Model tests with turbulence producing devices

,a

M ED DEL AlstiD E

ERA Ni

STATEN S SAC E PP S PR OV'N'IN G S A N'STALr

(pUBLICATIONS OF THE SWEDISH! STATE SHIPBUILDING EXPERIMENTALTANK).

Nr 18OOTEBOR,G

1951

.

MODEL TESTS WITH

URBULENCE PRODUCING

DEVICES

BY

11. F. NORDSTROM AND HANS ,EDSTRAND

1G1J1IPEBT.S AB

1. Introduction

The following paper gives an account of the investigations which

were carried out at the Swedish State Shipbuilding

Experimental Tank with a view to determining suitable

methods of artificially stimulating turbulent flow around model hulls. The experiments were extended below the normal test range to cover very low model speeds, i. e. speeds corresponding to < 5

knots for 15-20 knot ships.

The reason for extending the experiments to include these low speeds, which are of little interest from a practical point of view,

was that it was hoped thereby to obtain a wider knowledge of model

skin friction in relation to that of a plank. Resistance measurement

at these low speeds can in a way be considered as merely a matter of determining the frictional resistance, since in all such cases the

wave-making resistance is of relatively little consequence and can

probably be neglected in most cases.

For the same reason, the investigations dealt, not with normal

ship models, but with models which can be most easily described as

three dimensional bodies of ship form. It was thus hoped to be able to obtain some idea of the effect of form upon frictional resistance.

The test programme consisted of resistance experiments with a

number of models of different fullness and their main dimensions were chosen so that they could be said to be representative of normal models. Conclusions have only been drawn to a limited extent from the results of these tests. However, to enable the reader to work out

the results in various directions and draw his own conclusions

there-from, the primary test observations have been given in full.

2.

Symbols and Units

Model Dimensions

L = length on waterline

B = breadth

4

o =

immersed midship section area

S = wetted surface area (= mean girth x L)

V = volumetric displacement

= half angle of entrance on waterline (in degrees)

length of tripwire

d = diameter of tripwire

Ship Dimensions

The same symbols as above, but with the suffix s added, are used

for the ship dimensions.

Dynamic Symbols for Model

v = speed in general

V =- speed in knots (Metric) Ri = frictional resistance

= residuary resistance

R = Rf

=- total resistance

resitance of tripwire

Dynamic Symbols for Ship = speed in knots (Metric)

R, = total resistance

Dimensionless Ratios and Coefficients

length-breadth ratio, breadth-draught ratio length-displacement ratio VIlj V LB T block coefficient 0

L prismatic coefficient

Rf

Cf _{(212 S} frictional resistance coefficient

et°

e- /2 v2 residuary resistance coefficient

C

-tf2/2 v2 Tr. - Q/2 .1dv2 v L

Re =

REYNOLDS' number General Symbols

specific gravity of water (dimensionless)

= weight of water per unit volume

= density of water (mass per unit volume) kinematic viscosity of water

acceleration due to gravity temperature of water (in °C)

Vnits and Conversion Factors

Metric units are used throughout 1 metre = 3.281 feet

1 Metric ton =-- 1 000 kg 0.984 British tons 1 Metric knot = 1 852 m/hour = 0.999 British knots

Values of y. g and v

The following values have been employed for y, g and

7 = 1.000 (w =- 1 000 kg/ms) for tank water

= 9.81 m/sec.2

=

= 102.0 kg sec.2/m4 for tank water

total resistance coefficient

tripwire resistance coefficient

5

=

t

6

Table 1

y =- 1.000 for tank water y = 1.026 for sea water

The values have been taken from the S. N. A. M. E. Bulletin No. 1-2 and

con-verted to Metric units and degrees Centigrade by using the following relations:

1 ft.' = 0.092 903 m" 1° F = 32 + 9/5° C

Kinematic Viscosity of Water

Adopted by the American Towing Tank Conference in 1939

Tank Sea Tank Sea

Temp. _Water

Water Temp. Water Water

t 10' v 10" v t 10" v 10' . V

°C m2/sec. m2/see. °C m2/sec. m2/sec.

5.00 1.5189 1.5650 17.78 1.0632 1.1129 5.55 1.4928 1.5392 18.33 1.0486 1.0983 6.11 1.4674 1.5141 18.89 1.0343 1.0841 6.67 1.4428 1.4897 19.44 1.0204 . 1.0701 7.22 1.4188 1.4660 20.00 1.0067 1.0565 7.78 1.3955 1.4429 20.56 0.9933 1.0432 8.33 1.3727 1.4204 21.11 0.9803 1.0301 8.89 1.3506 1.3985 21.67 0.9675 1.0174 9.44 1.3291 1.3771 22.22 0.9549 1.0048 10.00 1.3081 1.3563 22.78 0.9427 0.9926 10.56 1.2876 1.3360 23.33 0.9307 0.9805 11.11 1.2678 1.3162 23.89 0.9190 0.9687 11.67 1.2483 1.2970 24.44 0.9075 0.9572 12.22 1.2294 1.2782 25.00 0.8962 0.9458 12.78 1.2109 1.2599 25.56 0.8851 0.9348 13.33 1.1929 1.2419 26.11 0.8743 0.9239 13.89 1.1753 1.2245 26.67 0.8637 0.9132 14.44 1.1581 1.2074 27.22 0.8533 0.9028 15.00 1.1413 1.1907 27.78 0.8431 0.8925 15.56 1.1250 1.1744 28.33 0.8331 0.8824 16.11 1.1090 1.1585 28.89 0.8233 0.8725 16.67 1.0934 1.1430 29.44 0.8137 0.8628 17.22 1.0781 1.1277 30.00 0.8043 0.8533 . 1 . . I H -.

7

The values of the kinematic viscosity of water have been taken

from the S. N. A. M. E.

Bulletin No. 1-2') and converted to

Metric units and degrees Centigrade by means of the following re-lations:

1 ft.' = 0.092903 m'

1 °F = 32

9/5 °C

The values so obtained are given in Table 1.

3. Models Tested

Seven models were investigated, all of which were made of paraffin wax and were symmetrical about midships. Originally all the models

were made and tested with sharp, vertical stems and sterns, but for some of the final experiments two of the models were given raked stems. In some other cases the stems were altered from 'sharp' to

'rounded' (diameter 5.0 mm).

The reason for making the models symmetrical about midships

was mainly that, as mentioned in the introduction, the investigation

was concerned in the first place with the effect of different types of boundary layer upon the resistance. Thus, since the character

of the boundary layer is influenced, apart from model size and speed,

principally by fore body form, it was the form and type of the fore body which were the main concern in this instance, while the after body was of minor interest. Each model was therefore given fore body form both forward and aft and was symmetrical about mid-ships.

The aforementioned sharp, vertical ends were adopted in order to obtain similarity as far as possible with planks of corresponding length. At the same time, such a form results in a clearly defined waterline length about which there can be no ambiguity.

The straight ends and the symmetry about midships mean that these models can be regarded as being between actual ship models

and planks, so that a certain amount of care must be taken in applying the experimental results directly to ship models.

Model No. 333 was made the parent form for the series. This

model was 20 ft. long, so that, assuming a scale of 1: 20, it corms-1) Uniform Procedure for the Calculation of Frictional Resistance and the Expansion of Model Test Data to Full Size. S. N. A. M. E. Bulletin No. 1-2, New York, 1948.

8

ponded to a 400 ft. ship. The lines, which had a rather pronounced V-form character, could be said to be normal fore body lines for a moderate speed cargo ship (about 14 knots).

Models Nos. 332 and 334 had the same principal dimensions (L,

B and T) as Model No. 333 and also exactly the same body sections. The latter were merely "closed up" (No. 332) and -spread out"

(No. 334) respectively in relation to midships, in comparison with

the No. 333 (see the sketch attached to Fig. 5). By this means, from

Model No. 333, which had a prismatic coefficient g) =- 0.70 and 20 % parallel middle body, were derived No. 332 with ep = 0.60 and no parallel middle body and No. 334 with (p = 0.80 and 40 %

parallel middle body.

Models Nos. 345 and 346 were similar to Model No. 332 but to

scales of 1: 40 and 1: 15 respectively in relation to a 400 ft. ship. There were thus three versions of the q = 0.60 form, namely No.

332 to a scale 1: 20, No. 345 to a scale 1: 40 and No. 346 to a scale

1: 15. The fullest form, Model No. 334 with 99 = 0.80, was also

repeated in another size, namely Model No. 352 to a scale 1: 40,

but there was no model of this form to a scale 1: 15.

Finally one model, No. 372, was made finer than any of those above. Since, however, Model No. 332 was already devoid of

pa-rallel middle body, it was not possible to develop No. 372 by means

of further "closing up" of the body sections. Nor could Model No. 372 be given the same midship section area as Models Nos. 332,

333 and 334, since. this would have involved too much alteration in

the character of the sectional area curve from that corresponding to the latter models. This was to be avoided, so that the principal dimensions (L, B and T) were maintained while the midship area

coefficient was decreased from # = 0.975 for Models Nos. 332, 333

and 334 to p = 0.938 for Model No. 372. Then the sectional area

curve was designed so as to give about the same difference in block coefficient between Models Nos. 372 and 332 as between Nos. 332

and 333 and Nos. 333 and 334 respectively. At the same time, this

sectional area curve was made to correspond in character as closely as possible with those of Models Nos. 332, 333 and 334. In this way Model No. 372 was developed having g) =- 0.52 and 6 = 0.488.

The principal model data are collected in Table 2. The body

plans and end contours are given in Figs. 1-4 and the sectional

area curves in Fig. 5.

stem (leading edge) of each model, as mentioned previously, was sharp, but for technical reasons the edge could not be made less than about 1 mm (0.04 in.) thick, so that in fact it can be regarded

as being rounded with a radius of 0.5 mm (0.02 in.). The same applies to the stern of each model.

As stated above, the vertical stems were replaced by raked stems of the same thickness (0 5 mm radius) for some of the final tests. Models Nos. 334 and 332 were altered in this way mainly in order

that the other experimental material could be related to a more

actual ship model. The models whose stems were made more ship-form in this way were re-numbered 334-B and 332-B respectively. The alternations are shown in Figs. 1 and 3 respectively.

In some cases the stem itself was rounded off to a diameter of

5.0 mm (0.20 in.) from 10 mm (0.39 in.) below the designed waterline

i) In relation to a 400 ft. ship. Table 2 Data 9 Unit Models Model No. . . .

-

334 352 333 332 345 346 372 Model Seale') . .

-

1: 20 1: 40 1: 20 1: 20 1: 40 1: 15 1: 20 L m 6.096 3.048 6.096 6.096 3.048 8.128 6.096 B m 0.825 0.413 0.825 0.825 0.413 1.100 0.825 T m 0.344 0.172 0.344 0.344 0.172 0.458 0.344 V' na. 1.349 0.1686 1.180 1.011 0.1264 2.397 0.8429 S m2 7.540 1.885 6.995 6.450 1.613 11.467 5.970 LIB

-

7.389 7.389 7.389 7.389 7.389 7.389 7.389 BIT

-

2.40 2.40 2.40 2.40 2.40 2.40 2.40 a

-

0.780 0.780 0.683 0.585 0.585 0.585 0.488

-

0.800 0.800 0.700 0.600 0.600 0.600 0.520 i3

-

0.975 0.975 0.975 0.975 0.975 0.975 0.938 19 degrees 32 32 23 18 18 18 10.5 0 m2 0.2765 0.0691 0.2765 0.2765 0.0691 0.4915 0.2660 Ships (400 ft.)

4

m 121.92 121.92 121.92 121.92 121.92 121.92 121.92 Vs m2 10 788 10 788 9 439 8 091 8 091 8 091 6 743 88 m2 3 016 3 016 2 798 2 580 2 580 2 580 2 388 L8Ir71,/3

-

5.52 5.52 5.77 6.07 6.07 6.07 6.45 . .

-. .

-...

.

-10 4 /0-14 SL /0-6 Fig. 1. Fig. 2.

{

No 334

No. 352

No. 334-B

/ / 2 I / ern Rounded - No. 334 /9

No.333

/91/2 -6 /I WL BL /9 /91/2 20 0 7 6 .5 W L4 2 20BL

IS

1

Ian

1111111111.

11/11/1111

KW=

Wan

5 6 7 WL 4 2 BL

-'1A/L4 BL VIL 4 Pig. Fig. 4.

(No. 532

No..345

I No,. 346

No.

332-8-/9

/

WL 4 BL 20

tat

itt:tast

twall

9 9 20 11

No

.

372

/402,46. WL 4 3 S/e/n Rounded 3. 9L 7 6 7 5 2

Area in rn2. c\I tc if; fr) 050-0.07-- 0.06 0.25 0.40 - 0.20 0.5o 0.20 0/0 0.04 0.05 -0.02 001 0 0. 0./0 0.05 0 0.5 0.5

Sechonol-Area Curves

Model Dirnerlsiohs 2 1 1_ f -0 0 Fig: 5. 346 2.5

332 , 333 , 334,372

I

34552'

1. 5 2 2.5 J. 5 , 4 /15 I -0-4 -005 -0 /2 /4 /5 /6 /7 /8 /9 20 1.5 0.5

13

downwards. This was done in the case of Model No. 334, before the alteration to a raked stem was effected (334-B), and also in the case

of Model No. 372; see Figs. 1 and 4. This rounding of the stem involved abandoning the vertical stem and rounding it also in the vertical plane, particularly in the latter model where the entrance was very fine (99 =-- 0.52).

Resistance tests, similar to those made before the sterns were

rounded, were of course carried out with the altered models. These experiments should, however, be considered in the first place in

relation to the investigations of different turbulence producing devices

and not regarded as tests on the altered models themselves. The

purpose of rounding the stem was to produce a local acceleration

of the boundary layer at the stem itself with a probable

tur-bulence stimulation effect.

The above alterations, which were made to Models Nos. 334, 332 and 372, gave rise, of course, to certain changes in the wetted surface area of each model. In this case, however, no account has been taken of this fact in the calculations and the results have been worked out using the wetted surface area of the model in question

before alteration.

4. Testing Particulars

All the resistance tests were carried out over a speed range of

0.1-2.2 m/sec., corresponding to a speed range for the ship, assuming

a model scale of 1: 20, of 1-19 knots. Over the lower part of the speed range a special pendulum apparatus was used for measuring resistance, since the resistances at these speeds were so small that they could not be measured accurately by means of the ordinary dynamometer. A description of this pendulum apparatus is given

in Appendix 1.

The accuracy of the arrangement was quite

satisfactory even for the small forces measured at the lowest speeds.

The apparatus was used for resistances up to 1 kg and at speeds

where the resistance exceeded this value the ordinary dynamometer was employed. Of course, the tests were always arranged so that ranges of the two methods of measurement overlapped each other.

The steering apparatus which is usually employed when the resistance is measured by means of the ordinary dynamometer was

14

thought to be unsuitable for use in conjunction with the pendulum

apparatus on account of its considerable friction and inertia. Another

more simple form of guide was therefore adopted for use with the pendulum apparatus. This is also described in Appendix 1.

With Models Nos. 332-334 and Nos. 346 and 372 the ordinary

dynamometer was generally used at speeds down to about 0.8 m/sec., corresponding to about 7 knots at a scale of 1: 20, and the pendulum

apparatus was employed in the very low speed range. In the case

of the smallest models, Nos. 345 and 352, scale 1: 40, it was possible

to use the pendulum apparatus over the whole speed range. As mentioned previously, the experiments were carried out at

the Swedish State Shipbuilding Experimental

T a n k. The dimensions of the Tank are length = 260 in, breadth

= 10 m and depth = 5 m (853x 33x 16.5 ft.). Before commencing

the first test series of the day, a dummy run was always made, in accordance with the usual practice at the Tank.

The speed of return after each run was generally about 0.5 m/sec.

while the interval between successive runs varied, of course, with model and model speed. In the case of the largest of the two fullest

models (No. 334, ç, =- 0.80), the interval was about 30 minutes at

the highest speed (2.0 m/sec.). For normal routine tests the duration

of the interval is adjusted in each particular case according to the

experimenter's estimation of the state of the tank water. Some

idea of the intervals between runs in these experiments can be

obtained from the tables in Appendix 2, where the primary results are given together with the starting time of each run.

In all the tests the models were run at draughts corresponding to 6.875 m for a 400 ft. ship and at zero trim. No appendages were

fitted to any of the models.

Due to the necessity of giving some attention to the routine

investigations

of the Tank, the different experiments with the

respective models could not be carried out in close succession and in some cases the tests were several weeks or even months apart,

as shown by the tables in Appendix 2. The models were washed

and dried before each set of tests, but since they were kept sunk

in water when not in use, in accordance with the usual Tank practice,

a slimy deposit on the wax surface of the models developed after

a time. This meant that continuous changes in the surface condition

of each model could not be avoided, in spite of the aforementioned

5.

Turbulence Stimulators

All the methods of stimulating turbulent flow, which are suggested in technical literature, can be separated into two main types, namely:

methods designed to produce turbulence in the boundary layer

of the model itself

methods designed to produce initial turbulence in the app-roaching water.

The first group thus includes such methods as the use of tripwires and sandpaper strips placed in various ways over the model,

roughening of the model surface itself (KEmples comb), rounding of the stem and vibration of the model.

The second group includes the use of swords, struts or grids placed

in different ways ahead of the model, spraying the water surface

with fine vertical water jets during the return run and vibration

of the tank water. Limitation of the interval between successive

runs, so as to take advantage of the turbulence remaining in the tank water from the preceding run, can also be regarded as a

methodin this group.

One of the earliest known of the above methods of producing

turbulence is the use of the tripwire. The first to use this device seems to have been OSBORNE REYNOLDS. In the article An Experi-mental Investigation of the Circumstances which Determine whether

the Motion of Water Shall Be Direct or Sinuous, and of the Law of

Resistance in Parallel Channels, published in the Philo so ph

i-cal Transactions of the Royal Society% 1883,

REYNOLDS describes experiments with tripwires in tubes. After a tripwire loop had been placed in the tube in question, REYNOLDS states regarding the flow in comparison with that without a tripwire "Eddies now showed themselves at a velocity of less than half the previous critical velocity

In the present experiments, turbulence wires (tripwires) were

used for the most part but tests were also carried out using

sand-paper strips, vibration of the model, swords and struts placed ahead

of the model, rounding of the stem and limited intervals between successive runs.

Two sizes of tripwire were used, namely 1 and 3 mm (0.04 and 15

1) Also published in Scientific Papers, Vol. IL by OSBORNE REYNOLDS, C a m-bridge University Press, 1901, from which the quotation is taken (p. 76).

16

Fig. 6.

0.12 in.) diameter. The turbulence wires were generally placed at stn. 19, but in the case of Model No. 334 different positions along the hull were investigated. Furthermore, special tests were carried out with Model No. 372 with double turbulence wires with a view

to finding a method of calculating the resistance of a tripwire itself.

The turbulence wire was fitted as close as possible to the wax model and fastened to it by means of staples placed about 100 mm apart. The effective length of the tripwire, which must be known

for calculating the wire's own resistance (see below), was made

independent of the bow wave by fairing it with plasticene. Fig. 6 illustrates how the tripwire was fastened to the wax model.

The sandpaper used for the sandpaper strips was of the so-called

waterproof type. It was made by Dur ex Abrasives Cor p.,

New York, and designated by the manufacturers as Hydro-Durexsil No. 60 D. In general, two widths of sandpaper were used, these

2

Fig. 7.

being tested in two successive experiments according to the method then extensively employed by Dr. K. S. M. DAVIDSON. The motive

for this was originally to obtain a measurement of the sandpaper's

own resistance and this is further discussed below.

The successive experiments with two different widths of sand-paper were arranged so that first a series of tests were carried out

with a strip of sandpaper of a certain width placed symmetrically at

stn. 19 (half the width forward of and half abaft stn. 19) and then another series was run with the after half of the strip removed. The

initial width of the strip was varied according to the size of the model. The edges of the sandpaper were in every case faired off with a small plasticene fillet. Fig. 7 shows a photograph of Model No. 332 fitted with a 25 mm sandpaper strip forward of stn. 19 (the after half

removed). An idea of the grain size of the sandpaper employed can

be obtained from Fig. 8 which shows a microphotograph of the material.

17

18 -Fig. 9_ swoo., --Nolowo"

t$'

r '00' A 0 a. t;,,i-1 _' 1a si. ',i1.4.... . t -Om ' T a le , 111 -7 . ., p i. ;I , A r 1 _r 0, ik _{, ,} .6 ,1 .I , 414% -.. , iv . -, "40 ... 0 1--. CI 4

tr I

' I. 4

'

/4 1.: -Jr f '.<.., il

,

1 i' 1 _tot. '..-4 I / , ' 1 ° ° ' r ': j-. ' ' '-' ..fi . lit ,,t,1 a. P 4PCJ , .,,,,,, N.., .., .. .. -

,'

_{,,E 3 ' '..'? i''''} , _{,r, r} ' _{.' .1)} k, je° # ts

"

. '_{. ..} ,010 r . '... '',0 s .

. 1il ....

4. 4 .0 ' I .. ' X.1_11 _ . , .. 13 .ri. '

Fig. 8. The sandpaper used for the strips ( x 10.),.

J

dimensionless form c

19

The stem rounding, which was carried out on Models Nos. 334 and 372 and described in Section 3 above, was also intended to stimulate turbulence and should therefore be mentioned here.

Attempts were made with Model No. 372 to stimulate a turbulent

boundary layer by means of vibrating the model. An unbalanced

motor was employed to set up the vibrations and the arrangement is illustrated in Fig. 9. The same model was also tested in conjunction with swords and struts as turbulence stimulators. The arrangements adopted are described in subsequent sections together with the experiments.

6.

Results from Tests with Different Types of

Turbulence Stimulator

In this section, the results obtained with the various turbulence stimulating devices are given. In the lower speed range, where the

resistance is mainly frictional, the results are expressed in the

as a function of REYNOLDS' number e/2 v2

(Re =v L . In the higher speed range, where the residual resistance

also becomes evident, the results are given as model resistance as a function of model speed. The ranges of the two methods of

presenta-tion have been chosen so that they partly overlap each other.

The corresponding ship speeds, based on the model scales given in

Table 2, have been marked in the various diagrams. In calculating the corresponding speeds in those diagrams which are drawn to a base of REYNOLDS' number, the kinematic viscosity (v) has been

taken as that for 15° C water temperature and sea water (7 = 1.026).

Particulars of the test series are summarized in Table 3 and all the primary results are given in the tables in Appendix 2, which

includes, besides model resistance and model speed, the temperature

of the tank water and the starting time of each run.

The suitability of the adopted methods of presentation can be debated. Particularly in the higher speed range, where model

resistance is given directly to a base of model speed, extraneous

effects from, for example, differences in the temperature of the

tank water between one experiment and another, can show them-selves in the results. This can also, of course, be assumed to be the

^

21)

Table 3

Resistance Tests. Series Nos.

(The Series Nos. are marked with 0 on the Figures)

case with the

dimensionless presentation at higher values of

REYNOLDS' number where the residual resistance of each model becomes considerable. However, it should be added that during the

experiments in question, the water temperature only varied between

the quite narrow limits of 12.8-17.7° C

Model No. 334 334-B 352 333 332 332-B 1345 346 372

Model Scale 1:.20 1:40 1:20 : 20 1 1:40 1:15 1:20

Prismatic Coefficient . . , 0.80 1 0.70 I 0.60

- 0.59

Without Turbulence Device 1 8 10 14 17 22 25 30 I 35

Tripwire 1 mm at Stn. 19 . 1 mm » * 18 ., . ,. 1 mm » » 191/2

..

1 mm, 25 mm abaft the Stem 3 mm at Stn. 19, .. 1 mm » * 191 1 mm > » 10 ' ' -1 mm * 191 3 mm ,»> 10i ' ' ' -2 3 5 6 . I 1 .1 , 11 Jr 6 18 19 , . 23, 29 3

3l36'

37. 38 39 Sandpaper 109 mm at Stn. 19 . ... 75 mm * » 19 . . . 50 mm » * 19 . . . 50 mm from Stn. 19 for'd ' 37.5 mm * s 19 * 25 ram * » 19 » 1 I I , I' ' 12 13 , , 20 21 28 33 34 ' Model Vibrating 40 Sword '

--41 42 Strut .. .... ,... .

.. ...

I

' Stem Rounded, Diam. = 5

mm 1 7

1 43

Diff. Time Intervals . . . 9

ii 94 99 1: 4 15 . . . . . . . . . . 27

21

Tripwire as Turbulence Stimulator

An increase in the resistance of a model fitted with a tripwire

compared with that of an absolutely naked model can be regarded

as being not only due to the turbulence in the boundary layer

stimulated by the wire, but also to the resistance of the wire itself.

Attempts have therefore been made to correct for the latter, by means of the following expression for the resistance of a cylinder of

infinite length moving in undisturbed water: RT,..= cr,.. e/2 ld v2

where RD.. = the resistance of the cylinder (tripwire), 1 = its length, d = its diameter, v its velocity and cr, = the resistance coefficient. Throughout the experiments dealt with here, the value 1.0 for the

resistance coefficient was used in correcting for both 1 and 3 mm diameter tripwires. The speed of advance of the wire was assumed

equal to the model speed.

In all cases, the effective length of the tripwire was made

independ-ent of the bow wave by fairing it with plasticene, as mindepend-entioned in

the previous section. The plasticene was applied from 10 mm (0.39

in.) below the waterline upwards on the larger models and from 5 mm (0.20 in.) below the waterline upwards on the two smallest

models, Nos. 345 and 352. Thus the effective length of the tripwire

on each model could be taken as being constant, regardless of the

bow wave, and equal to the girth to the waterline less 20 mm on the larger models and less 10 mm on the two smallest models; the method of attaching the wire is illustrated in Fig. 6.

As mentioned before, special investigations to try to determine the tripwire's own resistance have been carried out and are described in Appendix 3.

In Figs. 10-12 are reproduced the experimental results obtained with Model No. 334 (c) 0.80) without turbulence stimulators, with a 1 mm tripwire and with a 3 mm tripwire at stn. 19. Fig. 10

illustrates the very low speeds in the range Re = 6.0 105-4.5 106

and c is given as a function of Re.

In addition to the points

representing the measured values as calculated directly, the values

obtained after correcting for the tripwire's own resistance according

to the above method are also reproduced. Fig. 11 gives the results in the same way as Fig. 10 for the somewhat higher speed range

corresponding to Re = 6.0 105-9.0 106. The results in the higher

speed range are shown in Fig. 12 where model resistance is given

directly as a function of model speed. Corrected values of resistance

=

22 cc 0.006 0405 10.004 0.002 0.001 4 ' lig

II%

1 II

INk

'

Vir,

1./15/%, 11P--.7..-.r. _ /26t././...1.. . '.. 1 71111 =-_-- - --[ -=-_. . I 1 .-I 8 Re = v 5%106

Mode No. 334

0

No Turbulence Device, 1 pl.?, Tripwife at Stn. 49

Corrected for Tripw.Res.o(Rrr= e/2.1d v?

3 mm Tripwire at Stn. 19

Corrected for Tripw. Resistance

2 3 4 5 6 7 8

COrresp. Ship Speed,Vs, hnots (Scale h20,-Sea Water, 15.09C)

Fig. 10. In this and subsequent figures, the ringed numbers denote the respective

series (see Appendix 2) and, where it occurs, the letter s is an abbreviation for

second (sec.). 0.003

0

in 6-105 2 3 4 I

0 006 0.005 0.004 0.001 Model No. 334 No Turbulence Device mm Tripwire at Stn. 19

Corrected for Tripw. Res. (Ph.' 0.1d v 2 )

3 mm Tripwire at Stn. 19

Corrected for Tripw. Pes,

6 105 8 106 2 Re= v L

3 4 5 8

I I

2 3 4 6 8 10/2 16

Corresp. Ship Speed V5 , ir, knots (Scale 1:20, Sea Water, /5.0°C) Fig. 11. /07 93 ...,4 b _. 0. . Cm...AL. Pr., ,,e . cv 0.003 CC 0.002

24

Model No. 334

a No Turbulence Device

0

Corrected for Tripw.Res.(R,=4"/2.1d v2)trim Tripwire at Stn. 19

6 8 10 12 14 16 18

Corresp. Ship Speed,Vs, in knots (Scale 1:20)

Fig. 12. 12 10 8 6 4 2 .i. R a, CC

{°

3 mm Tripwire at Stn. 19 cs.)

N. Corrected for Tripw.Res.

r

s

,

_c.

1

_ipii

1

ii

ct 5

.41

1

. 10 .

.All

VW.

auiuu

0.7 0 /5 ₂₀ V in m/s

q;. .0I0 017 0.005 1/4., 0004 0002 0.0 0 2./0 4 Model No. 352' CD No Turbulence Device

{1

mm Tripwire at Stn. 19

- ---0--- Corrected for Tripw. Res. (Rrr=ep-id v 2

,00.008 6 ioRe =-9'-)) -

Ir

It 1 2 4 6 8 /0 /4 48

Corresp. Ship Speed, Vs fll knots (Scate 1:40,, Sea Water; 15.0 °C) Fig_ 11. 4. 10. 25 .11 _ Ii 1 I I 1 . I , I . 1

i

.

1

II

1 ifiplI IAI; rill1,1 I Ilp ill I

G13 .' I I-. . . , , 1 , I, I i. -. I '14 " ) I 3 2

96 Cc -4r Model No. 333 No Turbulence Device mm Tripwire at Stn. 19

Corrected for Tripw. Res. (R77 e/2-1dv2) 3 mm Tripwire at Stn. 19

Corrected for Tripw. Res.

ck .1110 . ---i, r-:_, AL Aita..._ ' ! '\I II I--.1 I I . I I 1I IPI 4. , .4 1 Pr.,,,,. --,N.: . Schoenherr's LinePr 6'/0 s 8 106 Re = v L 2 3 4 5.106 2 3 4 5 6 7 8

Corresp. Ship Speed,V, in knots (Scale 1:20, Sea Water, /5.0

Fig. 14. 0.006 0.005 0.004 003 0.002 000I /4 4

Mode/ No. 333

No Turbulence Device

mm Tripwire at Stn. 19

Corrected for Tripw. Res. (R1r= Old v2) 3 mm Tripwire at Stn. 19

Corrected for Tripw.Res.

)12

10

0.7 1.0 5 20

V in m/s

I I 1 I 1 i I

6 a 10 12 /4 /6 /8

Corresp. Ship Speed ,V, , in knots (Scale 1:20)

Fig. 15.

V in M/S

14 1.5 1.6 1.7 1.8

.28

Mode. No. 332

No Turbulence Device

mm Tripwire at Stn. 1.9

Corrected for Tripw. Res. (RT7E/2.Idv2) 3 mm Tripwire at Stn. h9

Corrected for Tripw. Res.

2 3 4 5 6 7 8

Corresp, Ship Speed,Vs, in knots (Scale 1:20, Sea Water, 15.0°C)

Fig. Hi. _ 1 1 7,_.__L. 1 :411 11111 1

illiiii-.

-di. 1 , i

-v,V4641

"011g1FINIPPNWIZE1.... d. . . ... Schoenherr's Line .L __ 1 1 , d' _5.=..Z -, 0.005 0.004 cs:, 0.003

c.?

I S 0,002 0.001 ' 6'105 8 106 Re= vL 2 4 5.10 0.006 0 I 3

Modeft No. 332

0

No Turbulence Device

I Min Tripwire at SM. 19:

Corrected for Tripw.Res. (Rrr= Id v2)

3 mm Tripwire at Stn, 1,9

Corrected for Tripw. Res,

in m/s 1.4 1.5 1.6 - 1.7' J.8 .49 11. 0,7 f,0 15 20 ,w mis L ----.--- r 1 ___,L_,_.._ _ --_11L 6 e 100 12 14 16 /8

Corresp, Ship Speed, i/s , in knots (Scat 1:20),

Fig. 17. 5 4 e/2 4 in

30 0.006 0.008 0.007 006 N 0.004 0 003 0.002 2 10 Model No. 345 No Turbulence Device 1 mm Tripwire at Stn. 19

Corrected for Tripw. Res. (RT= ep.id v2)

Corresp. Ship Speed, Vs , in knots

Fig. 18.

1

I IJ

1 1 1

2 3 4 6 8 10 /4 18

(scale /40, .SECI Water, 15.0 °C)

, ,

IL

_:ii

.

11/01/14

- ' ,. -...e.

I.

-

-. .Schoennerr's , Line 4 6 8 106 Re= v L 4.106 2 -o

0.004 0.00/ 0 0.006 0.005 a ("lode! No. 346 No Turbulence Device 1 mm Tripwire at Stn. 19

Corrected for Tripw.Res.(Rrr=0.1d v2)

3 mm Tripwire at Stn, 19

Corrected for Tripw. Res.

31

t i I I

I 2 3 4 5

Corresp. Ship Speed, V5, in knots (Scale 1:15, Sea Water, 15.0 °C)

Fig. 19.

ii-

e

I itiaiii

I

1

Re= vL 2 3 4 5/06 0.003 L,) cc 0.002 6.10 /06 -1

32 0.006 0005 0.002 0.00/ o Mode/ No. 346 No Turbulence Device I mm Tripwire at Stn. 19

Corrected for Tripw.Res.(R7.,=4,/2.1d v2)

3 mm Tripwire at Stn. 19

Corrected for Tripw. Res.

3 5 7 9 II

Corresp. Ship Speed, V5, in knots (Scale 1:15, Sea Water, 15.0 °C) Fig. 20.

\

,

...-, ---,.. --.-Schoenherr's Line---2406 4 Re = vL 6 107 0.004 cc 0.003 ci I

8. 10 12 14 /6 Corresp. Ship Speed, Vs in, knots (Scale 1:15)

Fig.. 21.. /6. 14 12 /C 8 6 4 2

,

,...: ti la, Cz ... CC k

- ...,-1mm Tripwire at Stn. 19 Corrected for Tripw.Res.(R

3 mm Tripwire at Stn. 19 ls. Corrected for Tripw. Res'.

r in m/s 4 45 1.6 1.7 Tr= e/2.6dv2) . A

rj,

I .,.. ° -..:

n i

0-, cr

111

I

,

NI

P

II

, r

TV

MO

1

FA

111111

IPA

, 1

11/11/11

II 1 ,

1111

rir:

I ,

ma

1 1 , II 1 1 1 1 , ,

III

1

II

33

Model

No. 346 0 Turbulence Device I.0 5 2.0 2.5 in m/s . IVo 0 7 :3

.34 cc 0.006 C.) 0.002 0.001 Mode l^ _{No. 372} No Turbulence Device 1 mm Tripwire at Stn. 19'

Corrected for Tripw. Res. (RT., = 0-Id )

3 mm Tripwire at SM. 19

Corrected for Ti-ipw. Res.

2 3 4 6' 7 8

COrresp. Sfrnp Spetd,Vs , in knots (Scale fi20, Sea Water, 15.0 °C) Fig. 22. I 1 , _. 1 , _ ,..a.,_ 11/11/1k . . . A, ,c, & Line __. - . _.

A

0.004 Schoenherr's ______ poll 1 11-11711111'. 1

gild

' 2 .106 . V 0 , 1 6.40 2 3 4 5./06 Re= 0.005 0.004 0.003 2 v L I 5

Mode/ No. 372

No Turbulence Device

1 mm Tripwire at Stn. 19

Corrected for Tripw. Res. (Ftrr= e/2, Id v2)

3 mm Tripwire at Stn. 19

Corrected for Tripw. Res.

6 8 /0 12 /4 16 /8

Corresp. Ship Speed,Vs , in knots (Scale 120) Fig. 23. 35 V in m/s /.4 1.5 1.6 1 7 1.8 0 7 10 /.5 20 v in m/s 4 { 2

36

Corresp. Ship Speed,Vs, in knots itScale 1:20, Sea Water,15.0° C)

Fig 94, C

Model No. 334

No Turbulence Device I mm Tripwire at Stn. 19' ..

.Corrected for Trip., Res. (R 0(d v2)

I mm Tripwire, 25 mm labaft the Stem Corrected for TriPw.Rel.

4 5 6 7 8 4 . ,,___...

iev

IIIIIIIibs.,

-.. _. I . _ ' .1 _...

11

Sch _... 46.1z6, A 19- '374. - 'el'. '.4,1*.t. id'E.,: I ' -111nalk.--, -.op-04 _ /40 ---.n... ---: --I , -, --;-I -I _ . , 0.006 0:005 0.004 A, 0.003 cc ,cs.1 0.002 o.occ4 6 105 8 006 2 Re= v L ii 3 2 I I

0

0

L

Model No. 334

Turbulence Device

0

Corrected for Tripw. Res. (Rrit- e/2-1d,v2)mm Tripwire at Stn. 19

1 mm Tripwire at Stn. 18

Corrected for Tripw. Res. s4mm .Tripwire at &tn. 19 //2 Corrected for Tripw. Res.

t mm Tripwire, 25 ram abaft the Stem

Corrected for Tripw. Res.

6 - a io '12 14 16 18

'Corresp. Ship Speed, Vs, in knots (Scale h20).

Fig. 25. 37 07 i.O 15 2.0 in m/s 5 6 in m/s 1.4 1.5 1,6 1,7 12 10 4 2 v 1

38

with 1 and 3 mm tripwires are shown, for the sake of clearness, only

as examples on an enlarged scale over a limited range of speed.

Fig. 13 illustrates the results for Model No. 352 in the same form

as those in Fig. 11. Here, however, it has been possible to give all

the results over the whole of the speed range investigated. The results shown refer to the naked model, the model with a 1 mm

tripwire and the same corrected as above for the resistance of the tripwire. The thicker tripwire (3 mm) was not used in this case.

Model No. 333 was investigated to the same extent as Model No. 334 above. The results are given in Figs. 14 and 15 in the same form

as those in Figs. 10 and 12.

The experimental results obtained with Model No. 332 are reproduced in Figs. 16 and 17 in the same way as for Model No. 333, while those obtained with Model No. 345 are illustrated in one

diagram, Fig. 18, using the same method as for Model No. 352. For the largest model, No. 346, the results are given in Figs. 19,

20 and 21 using, as before, two different methods of presentation for the low and high speed ranges respectively.

Figs. 22 and 23 illustrate the results for the finest model, No. 372. In Fig. 22, for the sake of clarity, all the values referring to the model without

tripwire in the range Re = 2. 106-3

106 have been

presented apart from the other results.

A special investigation was carried out with Model No. 334 fitted with a 1 mm tripwire in different positions along the hull. The results are given in Figs. 24 and 25.

Finally, Model No. 332-B (No. 332 but with a raked stem) was also tested over the low speed range both with and without a 1 mm

tripwire, the results being shown in Fig. 41.

Results from Experiments with a Tripwire at Station 19

In all the figures giving the experimental results in dimensionless form, SCHOENHERR'S line for frictional resistance along smooth

plates with turbulent boundary layers has been drawn in for

comparison. This line can be expressed as 0.22

Vet

r

On comparing the experimental results illustrated in Figs. 10-23

with each other or with SCHOENHERR'S line, it can be stated that

39

the models were apparently affected by laminar flow. In the case of the finest models, Nos. 332, 345, 346 and 372, the effect is most noticeable in the very low speed range, while with the full models, Nos. 334 and 352, the effect is greatest in the higher speed range.

In the case of Model No. 334 (92 = 0.80 and scale 1: 20) it is apparent from Figs. 10-12 that the model resistance was largely unaffected

by turbulence devices at Re < 2.5 106, corresponding to a speed

of about 4 knots (very low speed range). Furthermore, except for the

values for the model without -turbulence stimulator at the lowest

speeds, the spots lie above SCHOENHERR'S line for smooth plates.

These circumstances seem to indicate that no appreciable areas of

laminar flow existed during these experiments.

As regards the lowest speeds for the model without turbulence

device, where the values lie below SCHOENHERR'S line, it should be

pointed out that the measured values of resistance are particularly small at these low speeds (model speed 0.1 m/sec.) and any errors

become relatively large. Finally the spots in question only fall below the SCHOENHERR line to a slight extent.

On the other hand, in the higher speed range (Re > 2.5 106),

some effect on the model resistance was observed when using tripwires to stimulate turbulence. This is evident from Fig. 11 where the resistance values for the model with tripwires, both uncorrected and corrected for the tripwire resistance, lie above the corresponding

values for the model without tripwire over a considerable range of speed.

The same tendencies can be observed in Fig. 12. With a 1 mm

tripwire, the model resistance values in this diagram lie above those corresponding to the model without tripwire, this being the case for

both uncorrected and corrected values over the whole of the

practical speed range. With a 3 mm tripwire, some of the corrected values fall below those obtained from the model without tripwire, particularly at the highest speeds. This may be due to too high a value being chosen for the aforementioned correction coefficient, at any rate at these relatively high speeds.

The above remarks also apply to a large extent to the smallest

model, No. 352 (scale 1: 40), which has the same prismatic coefficient =- 0.80) as Model No. 334. In the very low speed range, it appears that the model resistance was largely unaffected by using a tripwire as a turbulence stimulator.

On the other hand, at Re > 106,

corresponding to a ship speed V> 5 knots, considerable differences

40

are evident in comparison with the "without tripwire" results and this could indicate that the latter were affected by laminar flow.

These differences are noticeable over the whole speed range from 5 knots up to the highest speeds conceivable in practice (15 to 16 knots), even though the method of presentation adopted is not suitable for illustrating the differences at these high speeds, where the residual

resistance becomes relatively great.

At the lowest speeds, the curve of resistance coefficient rises considerably above the SCHOENHERR line and this may be due to

the previously mentioned inaccuracies which are liable to occur at

such low speeds. However, this rising tendency at the lowest speeds

can also be observed in the results from other models, particularly

the second of the two smaller models, No. 345, (see Fig. 18), and it

therefore seems doubtful whether the occurence can be attributed

to pure chance. The cause might possibly be the appearance of surface tension forces in the water-air surface, which become relatively large at the small resistances in question.

It should be remembered here that the fact that experimental

values coincide with or lie above SCHOENHERR'S line for smooth

plates with turbulent flow, as for example in Fig. 10, does not

necessarily mean that the boundary layer of the model was also turbulent. Even if wave-making resistance can be neglected at

Re < 2.5 106 in Fig 10, it is probable that separation influenced

the resistance values in this region. In view of the full after body

form of Models Nos. 334 and 352, it is certainly reasonable to assume

that this can be the case. Other form effects with these full models can also, of course, be assumed to be present so as to increase the frictional resistance arising from mixed laminar and turbulent flow

up to or above the level of SCHOENHERR'S line for smooth plates

in wholly turbulent flow.

Three different cases are evidently possible as:

1. The resistance of the model with tripwire (corrected for the

resistance of the tripwire) can lie well above that of the model without tripwire. This could be attributed to turbulence in the boundary layer stimulated by the tripwire. At the same time, of course, any separation effect might have been reduced as a

result of the presence of the tripwire, but this reduction does

not outweigh the aforementioned increase in resistance. The

41

case obviously affected by laminar flow, in spite of the fact that they lie above the SCHOENHERR line.

The above circumstance may be reversed, i. e. the resistance of the model with tripwire (corrected for the resistance of the tripwire) can lie well below that of the model without tripwire. This might be attributed to the tripwire causing the separation

point to move aft with a consequent reduction in resistance. On the other hand, any appreciable laminar flow would be hardly conceivable.

In any case, the increase in resistance

consequent upon transforming the flow from laminar toturbulent

would be too small to outweigh the above decrease in resistance. The present case (in Fig. 10), where practically the same resistance was obtained whether the model was fitted with a

tripwire or not. This may have been due to one of the following possibilities:

That the boundary layer was wholly turbulent, even without the use of a special turbulence stimulator (in which case it is assumed that the tripwire correction is correct).

That wholly laminar or mixed laminar and turbulent flow

existed in conjunction with a form effect, such as separation "resistance", in accordance with previous remarks, and that neither of the turbulence stimulators (1 and 3 mm tripwires) was sufficient to transform the flow regime from laminar to turbulent to any considerable extent.

or c. That without a tripwire, wholly laminar or mixed laminar and turbulent flow existed together with a form effect

con-sisting of separation "resistance"

as in

b. and that the

tripwires employed were able to produce a transition from

laminar to turbulent flow over a considerable area, with the consequent increase in frictional resistance, but that

simultaneously the turbulence stimulator caused the separa-tion point to move aft and so decreased the resistance. Thus,

in such a case, the turbulence devices work in both directions, partly increasing the model resistance through increased frictional resistance, caused by the boundary flow over a considerable area being transformed from laminar to turbulent, and partly decreasing the model resistance to about the same extent through decreased separation effect, caused by the movement aft of the separation point. In these circumstances, the model resistance

remains roughly the same as when no tripwire is employed.

2..

3L

a.

42

It is impossible to say without doubt which of the three alternatives

(a, b or c) outlined above is in fact correct solely _{on the basis of the}

evidence in, for example Fig. 10. The existence of _{a form effect is}

possibly confirmed by the fact that the resistance coefficient for the

model with a 1 mm tripwire, at certain points in the region of Re = 2106 in Fig. 10 and Re = 106 in Fig. 13, lies below that for the model without tripwire. This situation should indicate that in the

region in question the tripwire caused the separation point tomove

aft with a consequent decrease in resistance.

The experimental results from Model No. 333, Figs. 14 and 15,

need not be discussed at length, since they can largely be said to

represent the mean between the results from the fullest model, No.

334, Figs. 10-12, and those from the finer No. 332, Figs. 16 and 17.

In the case of the finer models, as was pointed out previously,

it is evidently in the low and very low speed ranges where the greatest risk of laminar flow exists. The resistance coefficients for Model No. 332 without tripwire in Fig. 16 thus lie considerably

below the SCHOENHERR line in the very low speed range.

It is interesting to note from the latter figure that in this range the 1 mm tripwire did not apparently influence the model resistance

to any great extent,

while the 3 mm tripwire increased the

resistance more or less up to the level of the SCHOENHERR line. In

other words, a 1 mm tripwire was too small to provide enough

disturbance to cause transition from laminar to turbulent flow and

even a 3 mm tripwire was apparently insufficient at the lowest speeds.

Over the range corresponding to normal ship speeds, which is dealt with in Fig. 17, no effect apart from the added resistance of

each tripwire can be discerned. It appears, moreover, from the

corrected values given in the enlarged insert in Fig. 17, that the

correction coefficient adopted (cr, = 1.0; see above) is too great,

particularly for the 3 mm tripwire, as has been pointed out previously. These circumstances, however, are discussed in more detail in Appendix 3.

The results in Fig. 18 referring to the smallest of the finegroup of models, No. 345, largely confirm the results obtained from Model

No. 332, which had the same prismatic coefficient (9) = 0.60). Laminar flow evidently exerted a strong influence here, since the

values for the model without tripwire

lie considerably below

corres-43

ponding to less than 12 knots, turbulence stimulation with a 1 mm

tripwire produced a marked effect.

On the other hand, at the

highest speeds, i. e. above 12 knots, the corrected values for the

model with a 1 mm tripwire more or less coincided with those for

the model without tripwire. The latter can be assumed to indicate

that considerable areas of laminar flow are not prevented by the

presence of a 1 mm tripwire. In contrast with this case, the fullest of the small models, No. 352 (cp = 0.80, scale 1: 40), was, as

men-tioned previously, affected over the whole speed range; see Fig. 13.

In conclusion, it may be deduced from Fig. 18 that, as in the case

of Model No. 332, a 1 mm tripwire is not adequate as a turbulence

stimulator in the very low speed range. Further, the marked rising tendency at the lowest values, which has been mentioned above, is also to be found here.

For the largest model (scale 1: 15), No. 346, which had the same prismatic coefficient as Nos. 332 and 345 (99 = 0.60), the results

are illustrated in three diagrams, Figs. 19, 20 and 21. The effect

produced by the tripwire is considerable over the very low speed

range, while, as with Model No. 332, no effect is noticeable over the

range of practical ship speeds. It is also apparent here that the

1 mm tripwire was insufficient to produce turbulence in the very low speed range. An interesting detail of the experimental results for Models Nos. 332, 345 and 346 without turbulence stimulators

is evident from Figs. 16, 18, 19 and 20. The transition from mixed

laminar and turbulent flow to wholly turbulent seems to take place

very rapidly. This applies particularly in the case of the largest

model, No. 346, Figs. 19 and 20, where the resistance coefficient

at Re = 4

106 rises suddenly from 0.0027 to 0.0037. With the

other two models, this change over occurs at other values of

REYNOLDS' number, viz. Re 3 106 in the case of Model No. 332

and Re 1.5 106 in the case of Model No. 345. All these values

of REYNOLDS' number correspond to about the same model speed,

namely v = 0.5 to 0.6 m/sec. For this reason a number of extra

runs in this region were carried out in the experiments.

The above seems to indicate that the transition from laminar to

turbulent flow is not determined by REYNOLDS' number, as defined

here in terms of model speed and model length, but rather by a

local REYNOLDS' number defined in terms of model speed and a

certain definite length from the entrance to the transition point, as in the case of a plank. This length of laminar regime is clearly the

44

same for each of the three models in question and should be mainly dependent upon the angle of entrance of the model and the sharpness

of the stem. It can be further added that it is probably not the

model speed which strictly determines the transition from laminar to turbulent flow, as implied above, but rather the local velocity prevailing at the transition point (or more correctly, the transition

region) combined with the corresponding length of laminar regime.

The results illustrated in Figs. 22 and 23 referring to the finest

model, No. 372 (g9 = 0.52), confirm the earlier statements regarding the other fine models. Neither a 1 mm nor a 3 mm diameter tripwire

seemed to influence the model resistance in the range of speeds of

practical interest. It is then assumed that the value adopted as

before for the correction coefficient (c2,, .= 1.0) was too great. At the highest speeds this could apparently be reduced by more than

50 %; see Fig. 23 and compare also Appendix 3. On the other hand,

in the very low speed range, a marked laminar flow influence is evident, which seems to be unaffected by the presence of a 1 mm tripwire.

The values obtained when using the latter small diameter tripwire

even lie below those corresponding to the model without tripwire. This must, however, in this case, have been due to some special

circumstances. Possibly the condition of the model surface was

somewhat different in the two experiments due to such unavoidable changes as mentioned at the end of Section 4. It should also, however,

be pointed out here that the resistances measured at the low model speeds in question were small. Moreover, small variations in resistance were enlarged at low speeds, on account of the model speed being squared in the denominator of the dimensionless resistance expression. The results for the model without tripwire in the range Re= 2 106

106 in Fig. 22 have been presented separately for the sake of

clarity. It is of particular interest that, in this presentation, the

values separate themselves into two distinct curves more or less

parallel with SCHOENHERR'S line. One of these curves, which falls

above SCHOENHERR'S line, can be assumed characteristic of values

obtained when the boundary layer was turbulent, while the other

curve, which lies below SCHOENHERR'S line, can be taken to consist

of values obtained under mixed laminar and turbulent flow condi-tions. Some points (three in number) fall about half way between

these limits and can possibly be explained by the model having

45

side and mixed laminar and turbulent flow (as with the lower values)

along the other side. Thus, the conditions were obviously unstable

over the speed range in question and it was possible for the recorded values to move from one to the other of the limit curves in the course of a run. A definite transition, such as that found, for example, in the case of Model No. 346 in Figs. 19 and 20, could not be obtained

with this model, in spite of attempts in that direction.

It should be mentioned, with regard to the above, that the straight lines, which connect successive values in Fig. 22 and other diagrams where the same method of presentation is employed, are only intended

to assist in differentiating the various experimental series. They do not therefore illustrate the sequence in which the runs were made. Results from Experiments with Tripwires in Different Positions As mentioned earlier, some test series were carried out with the

fullest model, No. 334, with the tripwire placed in different positions

along the hull. In the low and very low speed ranges, tests were made with a 1 mm tripwire placed 25 mm (about 1 in.) abaft the stern, and the results obtained are compared in Fig. 24 with those

from tests with a 1 mm tripwire at stn. 19 and also with the "without tripwire" results.

In the range Re = 2.5. 106-4 106 (4-7 knots), the effect produced seems to have been less when the tripwire was placed at the stem than when it was at stn. 19. On the other hand, at very low speeds,

hardly any difference can be established particularly when it is

remembered that minor variations in the measured values are

magnified, as mentioned above, by the method of presentation. A

curious tendency is clearly evident in Fig. 24 in that the values vary so that the connecting lines have a zig-zag appearance, but this tendency can also be seen in earlier figures; see, for example, Figs. 14

and 22. The causes of these variations are particularly difficult to explain.

In the higher speed range, experiments have been carried out with a 1 mm tripwire placed at stns. 18, 19 and 191/2 and also at a distance

of about 25 mm (1 in.) from the stem. The results, together with

those for the model without tripwire, are illustrated in Fig. 25. Even though the tripwire raises the resistance values above those relating to the model without tripwire, as is evident also in the earlier Fig. 12, no such orderly differences as might be attributed to different positions of the wire are definitely evident in Fig. 25.

4 6 0.006 0.005 0.004 0.003 0.002 0.00!

g

(! 0.007 2 105

Model No.

352

No Turbulence Device'

mm Sand-paper from Sin. 19 for?!

50 mm at Stn. 19 4 6 8 106 vL Re = V. 1 I I

III Li_

2

Carresb. Ship Speed, V5, in /snots (Scale 1:40, Sea Water, 15.0 °C) Fig. 26.

6'

4 10

3C:r 5-)

0

9.006 0.005 0.004 0003 pi 0.902

Model No. 332

No Turbulence Device'

37.5 mm Sand- paPer from Stn. 19 for'

6.105 a 1,0

4T

- - - 91

2 3 4 5 6 7 8.

Corre'sp. Ship Speed,Vs,Zn knots (Scale 1:20, Sea Water, 15:0 °C)' Fig. 27, 75 mm at Stn. 19' 3, 4 .5-1.0 6 2 vL Re= 0.00/

Model No. 332

No Turbulence Device

(23o

37.5 mm Sandpaper from Stn. 19 forV

0A 75 mm

at Stn. 19

Correso. Ship Speed ,Vs , in knots (Scale 1:20 )

Fig. 28.

Sandpaper as a Turbulence Stimulator

The effect of sandpaper as a turbulence stimulator has been

investigated to a considerably less extent than that of tripwires. It

was mentioned above in Section 5 that two different widths of sand-paper were used, these being investigated in two successive experi-ments; in the first, a strip of sandpaper of a certain width was placed

symmetrically at stn. 19 (half the width forward of and half abaft stn. 19) after which the after half of the strip was removed and a

second series carried out. The original reason for this was to obtain a

measure of the resistance of the sandpaper itself. This resistance, however, is probably very small, particularly in comparison with that of a tripwire.

In some instances, an altogether higher model resistance was obtained when the model was fitted with a narrow strip of sandpaper

than when a full-width strip was employed. For this reason, it was

6 8 10 12 /4 /6 18 07 10 5 2.0 V in m/s 8 6 4 c CC 2

a--cc 0.00,7 0.006 0.00.5 0.004 0.003 0.002 0:00i

Model No. 345

4I No Turbulence Device

25 mm ,Sand paper from, Stn. 19 ford

50 mm 0

,

2. JO' 4 6 8 /06 v L Re= 2 3 4 6 8 10 .14 /8

Cort'esp. Ship Speed, V5,, in knots (SccVe Sea Water, 15.0°C)

Fig. 29., at Stn. 19 4./Q6 49 4 0 008 Schoenherr'sLine 1:40, 2

50

0

6.10

Model No. 346

No Turbulence Device

50 mm Sand-paper from SM. 19 for'd

at SM. 19

2 3 4 5

Corresp. Ship Speed,V,, in knots (Scale 1:15, Sea Water, 15.0°C)

Fig. 30. 106 5.106 8 2 3 4 Re- vL 5 10 004 0.003 0.002 0.001

-ii 0002

0001

Model No. 346

No Turbulence Device

50 mm Sand-paper from Stn. 19 ford

100 mm n _{at Stn. 19} Schoenherr's Line 51 2./06 4 Re= vL 8 107 3 5 7 9

Corresp. Ship Speed,V, , in knots (Scale 1;15, Sea Water, 15.0 °C)

Fig. 3L

0

0

0

0.006 0005 0.004 0.003 0 6

1 Ot

Model No. 346

0

-a- No Turbulence Device

® 0

50 mm Sandpaper from Stn. ,19 for'd

( 1001 4thm. . ii at .So. 4,9

5

111

a /0 12 14 /6

.Corresp. Ship Speed,Vs ,in knots (Scale 1:)5 ) v in m/s Fig. 32k, 20 2 52 12 10 6 4 0 25 18

53

not possible to deduce a correction for the resistance of the sandpaper

strip. Where a narrow strip, fitted at stn. 19, gave rise to a greater model resistance than a broad one, it may possibly indicate that the

trailing edge of the strip rather than the leading edge determined the

commencement of turbulence, since the trailing edge was moved

forward when the width was decreased by half as above. The widths of sandpaper employed were varied slightly according to the size of the model, as shown by Table 3.

The experimental results for those models (Nos. 352, 332, 345 and

346), which were tested in conjunction with sandpaper strips as

turbulence stimulators, are given in Figs. 26-32. These results need not be discussed in detail here, but they may be summarized by stating that the sandpaper investigated does not seem to be so

effective as a tripwire in stimulating turbulence.

Vibration of the Model and the Use of Swords and Struts to Stimulate Turbulence

It was mentioned in Section 5 above that some special devices for

stimulating turbulence were investigated, apart from tripwire and

sandpaper strips. These tests were carried out with the finest model,

No. 372, in the low and very low speed ranges. Particular attention was paid to the region about the model speed 0.5 m/sec., corresponding to Re 2.5 106, since the range in question can be regarded as critical for the transition from laminar to turbulent boundary flow;

see Fig. 22.

The special devices employed were an unbalanced motor placed above the stem of the model in order to vibrate it (see Fig. 9) and

swords and struts fixed to the carriage and placed in the water ahead of the model in order to induce turbulence in the approaching water. The results obtained are given in Fig. 33.

The experimental results in the latter diagram referring to the model fitted with an unbalanced motor show that no noticeable stimulation was produced at the revolutions employed (1 300, 6 000,

12 000 and 18 000 revs/min.)

The arrangement with an unbalanced motor was made on the

assumption that there should be a special frequency characteristic

for furbulence. By using this frequency when disturbing a state

similar to resonance was meant to set in.

54 0.005 0.004 0.00i Model No. 372 No Turbulence Device Sword 1.0 m in Front of Stem

11 2.6m Strut 0.3 m Vibrating Motor If Fig. 33. 1300 r/m 6000 r/m 12000 r/m 18000 rim,

I.,

Imulii

Mill

6 Ne . , //)0 . . 004 . 111111 ..

rapt' .

! .

i

0.003 2.106 3.106 5 i05 8 ,o6 2 3 4 5.10 Re - v I I L_ 2 3 4 5 6 7 e

Corresp. Ship Speed,V,, in knots (Scale 1:20, Sea Water, 15.0°C) 0.003

0.002

-

---- L

55

it is intended to investigate this method of stimulating turbulence

more carefully in another connection.

Fig. 33 also includes the results obtained both with a sword placed in two different positions (1.0 m and 2.6 m) ahead of the stem of the model and with a brass rod (strut) placed 300 mm ahead of the stem. The sword, as mentioned previously, was fixed to the carriage and it

projected vertically to a depth of 400 mm below the water surface. It was made of teak and was streamlined in form, with a maximum thickness of 10 mm and a breadth (fore and aft) of 40 mm; it was unpainted. The brass rod, which had a diameter of 8 mm, like the sword was fixed to the carriage and projected vertically to a depth of 400 mm.

Of the above devices, the rod (strut) appeared to be particularly

suitable for stimulating turbulence (see Fig. 33). It must, however, be pointed out here also that the experiments can only be regarded

as preliminary.

Rounding the Stem to Stimulate Turbulence

As stated in Section 3 above, certain alterations were made to

some of the models after the main experiments. In order to promote turbulence, the stems of Models Nos. 334 and 372 were rounded off to a diameter of 5 mm. The original sharp stem was, however, maintained down as far as the waterline in each case and the rounding was begun 10 mm below this, in order that the bow wave and residual resistence would not be too much influenced by the alteration. As was also mentioned in Section 3, rounding off the stems also entailed modifications in the vertical plane, particularly in the case of the finer model, No. 372, as shown in Figs. 1 and 4. No account

has been taken of the alteration in the area of wetted surface of each model consequent upon these modifications and the

experimen-tal results have been worked out using the wetted surface area of

the model before alteration.

The experimental results for Models Nos. 334 and 372 with rounded stems are given in Figs. 34-37. The first of these diagrams, Fig. 34,

also includes the results obtained with the model in question when

fitted with a ship-form stem, No. 334-B. These values, however, will be discussed in a later section.

The stem rounding, as carried out here, does not appear to have

promoted turbulence to any great extent. In the case of the full model, Fig. 35, in the high speed range, where tripwires produced a

0.006 0.005 0.004 0.003 L., 0.002 0.001

Model No. 334

0

Vertical, Sharp Stem

Rounded Stem, 0/am. = 5 mm

Model No. 334-8

Raked Stem A.

\

_\ A A.\ ...,...:,,,_,,

\

\

..4.-/ q .)8 . , 1,. \A Sc6 ' n6err, s 1/0, 6-105 106 Per vL 2 3 4 5.10 I I 1 2 3 4 5 6 7 8

Corresp. Ship Speed, V5, in knots (Scale 1:20, Sea Water, /5.0°C)

Fig. 34.

56

0

=

I

Model No.

334 Vertical, Sharp Stem

0 o

Rounded Stem, Diam.. 5 mm

12 a 6 CC 4 2 0 57 6 a 12 14 16 18

Corresp. Ship Speed, V5 in knots (Scale 1,20)

Fig. 35.

07 1.0 IS 20

V in m/s

0.006 0.005 0.004 n, 0.003 (Jr' 0.002 0.00/ Re= vL 2 3 4 5 5 7 8

Corresp. Ship Speed,V, in knots (Scale 1:20, Sea Water, 15.0°C ) Fig. 36.

noticeable effect before, the values for the model with a rounded

stem and those for the original model fall on the same curve. Furthermore, in the case of the finer model, Fig. 36, in the very low speed range, where a marked influence from laminar boundary layer flow was evident on comparing the original results with the SCHOEN-HERR line, the rounded stem does not appear to have any turbulence

..--1---ChOp_/21,,,,, ... No -I'l, e / / / ...' . 000 .

!mom..

lel

V ' lo, . 340

.

58

Model No. 372

(Di Vertical, Sharp Stem

Rounded Stern, Ohm.= 5 mm

6.105 106 3 .4 5 /06

-Model No. 372

0 o

Vertical, Sharp Stem

CD Rounded Stem, Diem.. 5 mm

59 3 Cc 07 10 /5 20 V in m/s 6 8 JO 12 /4 16 /8

Corresp. Ship Speed, V5 , in knots (Scale 120)

Fig. 37.

stimulation effect. Probably the stem radius adopted was too small

to produce the desired effect.

Limited Intervals between Successive Runs

Limitation of the interval between successive runs was also referred

to above in Section 5 as a method of promoting turbulence, in the

sense that the turbulence created in the tank water during the

previous run and the subsequent return run is utilized in the run in question.

60

It has been pointed out previously that the usual Tank practice is to adjust the interval between two successive tests according to the

experimenter's estimation of the state of the tank water.

It has

also been mentioned that the usual speed for the return run is about 0.5 m/sec.

In these experiments, through which it was hoped to determine to what extent the turbulence remaining in the tank water could be

utilized, the same speed for the return run, 0.5 m/sec., was used. The

intervals between successive runs, on the other hand, were varied.

In order to investigate the significance of the so called "dummy run", which is usually carried out every morning before the ordinary

pro-gramme of tests, intervals of up to nearly two days were covered

by the tests. Each experimental series was begun on a Monday

morning after the tank water had stood undisturbed since the

previous Saturday, and the same test speed was employed for the whole of that Monday, while the interval between one run and the next was successively reduced. The last test on a Monday formed

the last of that particular series and was carried out without any

interval between it and the preceding run. (The "intervals" were

measured as the time from the ending of the return run to the starting

of the next test run; compare the starting times given in the tables Appendix 2.)

Models Nos. 334-B, 332-B and 345 were tested in the above manner. Series of experiments were carried out as above at model speeds of 0.5, 0.8 and 1.5 m/sec. with Model No. 334-B, 0.5, 0.9, 1.5, and

2.0 m/sec. with Model No. 332-B and 0.5 m/sec. with Model No. 345.

The experimental results

are given in

Figs. 38-40, where

R R0

Ro s shown as a percentage to a base of the interval between

i

runs. In this expression R refers to model resistance after zero

interval and Rt to the resistance after the interval in question. For technical reasons, it was not possible to run all the tests of the respective series at exactly the same speed. The relative varia-tions in speed between the different recorded values are illustrated

in a special diagram in each figure. With the help of these diagrams, corrections have been applied to the model resistance values to compensate for the speed variations. A curve, parallel with the

model resistance curve for the speed in question and taken from earlier experimental results for the same model, is drawn through