ar md ships sailing m shallow water me demon-
shated for two hull forms
hough These is no w 11 defined limit for the water
depth h dividing shallow from deep water, the
behaviour of waves is w 11 k wn to depend on the
depth h he behc iour of vessels scilmg m shallow
water may be charateri:D:d by one cinematiccl
parameter, the dimensionless n mber For,, th depth
Frond m mber, defined es:
F.,, =
with V the speed of the ship md g The g avitatiomnl
acelemtion Fnr, clearly rules The wave resist mce of
the ship, by representing The ratio of V to the so celled
critical velocity ,/: leading thus to c division of
the whole velocity r mge into c subcritical md c
supercriticcl legion dep riding on Fnr, being smaller
or larger thm 1, in similarity with what happens et
high velocities m Hi, where the velocity of so md is
The critical velocity, separctmg The mbsonic fiom the
supersonic r mge he velocity r mge of V with values
of 0 9 < Fnr, < I I is termed The h mscriticcl r mge
So the rather pronounced ch mge m The mug itude of
The wave resist mce is characterized by c single m m-
ber, while the situation for the viscous resi tance is
different, as There is no critical velocity md Therefore
no n mber similar to Fnn
From values of Fnr, ~ 0 65 The wave resi tance
mcreses steeply for increai g velocity V becoming
higher 6 m The wave resist mce on deep water et the
same velocity he wave resist mce hr. c Icccl maxi-
m m in the h mscriticcl region ash re nl6honfh The
peed of the ship being kept con t mt, no rend flow
me may be attained, while so celled solitons
detach from The hull mming ahead of The ship ff the
vessel is forced mto the supemriticcl r mge, the wave
resistance becomes low r 6 m The one which would
be obtained et The same speed m deep water
A other key parameter for The i fluency of the
water depth on the resistance is The depth to d aft ratio
h T. For h T< 4 There cppe fi st charges even in the
viscous resists e for velocities cone po dmg to
values of Fnr, < 0 5 due to c dfffere t di tribution of
The flow aro md The hull
he VBD, Versuchsastalt folk Bim nschiff m
D isburg, Europe m D velopment C Ale for Inland
md Con till Navigation, has since its fo maroon in
1953 1 en dedicated to the Investigation of The shal-
low water effects on the behaviour of ships his
implies also the interaction of The ship with bottom
Ed b Inks of The waterways, cap Its es w 11 as rivers
Besides These activities on ship hydody tmics, the
ship as part of tTa port chtins in integ ted logistics
solutions is investigated m th departments of Tr ms-
po t Economics Ed T mspo t Engineering of the
VBD For the hyd odynamic Investigation, be it for
The indn try or in The f tme of projects for research
f mding mstit tions, The VBD is equipped with
excellent facilities, n shallow water lossmg tank
Iwhe~e water depth may easily be varied, current may
be simnlited ad waves may be generated) bemg the
central .! tem The department of compnhtiorLtl
OCR for page 969
L ~ 1 'I
Fig 1: Lines Pl m - Shallow river vessel (Ship A)
Fig 2: Lines Plum - Inkmd wate way ship (Ship B)
fluid dynamics (CFD) backs the department of expe-
riment~l fluid dynamics D)
The two selected examples of ship t pes are typi-
cal for the irme tigative pe formance of She VBD m
both fields FD md CFD h both cases the emphasis
is on She sailing on shallow water, md as the topic
h re is flow aro Ed She ship, no allusion will be made
to h im, smkage or resistmce values obtzired
MODELS INVESTIGATED
Shallow river vessel
The model investigated Fig 1) is z typical inkmd
wate way ship for extreme shallow water The stern
is, as cm be en from the lines plm, desigmed to
allow She installation of z sp cial flat f uster system
(Schottel P mp Jet), flush with the hull surface Its
scale was 1:12 She model was fitted with 120
pressme taps It 12 dfffere t stations h this paper we
will refer to it as Shdp A She main particulars me:
L ngthbetw perp
Beam
D aft
Displacement
Inland waterway ship
Lpp [m]
B [m]
T [m]
V [m ]
820
95
15
1054
his is z single scr w ship with th t pical form of
inkmd water vessels As c m be seen fi om Fig 2 it has
z characteristic turmeled stern, desigmed to ensme
good water supply to She propeller In these ships She
propellers have rasher small diameters md are highly
loaded Though only lesults for the scale 1:12 08 are
plesented, z series of g osim models was investigated
wish She scales 1:1208, 1:14, 1:1728 md 1:2154
h this paper w will refer to it as Shdp B She mam
particohrs me:
L nghbetw perp Lpp [m] 110 00
Beam B [m] 1145
D aft T [m] 3 00
Di placement J: [m ] 3312
EXPERIMENTS
She coordinate yst m used is nelihsnd d: Taxis
oriented m direction of ship motion, Taxis at right
modes pointing to starboard, z-axis crthogorudly
upward, the origin is It She intersection of aft perpem
dicohr wish base-lme
Ship A
She wave pattem on the water surface was
record d by z series of wave probes located It zppro-
priate y-positiom md stmdard pressme sensors were
used to obtain She hull-pressure di tribution for the
cases
OCR for page 970
h T | Fe | Fch | Rc
1 2 1 0 078 1 0 529 1 3 95~106
20 1 0098 1 0512 1 494~106 1
The velocity field w6 s mly mesured 6t h T = 2 0
with 6 3-c mponent Lcser-Doppler-Velocimeby
~DV) system, specific611y desig cd to be used in
sh611 wwatertets
Shdp B
He~e w will de61 only with 6he model 6t the sc61e
1:1208, comp6 i g some results obt~ined m 6he
sh611cw-water t wmg-tmk with computational
re mlts R suits 6r e p~esented for the h T values
h T Fn FCh Rn
I 5 0 138 0 685 I 19~107
3 0 0 180 0 681 1 44~107
Deformation of 6he fiee smf6 6md hull p~essme
w re detemmmed 6s in Ship A, while for the survey of
the velocity field (5 sections m 6he stern region) 6
spherical 5-hole p~essme probe was used
CFD-METHODSAPPLIED
RANSE-Solver CTX-S from AEA Technology
~dethods I & 2)
This solver 6pplies 6he fmite vol me-element
method Several tmbulence mod is of the scal6
eddy- iscosity t pe or 6 R y olds- tress model may
be chosff~ He~e 6he choice betw en blockshuctmed
hexalhed 61 ~thod 1) 6s well 6s completely mshuc-
tmed g ids wi6h teh6 hed 61 meshes ~dethod 2) is 6m
6ppeali g featme A mesh ~efmement in (eventuclly
nested) regions is easily perfommed for 6he mshuc-
tmed g id For 6he d tailed ch6 6 teristics 6md fe6-
tmes 6~ibble consult 6he sp cification sheet pro-
vided by AEA Techmology (Grotjams & Mbuter,
1998; N N,1999)
RANSE-Solver hased on the principle of artificial
eompressihiNty ~dethod 3)
T is is 6 finite vol me method using 6 tructmed
g id Inhoducmg 6m 6 tifici~l compressibility 6
coupling of the so obt~ined contmnity equation to the
moment m equations is 6chieved, 611cwmg 6m effi-
cient Roe flux-dffference- plitting techmique Th
method mcludes 6he comput~tion of the fre water
surf6 conside~ed 6s 6he bo md6 y betw en water
6md 6 ir 6md descobed by 6 so ca 11ed level set f mction
satisfymg 6m 6dditiomd equation (derived fr m th
bo md6 y condition) solved togedher with the 6bove
mentioned equations The turbulence model is the
tamd6 d k-8 model (St mt, 1999)
For the th ee RAN SE-methods 6he fo l low mg
bo md6 y cond6tions have been used:
Bottom 6md w611: no slip, movi g bo md6 y
(u = - Va), velocity norm61 to bo md6 y is :osro
Ship no slip, st~tiorury w611, velocity norm61
6md t mgenti6 1 to bo md6 y is :otro
W6ter smf6 e. center ckme: symmetry,
velocity norm61 to bo md6 y is :osro, viscous
fmces p6 611el to b md6 y 6re :osro,
Me6hod3: bo md6 y condition acordmg to
fiee smf6 e flow
Iniet: velocity V~ nomm61 to inlet, turbulence
intensity = 0 05, tmbulent to molecohr
viscosity ratio = I O
Ouflet: constmt pressure, Method 3: non
reflectmg bo md6 y condition (fiee smf6 e
flow)
Shallow water potential-theorede transeritical
treatment fi`dethod 4)
Applymg sh~llow water w6 fheory 6md 6 f6 -
field near-field heatment with 6ppropriate matching,
6m ing nious pote ti~l fhemetic method was devel
oped by hen ad Sh6 m6 (1994) 6md reimproved by
hen (1999) yielding 6 detsiled description of fhe
deformation of th fiee surfae An equation of 6
Kcdomtsev-Pet lash iii type for 6 depth 6 raged
potenti61 is derived for fhe f6 field 6md a improved
slender body theory for the ne6 field Though fhe
method was developed originclly to cope wifh the
mst~tionary c6 se of the t mscritic6 1 ~egime (includmg
fhe solitons), it is aplicable over 6 wide ramge of F h
n mbers Th mmerical solution is obtamed by
6pplyi g 6 finite dffference method The topog 6phy
of the waterway bottom may vary m di~ection per-
pff~dicohr to fhe di ection of ship motion 6md the hull
is ~epresented me~ely by its cross-sectiomd 6 e6 dis-
h ~bution 6md the loc6 I beam of the water line
EFD RESULTS
Shdp A
The pressure di tribution on fhe hull is sh wn in
dimem iorul form by colours 6md isolmes on the hull
surfae The Iccation of fhe pressme taps is show
(red dots), Figs 6 6md 9 The ~esults (G mur6 et al,
OCR for page 971
~~ :Y #~:5
~# i::ii:S'S<''7~:~< AS:<''
S:S:~ ~.~.!{,~.SS~
#: : : ~ ~ ~ ::
Fig. 5: Co~ut~ional grid (flood 2), A)= 2.0
. ~
. ~
I
I
~ )
-1=I
1
--~I
-2=
Fig 6: Mull pressure distribution. Experi mental
results A~ = 2.0, ~ = 0.098, Ash = 0.512,
An = 4.94~106
~ J.
1 _.
11 ~ .
iI ~ ~
'~ 11
I ~ I
I ~
Fig. 7: Hull pressure dls~lbutlon. Coypu t~lonsl
results (method 1 ) A~ = 2.0, ~ = 0.09E,
= 0~12, An = 4.94*106
1
.. .
.>I
-1~
1 .
~ ~ I .
1 ~ .
~ I .
~ I
_ ; .
_ ; .
~ I I
_ ~ 1
..~ ~ 1
:
°I
-a 1~?
-100 ~
~~] ~
-180 I
ELI
Fig. 8: Hull pressure distribution. Coypu t~ionsl
results (hotbed 2) ~ A)= 2.0, ~ = 0.098,
Ash = 0.5 12, An = 4.94* 1 06
::-
-
-
-
-
-
-
-
5p ~1
# ~~
-50 ~~
1
-150
Fig. 4: Mull pressure distribution. Experi mental
results at A) = 1.2, ~ = 0.078, Ash = 0.529,
An= 3.95*106
~ go']
Fig. 10: Hull pressure distribution. Coypu t~ionsl
results (method 1) A) = 1.2, As= 0.078,
Ash = 0~29, An = 3.95 + 106
OCR for page 972
\
\
-
~ ~ - ~ ~
=~
~ - /4
'.
~ - ~ ~
~ - ~ ~
~ 7
Fig. 11: Velocity distribution (stern section
x/Lpp = 0.14. LDV-measurements at h/T = 2.0,
Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
1
i
~,
Fig. 12: Velocity distribution (stern section
x/Lpp = 0.1~. Computational results (Method 1) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
Fig. 13: Velocity distribution (stern section
x/Lpp = 0.1~. Computational results (Method 2) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
\
-
-
Fig. 14: Velocity distribution (stern section
x/Lpp= 0.0~. LDV-measurements at h/T = 2.0,
Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
....
1
~ ~ ~ ~ .~ j, ,.,, ~ ~ ~, ~ ~ .,~., ,~ ~ ~ ~ ~ ~
~ ~ ~ ~ ...~ ~ ~:..: :
-~ ~ ~ ,s'.'...'..'.
~ ~ . .
~ _ ~ ~ i l ~ _
~ /-' ~ W.'`
+ ~~ ~ ~ W0
"
. ~ - /~ .t
A~ ~ ~ _
> ~._ _.,
1
Fig. 15: Velocity distribution (stem section
x/Lpp = 0.0~. Computational results (Method 1 ) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
- _'.'.....
_4'.
-
_
~ _ ~.~.~.~.~ ~ ~ ~ ~ ~ ~
—i
- ~ ~
~ ~ t
.'
~,p,~o
,'.. -
. .~ - , .~
Fig. 16: Velocity distribution (stern section
x/Lpp = 0.0~. Computational results (Method 2) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
The colour of the velocity vectors of the computational results for Ship A indicates the absolute value of the
velocities, with warm for high and cold for low speed.
OCR for page 973
\
~-~- ~
~ ~ J
_ ~ ~
_
\
~n
-
1
Fig. 17: Velocity distribution (stern section
x/Lpp = -0.1). LDV-meas urements at h/T = 2.0,
Fn = 0.098, Fnh= 0.512, Rn = 4.94*106
. .
.~
~'
Fig. 18: Velocity distribution (stern section
x/Lpp = -0.1). Computational results (Method 1) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
. -
Fig. 20: Velocity distribution (stern region). LDV-
measurements at h/T = 2.0, Fn = 0.098,
Fnh = 0.512, Rn = 4.94*106
'~: ::
. ~.~.~:~.~ ~ ~ ~ ~ ~ ~.
...
Fig. 21: Water surface deformation. Experi mental
results at h/T = 2.0, Fn = 0 098, Fnh = 0 512'
Rn = 4.94*106
............... ;
Fig. 19: Velocity
.
.
distribution (stern section
x/Lpp= -0.1). Computational results (Method 2) at
h/T= 2.0, Fn = 0.098, Fnh = 0.512, Rn = 4.94*106
-10 -5 0 5 r
., _ (7 [mm]
Fig. 22: Water surface deformation. Compu tational
results (Method 4) at h/T= 2.0, Fn = 0.098,
Fnh = 0.5 1 2
OCR for page 974
Ship B
Overview of figure numbers showing results
hull presssure
surface
deformation
velocity
distribution
velocity
distribution
velocity
distribution
velocity
distribution
streamlines
surface
deformation
h/T
1.5
1.5
1.5
1.5
1.5
1.5
3
. ~
x/Lpp
-.1098
.0274
. .0640
006
:=
;=
EFD
Exp.
23
29
51
33
36
39
42
=
52
34
37
40
43
CFD-Method
2
24
35
38
41
44
48
4
25 _
30
31 51
53
~-
46
49 _
—52
(Remark: The calculations with Method 3 have been
carried out at h/T= 2.0 instead of 1.5)
The computational grid for the Methods 1 and 2
(Fig. 26 and 27 on the next page) extended in x-
direction from 1.5 Lpp in front to 0.5 Lpp behind the
ship, from the water plane to the bottom and from the
center plane to a channel width of 4.9 m (half breadth
of the VBD towing tank).
The calculations with Method 3 used a structured
grid (Fig. 28 on the next page) which extends in x-
direction from 0.82 Lpp in front to 1.82 Lpp behind the
ship, from the water plane to the bottom and from the
center plane to the channel wall. The structured grid
used consisted of 160 elements in longitudinal, 50 in
transverse and 33 in vertical directio n.
The volume meshes for calculations carried out
with the 3 RANSE-methods had the extensions
' Elements |
780.606
986.935
264.000
-
~ ~.
Fig. 25: Hull pressure distribution. Compu tational
results (Method 3) at h/T = 2.0, Fn = 0.138,
Fnh = 0. 546, Rn = 1.19*107
1 (Hex)
2 (Tet)
3 (Compr)
843.867
217.618
279.174
The resolution used for the calculations with
Method 4 was 60 sections for the model, 420 cuts in
front and 840 behind the ship. The tank width
(9.81 m) was divided into 61 intervals.
_s
-
-
_ 300
-
_~r
', ~` T. ~ 31
——~ Ll~lm J
n
-too ...
Fig. 23: Hull pressure distribution. Experi mental
results at h/T = 1.5, Fn = 0.138, Fnh= 0.685,
Rn= 1.19*107
.
__
300'
G
p [N/m3]
-500
............... ....... ,, .. W.
Fig. 24: Hull pressure distribution. Compu tational
results (Method 2) at h/T = 1.5, Fn = 0.138,
Fnh = 0.685, Rn = 1.19*107
30,
OCR for page 975
Fig.29:W~ersurF>edd~nnation (.
Expc~imontsl~esults at ~/F = 1.3, ~=0.138,
Ash ~ 0.685, An = 1.19*107
- a Saks-
Fi8.26:Co~ ut~ib0~lgrid(~1hod 1,hc~abcdrat
block~Uuc~rcd),~=1.5
Fig.27:c0~utationalgrid(~hod2,tolr~hedr
6~ l.i
s ~
_ ~ {~1]
fig.3Q:W~orsur~c~de~rmabon A.
Cpmput~Jon~ltosults(~1hod 4)al 6) ~ 1.5,
-1C -5 0 S ~
~~ <~E~ESESESESE~E~E~E ~$# ~ [_]
Fi~.31:W~ersnr~ced<~rm~hon (.
Co~,u1~ioni1resuLs (redbud 3) at /# ~2.0,
= 0338, Ash = 0 5456, On ~ 139*107
Fig.28: Co~ut~iobslgrid (Method 3,s~uc~rod,
~h~k~\ ~=2(
Fig.32:Seloct~d Sections The measuremc~t Id
co~ntabon~of~ev~loc1Vdistr~ution
OCR for page 976
~ - 1 4 VX [mls]
Fig. 33: Velocity distribution (behind stern,
x/Lpp = -0.1098).
Computational results (Method 1) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn = 1.19*107
05 ~ ~ 14 VX [mis]
Fig. 36: Velocity distribution (stern section
x/Lpp = 0.0274).
Computational results (Method 1) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn= 1.19*107
0 05 ho 1.4 VX [awls]
Fig. 34: Velocity distribution (behind stern,
x/Lpp = -0.1098~.
Computational results (Method 2) at h/T = 1.5,
Fn = 0.138, Fnh= 0.685, Rn= 1.19*107
0 05 1.o 14 VX ['n/s]
Fig. 37: Velocity distribution (stern section
x/Lpp = 0.0274~.
Computational results (Method 2) at h/T = 1.5,
Fn= 0.138, Fnh= 0.685, Rn = 1.19*107
0 05 ~ ~ ~ 4 VX [IS]
Fig. 35: Velocity distribution (behind stern,
x/Lpp = -0.1098).
Experimental results (5-hole-pressure probe)
at h/T=1.5, Fn=0.138, Fnh=0.685,
Rn= 1.19*107
,'
~ ::
,~,,4 id, ~
/~ ~:~ ·.'5 '5, `:~.
1 _
0 0.5 1.0 1.4 it [mls]
Fig. 38: Velocity distribution (stern section
x/Lpp = 0.0274).
Experimental results (5-hole-pressure probe)
at h/T= 1.5, Fn=0.138, Fnh= 0.685,
Rn= 1.19*107
OCR for page 977
0 O.5 1 0 1.4 Vx [ - S]
Fig. 39: Velocity distribution (stern section
x/Lpp = 0.0644.
Computational results (Method 1) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn= 1.19*107
___ I T7x LAPIS]
0 0.5 1.0 1 5 1 8
Fig. 42: Velocity distribution (stern section
x/Lpp = 0.1006).
Computational results (Method 1) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn = 1.19*107
0 05 ~ ~ ~ 4 VX [IS]
Fig. 40: Velocity distribution (stern section
x/Lpp = 0.064~.
Computational results (Method 2) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn= 1.19*107
Fig. 43: Velocity distribution (stern section
x/Lpp = 0.1006~.
Computational results (Method 2) at h/T= 1.5,
Fn = 0.138, Fnh= 0.685, Rn = 1.19*107
Fig. 4 1: Velocity distribution (stern section
x/Lpp = 0.064~.
Experimental results (5-hole-pressure probe)
at h/T= 1.5, Fn=0.138, Fnh=0.685,
Rn= 1.19*107
Ax Em/si
0 0.5 1.0 1.5 1.8
Fig. 44: Velocity distribution (stern section
x/Lpp = 0.1006~.
Experimental results (5-hole-pressure probe)
at h/T= 1.5, Fn=0.138, Fnh=0.685,
Rn= 1.19*107
OCR for page 978
0 0.5
1.0 1.4 Vx [mls]
Fig. 45: Velocity distribution (stern section
x/Lpp = 0.02744.
Computational results (Method 3) at h/T=2.0,
Fn= 0.138, Fnh= 0.546, Rn= 1.19*107
0 0.5 1.0 1.4 Vx [m/S]
Fig. 46: Velocity distribution (stern section
x/Lpp = 0.064~.
Computational results (Method 3) at h/T=2.0,
Fn = 0.138, Fnh = 0.546, Rn= 1.19*107
Vx [m/s]
Fig. 47: Velocity distribution (stern section
x/Lpp = 0.0274~.
Computational results (Method 3) at h/T=2.0,
Fn = 0.138, Fnh= 0.546, Rn= 1.19*107
~~.~.~
~d ~ ~ ~
Fig. 48: Streamline visualization by ribbons.
Computational results (Method 2) h/T= 1.5
Fn = 0.138, Fnh = 0.685, Rn = 1.19*107
Fig. 49: Streamline visualization by ribbons.
Computational results (Method 3) at h/T=2.0,
Fn= 0.138, Fnh= 0.546, Rn = 1.19*107
OCR for page 979
Vx [mls]
Fig. 50: Dependence from the water depth: Velocity distribution (stern section x/Lpp - 0.0274~.
Computational results (Method 1) at Fn = 0.0426, Rn = 3.64*106
0.2 . . . . . . . . .
O .1 ~ _
- o 1 ~y,h= 1 7~ a . _
-1 o 1 2 3
z/h o :~ _ t,h ')
- O . 1 y/h=2.684 . .
- 0 . 2 ~
-1 o 1 2 3
0.2 . . . . . . . . . . . . . .
0.1
o ~ ~ ~ ~
-o 2 y/h=4.026 ~V-~ - =~ =
. . . . . .
-1 o 1 2 3
0.2 . . . . ~ . . . . . .
0.1 ~ 1
z/h.o' ~=~._~ ,
-o .2
-1 o 1 2 3
o 2
O . 1
z/h o
-0.1
-o .2
-
- 1 o tUR 2 3
Fig. 51: Comparison of measured (solid line) and
computed (dashed line, Method 4) wave cuts for
different y/h at h/T= 1.5, Fn = 0.1406,
Fnh = 0.6302, Rn = 1.097*107
z/h o
-1 o 1 2
0.1 .. .. . 1 ~
z/h o' ~ 6~ _ _ _ ~ _
-1 o 1 2 3
0.
~OoO1 y~=4.026r ~
-1 o 1 2 3
z/h o~'
-1 o 1 2 3
~'' '1~'''1''''1''''l''''1''1
o . 1 ~ ~ ,' ~ '~-~1
-1 o 1 2 3
t U/1
Fig. 52: Comparison of measured (solid line) and
computed (dashed line, Method 4) wave cuts for
different y/7' at h/T= 3.0, Fn = 0.1803,
Fnh = 0.6805, Rn = 1.440*107
OCR for page 980
2 0 ~y,/
60
Fig. 53: Computed 3-D-wave pattern showing
reflection on tank walls (Method 4) at h/T= 1.5,
Fn= 0.1406, Fnh= 0.6302, tDomain comprising
the full tank width, vertical scale exaggerated 8
times]
-n
Fig. 54: Computed 3-D-wave pattern showing
detaching solitons (Method 4) at h/T = 4,
Fn = 0~353, Fnh= 1.012, [Domain comprising the
full tank width, vertical scale exaggerated 8 times]
COMPARISON OF RESULTS
The correspondence between hull pressure distri-
butions obtained by the different computational
methods and between computation and experiment is
disappointing (Figs. 6 - 8 and 9 - 10 and 23 - 254.
This applies to both hull forms and to any of the h/T
ratios presented. The computed distri buttons show a
broader range of variability than the experimental
distributions suggesting that the (three-dimensional
and probably rather thick) boundary layer in the stern
region has a certain equalizing effect and is probably
not well reproduced in the compu tation. A pressure
variation across the layer (contrary to the assumption
for thin boundary layers) strongly dependent on the
location on the hull is possibly present too but not
reproduced in the computation. For Ship B in addition
the experimental values as shown by the color distri-
bution are misleading, as pressure taps were not
located precisely on the sharp edges bordering the
tunnels but on the sides of these edges avoiding thus
likely cusps in the real pressure distribution, the
interpolating postprocessing routine producing rather
a smoothed distribution.
Advancing to the distribution of the velocity as a
vector field we are nevertheless faced with a better
correspondence. For Ship A (velocity measured by
LDV at the h/T ratio 2) this is fair at the section
x/Lpp = 0.1 while at the section x/Lpp = 0.0 there
seems to be a suspicious deviation from symmetry in
the experimental values as displayed by the arrows
representing the velocity vectors in the plane y= 0.
For Ship B (velocity measured by f~ve-hole pressure
probe at h/T = 1.5) the computed distributions of the
velocity obtained by Methods 1 and 2 in the four
selected transverse planes (Fig. 32) show the charac-
teristic vortex well known from the expert meet,
though its location appears slightly altered, the corre-
spondence being somewhat better for small x/Lpp
(Figs. 33 - 35, Figs. 36 - 38, Figs, 39 - 41 and Figs.
42 - 44~. Due to difficulties in the generation of the
structured grid for the Method 3 here an h/T ratio of 2
and not of 1.5 was chosen. The results are displayed
in the Figs. 45 - 47.
The change of velocity field with decreasing water
depth presented in Fig. 50 (computational results
only) gives a good impression of the so called
shallow water effect. It can be seen, that the vortex
core is displaced outward with decreasing water depth
and the influence of the hull pressure field influences
the bottom pressure more and more.
The deformation of the free surface is not well
reproduced by the computational methods, neither for
Ship A, where only results from the potential theo-
retic Method 4 (Fig. 22) may be compared with the
experimental results (Fig. 21), nor for Ship B. where
results from Method 3 (Fig. 31) and from Method 4
(Fig. 30) should match the experimental pattern (Fig.
29~. The comparison of wave cuts for Ship B shown
in Fig. 51 (h/T= 1.5) and Fig. 52 (h/T= 3) gives an
impression of the quality attained by Method 4.
The 3-D wave pattern shown in Fig. 53 demon-
strates the ability to reproduce wave reflections from
the side walls, while in Fig. 54 the generation of soli-
tary waves detaching from the bow at a speed near the
critical Froude number has been computed.
OCR for page 981
CONCLUSION
As a towing tank institution the VBD has a para-
mount interest in deliver reliable data to its
customers. This applies nowadays as well to CFD
results as it has been always expected for the EFD
results. Independence of the computational grid used
is one of the first achievements to be reached. We see,
that for us, there remains some work to be done.
Realistic results of the flow around ships in
shallow water will only be obtained if the local
surface deformation and the squat are appropriately
worked out. In addition to model scales full scale
cases should be computed too. In the future the
influence of the turbulence model applied has to be
clarified. So far the numerical treatment corresponds
to the situation in the standard resistance test. The
dependence of the flow around the ship on different
canal widths will have to be one of the next steps. In
the future the appropriately simplified simulation of
the propulsor will be integrated into the
computational treatment as well as rudder and
appendages thus corresponding to the situation in the
self-propelled-test. This will finally lead us to more
thorough investigations of the instationary flow and
the manouevring of ships in restricted water.
Acknowledgements
We acknowledge the dedicated work of all the
members of the VBD engaged with those projects
which lead to the results (EFD and CFD) presented in
this paper. Prof. E. Muller and Dr. J. Kux contributed
by their guidance in the preparation and formulation
of this contribution. Thanks go to the institutions
from the state Nordrhein-Westfalen and the Federal
Republic Germany which funded the research
projects involved.
REFERENCES
Chen, X.-N. (1999): Hydrodynamics of Wave-
Making in Shallow Water, Dissertation, Faculty of
Mathematics, University of Stuttgart
Chen, X.-N. and Sharma, S. D. (1994~: Nonlinear
theory of asymmetric motion of a slender ship in a
shallow channel. 20th Symp. on Naval Hydro-
dynamics (ONR), Santa Barbara, California, National
Academy Press, Washington, D.C.
Gronarz, A., Grollius, W., Rieck, K. and Pagel, W.
(1995~: Experimentelle und theoretisch-numerische
Stromungsuntersuchungen an Binnenschiffen. VBD-
reportno. 1366
Bet, F., Stuntz, N., Hanel, D. and Sharma, S.D.
(1999~: Numerical Simulation of Ship Flow in
Restricted Water. 7th International Conference on
Numerical Ship Hydrodynamics, Nantes
Grotians and Menter (1998~: Wall Functions for
General Application CFD Codes, ECCOMAS 98,
Fourth European Computational Fluid Dynamics
Conference, Athen
N.N. (1999~: Using CFX-S for Unix & Windows NT
User manual from AEA Technologies, Harwell, UK
OCR for page 982
CONCLUSION
As z towmg t mk institution fhe VBD has z pma-
moumt i te~est m deliver reliable dats to its
customers 7his zpplies nowadays as w 11 to CFD
remlts zs it has been zlway expected for fhe E D
remlts Independence of the computatiomd g id used
is one of the flr t zchievements to be reached We see,
that for us, the~e remains some work to be done
Realistic resuts of fhe flow aroumd ships m
shall w water will only be obtained if fhe local
suface deformation md the squ~t me zppropriately
worked out h zddition to model scales full scale
cases should be computed too in the futme fhe
i flu e of fhe tu bulence model zpplied has to be
ckr ffied So far fhe m merical treatment conesponds
to the situstion m fhe t mdard resistmce te t 7he
dependence of fhe flow aroumd fhe ship m diffe~ent
carml widths will have to be one of fhe next steps in
the futme fhe zppropriately simplifled simoktion of
th propu sor will be integ ated into the
computatiorul t~eatment as well zs rudder md
zppendages thu conespondmg to fhe situation in the
seff-propelled-test 7his will finally lead us to mme
thorough irme tigations of the in tationary flow md
the m mou ing of ships in restricted water
Acknowledgements
We zck owledge the dedLcated work of zll fhe
m mbers of the VBD engaged wifh those projects
which lead to the re mlts FD md CFD) p~esented m
this paper Prof E Mflller md D J. Ku contobuted
by thei guid mce m fhe preparation md formu ztion
of fhis conh~bution 7hmks go to fhe mstitutions
from fhe tate Nor d h in-We sffzlen md fhe Fe deral
R public Germ my which fumded the research
projects involved
REFERENCES
Chea, X.-N. (1999): Hydrodyn mics of Wove
Mohng in Shollow Wot r, Dissertation, Faculty of
Mzfhematics, University of Stuttgart
Chea, X.-N. and Sharma, S. D. (1994): Nonlineor
theo y of arymmet ic m tion of o slender ship in o
shollow chonnel 20th Symp on Naual Hyd o-
dynamics (ONR), S mtz Barbma, Czlfforniz, Nztiorud
Academy Press, Wzshmgton, D C
Gronarz, A., Grolbus, W., Rdeek K. and PagA, W.
(1995): Ezperimmt lie und theoretuchmumerische
Stnomungsuntensu~hungen on Binnenschifm VBD-
reportno 1366
Bet, F., Stuntz, N., Hiinel, D. and Sharma, S.D.
(1999): Numericol Simulotion of Ship Flow in
Rest icted Wote': 7~ Internatiomd Co fe~ence on
Numerical Ship Hyd odynamics, N mtes
GroUans and Menter (1998): Woll Functions for
Gmerol Applicohon CFD Codes, ECCOMAS 98,
Fouth Eu op m Compubtiorud Fluid Dynamics
Co ference, Athff.
N.N. (1999): Using CFX 5 fw Uniz d Wndow N.
User marmal from AEA Techmologies, Harw 11, UK
Representative terms from entire chapter:
stern section
