On the feasibility of model tests with fishing nets

T

ON TRE PA$IBILITT OF MODLTE8T2 WITH

FI3RING NET8 by

Ir. J. J. van den BOSCH

Deift Shipbuilding Laboratory Report No. 91

October 1962

. a.

-ntroduo tion

Tests with full-sized fishing neta carried out in order to judge the set or the distortion of the nets, or to carry out measurements, are expensive and complicated. So it seems that the development of efficient fishing gear would benefit greatly if it proves possible to have reliable and accurate modeltests under the relatively favourable measuring condi-. tiene provided by an experimental tank.

As in all model work, the reliability of the tests depends largely on the possibility to comply with certain conditions relating the different scale ratios to each other. (i.e. the scales of length, time, force, etc.). These condi-tions are a,amm*rized. under the naine of "laws o! similarity t', In practice it proves nearly always impossible or impracticable to satisfy these rules completely, with the result that

divergences are introduced, which are termed "scale effects".. A olear idea o! the natura and the magnitude of these affecta

is needed tÖ interprete the test results.

Laws oj' similarity.

To ensure similarity of flow the first requirement is that object and model are geometrically similar. Any fluid particle in the model should follow a path which is geometri-cal].y similar to the path of the corresponding fluid particle in the object, so the time-force-path relation in the modal is an exact representation of this relation in full-scale.

the fundamental equation of dynamics: "force a _{masa x}

accele-ration".

For the object applies P M

and for the model

/

m

_dt

and so it follows that:

'C--Now let the scale of the forces be

_E

,/

_*

f

the length Coals

¿

₌

the mase scale

/'

and

the time scale Z

then the following relation existe:

'/=/"

which is

known

as the quation of Bertrand.

As

_/'

can

be written as the ratio of the products of density and volume:

A'

1

it f

oll,wa

that:

A=

where is the density of the fluid in the object and the density of the model fluid.

By introducing the ratio of corresponding areas

--= «

and writing the velocities as V and 2/=. the equation

of Bertrand yields:

-'=

whioh also can be expressed in the form of

two

equations:

F=

¿

,oV4

2

and

where

C

represents a coefficient which is the same

object

and

_{model for the case that the flow paterne are indeed} exaotlp:aimilar. Deviations from the similarity of flow result in differences in the coefficient

C

L

-2-

-3-Forces acting on a fluid particle can be: gravity forces, sheai forces due to viscosity, capillary forces, pressure for-ces etc. If the flow le steady (as lt will

_be

in moat cases with model nets), and the nets are towed at a reasonable depth below the surface, mass forces and gravity forces can be neg].ec ted. The only forces which come into play are viscous forces and pressure forces.

Let us assume for the moment that the only forces to be considered are of viscous nature. Then the internal

friction

forces in the fluid balance

the inertial forces. The shear force on a small area depends on the velocity gradient in the direction normal to the area in question and on the

viscosity coefficient 17 _{of the fluid. The ratio of the shear}

forces for object and model is:

'VA

/1

I ..5..

t

And as the inertial forces must balance the frictional orcea,

it follows that:

or

t

oC2 - - 4:2

y

The ratio ¡ is called the

kinematic viscosity coefticiert and is written

''.

It follows that i

«

_z.

-

ori

.±!ZL = _{or which is the same :}

VL_ v.1

V M,,

This ratio

Re-

4L

ja called Reynolds number.

It will be olear that

the requirement of equal Reynolds

number for

object and model is a

very unfavourable one with

G)

regard to mode].work in a towing'tank.Sea water and fresh water have practically the same kinematic viscosity coefficient, so the condition of the same Reynolds number virtually means that the modelapeed should be increased when the model dimensions grow smaller. Moreover this condition implies that the hydre-dynamic forces acting oLtbe model are as high as the Lull-size forces. It would take a very strong model to withstand these forces.

From the foregoing it will be clear that it te not racti-cal to adhere to Reynolds law Fortunately it proves to be

possible to use much. smaller speeds without introducing undue large scale effects. 1everthelese in each case we muet stay alive to possible discrepanoes due to too low a Reynolds number

Pressure forces are given by Bernoulli 'e law. In reality only pressure difference, count. The pressure difference be-tween two pointa in the fluid amounts to:

-where

flow velocity at point 1.

va flow V'elocity at point 2.

acceleration of gravity

z, height of point I above a reference level.

height of point 2 above that level

If the flow is not diwturbed by other causes, presaure forces are not subject to scale effects.

Application to model nqte,.

Before we can examine what scale effects are introduced in the particular case of modelteeta with nets, we have to make some assumptions as already pointed out by Kawakami:

the elongation of

the twines

can be neleoted,

the twines are perfectly flexible, the motion is steady.

L'

s

-5-As the model under water ehould haire the eame shape as the original, all external torees acting on parta of the model should. bear the same ratio to each other. Dickson

(3) explains

that when a model i. scaled down from the original weights and buoyancy decrease by the cube of the model scala.

ssentially this only holds true for buoyancy, as from the point of view of the experimenter there is no reason why the used materiale should be the same so long the above mentioned conditions are fulfilled.

Dickson ules the same materials for both original and modal and as a consequence in his case the weights and the buoyancy decrease as the cube o! the scale.

The lifts and drags should also decrease as the cube of the scal. and consequently the velocities should decrease as the square root of the model scale. Dickson has reached good results with a uart.r-acale model o! a 30' Aberdeen trawl, but he does not think the results with a eigth-ecale model trustworthy presumably because of too low a Reynolds number, and probably also beoauae of difficulties with the measurements

Let us assume for the moment that for the model we are not committed to us. the same materials as for the original and let us suppose that the quarter-scale model as used by

Dickson gives a fair representation of the original 30'Aberdeen trawl. The warp pull would be about 50 kilograms, which is a

reasonabl. torce

to handle in the tewing tank, but the actual

dimensions of this

model would still be far to

large. Even an

eight-scale model would be to large and for the towing tank in Deift, which of course I have tn mind for this sort of worc, I would prefer a model scale of about one sixteenth. In the ease of the Aberdeer trawl thea would correspond to a spread of the otterboards oi about half the width of the

tank.

Let us assume that this small model is a quarter-scale model of the above mentioned quarter-scale model of the Lull.. sisad net. To avoid confusion we shall call the small model M 16, the quarter-scale modal M ¿1., and the original 01. We can aleo say that M 16 M ¿I(M 4). Suppose that we want to comply * Tankdimensiona length 150 ni.

yidh

0 ni.

-6-.

with Reynolds law for the models

M1

and

M16,

thinking of M4 as

of the original net. The velocity quoted by Dickson for the

net 01

is 6 knots, the velocity of M4 is

1f kn, Using the same

Reynolds number for M4 and

M16

means that the velocity of M16

would again be 6 knots, which speed can be attained without

problema. The bydrod.ynamtc forces would be the same for M4 and M.16, but the hydrostatic forces, i.e. the buoyancy forces would be 54. times as small in the case of M 16 a. in the case of M4.

Por the model M being of

the same material as the original, the difference between the weight density of "twine" and water is about 0,25. For the model M 16 this difference ought to be

64 tim.. as large, or about 16, so the weight density of the twine material for the model M 16 should be

17. This cannot be

attained, but this example shows the line of thought. There are still other possibilities to *hiev. a higher Reynolds num-ber for the twines.

A model on the sa*le of 1/16 would be difficult to con-struct as the mesh size would be very small. As long as the mesh size stays small relative to the panel.size there is no objection to using a lower number of larger meshes, provided that the twine diameter is also increased in the same propor-tion as the size of the meshes. This is a fortunate circum-stance, as by increasing the twine diameter we also increase Reynolds number for the twines and. so we can decrease the speed Let us suppose that the mesh size is increased four times, and at the same time the speed of model M16 is decreased from 6 knots to 1f knots. We would still have the same effective

Reynolds number but the forces would be only 1/16 of the forces in the former case.

From this it followe that the weight density of the twine material should be 2 in the latter oase.

In fact the Reynolds numbers for the otterboards, floats, etc. are not increased by this artifice, but they are of minor importance. The differences between weight and buoyancy of these accessories are easily taken into account by ballasting.

-7-.

Twine materials.

The realisation of the above mentioned suggestions depends largely on the possibility to find a material which has a much higher weight density than ordinary twinee,less stretch but not much less flexibility. To my opinion it must be possible to Lind such xnaterials,for example glass Libres, cotton impregna.-ted with red lead in a not hardening oil, or cotton entwined with very Line copper wise etc.

Conclusions.

It has been shown that by juggling with the twine material the mesh size and the tGw velocity, much can be done to avoid scale effects due to too low a Reynolds number. With regard to the methods of measurement and. observation there are no large problems. Only the fabrication of the modele needs a certain

8 References

Dr.Ir. W.F.PA. van Lamneren c.s.:

Resistance, propulsion

and steering of ships.

W. Dickson, D.Sc. Trawl Performance.

A study Relating Modela to Comniercial Trawle.

Department of Argiculture and Fisheries for Scotland. Marine Research 1961. No.1

Tasas Kawakami.

Develop.nt of mechanical studies of fishing gear. Modern fishing gear of the world.