Added resistance and vertical oscillations for cylinders at forward speed in still water and waves

ADDED RESISTANCE AND VERTICAL OSCILLATIONS FOR CYLINDERS AT FORWARD SPEED IN STILL WATER AND WAVES

Ing. W. Bèukeiman

Report

Nr. 873-P

Aùgust 1990

Written contributiòn forthe seakeeping

coittee of the

19th International Towing TankuConference Septémber 1990, Madrid,

Spain.

DoiftUfliversityof Technology

Ship Hydromechanics Laboratory

Mekelweg2

2628 CD Deift The Netherlands Phone:015 - 7868 82

WRITTEN CONTRIBUTION FOR, THE SEAXEEPING CONMITTEE

_{OF' THE}

l9

_{INTERNATIONAL TOWING 'TANK CONFERENCE}

_{SEPTEMBER 1990}

(1TTC" 90) MADRID - SPAIN

by

W. Beukelman

AUGUST 1990

Ship Hydromechanjcs Laboràtory

Deift University of Technology

Mekeiweg 2, 2628 CD Deift

ADDED RESISTANCE AND VERTICAL OSCILLATIONS FOR CYLINDERS

AT FORWARD SPEED IN STILL WATER AND WAVES.

By

W. Beukelinan

Ship Hydro]nechanics Laboratory

De]. ft Unïvergity of Technology

The Nethêrlands

The present research is based on two Bets

of experiments as described in

(1] and (2]. The first Bet is related to forced vertical oscillation tests with a Planar Motion Mechanisme (P1414) for two

cylin-ders at forward speed in still water,,

while the second set is related to

expe-riments on vertical motions and added

resistance. in head waves with the same

cylinders at the same forward speeds

viz.: Fn 0.16 and Fn = 0.26/0.27. The cylinders considered

(L * 3 * H * T =

2.50 * _0.25 * _0.25 * O.Ï5 rn) had a

constant rectangular or triangular

section form over 2 m length, while. the

fore- and aft ends had a decreasing: sectional area' over 0.25 m.

For

non-dimensional parameters the following

valües have been used respectively for

the rectangular and triangular cylinder:

L' 2.333 a, B' = 0.25 a and L' 2.167 m, B' - 0.15 a.

in (1]

the results of forced vertical

oscillation tests are shown. The tests

have been performed in order to measure the added resistance and the ivdrodvnamjc

coefficients for both cylinders. The

main objective of this study was to show that the added resistance experienced by á forced oscillated model in still water

is älmost zero except some small

resistance increase due to non-linearity.

Figure 1 shows the results of the added resistance RA for the triangular cylinder whIle Carrying out forced heave oscilla-tions at Fn 0.27.

I

100 N N Il 50 O Fn 0.27

fOrO1in

JXPERDIENT

Or

02m

Ar

.03aii

CALCULATION ACCORDING TO THEORY

- - WITH EXP. COEFF.

o

'

o

0 1 2 3 4 5

Figura 1: Heave and added resistance coefficient for triangular

cylinder.

The calculated added resistance RA has

bedn determined by the method of

Gerritsaa-Beukelman (3]. Added resistance

calculations have been carried out using

both the calculated and measured

hydrodynamic coefficients. For pure heave oscillation the added resistance will be:

w2r2

RA=

b

2V

with w - oscillation frequency r - oscillation amplitude V - forward speed

= calculated or measured

An important conclusion of this

inves-tigation was that the added resistance in waves cannot be determined by forced

oscillation experiments in still water.

The flow of energy appears to be directly

from the

oscillator into the damping waves so that no resistance increase arises. It is therefore worthwiie to

consider the measured results of Ueno

et al [4, 5) in this respect.

Comparison between measured and.

calcu-lated hydrodynamic coefficients, based

on strip theory, shows satisfaçtory

agreement for the triangular cylinder.

For the rectangular cylinder, however,, it

was obvious that especially with respect to the damping coefficient considerable differences are present.

For this case

see Figure 2

The large damping for the rectangular

cylinder is caused by viscous effects due to the sharp edges of this cylinder under water.

By analysis of the experimental

results

it was possible to distinguish

both the vertical speed influence,

2

o.

Figure 2. Heave damping coefficient.

I I

TRIANGULAR CYLINDER

Fn0.27

o

dependent on the oscillation amplitude

and frequency, and the forward speed

influence on the viscous part

of the damping.

A plot of the total damping

coefficient for constant forward speed to a base of osciÏlation amplitude shows for each oscillation frequency a linear function of the amplitude of oscillation. Sea Figure .3.: for.. these, relations.

'For' the rectangular cylinder

extrapola-tion to zero amplitude of oscillaextrapola-tion

resuited, in' damping coefficients which vary ]inearly. with the forward speed squared, while

for zero forward speed

these values equalled the calculated potential damping values.

See Figure 4.

It could be expected that the viáooua

damping should significantly influence the vertical motions as well as the added

resistance In waves.

It. was therefore decided to carry out

experiments' in waves to measure these

parameters for both cylinders (2').

The measured results for the heave- and

Figure 3. Heavedamping

coeffioientrela-ted to amplitude of oscillation för Fn = 0.26/0.27.

CALCULATION

D DERIVED FROM EXPERI-MENT FOR RECTANGULAR

ICYLTNDER

Figure 4. Heave damping coefficient for zero amplitude of Oscillation related to forward speed

squared.

pitch response

function are

shown In

Figure 5 and for the added resistance in

waves in Figure 6. 0.5

ro

0.5 o CALCULATION 40 3O 20

RECTANGULAR CYLINDER TRIANGULAR CYLINDER

50Fn .26 Fn .27

O I

01

23

CALCULATION

EXPERIMENT

Figure 6. Added' resistance in waves, Fn = 0.26/0.27.

The results calculated, by strip theory

are also presented in' these figures. Comparison of experimental and calculated

vertical motions and added resistance in

waves shows good agreement for the

triangular cylinder (See Figures 5 and

6).

A strong deviation could 'be established

for the rectangular cylinder which of

RECTANGULAR

CYLINDER ''

TRIANGULAR CYLINDER Fa .27

I

r .-in

r -. rn

Figure 5.Heave andpitch, Fn = O.26/O.:27

O. a' .02 ni

A

Ca ' .03 ni

D

Ca

.04m

CALCULATION WITH EXP. COEFFICIENTS (r .02 n) 1 2 '3 4 We/i77g ___ 0 1 2 3 4

e/ig

_-_ EXPERIMENT (

O Ca

.02 ni

A Ca

.03 ni

1 oc

.04 in

CALCULATION WITH EXP. COEFFICIENTS (r .02 ni)

o 0.05

frequency to

lower values

demonstrated.

A better agreement between experiment and calculation was achieved by insertinq the measured hydrodynamic coefficients in the calculation method.

These results are also shown in the 'Figures .5 and :6.

It, is. 'bvious from-the preceding.results that for some cases where viscous damping

ffects play an important role this part.

of the damping should not be neglected

f

the .. calculation . of the vertical

motions and the added resistance in waves. This is especially true for higher Froude: numbers.

Such cases may not only be restricted to

sharp rectangular ship- or barge sections

but also to bilge keels which for high

forward speeds may also show a

signifi-cant influence on the vertical motions

and added resistance in waves.

REFERENCES

Beukelman, W.,

"Added resistance and vertical

hy-drodynamic. coefficients of oscilla-ting cylinders at speed",

Ship Hydromechanics Laboratory, Delft University of Technology, Report nr. 510., September 1980..

Beukèlman, W.j.

"tertical motions and added

resis-tance of. a rectangular and trian-guiar cylinder in waves",,

Ship Hydroinechanics Laboratory, Deift. University of Technology.,

Rèort nr. 594, July 1983.

Gerritsma, J. and' W. Beukelman, "Analysis of the resistance increase in waves of a fast cargo ship"

is clearly

.( 4] Ueno, K. etal,,

"Some experiments of heaving effect on ahead resistance of ships",

Journal

of the

Society of Naval

Architects of West Japan, Nr.

3.7,

February 1969 and 12h. XTTc,

page 112, 1969.

(5] . 'Ueno, K. etal,,

"Some, experiments, of' pitching effect on. .ahead resistance: of ships",

Journal of the

society of

Naval

.Architects of West. Japan, Nr. 37, ..February.'l969 and 12th .ITrc, page

114, 19.69.

course should be due to the viscous part - _{International Shipbuilding Progress,,}

of the damping. Vol. 19, No. 217, 1972 and 13th