Investigation of hydrodynamic characteristics of a plate intersections the free surface in shallow water

KoHEpEHu4q COf-ERENCE

00

PEX%

KA-IEDBAM CWB SEAC)NG LES OF SH?S

ß5'-81X TEX}-fECKIíX COU KEH ANO MARNE STJCRPES

1983 &

_j

Sterer 1983

rrc

tNVEST!GATIDU F KY)RC3ArIlC CHARACTERISTICS CF PLAIC TEECTZ1 FREE S'JFACE ;i SLLCl.:'1ATr

. i-:ilano, 'I. Lefterova, i. Vass:le.

.trnduc tien

The decrease in rateray.depth H to shin _draft T ratio leads to considerable chance in the set of hydrodynanlc forces acting on hull, rooeilors nd

control surfaces. As 3 result, besides ship erorul-sion characteristics strong changes underco its ca-noeuvring qualities as weil. In view cf the svoiien dirensions of the contenoorary ships,tankers in

mar-ticular, as well as the jncre5siflc number of _Ships for coastal navigation, the problem for studying nd

determining tue s4noeuyring qualities ir shallov

wa-ters appears very tooical

l:owevar, in this flQ!d te nuist'er o theoret,-ai _{and experimental investi'ations i5 yet rather} llurit diost1y, the thec':tical investications are

based on hull schematizetcn to flat plate [lj, 1

or equiv3lent ellipsoic

_{[i). [4]}

_{In t'im first} as'-proach, supposing trat the rdrodynaric load _{rin the} plate in shallow waters consists c potential arid

vortex cnponent. and acceotthr t;ie _{predetermined} circulation distribution aionc the chord, trie sway

and yaw dasmping as a function of HIT ratio is deter-mined after the singularity method. The influence of H/T parameter ori addes masses is usually numerically Investigated using the potential methods or

electro-dynamic and magnetoelectric analogy.

In the pres'nt peper,trie prtblea' or qualita-tive and cjantitatiye evaluation of the change in

damping and added masses of flat plate in _shallow

water _{at different Froude nurbers is forrejlatd,aud}

experimentally solved. Static drift anale tests of plate arid forced sway and yaw tests v'ers :arric ot using planar motion mechanism. For evaluatirip _the plate approximation towards the b'dy hull , t'te expo-rimer.tal results are ccnparad with analocous for two ships, differino Lasicall;' n fullness of body i ine

2. Experirental deter-matSon n Fiat plate hvd rodynamlc characteri stics irr shallow water

Foil model basic charactcríszrcs : te:

Con-ditions are shown ir, Tat±

As can be seen frt the Table, the

ts' -.:3ect

42 .- i

is a plate with aspsct rett A

L ':::1.

ci.'ating strcn' chane in the rj.lrQC.'r.a'tC :e-:-t's-rmstics at snall HIT ratios, t- teSts :.tr

out at the following deoths: H 1.2; 1.5; arid The depth . 4.2T ir so'e cases ori o'. _r'.

the deec vater t,hi:h is confi rien, o:. te

:e'a

t-al dsta.

Table i l'lodei characteristics and test cpnitc'i

ao M

(//////////////////////// f//////7///T//// ///'

The advance speeds of thé :ia"s sts dor"n speeds c 1 erIc 7 krittS of '.' "ca

lariner tyra s'is' and fufl-ui-ieo s-i.. s-:

.ectively ac'j'i tc:

V1 = i.;;2 /S2C fl 0.1941

arid V2

C34 'isec

n

TSkiniC into accrunt 'chat thc

i.

i -noeJvres cari be rearded as oSclCt1Oi5

. t'

erlod, the f'-scuen:y f C. 6 'z w cmicse'

sic for the exe'ìer'..

0'na:ioetr sionais dt

"s'cssr

fer hartrsc lineriztttr r'

resi

-:: -t.::

oraete

derieridencres, ¿

..-r

'5 - . .n

1.0

s

Cm

Aiy.m. COS Gt + Biy.çn . sinGt exdiu _{Cy ( pendencies.(The symbol}

.

used for definition of the respective values

ineasu-comoared with analogous results for 'lariner type ship and tanker Tokyo Maru f3J and for plate with aspect

ratio ?L= C.lzO tested in the Bulnarian Ship Hydro -dynarics Centre (BSC) deep water tank f5].

3. Rer1ts and analyses

The dependencies of lateral force C and moment

C nondimensional coefficients on the drift angle B V) and te nodirr,ensioflal yaw rateca and the ras-etive accelerations 3re presented in graohic form

ei's i

6. Attention should be paid to the fact

10G -.- f) drci 1.0 Fig i Lateral force coefficient _{at oblique tow}

that the nonlinearity of C becomes very large as

the ratio F!T decreases. The cor.narison ricade _with the plotted foil characteristics in deep water (H/T = o) shows that the differences between the test resul ts a t ratios P/ T = 4.2 and are very small

Fig 2 Yawinc moment _{coefficient at oblique} tow A 1,0 O r. -0,1 -C.0 -0.3

Fig 3 Cos-component of lateral force versus The increase of C at static tests in the

dif-ferent depths (Fig. 1) is larger than from forced

sway tests (Fig. 3) which presupposes _{presence of} nonstatlorrary effects in shallow water.

Fig 4 Sin-cocnponent of lateral force versus V_y

B 0.1

-055 -0.4 -03 -0:2

Fig 5 Sin-cononent of lateral force versus w

42 - 2

0.1 The neasured hydrodymamic characteristiCS are _{red at approxiciately infinite water depth).}

008

0.06

-004

a- tS

D--05 -as -0 -0.3

-2

j

F10 6 Cos-coiiponent of lateral force versus i

The plate curvilinear motion in horizontal olane of a linear approach, can be followed with th:

;ell-known system of differential equaticins [71.

m22j

+npm25.ii

(1)

-m26j -

rn - fi +

-

m.0 -

_O where: rr _{, - sway damping derivatives}

- yaw damping -otary)derivaives in22, m66 - added mass and inertia.

The vvlues of these derivatives as well as those of the added mass and inertia at different HIT

ra-tios, are ='en in Tables 2 and 3.

Table 2 Derivative values at En = 0.0637

y

002

001

ici oruìr to receive more clear qualitative nit-

-ture of cha low water effects on each derivative, it is necessary to trace the chancie in its relation to

tPe respective characteristic in deep water.

42 -

j

Table 3 Derivative values at En

Figures 7 12 show the

:endcet

parate ratios:

fly11H mZPH

ní1o.

The subscripts H and wean the finit c:t approximately infinite d-pth. Fr the sa-s c :c--parison, the sane graphs contain the analoc:s de-pendencies for shios types ariner ari Tc.<c cru [3_J.

3.1. shallow

ter effect or. ttatic :-.et-.as

e L

an mZH

Froni the analysis 0f Fi.s. 7 acid 8 't ce- te

seen that: W MARINE R -. - .J,;_. I to ----, W 13 213 2 '

Fig 7 Shallow water e'ect on dercet'e

Fn 0.194 H/T 1.2 1.1 4.2

L583 0.878 0.418

s _0.218

0.185 3.128

Sway Z

and yaw tests 0.130 0.098 0.065

-0.128 -0098 -3.057 - ri22 0.487 0.418 0.29; 0.028 0.023 0.311 Static n 2.110 1.116 0.41c tests m,E _{0.229 0.176 0.022} Fr = 0.0637 H/T 1.2 1.5 4.2

r5

0.875 0.624 0.427 0.117 0.105 0.064 nd ya- tests

-;

0.071 0.060 0.052 -0.072 -0.068 -0.049 0.405 0.355 m56 0.025 0.021 I 0.016 Static n8 Loe 0.709 tests rn,5 0.128 0.109 0.064 J

- the shallow water effect on the ste tic derivatives

becomes greater as the advance speed increases; - the increase of the nHderivative is particularly great at water depth H = 1.2T: it increases 2.5-fold st Fn = 0.0637 and abeut 5-fold at Fn 0.194;

- comparing with the rates of increment, it can be deduced that the ratio nVH1ncreases rerr.arcably

than the ratio 0H/0Z as the ratio HIT decreases, i.e., the point o application of sway dar.ping for-ce, that is the ratio OzHIfl.H , shifts far a.ey in

front of the midship.

eo rn1

I'

20

3.2. Shallow water effect n rotary

derivati-ves and

The followirg conclusions can be made from Figs. 9 and 10:

- the çreater the advance speed is, the greater is the shallow water effect on

5.0 -KC13 ny n-F155 M4-:4EH F--. -0.03

_{roy uaR}

-ç-.

r7

1.0 to ao-TOKYO MARU M A R NE R K013 115 210 _{25 4.0} H/ T

Fig 8 Shallow water effect on derivative

TOKYO MARU

O

10 1.5 _{2.0 2.5 V}

H/T

Fig 9 Shallow water effect on derivative flyUJ

- the shallow water effect on the der'vative

!H

greater than that on the derivative n1. 0H increa-ses 1.7 and 2.3 tires respectively;

42 - 4

Fig 10 Shallow water effect on derivative

- in connection with the creater increase of the

me-rnents dervative, the point of application of yaw

damping force moves to the ar end in front of the

mldship.

3.3. Shallow waer effect on added mass m22 and added inertia 066

From the analysis of Figs. 11 and 12 it becomes clear that:

- the larger the advance speed is, the greater is the shallow water effect;

- at water depth H = 1.2T, 022 and 066 increase about 1.5 times;

- the nature of the dependences _m65HImE.

f(/T)

is alnust one and the same for the foil and a

Ma-riner type h. '.0 rn22 m22 1.0 K 01 K û1 MARINE R TOKYO MARU TOKYO MARU MARI MER HIT Fig 11 Shallow water effect on added mass

JjJ

m'.5 m'.'.

1-O

1.0 l 21) 215 '.0

Fin- 12 Shallow water effect on added inertia 065

.4. Analysis of course stability changes in low water

It is known that the hendling capat.iiity of the closed loop system "s.11-propulsers-control sur-faces is determined by the properties of the oton loop system, i.e. by It; siability. In order to in-vestigate ship stability in shal uw water the SystsiT of linear .quations il) of the free motor can be written In the

or:

-

C _í 012.LJ

(:)

J ù -

a +Q22.Li

r as a .Thd order linear differential constant coefficients:

1.0-

0.5-e On

(Qi1+a22)-(a12.a_a11a22)p_o(3)

The condition of stabe sLat:Iil.y is that ail of the roots of the equation (3 iist have negativa 'eal

parts

and in ti2

case the necessary and sufficient conditions for stable stability are qiven by aouth-I4urwitz as follows:

- li

+ a22) > o

(4)

-

(an.

a21 - a11. ₂₂

>0

After transforming the last inequality, ano taking into account that m5 0, ee o'tain:

w

>

(Tlz (5)

fly fly

Fig.13 shows the values of these ratios for the foil (denoted by 1 and l, respectively) at dif-ferent ter depths. The comparison with the levers

e MARINER Fn0.155

£TOKYO MARUFrn-103 c

with

42 - 5

I and l for Mariner and Tokyo .aru type

t;:

shows that the foil stability range it muon croacem and the dependencies l f(H/T) for

it

and a

'a-riner type ship are very close.

In order to gain a more complete idea c tre

stability

change during rtion along t s' at a

result of the instant external disturbances

Influ-erce these parameters at dfferent water depths, the rvturC of free notion i investigated. Por tre

rpos,e, f-ee onton s decribed by the interals

[2):

2I

pp2L

1 ₂

Jì

wo fl(s) rnzu _(gP1. s_ m65 - __i- - ₍ 1 )

pp2

rn,2 i m P (fP5

t5

pi-p2

I

u(s)

i

_{[(o.E'_p}

Pe fl

D-

2 o fly

PSP5:]

m22

woere: - amplitude of the initial disturbance along the drift angle;

amplitude of the initial disturbance along the angular speed;

p1,p., - roots of the characteristics

aoje-tion of (3);

S - dimensionless time.

The results of toe calculations for the plate and both ships are plotted in Figs.14-17.

From the analysis of the nature of develo3nert in time of the motion parameters t(S) and (S),ider-tical with the disturbances (Fiqs. 14 and 15) it

becomes clear that: the foil, as well as the ships, are stable with respect to disturbances caused by a" initial drift angle and angular speed at the trree depths investigated; s:ith the decrease of the I!T ratio, the values B(s)/S and (s)/. decreas at

a considerably faster rate; th nature of changes

of the ratios s(s)/a and at decrease o

ter depth is analocous for the foil and the ships, and the dependences for the foil are re similar to those of a ariner :.eso o.

After analysing the change in time of the parairters at the presence of opposite disturbances, (Figs.16 and 17), the following conclusions can be drawn: the foil, as well as toe sniiS, are stable with respect to disturbances caused by an initial

o

to 1.5 ZU

HIT 2.5

Fig 13 Variation of the point of application of sy and yaw damping forces

V

0.5 o 0.5 C O 1.0 fì)sI Io 05 TOKYO MARU MARINER

:

I

_o : o e s ¿o

f5

KOl.) 4 +

I

e C A Q in 00 40 u)s) Li0 0.5

io.

Li0 0.5 TOKYO MARU s Fn_3.194 KOl) .i-O0637 ° n-O.i55 MARINER Fri-O.0905 IO Fri-0103 ITOKYO MARU ¿ _n-0O75 J

55

S X013A A ¿ G _MARIN°R

..I '+

H/T1.2

G o5 S if ß TOKYO MARI.)

z'

S + 2 $

5+

* + MARINER s + o

++

H/T1.5

G + ₊ TI Y + + a to

i

MARINER s

t

t

t

KO

H/T4.2

+ 0.5 - SSC ha'ie o' .(s) in 'ree oton et - disturbenr.e

f

i? G

,

R s

f

_f

TOKYO MARI.) LO LICs) C A + Q a Q

fa

45

+ a

5+

G G G S e s 4 Q o A

f

LI0

0.5-f V;

f,

MARINER + f _s + +

H/T 4.2

rs _to

drift angle and angular speed for the thVe depths for the foil and the ships at HIT &2,

t'

T

o-, G _{0.5 in} 005-i-Jo 010

H/

1.2

H/T1.S

HIT4.2

a

¿a

A

e,

a u ¿ MARU e 3 MARINER o C _4/ a ₄ e

0G

a C

sa

f

0.0 K 013

t

.+++++++++I+++

a

5+

f +

a

.

s s

s 4

e A + e TOKYO MARL £

/t:A

aoaa

a a a A a K0i3 MARINES

42 - 7

decrease of kater depth, foil steb1li,

',r'-'''

1.0 LJ(S) po in o

H/T1.2

e a e

H/T1.5

o a

33 ea0 a

TOKYO rc MA R .EP

C

/-L

Lo

95

C0

è & C + G

_f

a + s +

se

05 a a

eo

e Q 0 MARINER e e o G

-3

TOo(YC MtR

¿

+ +

f

. f

t

+

4ff

1 4, +

.ea.

+ e ¿g3 1'

5

a s MARINER

H/T'z4.2

3 s ¿ Il, J

,

4+4

₊₃

e,

+

,

TO<YO.'AR Oh-02 05 in o _6s

Fig 16 Change of a(s) in free 'itIon at - disturbanceFig 17 Change of .(s) in free -iotio1 at

- dst.roa:

a L e

_.1

e

!+.4l+

J s.

e

;

i

a

investigated, with the decrease of the H/T _ratio there Is a decrease of the drift angle (s) genera-ted by the initial angular speed. It uld be inte-resting to mention that this change is greatest for

the Tokyo iaru ship, the nature of the change In

ti-me of tne ratio(s)/

is aloost one and the same

f(s1 K013 TOKYO MARU ao

1+

-

*4

+ O

++

+4f

+ pa MARINER/ O o s to

4. ConclusionS

As a result of the investigations nerformed and after sunmnarisirig the analyses, the following

conclusions can be made:

- ship schematization as a thin foil for shallow wa-ter conditions yields comparatively good qualitative and quantitative results for the hull 's static and

rotary derivatives;

- in the deteriination of added masses the

account-ing of real ship hull form is necessary. Due to this reason, the equivalent ellipsoid apprjximation is more appropriate;

- the conclusion is imposed that the shallow water

effect is expressed primarily in the increase of the

hydrodynarnic forces absolute values, which, for the foil and ships considered, leads to an increase in

stability;

- attention should be oaid to the increasing aonli-nearities of force - rest parameters dependences which reflect the mathematical model of ship

ma-noeuvring motion in shallow water;

- nonstationary effects at Pf''i tests in shallow Wa-nr can be expected.

References

Basin, Velednitsky, Liahovitsky Hydrodynam-ics of Ships in Shallow Water", Sudostroenie, Lenin-grad, 1976 (in Russian)

Eujino li., "anoeuvrability in Restricted Wa

ters: State-of-the-Art, the University of Michigan, 14o 184, August 1976.

Fujino 1.," Experimental Studies on Ship Ma-noeuvrability in Restricted Waters Part

1,Interne-tional Shipiiding Progress, vol.15. 1968.

'likelis N. E. "Calculations of Hydrodynamic Coefficients for a Body Hanoeuvring in Restricted

Waters using a Three Dimensional Method",Trans. RINA 1980.

5, i'lilanov E. M., Vassilev P.. Lefterova 1." Ex-perimental Evaluation of Hydrodynamic Loadng on Os-cillating Thin Airfoil", Jubilee Scientific Session, BSHC, Varna, 1981. (in Russian)

Hess F. "Ship in Shallow Canals:A Tneoreti-al Model for LaterTneoreti-al Forces, Rudder Effectiveness and Course Keeping Stability", International

Ship-building Progress, vol . 26, 1979.

Sobolev G., "Manoeuvrability of Ship and Auto-mated Ship Steering', Sudostroenie, Leningrad, 1976,

(in Russian)

uiianov E., Dipl. Eng.

Vassilev P., Dr.

Bulgarian Ship Hydrodynanics Centre Varna 9003, Bulgaria

Lefterova I., Dipl . Eno.

Higner Machinebuilding and Electrotechnical Institute

Yama 9010, Bulgaria

42-8

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