Some effects of tank wall interference on the results of experiments in waves

BiEtotheek van de AfdeIng Schc::. :r'ï- _{m Sche3pvart!une} Techn;-he Hccc

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DCCUME,J.hE

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. DATUM1 TECHNISCHE UNIVERSITEII Laboratorium voor Scheepshydromechanica Archlef Mekelweg 2, 2628 CD D&ft Tel: 015-786873- Fax: 015. 781828 VICKERS LiMITED

SHIP MODEL EXPERI'LENT TANKS

ST. ALEANS AND DUARTON

SOTYLE EFFECTS OF TANK WALL INTERFERENCE ON THE RESULTS OF EXFERITYNTS IN WAVES

BY D. C. MTJRDEY

ROTM 71/25 DCM/JML

SOME EFFECTS OF TANK WALL INTERFERENCE ON THE RESULTS OF EXPERINNTS IN WAVES

BY D.C. MURDEY

SUNMARY

Response curves measured in regular waves in the St. Albans Tank are examined with the object of estab-lishing and quantifying some effects of tank wall inter-ference due to the reflection from the tank walls of waves generated by the motions of the model.

Such interference is found to cause two "jumps" in the motion response curves and a peak on the propulsion

response curves. The location and magnitude of the

interference effects depends on the ratio of wavelength to length between perpendiculars corresponding to the onset of interference given by the nomogram published in References (1) and (3).

Diagrams are presented which may be used for estim-ating the quantitative effects of interference on experi-ment results.

SYMBOLS

B Moulded beam, ft.

Froude number.

g Acceleration due to gravity, ft/sec2.

k Wave number = 2Tr/,\ , ft.

L,LBF Length between perpendiculars, ft.

Sn

Increase in propeller rate of rotation,

revolutions per second.

2

RPS Propeller revolutions per second.

5T Increase in propeller thrust, lb.

y Model speed, ft/sec.

Za Heave amplitude, ft.

Wave amplitude, ft.

ea

Pitch amplitude, radians.

Wavelength, ft.

Frequency of encounter? radians/sec.

(X/L)INT Minimum value of /L at which tank wall

interference effects may be expected.

"9l'

l' (/L)&2, 2' /L)N and

quantify the effects of tank wall inter-ference on response curves and are def-med in Figure 6.

1 INTRODUCTION

In 1966 Moor, Reference 1 , published a nomogram

based on theoretical work by Brard, Reference 2, for calculating, for particular values of the ratio of tank breadth to model length, the ranges of wavelength and model speed for which the results of experiments in waves may be affected by tank wall interference due to the

reflection from the tank walls of waves generated by the motions of' the model. This nomogram has been incorporated into the "International Towing Tank Conference 1969 Stan-dards for Seakeeping Experiments in Head and Following Seas",

Reference 3. Whilst predicting that certain experiments

may be influenced by tank wall interference, it gives

neither an indication of how the results may be influenced by such interference nor of how large (and hence how

-3

Very many of the response curves measured on models in regular waves in the St. Aibans Tank are expected, according to the nomogram, to have been affected by tank

wall interference to a greater or lesser degree. This

paper presents in detail examples of these effects for

one model together with an overall summary of the effects

on other models. These data are analysed to provide

diagrams for use in estimating quantitatively the effects of tank wall interference on response curves of pitch and increase of propeller rate of rotation.

2. DATA

The data used in this analysis are several hundred response curves measured during the last ten years as part of the routine testing of models in regular waves

in the St. Al'oans Tank. The Tank is 20.83 feet wide

and 10.5 feet deep. Most of the mo.dels were between

16 and 18 feet long between perpendiculars ( LEE)

although experiments have been carried out on models as short as 9 feet LBE and as long as 20 feet DEP. Details of the majority of the models are given in

Reference 4. In each case the model was self propelled

in head waves with the height maintained at a constant value, usually LEE/SO, and the wavelength varied in not

less than twenty steps from 0.5 lEE to 3.0 LBP.

Experi-ments were often repeated with the model in a different

loading condition and at several speeds. Measurements,

relevant to this paper, were made of pitch and heave; and of the increases in propeller thrust, torque, and

rate of rotation. The results were plotted on

where ?.. is the wavelength and L the length between

the model had been run at several speeds the experiment.. results were faired simultaneously on speed and)/L.

The interference nomogram, Reference 1, shows that interference may IDe expected to affect to some extent one hundred and eightyseven sets of response curves. When using the nomogram allowance has been made for the relationohip between frequency and wavelength in shallow

water; the nomogram strictly applies only to deep water.

A check was made on those response curves where interference affects were not predicted to establish if

this was, in fact, correct. In every case the pitch and

heave responses tended smoothly to unity and the increases in propeller thrust, torque and rate of rotation to zero as the wavelength increased from 2.0 IJBF, with no more experiment scatter than average over the whole wavelcngth

range. _{The general character of the response curves for}

models run at low speeds was similar to those for the

same models run at higher speeds. It was therefore

concluded that there was no evidence of tank wall inter-ference, confirming the prediction obtained for the

nomo gram.

There was, furthermore, no evidence of interference on any response curves for which the minimum value of

/L at which interference was predicted, (X/L)INT, was

greater than 1.64. The analysis described below is based

on the remaining fiftyninesets of response curves which do show evidence of tank wall interference.

3. AN EXAMPLE 0F THE EFFECTS 0F TANK WALL INTERFERENCE

The effects of tank wall interference in waves may be expected to show up most clearly for large models run

-5

at low speeds, where interference is predicted over a

large proportion of the response curves. For this reason

the results of experiments carried out at speeds corres ponding to Froude numbers 0.150, 0.171 and 0.192 with a 20 foot LBF model of a tanker form were selected for an initial investigation.

The increases in propeller thrust, torque and rate of rotation measured at Froude Number 0.150 are shown in

Figure 1. At this speed interference may theoretically

effect the results of experiments in waves with

_XIIi

greater than 1.03, and for these wavelengths the lines faired through the experiment data are shown dashed in

the figure. All three response curves show similar

variations withX/L including an unexpected second peak

at a value of X/L approximately 1.25. Because of this

similarity only the results of measurements of propeller rate of rotation are described in detail in this paper.

Figures 2, 3 and 4 show for Froude numbers 0.150,

0.171 and 0.192 respectively the measured pitch, heave and increase in propeller rate of rotation plotted on

and the lines faired through the experiment spots

are compared in Figure 5. The range of

X/L

over which

interference may be expected is indicated in the figures by dashed lines, and the critical value of,\/] (corres-ponding t6 the wavefront of the model generated waves

being at ninety degrees to the model centrelie) indicated

by a vertical arrow. At Froude number 0.192 (Figure 4)

the critical value of/L is 3.45, which is outside the range of the experiment data.

-6

The response curves measured at the highest speed show very little evidence of interference, being

gener-ally smooth in the long wavelengths. The qualitative

effects of the interference may therefore be estimated by comparing the response curves measured at the lower speeds

with those measured at the highest speed. The general

effects of changing speed alone are known from sets of

response curves run (on other models) at higher speeds,

where all the results are free from interference.

Decreas-ing speed may change the magnitude of the peaks in the response curves, and cause them to shift towards shorter wavelengths, but it is not expected to cause any major changes in their overall character.

It is cohcluded from Figure 5 that the peak in the propulsion response curves at Freude number 0.150 which

occurs at /L 1.25 is caused by tank uall interference,

as are the steep rise in the pitch response curve between

X/L

1.2 and 1.3, (and the associated sharp maximum and

minimum) and the smaller jump at about)/L 2.1. At

Froude number 0.171 there are similar, but smaller effects on the pitch response curve, but no evidence of

inter-ference on the propulsion results.

At Froude number 0.150 the heave response shows interference effects corresponding to those in the pitch response, but the jumps are much smaller, and there is no evidence of interference affecting the heave at either of the two higher speeds.

- 4. INTERFERENCE EFFECTS ON OTEER MODELS

The effects of tank wall interference described in section 3 are typical, and in. all, fiftynine of the sets

7

of response curves considered show similar characteristics which differ from the example shown only in their magnitude

and in the value of\/L at which they occur. A

quantit-ative summary is given in Table 1, which also includes

details of the principal particulars of the models, loading conditions and speeds at which the experiments

were carried out. Further hydrostatic particulars are

given in Table i of Reference 4. Details of the

inter-ference effects given in Table 1 of this paper are the values '\/L at the middle of each of the two jumps in

the pitch resoonse curves and the corresponding heights

of the jumps expressed as percentages of the pitch

res-pense estimated to apply in the absence of interference; and the value of )./L at which the interference peak in

the propeller rate of rotation response curves occurs, and the corresponding total deviation from the response estimated to apply in the absence of interference,

expres-sed as a percentage of the maximum increase in propeller rate of rotation, all as defined in Figure 6.

As mentioned above, the interference effects on the

heave response are smaller than those on the pitch response,

and they have proved very difficult to establish reliably. For this reason effects on heave are not considered in this section.

The expectation that the pitch responses should, in the absence of interference, tend smoothly to unity as?/L, increases from about 1.5, aids the definition of the jump

which occurs between \/L 2.0 and 3.0, but, with the

excep-tion of cases of very large interference effects, it has

only been possible to establish the jump in the pitch

-8

at several speeds, and the form of the response curve

without interference most easily estimated. Insufficient

or inconclusive evidence of interference is indicated

by a dash in Table 1, and no evidence of interference is denoted by 'TNOJTE".

The minimum values of >./L at which interference may

be expected, /L)INT, are also given in Table 1. Figures

7, 8 and 9 show the interference data from the table plot-ted on (>\/L)INT. In each case there is a strong dependence of the observed effects of interference on the minimum wave-length for interference, the effects becoming smaller as (/Ij) increases. No interference effects at all are

found when (/Ij) is greater than 1.64, and all the

effects are very small for ()/L)INT greater than about

1.4. To run experiments only in the interference free

region defined by the nomogram in Reference T would

therefore lead to unnecessarily small models or an undue curtailment of a test programme.

On average, the/L of the interference peak in the propeller rate of rotation response curve differs neglig-ibly from that of the jump in the pitch response which occurs between)/L 1.2 and 1.7, and. it is concluded that the propulsion is influenced only by the very large

variations of pitch withX/L which occur when the minimum wavelength for interference is less than about 1.1.

It is noteworthy that the jumps in the pitch responses which occur betweenÀ/J 2.0 and 2.8 are not

critical phenomena. The latter are defined by a constant

value of the frequency parameter, _{wv/g (where}

e is

the frequency of encounter, radians per second, y the

model speed, and g the acceleration due to gravity) _of

-9

in the pitch response curves takes on values between 0.27 and 0.35.

The lines fitted to the experiment data in Figures 7, 8 and 9 are a quantitative guide to the effects of wall interference in waves in the St. Albans Tank and

are a useful supplement to the nomogram of Reference 1.

CON C LUS IONS

By comparing response curves measured at speeds where tank wall interference is not expected, with response

curves measured at lower speeds, it has been possible to quantify some effects of tank wall interference.

Interference does not cause scatter in the results,

but seems to be the cause of two "jumps in the pitch

response and a peak in the propulsion responses. The heave

response is affected in a similar way to the pitch, but the jumps are much smaller and usually difficult to define.

The wavelength at which the interference effects occur and their magnitude depend on the minimum wavelength at

which interference is expected. Interference does not

appear to influence the results of experiments when the minimum wavelength for interference exceeds about 1.7 LBP, and the effects are unlikely to be important when minimum wavelength for interference is between 1.4 and

1.7 LBIP. Interference effects are most serious when

lo

-There may be other effects of tank wall interferenc;e

in waves which have not emerged from this analysis. Any

such effects may only be established by running geosim models in one tank or running one model in several tanks of different widths.

REFERENCES

Moor, ID.I. : "Longitudinal Bending Moments

on Models in Head Seas". Trans.

R.I.N.A.

Vol.109 (1967) p.117.

Brard, R : "Introduction a

Thorique

du Tanage en Marche" A.T.M.A.,

Vol. 47 (1948) p.455.

Goodrich, G.J. : "Proposed Standards for

Sea-keeping Experiments in Head and

Following Seas" Appendix I of

the Report cf the Seakeeping

Committee to the 12th International

Towing Tank Conference, Rome

_1969.

Moor, D.I. and : "Motions and Propulsion of Single

Nurdey, D.C. Screw Models in Head Seas, Part

II" Trans. R.I.N.A. Vol.112

TABLE i

QUANTITATIVE EFFECTS OF TATK WALL INTERFERENCE

PITCH RFS INCREASE

MODEL COITION

L B T F (/L)INT

(/L)1(%)1 (X/L)2

&2 (X/L)N 600 1 16.OQ 2.291 0.733 0.160 1.51 NONJ 2.75 15 NONE 832 1 17.00 2.468 0.930 0.149 1.21 1.50 35 2.30 40 NONE 0.164 1.46 1.70 5 2.80 20 NONE 835 1 16.00 2.091 0.896 0.149 1.28 1.50 20 2.35 15 NONE 0.164 1.54 1.70 5 2.70 20 NONE 1050 1 16.00 2.163 0.953 0.149 1.28 1.50 15 2.40 15 1.70 8 0.164 1.54 1.70 5 2.60 15 NONE 2 16.00 2.163 0.600 0.149 1.28 1.70 lO 2.40 25 NONE 0.164 1.54 1.70 5 2.70 lO NONE 1155 1 16.00 2.439 1.098 0.160 1.48 1.60 15 2.60 lO NONE 2 16.00 2.439 0.602 0.160 1.48 NONE 2.60 40 NONE 1156 2 9.20 1.402 0.346 0.133 1.50 NONE NONE NONE 1194 1 18.00 2.630 1.005 0.120 0.74 1.15 lOO

-1.20 70 0.134 0.93 1.30 70 2.10 30 1.30 40 0.149 1.14 1.40 50 2.30 40 1.40 5 0.164 1.38 1.50 15 2.40 lO NONE 0.179 1.62 NONE NONE NONE 1194 2 18.00 2.630 0.548 0.134 0.93 1.30 40 2.05 30 1.30 10 0.149 1.14 1.40 25 2.30 15 NONE

MODEL STA CONDITION B TABLE 1 - CONTIN1JED

(/)

(%) NONE NONE PITCH

(A/L)2

2.60

NONE &2

10

RPS INCREASE

(/L)N

NONE NONE T

0.164

0.179

(À/L)INT

1.38

1.62

1201

1

17.50

2.408

0.923

0.149

1.18

1.40

40

2.30

25 NONE

0.164

1.43

1.55

15

2.55

lO NONE

1201

2

17.50

2.408

0.581

0.149

1.18

1.45

30

2.30

25 NONE

0.164

1.43

1.60

10

2.50

20 NONE

1304

1

17.15

2.586

0.998

0.172

1.59

NONE

2.80

10 NONE

1328

1

17.63

2.441

0.913

0.160

1.24

-2.60

15

1.45

2

1328

2

17.63

2.441

0.604

0.171

1.55

NONE

2.50

10 NONE

1331

1

18.00

2.633

1.005

0.151

1.18

1.40

40

2.30

35 NONE

0.171

1.50

1.60

15

2.50

lO

NONE

1331

2

18.00

2.633

0.548

0.161

1.33

1.60

20

2.70

lO

NONE 1334B 1

17.63

2.441

0.913

0.160

1.24

-2.50

10

1.55

2 1334B 2

17.63

2.441

0.913

0.171

1.55

NONE

2.70

10 NONE

1347

1

17.63

2.441

0.604

0.160

1.24

-2.30

10

1.50

5

1347

2

17.63

2.441

0.604

0.171

1.55

NONE NONE NONE

1414

1

16.00

2.552

0.880

0.149

1.28

1.50

35

2.35

35

1.45

12

1414

2

16.00

2.552

0.554

0.149

1.28

1.50

30

2.35

20

NONE

1425

1

16.00

2.552

0.880

0.149

1.28

1.50

30

2.45

20

1.45

9

1425

2

16.00

2.552

0.554

0.149

1.28

1.50

35

2.35

30 NONE 1458A 1

20.00

2.903

1.136

0.150

1.03

1.25

95

2.10

30

1.25

66

0.171

1.34

1.40

40

2.40

15 NONE

FITCH RFS INCREASE

('\/L)1 (%)

(,\/L)2

()'/L)

(%) N N

1.50

4

NONE NONE NONE NONE NONE

1.55

7

NONE

1.60

4

NOIfl NONE NONE NONE NONE NONE

1.20

50

1.00

40 NONE

1.50

30

2.30

45 NONE

2.50

5

1.40

45

2.40

15 NONE

2.50

10

1.40

40

2.40

10

NONE

2.40

10

1.60

35

2.50

15 NONE NONE

1.55

30

2.50

20

1.70

15

2.70

20

1.60

20

2.55

30

NONE NONE

1.60

30

2.50

45 NONE

2.60

10

NONE

2.60

10

1.20

70

1.60

50

1.20

75

1.55

20

1.70

5

2.40

10 MODEL STA CONDITION L B

TABLE i - CONTIIfUED

T F

n

(\/L)INT

1458A 2

20.00

2.903

0.759

0.160

1.08

0.182

1.50

1458B

1

20.00

2.903

1.136

0.171

1.34

1458E

2

20.00

2.903

0.759

0.182

1.50

1458E

1

20.00

2.903

1.136

0.171

1.34

1458E

2

20.00

2.903

0.759

0.182

1.50

1496

1

16.00

2.200

0.880

0.149

1.28

0.164

1.54

1551

1

16.00

2.150

0.921

0.149

1.28

0.164

1.54

1551

2

16.00

2.150

0.585

0.149

1.28

0.164

1.54

1547

1

16.19

2.313

0.925

0.150

1.29

1766

1

18.00

2.447

0.759

0.179

1.64

1766

3

18.00

2.447

0.690

0.179

1.64

1767A 1

12.00

1.886

0.730

0.117

1.00

1767E

1

12.00

1.886

0.730

0.117

1.00

AEW DAL 1

15.78

1.687

0.501

0.159

1.48

06

04

02

r

THRUST

INCREASE

TORQUE

/ INCREASE

RPs

INCREASE

t O _CRITICAL O

0-5

10

I5

20

₂₅

30

WAVELENGTH

LBP

FIGURE i:- PROPULSION RESPONSE CURVES _{MEASURED ON A}

MODEL 20 FT. LBP. IN THE ST. ALBANS TANK AT _{FROUDE NUMBER}

0150.

DASHED LINES INDICATE TANK WALL INTERFERENCE _REGiON.

0

4

O5

05

PITCH

- _O_

--Q/

-O

HEAVE

RPS

INCREASE

CRITICAL

a

1 J -

_{-Q -e- -O--}

_{- G}

---O

O

0.5

10

15

_2O

25

_3'O

WAy E LENGTH

LBP

FIGURE2: RESPONSE CURVES MEASURED ON

_{A MODEL 2OFT.LBP}

IN THE ST. ALBANS TANK AT FROUDE

_{NUMBER OI5O}

15

05

Z

10

05

¿n 4 2 O O

05

1'O

LB P

PITCH

o

-HEAVE

-

-RPS

IN CREASE

CRI TICAL ?/ L

15

₂₀

WAVELENGTH

25

30

FIGURE3: RESPONSE CURVES MEASURED ON A MODEL 2OFT.LBP

IN THE ST. ALBANS TANK AT FROUDE NUMBER 0171

15

Oct

Ka

10

05

Za

A

I0

05

HEAVE

®_o_ac

-RPS

INC REAS E

FIGURE 4:

RESPONSE CURVES MEASURED ON A MODEL 2OFT LBP

IN THE ST. ALBANS TANK AT FROUDE NUMBER 0.192

DASHED LINES INDICATE TANK WALL INTERFERENCE REGION.

05

15

WAVELENGTH

LB P

20

i_5

05

O. 5

0150

Q1 7

0192

_T

i

'

Fn

0-150

0171

O $92 I I

-

_{-._7- -. -.} '---..

-Fn

0150

HEAVE

0471

0192

/

20

PITCH

RPS

INCREASE

O

05

15

25

3.0

WAVELENGTH L BP

FIGURE 5: COMPARISON OF RESPONSE CURVES MEASURED ON A

MODEL 2OFT LBP IN THE ST. ALBANS TANK.

(O/ _IOOD 10104 _C

fOj\

100F

E - MEASURED

- ESTIMATE

FOR NO INTERFERENCE IOOB /01 A

(YL)

_(/L

PITCH

RPS

INCREASE

MEASURED ESTIMATE FOR NO INTERFERENCE ENVELOPE OF INTERFERENCE PEAK

05

1.0

15

20

25

30

WAVELENGTH

LBP

FIGURE 6:

QUANTITATIVE DEFINITION OF TANK WALL

INTERFERENCE IN WAVES

20

K''a

.5

10

05

(0 /0

I00

80

60

40

20

el

pl

o

10

16

/L)lNT

FIGURE 7: MAGNITUDE AND LOCATION 0F THE FIRST

JUMP IN THE PITCH RESPONSE CURVES CAUSED BY

08

1'0

I2

14

I 6

18

FIGURE 8: MAGNITUDE AND LOCATION OF THE SECOND

JUMP IN THE PITCH RESPONSE CURVES CAUSED BY TANK WALL INTERFERENCE.

(o,

'°1N

80

60

40

20

15

10

I

06

08

o

o

10

I t

I 2

14

1 6

FIGURE 9: MAGNITUDE AND LOCATION 0F THE PEAK IN THE

RESPONSE CURVES OF PROPELLER RATE OF ROTATION CAUSED PY TANK WALL INTERFERENCE.