On the effects of different turbulence exciters on BSRA 0.75 block models made to various scales

A )'-

r"

Siudjecentrum T. N. O.

voor Scheeps0 _en

Aid. Scheepsbouw

SKIP SM ODE L L T A N K E N

NORGES TEKNISKE HÖGSKOLE

ON THE EFFECTS OF DIFFERENT TTJRBULENCE-EXCITERS ON

B.S.R.A. 0.75 BLOCK MODELS MADE TO VARIOUS SCALES

by

I

E. SUND

(WITH A NOTE BY J.K. LUNDE)

SKIPSMODELLTANKENS MEDDELELSE NR. 11 AUGUST 1951

NTH - Trykk

Trondheim 195e

Lab. y. Scheepsbouwkunde

Technische Hogeschool

DeLft

ON THE EFFECTS OF DIFFERENT TURBULENCE-EXCITERS ON

B.SR.A. 0.75

BLOCK MODELS MADE TO VARIOUS SCALES

by

E. SUND

(WITH A NOTE BY J.K. LUNDE)

1. GENERAL DESCRIPTION OF THE TESTS. In order to study the

effect of different turbulence-exciters, a series of experimental tests on a full type ship were carried out, last year, at the

Skipsmodelltanken in Trondheim. The

0.75

block hull form which

has been the subject of these experiments originated at B.S.R.A. It has also been studied at other towing tanks in connection with the nature of frictional resistance.

This liné form has been selected for investigation because of the relatively great change in towing resistance which occurs for models of this form with, and without,

turbulence-exciters. Similar experiments carried out at the

National Physical Laboratory, Teddington, are described by J.F. Allan and J.F. Conn in Transactions of I.N.A., vol. 92,

1950, p.

107:

"Effect of Laminar Flow on Ship Models." On

Fig. 5 of this paper are shown the lines of the model.

The tests here described were planned to bring out the effectiveness of different turbulence-exciters with

various model sizes and values of Froudes number. Stated

another way, an attempt has been made to ascertain the limits of velocity and model sizes within which reliable test results may be obtained with the various turbulence-exciters.

To obtain results which could bring this out, the

-

z-i) The models tested had tobe geometrically similar,

but to different scales.

The type of turbulence-exciter and its location

had to be similar for the different models. It had also to

conform to types customarily used in model tests.

The speed range of the tests had to extend down to low velocities in order to include the case where the

turbulence-exciter in question completely or partially ceased

to cause turbulence.

Different draughts had to be tested to determine whether this effected the relationship between turbulence and

laminar flow.

Customary model building techniques had to be

used.

From the same prototype four models were made to scales of 1:15, 1:22.5, 1:30, and 1:45, using ths stock wax

of the Tank. Line draughtings were prepared on thin steel

plates to eliminate paper shrinkage and the accompanying

inaccuracy between different models. After the lines were

cut, the hulls were finished with the same degree of precision

as commercial models.

Dimensions and coefficients of the prototype and

the scale models are shown in the tables i and 2.

Scales have been so selected that any model used In

customary testing should lie between these limits.

The tests have included some of the devices which

are regarded as suitable for producing turbulence. It is

known that sharp edges along the stem in itself can disturb

an otherwise stable, laminar flow. This phenomenon has also

been investigated.

To conform with the shape of this ship, the water

line should terminate in a rounded bow. For the specific

purpose of producing sharp edges along the stem, the

Scale

LLWL LBP B

dLE

' LWL d1 WL 1(MLD)

dL

II

VL 11(MLD) TABLE

1.

Ì1AlN DIMENSiONS .

Prototype

M i

M 2 M 3

M 4

1:1

1:15

1:22.5

l:3o

1:45

41o'-o"

124.87 in

8.325 in

5,55 in

4.162 ni

2.773 'a

400'-o"

121.92 in

8.128 in

5,42 in

4.o64 ni

2.710 ni

55'_"

16,76 n'

1.118 in

o.745 in

o.559 ni

0.373 ni

26'-o" =

7.92 ni

o.528 ni

o.352 ni

o.264 in

o.176 in

ll9oo tons (MLI))

l2loo ni3

3.585 ni3

l.o61

ni3

o.448 ni3

o.133o

21'-o"

6.4o in

o.427 ni

o.285 ni

o.213 ni

o.142 in

936o tons (MLD)

9515

nì3

2.819 In3

o,835 ni3

o.352

in3

o.1o45 ni3

16'-o"

4.88 ni

o.325 ni

o.217 in

o.163 in

o.1o85 ni

692o tons (MLD),

7o33

ni3

2,o84 ni3

o.617

ni3

o.261 ni3

o.o772 ni3

*Mti

Units

-4

a transverse surface at the bow. This transverse surface

tapers off below, after which the bow becomes a knife-edge.

In itself a bow of this form may cause turbulence. Only to

an insignificant degree, however, was this shown to be true. A significant effect was obtained only with the largest model at

maximum draught. Further tests with this device were

con-sequently only carried out with the models loaded to maximum

draught. Upon conclusion of these tests the bow was rounded

off to its proper shape.

Turbulence was also produced by an incrustration

of sand on the surface of the model. Granular sand was sieved

to yield a uniform size with a mean diameter of 0.7 mm. This

relatively homogeneous sand was applied with a density of

approximately 300 grains per cm2.

TABLE 2. COEFFICIENTSP

LWL

WLI

WLII

CB 0.746 O.72 0.705

C

O.96

O.9l

0.976

0.757 0.742 0.723

O.42

O.l0

O.77

LCB

- LBP 1.49 % F 1.71 % F 1.72 % F

LBP/B _{7.27 7.27 7.27}

B/d _2.12 2.62 3.44

*

The coefficients are calculated from the displacements

including cruiser stern and using the different water-line

-5-Two methods of placing the sand were used, and each

subject to complete tests. In the first method a one cm. wide

sand strip was laid along, and one cm. from, the bow, running from the water-liné to section 9 1/2

In the second alternative the original sand strip was retained, but in addition a similar strip was placed just under the water-line, running from the bow and aft to section

8 on both sides.

A trip wire was the device in another set of tests.

For this the trip wire equipment _{common in most towing tanks}

was used. _{The i rnm.-diameter, circular wire was placed around}

the model at a distance from the FP 1/20 of the total length

of the load water-line. The trip wire was kept at this station

independent of the particular draught run on.

Two criteria determined the velocity range for the

tests with the above-mentioned turbuience-.exciters. _{One, that}

the tests should serve to shed light on model tests in general.

The velocity range must therefore cover the general test range

for this type of hull. Two, that it must be, if possible,

clearly established where the various turbulenc'e.-exciters cease

to function satisfactorily. The velocity range could therefore

not be completely determined aforehand, but after a few

preliminary tests it was selected between the limits 0.04 to

0.22 of Froudes number. _{This corresponds to a range of Reynolds}

number from about 0.6 x io6 _{to 2.8 x} 106 _{for the smallest model,}

and 3.1 x 106 to 1.44 x lO for the largest. In the prototype

the range is 3.35 to 14.75 knots.

Earlier, in other towing tanks, experiments with this

hull type have been carried out with three different _draughts

of the prototype, to wit, 26'-O", 21'-O", and l6'-O". For ease

in comparing earlier results, the same draughts have been

selected here. These values are suitable in other respects,

In that they include the generally occuring draughts.

The models were formed in wax and treated in the same manner as commercial models tested for clients.

-6

Results of all towing tests are converted to the

dimensionless form CR=R/(l/2f SV2), where R is the towing

resistance in kg., the density of the tank water

(102 kg.rn sec ), V the model velocity in rn/sec., and S the

wetted surface of the model in m2. A test series has included

from 15 to 22 individual towings. The computed C values from

the tests are plotted on the basis of Froudes number F, and a

mean curve drawn through the points. The degree of accuracy in

this procedure has been the same as for ordinary model tests,

and as objective. Thereafter the test results are plotted on

the basis of Reynolds number, and values of resistance are

taken from the mean curve of the first plotting. Reynolds

number, Re, is here designated as Re

VL/V

where V is the

model velocity in rn/sec., L the length of the model in m and

' the kinematic viscosity in m2/sec. As previously

mentioned, the models were first made with sharp edges along

the stem, and tested in this condition. Thereafter the bows

were rounded to the appropriate shape, and all subsequent

tests made in this condition.

All models with rounded bows were first subjected to

complete towing tests with a smooth hull, i.e., without

turbulence-exciters.

Tests were similarly carried out using the different

turbulence-exciters. Results are transferred to diagrams where

the spesific resistance, CR , is plotted on the basis of

Reynolds number, Re (Fig. 1-11). For comparison purposes the

results with a smooth hull and rounded bow are also presented.

There is further shown Schoenherr's curve for frictional

resistance with turbulent flow, and H. Lackenby's curve from

his publication: "Re-analysis of William Froude's Experiments

on Surface Friction and their Extension in Light of Recent

Developments" (Transactions of I.N.A., vol. 79, 1937, p. 120).

The following considerations are taken into account

inì the analyses of the results: For the models the specific

residual resistance shall be the same at the same Froudes

-7--models, the increase or decrease in specific residual resistance

should he the same. On the other hand, if the flow is turbulent,

the magnitude of the specific frictional resistance will be a

function of Reynolds number. With the different models the

same change in Froudes number will result in the same difference between specific total resistance and frictional resistance, and

will represent the specific residual resistance. If, for any

model, the flow changes from turbulent to laminar, the frictional

resistance will be effected. The resulting change in total

resistance will then not conform to turbulent conditions.

In the diagrams the specific resistance of the different models is plotted to a base of Reynolds number, and on the curves are indicated values of Froudes number from 0.05 to 0.22 in equal

increments of 0.01. One has attempted to ascertain the extent

to which test results wi.th the individual models will yield

equally valid values of specific residual resistance. This should

be the case if the frictional resistance of all models is of the

same turbulent nature at the corresponding velocity. On the

diagrams, therefore, curves are drrawn through points of specific

resistance with the same Froudes number, i.e., iso-F curves. If

the frictional resistance is turbulent for all models, these

curves will be uniformly spaced. If turbulent flow could be

maintained down to zero velocity, the curve through F O for

all models would represent the exterpolator to be applied in

computing the frictional resistance for models within the range

of Reynolds number here tested. Turbulence, however, will cease

with lower velocities, i.e., with smaller Reynolds numbers. It

is therefore impossible to determine the pure frictional

resistance on the basis of such tests. _{The superimposed iso-F}

curves are only drawn as far as they mutually agree, i.e., _are

equally spaced. _{The hypothetical curve for zero velocity,}

assuming turbulent flow, should have been equidistant from _any

one of the iso-F curves. _{It is because of the interest in}

-8-and Schoenherr are also drawn on the diagrams.

It will be noted that some points o not lie on the

corresponding iso-F curve. Such irregularities may be

attributed to instrumental errors and permissible inaccuracies

in readings. In drawing the iso-F curves regard is given to

the probable magnitude of these influences.

2. DESCRIPTION OF THE INDIVIDUAL RESULTS. Consider first the

results with smooth hulls. Here it must be assumed that the

flow, particularly with low velocity, tends to be laminar. This tendency is confirmed in the diagrams, in that the curves lie considerably below those where artificial turbulence has

been produced. As will he discussed later, the set of points

for the same Froudes number, are quite scattered for the different

models.

Test results with sbarr edges at the, stern but otherwise

smooth hull are shown on Fig. 1, for LWL, where the resistance

is plotted on the basis of Reynolds number. The two largest

models indicate that turbulence develops at relatively low

velocities. With a Froude number 0.13-0.14, the iso-F curves

of these two models are approximately equidistant from both

Lackenby's and Schoenherrts curves. Below F = 0.13 the

resistance of the smaller model drops rapidly and a iarked

laminar influence develops. The

larger model alDparentiv retains

its turbulence to a lower Froude number, but in the lower portion,

i.e., under F 0.0e, the sharp drop in the curve indicates that

laminar conditions are present to a marked degree. Both models

rapidly lose turbulence for Reynolds numbers less than about

4.5 x io6. For the third model, M 3, the resistance curve lies

far under the corresponding curves for the first two. Model M ¿4.

was not tested with sharp edges at the stem since its Reynolds

-9

With the turbulence-exciter _{here used, i.e. sharp}

edges at the stem, the results _{obtained indicate that towing}

tests with M i produce turbulence _{down to F o.og, with M 2}

to F = 0.13, and with M 3 probably _{to F 0.20.}

Tests with sharp edges at the stem and attached trip

wire for LWL were made _{immediately afterwards and the}

results

shown on Fig. 2. _{Data was here obtained for comparison later}

with the trip wire and rounded _{bow. Since sharp edges at the}

stem and the trip wire would both _{produce turbulence separately,}

one was interested in the determining _{whether the turbulence}

could be retained down _{to a lower limit. As later tests showed,}

the wire alone gave virtuelly _{the same results as the devices}

used, i.e., sharp edges at _{the stem + trip wire. Turbulence}

weakened at a Reynolds number of _{about 4 x} io6 _{for M 1, or at}

F _{0.06, for M 2 at about F}

0.09, and for M 3 at about F _0.13

Since the results otherwise are in so close agreement

with those achieved with trip wire alone, it is sufficient to

refer to the description of _these.

Tests with a sand strip along _{the how were carried out}

for all draughts and for _{the entire velocity range between Froudes}

number 0.05 and 0.22.

For LWL the resistance (Fig. _{3) for the two largest}

models can be cornrsred, down to a Froudes number _{0.12, or}

rerhaps 0.11. _{Models M 3 and M 4 can perhaps also be compare.d}

to the first two for Froudes _{number ranging from 0.22 to 0.19.}

At this latter limit the _{turbulence decreases sharply for}

the

two smaller models.

Turbulence ceases irregularly with the different model

sizes, i.e., the transition _{does not accur with the}

same Reynolds

number. _{It thus appears that M i}

rapidly loses its turbulence

with a Reynolds number of 6 x 106 _{and less. With M 2 the break}

comes at Reynolds number 4 _x io6.

In M 3 turbulence occurs only

at the upper velocity limit, _{but even then its complete}

presence

lo

-satisfactory turbulence down to Reynolds number 2.4. x

io6.

For WL I (Fig. 4.) models M i and M 2 can be compared

down to F 0.12, while neither M 3 nor M /+ can at all be

considered. With this draught M 2 shows an unexpected high

resistance with low Froudes numbers, immediately before turbulence

ceases. The cause is difficult to determine, and cannot be

attributed to instrumental or experimental errors.

For WL II (Fig. 5) the conditions are the same as for

the previous draught, but the two largest models show a uniform

residual resistance down to F = 0.10.

Sand strips of the type here used are not as effective

a turbulence-exciter as a trip wire. With the latter, turbulence

commences with a definite Reynolds number, whilst with sand strips

turbulence commences irregularly with the different model sizes.

In the test series with two sand strips, the sand strip

on the bow was retained from the previously described test whilst

a similar strip was placed on the model on each side just under

the water-line in still water. This sand strip was laid from

the bow aft to section .

This arrangement produces a slightly better turbulence

than the sand along the bow alone, but laminar tendencies are

noticeable even at relatively high velocities.

For LWL (Fig. 6) M 1 produces a decided turbulent flow

at velocities down to F 0.10, whilst model M 3 already deviates

from the others at F 0.16 or nerhaps 0.15. M 4 does not agree

with the others when Froudes number is less than 0.l.

For WL I (Fig. 7) it can be assumed that M 2 has good

turbulence down to F = 0.11, and M i even lower. At F 0.19

or 0.l, M 3 and M 4 suffer from laznínar conditions. The spread

in the test results is somewhat greater than for the tests on

LWL. This is particularly true for M 2 and M 1.

For WL II (Fig. ) it can be said that

M i and M 2 run

uniformly down to F 0.11, whilst M 3 can be followed somewhat

uncertainly to F = 0.15. The results should indicate that

although the points are somewhat spread. M 4 agrees down to

F = 0.17, but the further tendency of this curve and its scale

values must be considered rather unreliable.

These tests also show that turbulence occurs with

different Reynolds number for the different model sizes. The

tendency towards turbulence is apparent at Reynolds number

about 6 x io6 _{for the largest model, whilst the}

same is true for

M 2, M 3 and M 4 at Reynolds number about 4 x 106,

34

x io6

and 2.5 x io6 _{respectively.}

The results with a trip wire (Fig. 9-11) show that

this turbulence-exciter gives the most satisfactory _{results of}

all the exciters analysed. _{As previously mentioned, a 1}

mm.-diameter wire was used on all models. This is placed around

the model at a distance from the FP 1/20 of the _{total load}

water-line length and kept at this station independent _{of the}

particular' draught run on.

For LWL (Fig. 9) the results agree well for all

models down to F = 0.13. _{Here M 3 and M 4 drop out, whilst the}

two larger models may be compared down to F _{0.09. The iso-F}

curve for the largest model indicates that turbulence is present

in the entire velocity range test, i.e., down _{to Reynolds number}

of about 3 x 106. It will be noted that at lower velocities the

curve is parallel to and immediately4 under Lackenby's _curve.

This tendency of parallelism is reasonable, _{when one assumes}

that turbulence is intact and that changes in velocity will

result in only smaller changes in residual _{resistance. At these}

low velocities, however, it is difficult _{to obtain absolute test}

values. _{One is, therefore, on the safe side in judging only the}

relative tendency of the _{curve and not its scale values.}

For WL I (Fig. 10) all models may be compared down to

F _{0.14, after which the resistance for M 4. decreases. The}

same is true for M 3 at F = 0.12. _{The two larger models may be}

compared down to F 0.10.

12

-down io F = 0.09, but ceases for M 3 and M 4. at F 0.12.

From the results with a trip wire it can be concluded that the reliability of the tests, i.e., the comparison between models, is considerably better than with other

turbulence-exciters employed. The transition from a partly laminar to a

turbulent range evidently occurs here at a lower Reynolds number. The deviations in values of resistance for the different models, with regard to iso-F curves, are considerably less in the tests with a trip wire than with sand strips.

It will be seen from the diagrams that even at high

values of Reynolds number the curves for smooth and for turbulence.

stimulated models are not comparable. The variation is greatest

in the smaller models, tapering off, and even ceasing entirely,

in the largest model. This difference in resistance is due tc

two important causes. One cause is the resistance inherent in

the turbulence device itself. In the case of the trip wire, the

magnitude of this can be determined from approximate formulae

which have been developed. Lb is, however, a question whether

these formulae give values of sufficient accuracy. As a

consequence it is of problematic worth to separate the

turbulence-exciter in this difference between resistance curves. In two

of the tests with a trip wire, for LWL and WL II, the curves for the largest model are comparable at high Froudes number,

whilst for WL I there is still a small difference. This should

indicate that the trip wire in itself does not result in a

significantly large resistance. With decreasing velocities its

inherent resistance will also decrease. The other cause is the

extend of the area of laminar flow for the smooth models. This

area is comparatively larger for the smaller models leading to a greater difference in the smooth and stimulated curves for these

models.

In conjunction with the test carried out with the trip wire, the trimming of the different models has also been

recorded. To determine if he trimming was similar it was

13

-satisfactory turbulence-exciter. From fig. 12 it will appear

that the values obtained show no significant difference between

the models.

3. SUMMARY OF THE TEST RESULTS. The results of the aifferent

tests are Dresented in purely graphical form. _{Figures 13,} 14.

and 15 show, in terms of Froudes number, that part of the total

specific resistance which lies above the Schoenherr line. Where

turbulence-exciters have been used, only that part of the curve

is shown, where it could be assumed that turbulence was present,

i.e., that rart of the curve for which there was an agreement

between the different models. The curves for smooth hulls of

the different models are quite different over the entire range.

These are drawn down to the selected datum, i.e., to the point

of intersection with the Schoenherr line. These curves for

smooth hulls strikingly illustrate how the laminar effect is

peculiar for each individual model. It is significant that M 2

lies above M 1, M 3 and M 4 for LWL and WL I.

As previously mentioned, iso-F curves have been

superimposed on the resistance curves, insofàr as they mutually

agreed. _{Since various values of resistance lie partly over and}

partl.y under the curves, due to experimental errors, the curves

on figures 13, 14 and 15 will represent the _{mean for all models.}

The deviation, however, is small and of _{no importance when}

comparing with results for smooth hulls.

Figures 16, 17 and 1 _{illustrate graphically the}

limitations of the effective _{range of turbulence-producing devices.}

The diagrams show the lower limit _{of Rroids number, for which}

turbulence exists depending _{on the length of the different models.}

The limits must not be strictly interpreted, _{in that they are set}

up from diagrams where specific resistance has been _{plotted on}

the basis of Reynolds number. _{In general it can be said that the}

transition from turbulent to laminar flow _{is slightly nebulous}

14

-model re most difficult to determine, in that the lower part

of the resistance curve cannot be compared with any other model. The determination of transition from turbulence is then made by considering the resistance tendency compared with the tendency

o.f the curves for frictional resistance.

In general these tests have shown that the trip wire must he designated as the superior turbulence-exciter among

those tested. The results using this exciter have been far more

uniform, with considerably smaller spread, than with the other

excit ers.

The tests further show that turbulence arises about

the same lower limit for the various draughts. This is rather

conclusively shown in the data collected from an extended range

of draughts.

These tests have been so planned, and the results so presented, that they can serve as a guide for the ordinary model tests which frequently are performed with similar full type models.

On the basis of themany sided problems which arises in connection with the phenomenon of flow, the field which has

here been investigated may unfortunately be somewhat limited. It

would therefore be of great importance to undertake further tests to investigate, in a pure form, how turbulence arises in models.

Thus, it could be of interest to undertake experiments with a

view to clarifying the effect that different degrees of

smooth-ness on the surface of the model has on turbulence. A desired

continuation of the exneriments here performed would be an

extensive series of tests for this purpose.

4. ACKNOWLEDGEMENTS. The research described in the foregoing

was sponsored by the Royal Norwegian Council for Scientific and

Industrial Research.

The Author wishes to record his thanks to those of

the staff at the Skipsmodelltanken. who have assisted with both

15

-A NOTE BY J.K. LUNDE. It has been suggested in the tast that the

iso-F curves should all be parallel to each other in order that

Froude's law of comparison shall be satisfied. It will be noted,

however, that this suggestion of parallelism requires the iso-F

curves to be straight lines, and it therefore appears to be more

correct to suggest that the vertical distance between any two

of the iso-F curves for a family of geosims, should be constant

for varying values of Reynolds number. This, as indeed Froude's

law, requires the conception of a perfect fluid. On the other

hand, if we use the residual resistance, including as it does,

items which do not follow this law, the suggestion of constant

vertical distance between any two iso-F cu'ves may not be

strictly true.

It is also of interest to note that the wave resistance

itself in the case of a real fluid, is influenced by the scale

effect. The vertical distance between any one of the iso-F

curves and the minimum turbulent friction line can, therefore,

never be constant for varying Reynolds number. To show this we

takethe origin O amidships in the free fluid surface. Ox in the

direction of the motion, Oz vertically upwards and Oy transversely.

Using the non-dimensional co-ordinates ,', , defined by

7=Y/6,

z/d

where

21

,

26

and ci' are the length, maximum beam and draught

respectively pf the form, we have that the wave resistance in

the case of perfect fluid may be written

(1)

_{R =}

¿2dy2''2 Q,de)5e658

de

where

cos(fk.b'sec

9)

16

-and here the model is given by

It has been known for sorne years now, that it is not only the form of' the model hull itself which is the cause of the

wave resistance in a real fluid, but rather, that it is the shape

of the hull modified by the boundary layer. As the displacement

thickness

6

gives a measure of the outward deflection of the

streamlines, "the wave making form" of the model may be taken to

be given by

The wave resistance may now be written

R

pydI/(Ç2Q,22se39

da

a

#jï(p2

_c)secade

q Qa)3û

d1/

o -o

where

P

_{, Q} are given by 2) and where , , Q2 are also given

by (2) hut with replaced by

If the model is very narrow we may exnress the displacement thickness as

(6)

Olo46es6,,)v

17

-the non-dimensional f.rm,

Rer'aV'/i

is

_{the Reynolds number.}

This expression of the displacement thickness will of cource not

alter the first term in

₍₅₎

_where ' , Q, are given by (2),

and which is the part corresponding _{to the wave resistance}

experienced by the model moving in _{a perfect fluid. Neither will}

the next two terms in (5) be altered, _{but ,' now becomes}

(7)ìO37e'/h/

oJ %4,) '/s

E-

(

_{sec il}

ep'ds4. SS/ a'1

From (2), _{(5) and (7) we note that the wave resistance}

experienced by a narrow model, moving _{at constant speed of advance}

in a real fluid, is the sum of three terms, namely:

The wave resistance experienced _{by the model when moving in}

a perfect fluid.

The wave resistance experienced by _{a form corresponding to}

the boundary layer represented _{by its displacement thickness}

and moving in a perfect fluid.

The interference between the wave resistance due to (a) arid

(b).

It will be seen from (7) that both (b) and (c) depend

upon Reynolds number, and that its influence _{is greater the}

smaller the model is made. _{This in itself advocates the use of}

the largest possible models in order _{to obtain reliable resistance}

results. _{As no calculations have been carried}

out, it is perhaps,

unsafe to prophesise beforehand the extent of the influence of

(b) and (c) on the general _{run of the iso-F curves, although some}

calculations by Havelock (Calculations _{Illustrating the Effect}

of the Boundary Layer _{on Wave Resistance, Transactions of I.N.A.,}

Vol.. 90, l94, _{p. 259) on a plank indicates that the influence}

18

-These terms, however, cause the wave resistance to be

a function of Reynolds number and accordingly influenced by the

scale effect. Thus the specific wave resistance for a real fluid

is not strictly constant along the iso-F curves as it would be for a perfect fluid in accordance with Froudets law, nor will the vertical distance between any one of the iso-F curves and the minimum turbulent friction line be constant for varying Reynolds

number. The use of (6) does, however, make the vertical distance

between any two of the iso-F curves constant for varying values

of Reynolds number.

A different expression of the displacement thickness has, no doubt, to be used when considering more ship shaped models for which account also will have to be taken of the

possibilities of both transition and separation. For such models

the rapidly increasing thickness and appreciable boundary layer at

the stern, caused by the curvature of the form in this region,

plays a greater r1e on the wave resistance result than does the

more slowly increasing boundary layer thickness along the sides

FIG. I. SHARP EDGES AT BOTH SIDES OF STEM. LWL.

SCALE OF REYNOLDS NUMßER, eF

FIG. 2. SI-IARP EDGES AT BOTH SIDES or SEEM AND TRIP WIRE..

L

SCALE OF REYNOLDS NUMBER,

00. ROUt'IØE STEM (MOOTH AT STEM H LL) EDGES

.

-o

oo4t.

0.003 1x106

-

2 3

______EÇ

4 5 6 Ô -LAC N8y 7 9 I*I0 - I I 1.2 1.3 1.4 ROLNDEP STEM (.MC.TH 6TEr1 NU D TkIP WI L) E. EDE5 A

F

4

0.0O4UáAl

6

pii

--____

1.3 003 1x106

-2 3 5 7 -i)L 11H 8 9 I.I0

Ii

1,2 ER 4

SCALE OF REYNOLDS NUMBER,

R.-9--NG BOTH SIDES OF STEM. WL I

SCALE OF REYNOLDS NUMBES, Re4

FIG. 5. SAND STRIPS ALONG BOTH SIDES OF STEM. WLL

SCALE OF REYNOLDS NUMBER, R&'»

.00 -J5JD 5TR%5 Tr1 (SM ALON6 0m HULL -0.003

o___

__

NO6 a .4 5 6 7 8 9 L2 1.3 sj07 1.1 0.00 . ROiJNPt) 5AND ST STEM (S IPS ALON 00TH 5TE.I1 NUL J . -0004 0003

*..

4 5 6 7 8 9 1x107 I

-!!t:

I 1.2

__

1.3 4l. -bJ06 2 1.4 'q

0"

p'

__

0003

-J

-h

6 8 9 IxI0

-.--??:?T

I la NO6 2 'I 4 7 I 1.3 1.4

FIG. 3. SAND STRIPS ALONG BOTH SIDES OF STEM

>

L) u L)

HG. 6. SAND STRIPS ALONG BOTII SIDES OF STEM AND WATERLINES, LWL.

SC.AL

OF REYNOLDS NUMBER,

7. SAND STRIPS ALONG BOTH SIDES OF STEM AND WATERLINE5.

VIL I.

SCALE OF REYNOLDS NUMBER Re

F STElI AND WATERLINES.

VIL

.

SCALE OF REYNOLDS NUMBER, Re

00. 5 NDWAT LINE fr106

-3

__

5 6

Ei_.5

.

_______

--

-4 8 1.3 7 2 4 -9 fr107 I i 1.2 Q . s

-STEM TRIPS ALO .Öc,TH,,tLJ 6 STEM NC) WATE -. INES ________ RcUNOD . 5ANO

u

-

---1

'LTr'

- -.. 6 7

-==r----.---8 9 lxlO

-SC i 1.2

'i

0.003 I s NI-IRR 1.4 1s106 ¿ 3 4 5 1.3

00'.

--i,1.1I.0 C) ,flI-1 ALO ).MQ(PI-1 -I f.rLM NOATL-Lir4E' .5414t) rRlps

_=__I

0004 O 00.3

h.

. . r L.A

i.

IçENB,' fric6 Z .3 4 5 6 7 8 9 fr101 1.1

'L4

1.2 1.3 1.4

L) U] t.) z Li L) U) û-ti) L. o LI J

SCALE OF REYNOLDS NUMBER, Re

WL

SCALE OF REYNOLDS NUMBER, Re

\JL. 11. SCALE O REYNOLDS NUMBER, R CZD &TE (Si-lOOT HULL) -L 5 6 7 8 9

-1.1 LACN,' SCHØENER z 3 1.2

O'.

________ . IUNOD 5TE.1 IP '..jIP.t. (SMOOT- HULL)

-T 000

-7 _____________ 8 -9 lI,o' I i l.a 6 LACKNBy HERR. 1406 2 5 1.3 1.4 s s s

__mi4

r itji L) 2 _. . s00 -M I IA 106

:OR

1.4

'J

FIG.

IS. SINKAGE

FIG

14.

PART 0F SPEC. RESISTA'LCE EXCEETNIS SO-ENHRR FRICTION LiNE. WL.

iao : : : ° o. 55 cl,, 300 4(10 ..& G ,, , + LWL loo soc . 000. SG G ' ' 300 400 e. LS. WL I 300 400 MODEL Na , 0I 016 0.14 I 5 S 4 0.17 AP, PP

_o.,..

L 0.10 WLt[ 0.11 0,12 OIS 018 019 QaO oaI 022

UL

U

.1

IIUPÁ1

!!!!!!! .I!!!!4

000)4 ME N 5 00TH IP WIR t.

--. 0001 THE ESTS IPS AT

-510M

111111

r

VA

:

-__

..!I!,

14 16 IB 20 25 24 26 ) MCSJ4

f'--I.

_

111111

I..,.

II

u..

'02 '04 24 26

SCALE OP FROUDES NUIIBER, F.

SCALE OP PROUDES NUMBER, F.

FIG.

IS.

PART OF SPEC. RESISTANCE EXC.EDIN6 SCNOEJ'II-ILRR FRICTON LINE LWL.

F1615.

PART OF SPEC RESISTANCE EXCEEDING SCNOENI-IERR FRICTION LINE WLJI.

SCALE 0F FROUDE5 NUMBER, F

-24-f16. 6 LOWER IJMIT CF Tb.B&JL E, LWL.

SCALE OF RVNOLO& NUMBtR

F16. 7. LOWER U?9T CF Tt&ILENCZ. '-1- I

5C.ALE OF REVLD5 NUM8R

b/

5CUX O RYt6LC8 NIJM8R

e 9 4 5 6 e s

a,-Mr!

aIO9 5 4 5 6 e

Ir,

5 s v 8