The longitudinal distribution of low frequency hydrodynamic derivatives for lateral motions in shallow water

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624825

TECHN!SCHE HOGESCHOOL DELFT

AFDELING DER MARITIEME TECHNIEK

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

2628 CD DELFT

The Netherlands

Phone 015-786882

THE LONGITUDINAL DISTRIBUTION OF LOW FREQUENCYiHYDRODYNAMIC

DERIVATIVES FOR LATEPAL MOTIONS IN SHALLOW WATER.

W.Beukelman and J.Gerritsma

Report nr.6O3 november 1983

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Contribution to the 17th ITTC Manoeuvrabïlity Committee The longitudinal distribution of

low frequency hydrödynamic derivatives for lateral motions in shallow water.

W. Beukelman and J. Gerritsrna

The longitudinal distribution of the horizontal hydro-dynamic forces actIng on a slowly oscillating ship in shallow water is of interest fOr the determination and

analysis of the steering and manoeuvring characteristics of ships in ôonfined waters.

As a first exploration of the problem of this

long.itudi-nal distribution forced oscillating experIments have been carried out with a segmented model in shallow water,

per-forming very iow frequency yaw- and sway oscillations.

Also some static yaw tests were included for comparison

with the corresponding low frequency values..

In this report the reailts .of experiments with a model con sisting of seven segments carrying out low frequency

yaw-and sway motions in shallow water are given. Two forward

speeds and a range of water depths have been considered.

The measured total hydrodynamic forces, as well as their

distribution along the length of the. model are compared with calculations according to the. strip theory, taking

int account the effect of shallow water [4J

The experiments, have been carried out with a 2.3 m model

of the Series Sixty. This model had been used earlier

for a similar investigation for higher oscillation

fre.-quencies, of interest for the analysis of shIp motions in waves, in deep water as well as shallow water

_Li,

2, 3J The hydrodynamic derivatives have been determined. .by means

of forced oscillation.experiments for pure:sway and yaw

motions of the..ship model. .

In Table i. the model speeds (Fn, U), the oscillation

fre-quencies w and the oscillation amplitudes

a of the

sway-and yaw motions are given. It should be remarked thát the

amplitudes of the horizontal displacement of the

thfstening.

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by the angle .

The length between. perpendicu1ar is taken as the reference length

.Table.1: Test Conditions.

The static drift angle experiments have been carried out

for a range 1,O° < . .

.< loo _{in steps of Ï degree.}

For this condition ' = r O.

For the forced oscillation tests and the static drift angle

tests the following waterdepth/draught ratio's.have been considered:

h/T = 1.15; i.2 1.5; 1.8; 2.4.

Resuits of the model experiments and the calculations.

The experimental distributions and Y aregive.n in the

Figures 1 and 2 as solid lines, for the two forward speeds

of the model, the. osciilation.frequencies and the waterdep.th-draught ratio's considered. For. constant waterdepth variation of the low forward speed and the. low oscillation frequencies h'ave only a small influence on the distrïbutions Y" and Y

y y

This influence is certainly small in comparison wIth the in

fluence of waterdepth.

In Figure 3 the distributions o.f Y for the case of w = O (static tests) are giveñ for two drift angles ( = 5° and

Fn U mis r= rad/ r'= rad/s degrees

2_rr.

',,wL . (À)S1fl-2 meter -, 0.0675 0.318 0.0.376 0.267 0.26

050

0.75 22.2 38.2 49.7 . 0.191, 0.061 0.033 1.85 3.55 5.33 0.26 15.0

O249

.1.21 0.103 0-.485 0.0335 0.156. L 0.50 27.3 0.073 2.33 0.75 H 37.7 0.037 3.49

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3

= 10°) and for two modeispeeds and five waterdepth/draught ratio's.

For the waterdepth/dra.ught ratio's h/T = 1.15, 1.5 and 2.4 the measured y" and y'! distributions forthree oscillation

V V

frequencies and for the static tests are plotted in Figures 4 and 5.

Of interest are the negative side forces occurring for the sègments , 2 and 3 in the aft part of the shipmodel.

The experimental values of the sideforces as fòund. with the

static tests agree satisfactory with the values found with

the lowest oscillation frequency '(w = 0.26 rad/s).

The dis.tribÙtiôn: of Y in the aft part of the shipmodel is slightly dependent on the oscillation frequency. To a lesser degree this is also: observed in the forward part of the shIp model.

in Figure 4 also the values of Y based on strip theory

calcuations are depicted. It is emphaized that no

vis-cosity effects are included in these values.

In comparison with the experimental values it is shown'

that viscosity has an important influence on the sideforcs. in the after part of the shipmodel, probably as a result of separation, but the influence in the forward part is

much 'smaller.

For the smallest .waterdepth 'ratio. (h/T = 1.15) the corre-lation between calcucorre-lation and experiment is not

satis-factory. .

The distribution of the hydrodynamic mass (Y,) over the length of the shipmodel (see Figure 5) agrees fairly good with the ca1cuiation,except for thé smallest waterdepth

ratio.

In general the influence of forward speed In the considered range is not important and the same applies to the influence of the oscillation-frequency for waterdepth-draught ratio's

exceeding 1.5.

For smaller waterdepth:ratio's Y'! increases with thé

oscil-V

lation frequency.

The alues for Y' and Y! for the whole model and the cross

y y

coupling, derivatives Y and Y are given in thé Figures 6 and 7.. Also the corresponding calculated values are de-picted in these Figures

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4

To söme extent the tendencies as already mentioned follow. from these figures. The important increase of the hydro-dynamic mass for very small waterdepth ratio' s is known also from other sorces..

The measured and calculated values of Y" and Y'. are given

V V

in the Tables 2 - 7 for comparison with other and future calculations.

The statï.c drift angle results are.given in Table 8. In generai it may .be. stated that the agreement between experiment, and calculation is better when the wäterdepth ratio as well as the frequency of oscillation increase.

Reference s.

'[iJ

'Gerritsma, J. and W.. Beukeiman,,

The distribution of the hydrodynamic forces on a heaving and pitching ship model in stili, water.1

5th Off ice of Naval Research Symposium 1964, Bergen,, Norway.

[2] Gerritsma, J.. and W. Beukelman1

Analysis of the modified strtheoryfôrthe

calcula-tion of ship mocalcula-tions and wave 'bending moments, international Shïpbuilding. Progress, 1967.

BeUkelman, W. and J. Gerritsma,

The distribution of hydrodynamic mass and damping of an oscillating shipform in shallow water,,

International Shipbuilding Progress, 1982..

4J Keil, H.

Die Hydrothechaniche Kräfte.bi.der periodischen

B.ee-gung 'zwei dimensionaie.r Körper an der Oberfläche. flacher Gewässer,

Bericht nr. 305, Institut für 'Schiffbau der Universität Hamburg, 1914.

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Table 2: Sway (Experiment.) h/T = 2.4 Y; i0.. y'' * i Section Nr: Fn _9.0675 _Fn _{= 0.103} _Fn = 0.Q675

Fn= 0403

CL) w w w 0 26 0 50 0 75 0 26 0 50 ô 75 0 26 0 50 0 75 0 26

-08-06=08

0 o 0 75 1

-60-31+1.1

-55-35-05 -lo -08-18

2

+37 +69+9.3

+56 +86 +99 -47-53-59

-48-53-57

3

+33 +57+60

+42 +64 +69 -70-75-80

-71-76-80

4

-4.3 -30-41

-3.1-25-28 -77-81-87

-78-81-85

5

-106 -118-128

-92-98-113 -77-78-80

-79-80-81

6

-163 -164-176

-155 -161 -172 -61-63-67

-64-64-66

7 -42..2 -40.4 -41.5 -41.6 -41.6

-4.0

- 33 -3.7

- 3.8 - 3.3 = 3.5. Whole Y' *

i0

Y * model -23 6 -20 1 -19 2 -21 2 -19 0 -18 4 -12 1 -12 7 -13 8 -12 3 -12 8 -13 4

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Table 3: Sway (Experiment.)

h/T = 1.5

Y" 4

V i0 Y * V Fn =

0.0675

Fn =

0.103

. Fn =

0.0675

Fn =

0.103 Section

Nr: W (A) (A) W

0.26

0.50

0.75

0.26

0.50

0.75

0.26

0.50

0.75

0.26

0.50

0.75 i

- 4.0

+ 2.4

+ 6.5

- 4.0

+ 0.0 +

7.3 - 0.9

- 0.9

- 2.8

-

1.1 - 0.0 -

1.3.

2

+ 7.1

+17.1

+24.4

4 9.9

+18.2

+25.2

- 6.2

- 7.7

-11.3

- 6.8

- 7.9

-10.1

3

+ 2.3

+ 9.0

+11.1

+ 3.9

+10.8

+12.4

- 9.6

-12.0

-13.7

-10.8

-12.3

-15.3

4

- 9.6

- 6.4

- 7.4

- 9.0

- 5.1

- 7.1

-10.6

-12.9

-14.9

-11.5

-13.0

-16.0

5

-19.7

-21.5

-25.6

-19.5

-19.2

-26.9

-11.5

-12.9

-14.4

-12.3

-13.6

-15.8

6

-31.5

-34.1

-38.0

-32.3

-33.2

-41.2

- 8.2

-10.0

-11.0

- 8.9

-10.2

-11.4

7

-58.3

-60.7

-64.8

-59.3

-59.1

-65.7

- 2.3

- 4.8

- 5.3

- 2.8

- 4.3

- 4.1

Whole

model .

Y' * 1O

Y! * 1O

-36.8

_1-30.2

_{t_30.0}

-28.2

-30.7

16.0 -19.8

-23.8

-17.5

19.8

_j

-23.9

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Table 4: Sway (Experiment.) hIT = 1.15 y" * io3 V

y': *

V Fn =

0.0675

Fn =

0.103

Fn

= 0.0675

Fn =

0.103

Section. Nr: () (A) (A) W

0.26

0.50

0.75

0.26

0.50

0.75

0.26

0.50

0.75

0.26

0.50

0.75

1

- 3.5 +

1.0 -

8.1 - 3.8 + 6.2

-18.8

- 2.4

- 3.2

- 8.6

- 1.3

- 1.5

-13.8

2

+ 5.2 +19.3

+10.7

+ 6.3 +29.4

-32.4

- 9.5

-13.6

-25.2

-10.8

-13.9

-43.9

3

- 8.1 + 3.9

+31.7

- 8.4 + 8.8

-127.4

-15.5

-22.1

-35.4

-17.4

-23.4

-55.1

4

-32.7 -27.8

-88.9

-35.5 -26.5

-223.8

-16.9

-25.3

-38.3

-16.7

-24.8

-45.6

5

-52.1 -48.7

-127.9

-55.5 -52.1

-264.4

-15.4

-23.1

-33.9

-15.3

-23.7

-25.6

6

-76.3 -80.3

-159.4

-83.7 -84.1

-267.3.

- 9.4

-17.4

-23.2

- 6.2

-14.9

- 4.9

7

-111.6-109.6

-168.3

-119.1-109.4

-200.1

- 3.4

- 5.3

- 3.9

- 8.6

- 0.4

- 3.9

Whole model y' * *

iø

-93.5 -78.1

-185.3

-96.8 -73.2

-366.5

-21.3

-35.6

-54.7

-19.1

-33.1

-45.3

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Table 5: Sway (Calculations.) hIT = 2.4 " * V

y' *

V Fn = 0.0675 Fn = 0.103 Fn = 0.0675 Fn = 0.103 Ord. Nr: ü) w 0.26 0.50 0.75 0.26 0.50 0.75 0.26 0.50 0.75 0.26 0.50 0.75 0 +82.0 +82.1 +82.2 +82.0 +82.1 +82.2 - 0.2 - 0.2 - 0.2 - 0.2 - 0.2 - 0.2 2 + 8.4 + 8.0 + 7.3 + 8.4 + 8.1 + 7.6 - 4.4 - 4.4 - 4.4 - 4.3 - 4.4 - 4.4 4 +21.9 +20.9 +19.2 +22.1 +21.4 +20.2 - 6.2 - 6.2 - 6.2 - 6.2 - 6.2 - 6.2 6 +19.5 +17.8 +14.9 +19.7 +18.6 +16.6 - 8.6 - 8.5 - 8.5 - 8.6 - 8.5 - 8.5 8 + 5.4 + 3.4 - 0.1 + 5.6 + 4.3 + 2.0 - 9.9 - 9.9 - 9.8 - 9.9 - 9.9 - 9.8 .10 - 0.8 - 2.8 - 6.3 - 0.5 - 1.8 - 4.1 -10.0 -10.0 -10.0 -10.0 -10.0 -10.0 12 - 3.5 - 5.5 - 9.0 - 3.3 - 4.6 - 6.8 -10.0 -10.0 -10.0 . -10.0 -10.0 -10.0 14 -14.0 -15.7 -18.6 -13.8 -14.9 -16.7 - 9.3 - 9.2 - 9.2 - 9.3 - 9.2 - 9.2 16 -18.3 -19.3 -21.0 -18.1 -18.7 -19.7 - 7.6 - 7.6 - 7.5 - 7.6 - 7.6 - 7.5 18 -13.0 -13.4 -14.2 -13.0 -13.2 -13.6 - 5.9 - 5.9 - 5.9 - 5.9 - 5.9 - 5.9 20 -107.2 -107.3 -107.5 -107.2 -107.3 -107.5 0.0 0.0 0.0 0.0 0.0 0.0 Whole. model y' * -17.0 _-16.9! Y * _1:.91 -17.01 -16.91 -16.9 - 1.6 - 4.4 - .2 - 1.2 - 3.1 - 6.2

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Table 6: Sway (Calculations.) Y" * V h/T = 1.5 Y * V Ord. Nr: W W W 0.26 0.50 0.75 0.26 0.50 0.75 0.26 0.50 0.75 0.26 0.50 0.75 0 +101.1 +101.0 +100.9 +101.1 +101.0 +100.9 - 0.2 - 0.2 - 0.2 - 0.2 - 0.2 - 0.2 2 + 26.0 + 24.5 + 22.0 + 26.2 + 25.0 + 23.0 - 6.0 - 6.0 - 6.0 - 6.0 - 6.0 - 6.0 4 + 50.0 + 45.2 + 37.2 + 50.4 + 46.8 + 40.7 -10.3 -10.2 -10.0 -10.3 -10.2 -10.0 6 + 42.4 + 33.5 + 19.3 + 43.2 + 36.7 + 26.3 -15.6 -15.3 -14.8 -15.6 -15.3 -14.8 8 + 10.3 + 0.7 - 14.8 + 11.5 + 4.9 - 5.6 -18.6 -18.1 -17.3 -18.6 -18.1 -17.3 10 - 3.5 - 12.7 - 27.4 - 2.3 - 8.3 - 18.0 -18.9 -18.4 -17.7 -18.9. -18.4 -17.7 12 14 - 9.8 - 34.3 - 18.6 - 40.4 - 32.8 - 50.3 - 8.6 - 14.2 - 23.3 -18.9 -18.4 -17.7 -18.9 -18.4 -17.7 - 33.2 - 36.6 - 42.2 -17.2

-i68

-16.1 -17.2 -16.8 -16.1 16 - 47.3 - 50.0 - 54.5 - 46.7 - 47.8 - 49.7 -13.0 -12.8 -12.5 -13.0 -12.8 -12.5 18 - 37.9 - 38.8 - 40.4 - 37.7 - 38.0 - 38.6 - 8.6 - 8.5 - 8.5 - 8.6 - 8.5 - 8.5 20 -137.8 -137.7 -137.5 -137.8 -137.7 -137.5 - 0.0 - 0.0 - 0.0 - 0.0 - 0.0 - 0.0 Whole model Yt * 1O V Y * V 1O - 5.1 - 17.0 - 36.3 - 35.3 - 11.3 - 24.0 -29.6 -29.0 -28.1 -29.6 -29.0 -28.1 Fn = 0.0675 Fn = 0.103 Fn = 0.0675 = 0.103

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= 0.0675 Y" * ]0 V Fn = 0.103 = 0.0675 Y *

io3

V = 0.103 Ord Nr w w W W 0 26 0 50 0 75 0 26 0 50 0 75 0 26 0 50 0 75 0 26 0 50 0 75 0 +146 3 +145 7 +144 6 +146 3 +145.7 +144 6 - 0 3 - 0 3 - 0 3 - 0 3 - 0 3 - 0 3

2+790 +717

+598

+795

+732

+633

-102

-101

-99

-102

-101

-99

4 +137 3 +102 8 + 54 4 +139 3 +109 8 + 68 9 -22 2 -21 1 -19 4 -22.2 -21.1 -19 4 6 +125 9 + 51 4 - 34 5 +131 2 + 68 9 - 'i 6 -37 6 -33 3 -27 8 -37 6 -33 3 -27 8 8 - 0 2 - 58 1 -122 2 + 7 8 - 33 2 - 77 9 -46 3 -39 1 -30 9 -46 3 -39 1 -30.9 10 - 23 2 - 72 4 -128 7 - 15 2 - 47 5 - 84 4 -46 3 -39 1 -30 9 -46 3 -39.1 -30 9 12 - 5.9 - 61.2 -1.228. + 2.1 - 36.3 78.5 -46.3 -39.i 3O -46.3 39.1 -30..9 14 -137 4 -141 2 -155 2 -130 6 -119 5 -115 7 -42 7 -36 8 -29 8 -42 7 -36.8 -29 8 16 -145 2 -140 3 -138 8 -141 9 -128 9 -116 0 -29 8 -27 5 -24 4 -29 8 -27.5 -24 4 18 -118.6 -116.5 -114.2 -117.6

-1129

-106.5 --16.5

--11

1.5.5 -'16.5 -16.1 -15.5 -20 -223.6 -22.1.9 .- ---218.9W -223.6. -221.9 -218.9 0.0 0.0 0.0 0.0 0.0 0.0 Whole model . . y' * V . . . y

*

V

io

---

29 0 - 91 9 -168 9 - 68 8 - 60 6 -110 8 -68 8 -60 6 -50 8 -68 8 -60.6 -50 8 Table 7: Sway. (Calculations.)

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Y" V *1 Y V 1. s Fn Section Nr - _- _y' h/T 1, 2 3 4 5 6 7 _Whole model O675

_-39

_-10.8 _- _4.6 _{- 98. -20.4} _-33.5 _60.6

_-395

1.5 .103 3.4

_{-12.3 - 5.9}

- 8.2 -18.3 -31. -58.0 -32.7 _1.5 .0675 -4.3 - 5.5 - 2.8 - 3.8 - 9.3 -16.5 -4.1.0 -21.6 2.4 .103 _-1.8 _{- 7.5} _4.0 _{- 3.1} _{-. 9.5} _-16.1 _-41.7 _-19.6 2.4 .0675

8O

_13.8 _-28.2 _-s6.i _{80.6 -ilO.3 -15r.5} _-144.9 1.15 .103 -8.3 - 3.3 -14.2 -4f.5. -63.2 -93.5 -127.9 -113.8 1.15 Table 8: Static measurements.

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Fn0.1O3 W: Q50

12 -- Experiment

Fn:10675 w =075 Fn:O.103 w:O.75

Figure 1: Experimental distribution of the damping coefficient

SWAY Fn:0.103 - :Q26. FnO 0675 w:0.26 Fn:0.0675_wC.5O :21. :1.8 h h t2 :1.15

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o -20 o -20 yx10 -20 O -20 O -20 o -2d o -20 y xiØ -2Ó o -20 -20 2 3

4:5

Fñ0.1O3 w:O.50 13 -1 2 3 - Experiment,. SWAY Fn:Ç10675

w 75

Figure 2: Experimentai distribution of the added mass coefficient.Y Fn: Q0675 W:O.50 2 3:

---Fnr1O3 w:0.75 h T h 12 2.6 :1.8 :15 Fn0.0675 Fn0iO3 w026. w=U26 4 5 7

23

1. ₅ ₆ ₇

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o -40 o -40 o -40-yÇm'103 -40 O -40 Fn :0.0675 (3:50 Fn: 0.0675 13:10°

14

-STATIC TESTS 6\

J

_lili

1111m:

--ìi!!uÏ

vi

V

Fn:Q103 ¡3 = 5° 2 Fn :0.103 (3:100

r

:15 :12 :12

Figure 3: Distribution of the damping coefficient from static tests. o -40 o -40 o -40 y.103 -40 O -40

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-80 -too APP

-

15 -FPP -80 -loo APP 'o .20 u

O

to = 0.26 Experiment f

_{- w=0.75}

(0 = 0.50 w = 0.26 - - - Calculation

f £

_{w = 0.50}

w= 0.75

+ - Static ß 50.

:FigÙre 4: Measu..ed and ciculat.ed distribution of Yfor

hiT = 2.4., 1.5 and 1.15.

FPP

-FP -loo

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16 -r O w = 0.26 Experiment w = 0.50 a = 0.75 r = 0.26

-

Calculation

_t

£ w = 0.50

S, w 0.75

Fiqure5;: Measured and calculated distribution of for h/T = 2.4, 1.5 and 1.15.

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.3 Yç1 "10 50 -SWAY wO.26 w0.50

4,.

12 1.5 E8 2i w 0.75 1.2 15 1.8 I I I! 1 2.4 h

___

12 15 18 21 2.4

17

-.3 -100--200 -12 15 L 2) = 0.0675 --+-- = Calculation

o = Experiment

= Static 8 50 Fn = 0.103 --x-- Calculation

A = Experiment

A = static ß 50

Figure : Comparison of measured and calculated coefficients for swaying as function of the waterdepth draught ratio.

o

4t2

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10 y1 .io O

't

uj:0.26 0 1.2 1.5 1.8 W;O.75

i

1.2 1.5 1.8

2.12.4

O w t2 1.5 1.8 2.1 2.4

3

-'h

-

w-T 1.8 2.1 1.2 -.

18

-YAWING w0.S0 h 12 1.5 1.8 Fn, 0.0675 = Càlculation

o = Experiment

Fn = 0.10.3

X--

= Calculation

-a-

Experiment

Figure 7: Comparison of. measured and aiculated coefficients for

yawing as function of the waterdepth - draught .ratiò. -10 -20 -30 X-X

_,

,

__x

-.1

/

-1-I 4.