The design of high speed free surface water channels

The Design- of High'-' -Speed :Free Surface

'

'Water

by

josEPti

H. PRESTbiki:

Proceedings of the NATO Advanced Study Institute

an 'Surface; HydrOdYnnmi

es!

Bressanone, August 26 September 7 1966

".Tedmitche._

The Design of High Speed Free Surface Water

Channels

by JOSEPH H.

PRESTON

1. Introduction

The definition of a high speed water channel adopted in this paper is not restricted to supercritical conditions of

flow. For the present purpose a Channel with a maximum velocity greater than 5 ft/sec. say will be called a high speed channel.

- The design of high speed water channels is particularly

difficult, since not only must the velocity distribution through-out the working section (excluding the boundary layer) be

uni-form as in,a wind tunnel, but the free surface must be free from waves and remain level. Air entrainment must be avoided, as must cavitation on the impeller and cascades if the channel

is depressurised. Leakage of water out of joints and seals must be prevented and also the leakage of air into the system when depressurised. High water speeds involve high dynamic 'forces on the structure -- for instance 2D ft/sec with water

introduces forces comparable with those of a wind tunnel of 600 ft/sec -- thus the structure tends to.be expensive. The need to avoid corrosion limits the choice of the materials of construction or precautions must be taken and these raise the

The first circulating water Channel with a free surface appears to have been a small one constructed by L. Prandtl in 1904 for the observation of vortices. Other channels were de signed between 1920 and 1930 for ship model testing with

di-mensions of about 5 ft wide x234 ft deep and low

velocities.-References to these will be found in ref. [2]: Generally, the

velocity distribution and the quality of the free surface of these channels was poor,by modern standards and not much.uae

appears to have been made of them.

In Germany (at the V.W.S. - in Berlin) a free surface

water channel with working section 7 m long x 1.8 m wide x 1.2m

deep and a top speed of about 6.m/s was built in the 1920's and then rebuilt in 1957. This channel had a compact return circuit resembling that of a wind tunnel (see ref.

_Ii]

and Fig. 1) and the water emerged into the working section via the closed contraction nozzle. The free surface was held level and

free from major waves by means of a false tilting floor. This device is now an essential feature of all successful recent water channels. Also the upper part of the flow was diverted

at the exit from the working section to prevent wave reflection

and to get rid of air bubbles. This channel must be regarded. as the first successful channel for ship model testing aid has

set. the design pattern for a number of recent channels!:

A very.large channel was designed for the David Taylor

Model Basin and completed in 1944. This is described in ret.Efl:

The circuit was of the wind tunnel type with an enclosed con-traction nozzle and the test section was 60 ft long x 22 ft

wide x 9 ft deep. The maximum speed was about 16 ft/sec

Ob-tained.from an input of 1250 h.p. The overall length was 157 ft_'.

No details of the performance is given in reference [2]; but

it is understood to-have not been very. successful. _{An outline}

sketch of its elevation is shown

in

Fig. 2.

: In the U.K.;theBritish Ship Research Association sponsored research at Cambridge under Bihnie on the design

of

high speed

Ele..1E4.3,

Elbe-Fi gr.

a

De s ign of the V W S

Water channel

Ver.ticar. longitudinal section- through. T

1

I

water,..chaurret (from ref.

,.

.

water channels. Binnie 16J studiedthe discharge from a large stilling tank into a long channel via a nozzle. He found that

at high speeds a trough' water surface developed which he could

not sufficiently improve by skimming. Also at subcritical

speeds, and particularly as the critical speed was approached,

large waves could develop. He then turned to a natural draw

down instead of a closed nozzle and by development of a cascade type of weir at exit from the working section was able to hold a satisfactory level surface up to a Froude number of 0.6 (see

ref. [7]). Following this research, the N.P.L. Ship Division considered the design of a large flume and built a 1/10 scale model (Fig. 3 and ref. [8]). This model operated extremely

satisfactorily when suitable smoothing screens were introduced

into the stilling tank upstream of the working section. The full scale channel was then built and completed in 1966. The

working section is 50 ft long x 12 ft wide x 8 .ft deep and the top speed is 12 ft/sec corresponding to a Froude number of 0.75.

The water flows from a stilling reservoir via a natural draw down through a 9:1 contraction into the working section. This

leaves' via a cascade type weir and falls under gravity into a large sump from 'which entrained air bubbles escape before being

pumped into the upstream reservoir through a 2000 h.p. axial flow pump: The overall length is 350 ft approximately.

A water channel has recently been installed at the Duisburg

Technical College. This was designed and built by Kempf and

Remmers, Hamburg. The working section is approximately 5 m long x.11/2 m wide x 1 m deep. The top speed is 8 ft/sec (Z%

m/s)-This follows, the design of the Berlin channel in having a tilt-ing floor and a closed contraction nozzle (2:1). Entrained air

is removed by diverting the Upper layers of water leaving the working section over a plate and through screens, so that the water is slowed down in a passage of increasing area before being returned to the main circuit between the first two

cas-cades. Flap controls, at the end of the nozzle, at the beginning

DI FF USER UPSTREAM STIU.ING ICoNTRACTIoN SECTION

Fig., 3

-:. WORKING SECTIj WEIR _SECTION .

-Fig.

3 a- General layout of circuit

,

.

W TER ' LEVEL. IN: /

"fAWOi

WORKING:SECT . . D . . l grRP-.: GUMP_ wxrgit 'T :,, LENEL , SUMP ' c

f tilting weir

di:mined

(- [rola re 1..

,

.-with the main return, help in maintaining a level surface and in preventing gulping of air into the main circuit. We were

priviledged to see this channel in operation and were impressed

by the level water surface and its ease of control _by tilting the floor.

At Liverpool we have very recently replaced an old low

speed water channel, installed in 1925, _by a new channel. The new channel has a working section 14 ft long x 43 ft wide x

23/i ft deep and a top speed of nearly 21 ft/sec. The channel was

designed in conjunction with Kempf and Remmers who built-it (Fig. 4). It follows the now established German design with a

closed contraction nozzle (4:1) and a false floor which can be

raised and lowered and tilted. Entrained air is removed as in

the Duisburg flume by a diverter plate with controllable flaps,

which also prevent gulping of air into the main circuit. The design is novel, for a channel of this size, in that full

de-pressurisation of the free surface is intended. A model, 1:4.67

scale, was built by Kempf and Remmers to investigate the de-pressurisation aspects and the general flow features. This model was very successful. Results for the model channel and the full scale channel will be presented later in Part II of

this paper.

In the United States there are two very high speed water channels, one at C.I.T. and the other at Hydronautics near

Washington. Both have small working sections. which can be

de-pressurised and have large deaeration chambers through which the whole flow is passed. The C.I.T. channel has a working section 8 ft long x 2.0 ft wide x 14 ft to 2 ft deep. The miximum speed is 30 ft/sec and the free surface can be de-pressurised down to 1/15 atmosphere. The Hydronautics channel has a working section 11 ft long x 2 ft wide x 1.0 2.0 ft

deep-. _{The maximum speed is 40 ft/sec and it can be depressurised}

li/j3 (53.0.Frr)t &es . /3300 _03.6 rt) 5000 (LUTE) . rioxfraN4 Jsulem 7

.1.:iyerpool.,l:Rivers.it.rtwit;er channel'

hia:

5

Variablepressure, freesurface, highspeed

channel. Hydronautics Inc. (from ref.

5)

Fig. 6

The freesurface water tunnel at the Hydrodynamics

Laboratory of the California Institute of Technology (from

hig. 7

a

area ratio

Lriiversity water

channel,....

' 20,028 A4Tatranre..Darsra of Swcarcamty dicristrk. -Fig. 7la ,

-chann

_. .

Fig. 7 Effect of contraction ratio on size of channel

The design of this.is fairly straight forward. The sides

should be parallel and smooth, with the maximum of window area for viewing consistent with strength. The junction of the steel

and glass (or perspex) surfaces needs to be smooth in the neighbourhood of the water surface. Enough freeboard must be

left to cope with large solitary waves which can be accidentally.

generated when adjusting the false floor or if an emergency shutdown occurs. The top of the sides of the workinE section must be designed to carry a variety of instruments including the model suspensions and resistance dynamometers, and in the case of depressurisation be designed for sealing.

b) The first diffuser

The purpose of this is twofold. .Firstly, to slow up the

flow before it reaches the first two cascades of turning vanes,

for these can contribute very greatly to the power factor of

the circuit if the velocity is high. Secondly, to commence the necessary transition from a rectangular to square section before

finally changing to a circular section before the impeller.

The angle between the walls should be such as to avoid' boundary layer separation and alternate switching of the flow from wall to wall, the effects of which may be felt in the working section. The maximum angle which is permissible here

depends on the boundary thickness at entry to the diffuser and on the area ratio finally reached. References [10]; [11]; [12]'

and [13] and[14] should be consulted and appeal to model tests may be necessary.

c). The

guide vanes in the bends

The design of the guide vanes system for the first two

bends tends to be the most difficult, since the velocities and hence the forces are large, and, in the-depressurised channel,

is not : far belovWthe...free surface. _

A:variety

of

guide Vanes exists for 'Wind. tunnel use (see references "[10]-and-,[11]). 'Vanes for water =channels and

waterthnneig..haie

sharp leadingedges,andAhp sn11.4ce§

-are formed by .circular arcs A -modificationfhf this fdrin

based '

on

the assumption of a free vortex flow in the passage

between neighbouring blades..

Bladeg:Offthii'ddsigh:

have -.constant

pregatie

on each surface 'which is an advantage from-a cavitation

. _

-standpoint : For the guide vanes listed'. in

'refg3,11.61-

and,.[1.1];-the thickest sections have a minimum ' loSg. coefficient of 0. 25

for -a gap/chard. _raft&

of

0 5 whilst. for very

,thin

circular :alf&

profiles the minimum : loss coefficient is 0 15i for a gap/chord' . ratio of 0.3 strength and vibration requirements in

-profiles

of

some thickness essential

uhless:a..large

number Of

cidggeupportS are

:Used,

which 'liutS the cost 40.-::Wilesg the

flow is slowed up.. after leaving the Workini. section it is cidar

that the first twd,gets:-Of guide vanes will make' a considerable _

if not major contribution to the total ;losses in the circuit:

d) The Impeller and straightener design

The aim here is to achieve good efficiency and ,cavitation

performance In the case of the depressurised - channel .-_ The _latter

- is linked to thedePth:of the impeller below the free surface,

The blade profiles in .conjunction with the gelected-.radial-.

loading or lift coefficient, must retain as high

a

-value Of the

- ,

-.pressure minimum as possible. - The ..camber and fairing of the

:

profiles determines the .chordwise PreSSure'distribution which

should be nearly constant over the 'majorpett:Athe.,guctiOn

_surface_ Low circuit losses (i e. a low powerl factor) are

im--

-. .

portaht in that they reduce the disc loading of the

impellerLo*

lift coefficientsraise the minimum pressure Or reduce ' the

-.maiiinuth

velocity

over the blade. This leads to an .impeller of

-high :gol id ity ' which becomes difficult to design and also to

..:SOthe'ireduetioh

of efficiency Low blade velocities clearly

have

an advantageous effect on cavitation but again increase the

solidity. In appendix II, the influence of the various factors

on the cavitation performance is dealt with in an elementary

way. References [9]; [10] 'and [17] should be consulted. As regards the general design, this could be of the 'free vortex' type (as is usual in wind tunnels) with straighteners which are designed to remove all the whirl; or the design may be such as to make good the loss of total pressure in the boundary layer and thus give a uniform outlet flow. With this design no arrangement of fixed straighteners can completely

remove the rotation; zero rotation only is possible with contra,

rotating impellers and these are impracticable for a water channel. The behaviour of the diffuser which follows and the selection of its angle is undoubtedly linked to these aspects of impeller design. We may note that the presence of whirl downstream of impeller is undesirable since it may find its way through to the working section unless a fine honeycomb is used. On the other hand it is claimed that the presence of

whirl enables a larger diffuser angle to be used_ The available

information on this aspect and on the general problem of the impeller design on diffuser performance is meagre.

As regards the straightener (if one is employed) its de-sign depends on the magnitude and nature of the whirl. If the whirl is of the free vortex type and if the ensuing angle of

flow relative to the axial direction does not exceed 12°, then

the simple untwisted radial straightener can be employed (see ref. [19]). Otherwise a more complicated, twisted version is necessary. The whirl associated with a free vortex design is considered in appendix III.

A favourable point arising from the use of a low lift

coef-ficient at the tip, in order to avoid cavitation, is that the hub diameter comes out quite small and there is little danger of its `shadow' or wake penetrating to the working section as occasionally happens in wind tunnel designs, when a hub/tip

diameter ratio of 0.5 or 0.6 is usual.

e) The main diffuser downstream of the impeller

The purpose of this diffuser is to slow down the mean velocity to the value set by the contraction ratio of the

nozzle. It must do this in as Short a distance as possible

con-sistent with good efficiency and the absence of separation. This implies a fairly small cone angle. As regards minimising

the losses, little is gained by continuing the small angle dif-fusion beyond an area increase of 4:1. The angle selected here

varies a good deal in practice and the cost and length of the structure must be born in mind. Wind tunnels frequently keep

to as low as a 50 cone angle (refs. [1.0], [11]). Angles up to

8° have been used without separation occurring, but we think that this implies that the impeller has been deliberately de-signed to make good the loss of head in the boundary layer or

that swirl has been deliberately used to prevent separation and

also that the area ratio is less than 4:1. The whole problem

of diffuser design is a complex one and at present is not

com-pletely amenable to mathematical analysis, though an attempt is made in refs. [12]and [13]. Inlet conditions have an im-portant effect and scale effect is not understood. If a large

contraction ratio is employed, then, after the small angle

dif-fuser has reduced the velocity to 1/4 of the working section value, a rapid diffuser of large cone (200) angle can be em-ployed, using wire screens at appropriate intervals to avoid separation ref. 110, 111: Alternatively, the constant wall pressure diffuser suggested by Squire and developed by Gibson (ref. [15]) can be used. The constant wall pressure is achieved by correct shaping of the walls, plus the use of one screen whose resistance and position can be calculated. Another form of rapid diffuser is obtained by introducing partitions, so that in effect the diffuser is composed of a number of fine angle diffusers. The pressure recovery is poor and the flow uniformity is much improved by having a screen at the exit.

Settling length

This is placed after the last bend and before the

con-traction. Its purpose is to provide a place for smoothing screens

and honeycomb and a length of low speed flow to allow eddies and turbulence to decay. Its length will partly depend on how uniform the flow is after the last bend and how many screens are required. A long settling length adds to the cost, but it may be necessary for very high speed channels.

wire screens

Tne purpose of screens is to even out spatial variations in velocity and to reduce turbulence. They are also used to

prevent separation in large angle diffusers. Ideally, for recti-fying the velocity distribution, the resistance should be twice

the local dynamic head. Bradshaw [18] has shown recently that such screens can create weak vortex flows of large scale. He

has found that this is prevented by using screens of resistance

about 1.6 local dynamic head (open area ratio 0.57). It is

recommended that screens of this type be employed in the

settling length. It should be noted that screens in high speed

water channels have to support very high loads and they may need to be supported on a coarse honeycomb structure.

Pro-vision must be made for access to them for cleaning. Stainless

steel would seem to be essential from both the standpoint of

corrosion and strength. If a number of screens is to be used,

then a large contraction ratio is essential if the losses are to be kept small. with a contraction ratio of 4:1, only one

screen seems possible.

The honeycomb

The purpose of this is to remove large scale rotation such

as may arise from the impeller, secondary flows in the cascade passages and weak vortex flows from screens. It is essential that a uniform cell structure is maintained and the smaller

the cells. the better. The ratio (length of the cell to its cross

. dimension) should be large -- 6.to 8 seems satisfactory. For

water channels, the cells are usually square and the honeycomb

is built up by halfslitting long strips of brass _{or stainless} steel. With small _{'diameter' cells the cost can be high. A} honeycomb is essential in all channels!

1) The contraction nozzle

The purpose of this is to accelerate the flow from the settling region into the working section. It plays _{a very} im-portant part in reducing the longitudinal component of turbu-lence and the spatial variations of total head. A monotonic

behaviour of pressure distribution along its walls is desirable

and particularly at the high speed end in the case.of water

channels. To achieve this an exponential approach is necessary

and a slow approach to the working section for water _channels

helps in maintaining a wave free surface. There is a

consider-able literature on the design of contraction nozzle for_'wind

tunnels (references [9]; [10]; [16]. and Cl?];

Choice of Contraction Ratio

This has such a very important influence _{on the design,}

performance and costs that Some discussion of it is essential.

It is readily shown that spatial variations of total

pressure expressed in terMs of the mean local dynamic head are

reduced

(r

_{contraction ratio) between entry and exit.}

1.2

Thus it is seen that the contraction ratio plays a big

_part

in obtaining of uniform velocity distribution in. the working

section.

Also it is shown (ref. [10]) that the longitudinal

components are increased by a factor

A

.-Moreover, if smoothing screens of relatively high total resistance are to be employed, then a large contraction ratio

is necessary if the losses due to these are to be kept small,

1

since these losses vary Thus, hydrodynamic arguments tend rz

to favour large contraction' ratios, but economic considerations

indicate that both the cost of the channel and the building

-in which it is housed rise rapidly with increase in contraction

ratio and a compromise has to be effected. Generally it seems

that where the 'dimensions of the working section are moderately large (1.e..5' x 3' _{say) a modest contraction ratio between}

2 and 4 is chosen. Certain small, but very high speed, channels (working section 2' x 2' approximately) have large contraction

ratios. Provided that very low turbulence levels are not re-quired, then there, is evidence that a fairly satisfactory velocity distribution in the working section can be obtained with a.contraction ratio of about 41 and this might allow the

use of one smoothing. screen. However, significant gaits in the

level of turbulence and uniformity of velocity distribution are obtainable by going up to a contraction ratio Of 9:

Fig. 7 shows the Liverpool channel with a contraction ratio of

4:1 and also shown is a channel with the same working section and return portion up to the diffuser, but with the rest of

the circuit modified to accord with a contraction ratio of 9:1.

j) secondary flows

- These are cross flows associated with streamwise trailing.

vorticity in the boundary layers on the walls. Apart from the

variation of flow direction which they imply, they.have a much more important effect on the distribution of the boundary layer thickness. Generally their effect is to thin the boundary layer

on the side walls of.channels and to thicken it on the bottom

about the centre line of the bottom. It is this accumulation

which is mainly responsible for the gradual departure from

uni-formity of the velocity distribution in depth as the floor is approached. Also cross traverses near the floor show a region

of low velocity or total pressure about the floor centre line.

The origin of the trailing vorticity stems from three

sources: (a) the wall boundary layers in passing through the cascade passages are bent in their own plane and as a conse-quence generate streamwise vorticity which sets up secondary

flows in the cascade passages (see refs. [21 to 23]). On leaving, these vortices, which are all of the same sign for any one wall,

combine to form a large single vortex. Thus there are a pair of vortices of opposite signs associated with the boundary

layers on the side walls, (b) on passing through the contraction

nozzle, which has double curvature on each wall, the boundary layers are again curved in their own plane and the issuing

secondary flows may not always have the same sign as those under (a); see ref. [24] andFig. 17. Finally (c) there is the well known secondary flow associated with turbulent boundary layer

flow in corners whicn distorts the contours of velocity and total pressure, tending to produce a thick boundary layer at

the centre of each wall and hence on the bottom wall of a channel to add to the effect under (a). Appendix III outlines the main

results of secondary flow theory.

Clearly the source of trailing vorticity under (a) is as-eociated particularly with the boundary layer from the diffuser

entering the last two cascades and giving rise to a very poor distribution of total pressure at the entry to the nozzle.

The honeycomb,probably,is effective in killing much of the swirl associated with these secondary flows, but a screen is necessary

to even up the distribution of total pressure and perhaps a screen at the end of the diffuser is the best solution. The

secondary flows under (b) and (c) are not so amenable to control by correct design at present and further research is required.

2.2. Settling Tank - Sump Type of Channel

Fig. 3 shows this arrangement diagrammatically. Water flows

from a long settling length containing smoothing screens and honeycomb through a contracting nozzle with natural drawdown

to the working section. It leaves this via a special weir, falling under gravity into a large sump from which entrained air escapes. From the sump it is.pumped along a long pipe (of

area about equal to that of the working section) to the settling length which it enters via a rapid angle diffuser. This may be of the 'egg box' type i.e. partitioned or it may be controlled by screens. The power factor for this type of circuit is large

since all the K.E. of the working section flow is destroyed.

The return pipe has large skin friction losses and there are

4 bends in this duct (with cascades) for which the losses are high, since the velocity is high. Hence a motor of large power

is required and the impeller may be difficult to design since it is at a relatively low depth below the free surface.

It seems that this type of channel is likely to be employed when the dimensions of the working section are large, because

it is structurally and economically more attractive than the wind tunnel type of circuit. The design of the various indi-vidual features of the circuit e. g. impeller/straightener, guide vanes, screens, rapid diffuser, contraction is already

covered under 2.1 and reference [8] gives details of an actual

design. The pump intake may need special attention to avoid

vortices.

3. The Free surface

Ideally, the free surface should be level and free from long or short standing waves over the whole speed range. If the

speed range covers both subcritical and supercritical ve-locities this presents a severe problem.

The presence of waves and the nature of the surface (Whether -glassy Or rough) depends on (a) the speed of flow, (b) the type

of entry to the working. section (whether via an enclosed nozzle or natural.dram=down), (c) the provision of an adjustable floor,

(d) the nature of the exit (e) the water content.

3.1. The Entry

(a) Enclosed nozzle

Binnie and his associates (refs. [6]. and [7]) in their experiments with nozzles found that the water surface at exit

was 'rough', and this was particularly noticeable at high speeds. Attempts- to skim off the rough surface with a blade gave little

improvement and this is supported by the experience of Dr. Remmers of Hamburg. However, the designers and operators of the Berlin flume have accepted this limitation up to speeds of about 6.m/S, as also has Dr. .Remmers for the lower speeds of the Duisburg flume and we ourselves in conjunction with

Dr. 'Remmers for the new Liverpool flume. At Liverpool we find

that at speeds below the critical (9.4 ft/sec) the roughness is very small and that up to 15 ft/sec it does not exceed

1"

However, at topspeed 21 ft/sec.the surface is very rough

and this together with entrained air constitutes a serious limitation above 18 ft/sec (design top speed). we.think this roughness arises from the boundary layer of the nozzle, which

becomes a highly turbulent wake on the free surface. The

rough-ness is then a manifestation of the fluctuating velocities associated with this turbulence and possibly with the general

stream turbulence. Possibly some form of boundary layer control

on the nozzle surface would reduce the roughness.

Needless to say the nozzle surfaces should be smooth i.e., free from waves and roughness and have exponential approach to the working section sides and the free surface. A design' point to be .noted, if an enclosed nozzle is used, is that suction

to run full at low speeds.

b) Natural drawdown

The large N.P.L. channel (working section 12 ft x8 ft deep)

is based on tests of.

0'

scale model (ref. [8]) and has a natural

1

drawdown. Both the model and the full scale flume operate in . the subcritical speed range. The natural drawdown appears to

be very successful; there is no roughness of water surface, but

there are small wavelets which originate mainly from the con-traction side walls. Some are no doubt due to surface tension effects, but others could arise from contour imperfections on the contraction wall. It appears highly desirable to maintain continuous curvature of the surface of the contraction wall (with absence of even small waves in the contour) if dis-sturbances to the water surface are to be avoided.

so

far as is known, there are no research channels

oper-ating at speeds above the critical which employ natural draw down. There appears to be no fundamental difficulty, though there is a practical problem associated with the variation of head in the settling length when the speed is changed. In Ap-pendix I we have investigated, on a onedimensional basis, the form of the contraction nozzle to give an asigned monotonic shape of drawdown for different Froude numbers. Contractions in both the vertical and horizontal planes are considered. In

both cases it is seen that the contraction shape must vary with Froude number and, in particular, at speeds above the critical (F= 1.0) a bump appears on the nozzle (nonmonotonic behaviour). Provided the contraction is gentle, the calculations should be

correct and therefore, for an assigned shape of drawdown, adjustable walls must be incorporated to cover the required Froude number range. The need for variable wall shape perhaps

in part explains. the success of the adjustable floor which is dealt with below.

3.2. Adjustable Floor

With a fixed horizontal floor, Binnie Ds] found increasing

.difficulty in maintaining a wavefree level surface in the working section of his model channel as the speed was raised.

At speeds approaching the critical large solitary waves appeared. The C.I.T..water channel has a fixed floor and there are limited

ranges of speeds or rather Froude numbers for which wave free

flow is possible. The Hydronautics channel has a fixed inclined floor (to compensate for boundary layer growth) and satisfactory operation is claimed. over a wide speed range. Both these Ameri-can channels are primarily intended for very high speeds in the

supercritical regime. The very high speed channel now under design by Kempf and Remmers has an adjustable floor.

The Berlin flume (described by Schuster [I]) appears to

have been the first to have made use of an adjustable floor.

Both height and inclination of the floor can be varied to give

a wave free surface over the whole speed range. The Duisburg flume and the new Liverpool flume incorporate this device and all these flumes have enclosed contraction

nozzles. The

ex-perience at Liverpool is that there is one angle of inclination

which is practically satisfactory throughout the speed range and this is the angle estimated to be necessary to compensate for boundary layer growth. The large N.P.L..channel and its model operate below the critical speed and both have an

ad-justable floor, but in the large channel it appears to be used at a fixed setting.

It is clear that an adjustable floor must be considered as essential for channels' intended to operate from low sub critical Froude numbers through to supercritical conditions. It also has the. advantage that variable depth can be readily

obtained. The Hydronautics channel is interesting in that vari-able depth is achieved in the working section by incorporating

3.3. Exit from working section

A successful design of exit must prevent waves being re-flected upstream at subcritical speeds. It must prevent draw down and gulping of air into the return circuit and it must allow entrained air bubbles to escape so that they are not circulated around the channel.

(a) Wind tunnel type return circuit

In the German type of design some 5% of the main flow is diverted over a long splitter plate lying above the main exit and over the first bend. Because of the shallow depth of the diverted water, the initial flow over the diverter plate is supercritical and no waves can return upstream.

A number of wire screens intercept the diverted flow and

a 'jump' occurs at the first screen, or ahead of it at low speeds, causing bubbling and foaming. As the flow passes these screens the depth increases and its speed decreases so that bubbles of entrained air have a chance to rise to the surface. The diverted

flow rejoins the main flow behind the first cascade through a

passage the width of which is controlled by an adjustable flap.

Movement of this flap in a direction to further constrict the

main passage (which also has been reduced inarea)andix)increase

the secondary passage tends to prevent drawdown at the end of the working section at high speeds. It is used in conjunction

with an adjustable flap at the beginning of the diverter plate

to prevent air entrainment and splashing. The setting of the adjustable floor and increase of water content are important in this connection at high speeds.

These arrangements, though complicated, are quite satis-factory on the German type of design up to speeds of about 18 ft/sec. Above this speed more and more small air bubbles

are entrained into the main flow. If higher speeds are required

then other arrangements become necessary. A possible solution would be to carry the diverted water into a settling tank so

that the bubbles have time to rise. The water could -then be

pumped back into the main circuit and used as a means of boundary layer control to improve the velocity distribution- at the dif-fuser exit. In the very high speed channels of C. I. T. and

Hydro-nautics the whole of the flow at exit is passed to specially designed de-aeration chambers of large volume. The working sections of these channels are fairly, small and so this is possible but with large working sections this solution would

be very expensive. In the projected design for the Berlin channel

Kempf and Remmers adopt a similar solution of a large

de-aer-ation chamber but the geometry differs from the American type.

b) Sump type 'return circuit

In this design, the water in leaving the working section

falls under gravity over a weir into a large open -sump. The air entrainment is considerable, but, if the sump is large enough,

air bubbles have time to reach the surface ahead

of

the pump

entry.'

The weir needs to be of special design to avoid draw-down of the free 'surface in the working section and also the possible

formation of long waves at 'sub-critical speeds: Orkney [7]. carried out a number of experiments on this aspect of channel design and evolved a cascade type of weir which is employed

with, success 'in the N. P. L. 1/10 scale channel [8] and in the

full scale channel.

3.4. Water Content

In both the wind tunnel and sump types of return circuits the water level at rest is of some importance. In the former, for low speeds the channel is filled so that the level is very

slightly above that of the nozzle exit.. At high speed§ for optimum operating conditions the water content can be slightly

of air into the main circuit.

4. Free surface with Depressurisation

The very high speed channels in the U.S.A. at C.I.T. and

Hydronautics and new German high speed channel can be

de-pressurised down to atmosphere. These have relatively

15 11

snail working sections. The new channel at Liverpool (working

section 4% ft x 23 ft, top speed 20 ft/sec) has been designed for depressurisation down to about 1 ft of water absolute

pressure. This greatly increases the scope of the channel.

Ignoring viscosity and surface tension, the drag D (say

of a partially submerged body depends on the velocity U, a

representative length 1, gravity g, the density p and (p. - pvl where p0 is the pressure at the surface and pv is the vapour

pressure i.e.

D = f[U, /, g, p, -

PO]

There are thus 3 non-dimensional groups involved and hence

U

pn - p

2 2 =

f(

2 f(P, a)

½pUt

1 g

where F Froude number - Cavitation number

For dynamical similarity with the above yariables between model

(1) and full scale (2), F and a must be constant for the two systems. Now both g and p are the same for the two systems, and if

model .(1) , Or 12 (Fib

- Pv/,

(p0

.1)v 1 Pv U 2

(Po

12 (PO Pv)2.

l2

As an example, suppose we need to inVestigaWthe...7nose-i,

. - - ,,,

bility Of cavitation on the stabilisers, _{._} . a passenger

ship--.

,

_.

._.

.

or the behaviour of tbe:propeller. Take:

ft U

knots-F =0.274a =

Here we note that in the model test the

aPeedA'a'lWL-and.-ab-iia.

tfie:miriate-pressure.

-

This

test would be not possible if theObtraction:hW

to rmitull,' since suction below the free surface pressure has to tei.applie-d. However it is

possible thaty-at-AOW speeds';

.1 .

satisfactory flow can be obtained without the contraction

,

running full.

500 ft 20

As a second example we take the case of a small high speed craft e.g. hydrofoil boat.

-ft U knots

(po -

ft

F = 1.33

a =

0.0743

Here the surface pressure is higher than in the former example, as also is the speed, so that the contraction problem does not

arise. However, since the speed in the channel is 10 knots

and because 0- is small, it is necessary to consider the

cavi-tation performance of the channel; particularly in regard to

the impeller and the first set of guide vanes.

This has been done in Appendix II where the results have

been presented in non-dimensional form showing

acrit

v

-whilst, in theory, it is possible to predict the two constants appearing in the theory, one of these is best

ob-tained by model tests. The design of the Liverpool channel _was

based on tests of a complete model. Fig. _{16 shows the graph} of

a

. v

crit

for this case. and within the speed range of the full scale

channel cavitation trouble seems unlikely, but within the speed

range of the model channel serious impeller cavitation _can

occur.

8hiP

(2)

80- _{40 34}

5. Selection of Channel Size, Speed, Type of Design, and Materials of Construction

The selection of channel size and speed is governed prima-rily by the money available and by the need of the model under

test to be reasonably large whilst satisfying the full scale

Froude number and cavitation number -- if the latter is likely

to be significant. However, whilst small scale models require

low speeds on a Froude number basis, they require low absolute free surface pressures for the same cavitation number. Also, as a consequence of Froudes law, the Reynolds number of the model is the (scale) 2 of the full scale Reynolds number. This is

a serious limitation in those cases where the drag and boundary

layer is dependent on Reynolds number.

From the present survey it appears that the designs fall into 3 groups. The first relates to the testing of very high

speed surface craft and underwater weapons. These channels tend

to have small working section dimensions, high water speeds (30 50 ft/sec) and have depressurisation. The C.I.T. and

Hydronautics channels in the U.S.A. and the new Berlin University Channel falls into this group and references [s]' and [4] discuss

the design requirements. At the other end of the scale is the

large channel in which ship models are to be tested on a Froude number basis only. Large models are necessary to give'accuracy

in manufacture and to yield boundary layers which are thick enough to allow of their exploration with Pitot tubes for measurement of velocity and, or, skin friction. The size of model is not too different from the ship tank model so that

comparison of tests is possible. The D.T.M.B. channel and the new N.P.L. channel were designed to meet this need. The former has

a working. section 22 i4wide x 9 ft deep and for the latter the dimensions are 12 MOO x 8 ft deep. The complete structure

and the building are large and expensive, as is the supporting

instrumentation. Hence such a channel will only be found in a

national establishment. Finally there is the intermediate type

quantitative information from model tests on small to medium size high speed surface craft. It should be capable of pro-viding useful information relating to pressure distribution

and on flow directions in the boundary layer for models of large ships. However, its Reynolds number will be small so that drag measurements will not have much significance in this case, where skin friction is the major source of drag. The Berlin, Duisburg. and Liverpool channels fall into this category and have much the same size of working section 5 ft wide x 3 ft deep with a maximum speed of up to 20 ft/sec and operate over the whole

speed range. The flexibility and scope of such channels can be greatly increased by depressurisation. It would seem that

gener-al purpose channels which are smgener-aller than this have a re-stricted usefulness because of the small model size. On the other hand increase in dimensions rapidly puts the cost up so that firms and universities cannot afford a larger channel.

It is interesting that, for all three groups, the Reynolds number (based on maximum velocity and working section width)

comes out about the same value..

Type of Design

The small and intermediate sizes of channel

will

be of the enclosed nozzle wind tunnel type circuit because of the

relatively high top speed and the need for depressurisation. The material of construction will be steel -- preferably of stainless steel for the parts in contact with water. The

pro-tection of mild steel against corrosion appears to be difficult

for open channels where the supply of oxygenated air to the water is constantly being renewed. However, where cost is im-portant, a suggested formula for protection is two coats of phosphating solution, two coats of aluminium primer paint and a finishing coat of bitumastic paint. Of the two very large channels in existence, the D.T.M.B. channel has a wind tunnel

whilst the N.P.L. type has an open settling tank sump layout

with natural draw-down. The latter probably is capable of pro-ducing a smoother water surface and it is probable that structur-ally and economicstructur-ally it is more attractive. However, we think

that there is a third solution which utilizes a wind tunnel circuit laid out in a horizontal plane. The circuit could be

enclosed partially to give a natural _{draw-down. The exit from}

the working section would utilize the German design of a di-verter plate. The diverted water would be _{freed from bubbles} and returned to a constricted section or to a separate tank from which it could be pumped into _{the main diffuser. Fig. 8} Shows a layout of this channel. The power factor of such a channel could be as low as 0.5. Taking the N.P.U..dimensions

and top speed of 10 ft/sec it would require only about 100 h.p.. to drive it instead of about 1200 h.p. _{for N.P.L. design. The} material of construction for large channels will be reinforced

of concrete for the bulk of the _structure.

Again, in connection with the very large flumes and the very high speed channels, it is worth _{considering the} possi-bility of siting these near to _{a hydro-electric station. The} waste water or compensation water could be used to supply a

large stilling tank or small _{reservoir and then be led to the}

working section and returned to the river. Thus the expense of a return circuit and the problem of aeration and de-pressurisation disappear.

6: Speed Control

The main drive should be designed to give continuously. -variable control of speed down to _-L.the maximum speed in

200

the case of a general _{purpose channel, which may. be used to}

calibrate oceanographical instruments. For model testing a 1 to

-00" I./ :

-riS

SIDE ;ELEVATION

'Fig. 8

holding to 1.0 % for any speed in these ranges, which should

be by automatic control of Shaft r.p.m..The WardLeonard system is a well tried one and in our experience is capable of achieving

the above requirements without gearbox on a single pulley.

system with a toothed belt drive. There are alternative systems of obtaining continuous speed control such as hydraulic

trans-mission or by a variable pitch impeller, as is used in the large N.P.L..channel..

7. Basic Instrumentation

7.1. speed measurement

This will normally be obtained from the pressure drop

across the contraction nozzle, which has to be calibrated against

traverses by a Pitotstatic head. _{At very low speeds of the}

order of _{ft/sec it will be necessary to use an accurate} 10

tachometer of the kind which continuously counts impulses _or signals which are proportional to impeller.r.p.m..The cali-bration of this can be done by the timing Of a float. The ta-chometer reading can be also very useful at all speeds, but it

should be borne in mind that its calibration may change with settings of the various controls. Deaeration of all water Manometers should be provided..

7.2. False floor position and flap controls

The position of the floor can be obtained by direct measure-ment using a steel scale at.the.entry.and exit positions.

How-ever, it is wellworth the expense to have distant reading counters on the control panel, which record. the revolutions

of. the jacking motors and hence floor positions. The flap

7.3. Balances for measurement of forces

If the channel is not depressurised or when used in the depressurised condition for testing ship models, a drag dyna-mometer combined with trim and displacement meters will be

essential.

In depressurised channels, balances will need to be of

the strain gauge type'because of the limited head room available above the free surface. Serious consideration must be given to

the forces and moments.which are most likely to be required.'

It seems preferable to order a comparatively simple balance to

cover the most likely measurements and to improvise for the

others, rather than to order an expensive multicomponent balance

which may not be satisfactory for all the measurements..

7.4. gavemaker

Provision should be made in the design of medium size and

large channels for the mounting ofa wavemaker at the end of

the contraction nozzle.

7.5. Conversion to an enclosed water tunnel

It is worthwhile to make provision in the design for the mounting of a plate to suppress the free surface waves in the case of a medium size channel. This then converts the channel into a comparatively large water tunnel which, at 20 ft/sec, is equivalent to a wind tunnel of the same size operating at

230 ft/sec on a Reynolds number basis. As has been pointed out the dynamic forces are much larger and it is likely that certain

problems in industrial aerodynamics, involving the elasticity

8. Miscellaneous Problems

8.1. whirl and vibration of the impeller shaft

Generally whirl is not likely to be a problem because of

the low shaft r.p.m. and the necessity of having a fairly stiff

shaft to transmit the torque.

There is the possibility of resonance at the first natural

frequency of bending vibration if this corresponds to blade frequency. This can arise if the peripherial distribution of

velocity is nonuniform, as may happen when the main flap control (which controls the diverted water) is in an extreme position.. Then each blade is subjected to a fluctuating bending moment,

Which will provide an exciting force at blade frequency. The

cure of this, in the design state, is to ensure that the first

natural bending frequency is sufficiently high.

8.2. The fairing of instrument leads and the method of support

The fairing of Pitotstatic head leads is often in the form

of

a fine streamline shape formed by two biconvex circular .arcs cantilevered from a central support above the channel. The

centre of torsion is at midchord point and the centre of

pressure of the lift forces on the .fairing is at the quarter chord point. Clearly, with this arrangement, slight

misa-lignment in direction calls into play .a torsional moment tending

to increase the misalignment and thus to further increase the

lift and twisting moment. A critical speed is reached when the

elastic restoring moments are exceeded by the hydrodynamic moments and 'divergence' both in torsion and bending

occurs.-This will prevent the use of the instrument in this form at high speeds and large depths. The cure is to introduce a pivot ahead

of the centre of pressure so that the instrument has 'weather

cock' stability and will always align itself with the flow.

Small rubber pivots used in suspensions.are very suitable in this

WENN_

LW

stnt ELEVATION;

TILT1i1C _ FLOOR. : ' . 1

\\L\

-:,At:sugge-ated- design for:alarge water channelv:-'

DIVERTED. WATER

'holding to 1.0 % for any speed in these ranges _{which should}

be by automatic: control of shaft r.p..m. The Ward-Leonard system is a well tried one and in our experience is capable of achieving

the above requirements Without gearbox on a single pulley

system with a toothed belt drive. There are alternative system of Obtaining continuous speed control

_such

as hydraulic

trans-mission or by a variable pitch impeller, _{as is'useclin the.} large N.P.L. channel.

7. Basic Instrumentation

7-1, speed measurement

This will normally be obtained from the pressure drop

across the contraction nozzle, which has to-be calibrated against

traverses by a Pitot-static head. At very lo* speeds of the

order of _{ft/sec it will be necessary to use an accurate} 10

tachometer of the kind which continuously counts impulses or signals which are proportional to impeller r.p.m..The cali-bration of this can be done by the timing Of _{a float. The}

ta-chometer reading can be also very useful at all speeds, but it

should be borne in mind that its calibration _{may change with} settings of the various controls.. De-aeration of all water Manometers

_Should

be provided_

7.2. False floor position and flap controls'

'The position of the floor can be obtained by direct measure-ment using a- steelscale at the entry and exit positions.

How-ever, it is well worth the expense to have distant reading counters on the control panel, which record. the revolutions

of,the jacking. motors and hence floor positions. Theflap

7.3. Balances for measurement of forces

If the channel is not depressurised or when used in the depressurised condition for testing ship models, a drag dyna-mometer combined with trim and displacement meters will be

essential.

In depressurised Channels; balances will need to be of

the strain gauge type because of the limited head room available.

.

above the free -strface serious consideration must be given to

the forces and moments which are most likely to

be

required. It Seems preferable to order' a Comparatively simple balance to

.cover. the most likely. measurements and to improvise for the

others, rather than to order, an expensive multi-component balance which may not be .satisfactory for

all

the Measukeinents.

7.4.. Wave-maker

,

Provision

should

be made in the-design

of

medium size and

_

-large channels

for

the mounting of :a wave-Maker at the end

of

- the contraction

nozzle:

7.5. Conversion-to an enclosed water tunnel

It is worthwhile to make provision in the design. for, the

.

mounting....Ofr,a, plats to suppress the free surface Waves' in the case of a medium Size channel: This then converts the channel

.,

into a comparativelY, large water' tunnel which at 20. ft/sec, .

_

is equivalent to sa wind tunnel of the same size operating

j60 ft/sec on a :Reynolds number basia. As has been Pointed out

-*the. dynamic _forces are much larger:. and it is likely that

certain

problems 1.n.,indUStrial aerodynamics, involving the elasticity

8. Miscellaneous Problems

8.1. Whirl and vibration of the impeller shaft

Generally whirl is not likely to be a problem because of

the low shaft r.p.m. and the necessity of having a fairly stiff shaft to transmit the torque.

There is the possibility of resonance at the first natural

frequency of bending vibration if this corresponds to blade frequency. This can arise if the peripherial distribution of

velocity is non-uniform, as may happen when the main flap control (which controls the diverted water) is in an extreme position.. Then each blade is subjected to a.fluctuating bending moment,

which will provide an exciting force at blade frequency. The

cure of this, in the design state, is to ensurethat the first natural bending frequency is sufficiently high.

8.2. The fairing of instrument leads and the method of support

The fairing of Pitot-static head leads is often in the

form of a fine streamline shape formed by two bi-convex circular .arcs cantilevered from a central support above the channel. The

centre of torsion is at mid-chord point and the centre of pressure of the lift forces on the fairing is at the quarter-chord point. Clearly, with this arrangement, slight

mis-a-lignment in direction calls into plava torsional moment tending to increase the mis-alignment and thus to further increase the lift and twisting moment. A critical speed is reached when the

elastic restoring moments are exceeded by the hydrodynamic moments and 'divergence' both in torsion and bending

occurs.-This will prevent the use of the instrument in this form at high speeds and large depths. The cure is to introduce a pivot ahead

of the centre of pressure so that the instrument has 'weather

cock' stability and will always align itself with the flow.

Small rubber pivots used in suspensions.arevery suitable in this

counteracts any tendency of the P.V.C.. connection tubes to throw

the instrument out of alignment at low speeds.

9. Conclusions

Very high speed open channels can be designed. for satis-factory operation up to 50 ft/sec..In the two examples of these

in the U.S.A..it is probable that the inclusion of a tilting floor 'would widen the range of operation. The problem of de

aeration seems to have been satisfactorily overcome by the use

of specially-designed large deaeration tanks in circuit. It seems likely that improvement to the power factor of these Channels could be made by improved hydrodynamic design of the

circuit.

Water channels operating at these speeds are likely to be small because of the nature: of the testing to be carried out, the large powers required, and the high cost of larger

channels.-The medium speed channels (up to 20 ft/sec) of medium size

can be designed with a very efficient circuit from the stand-point of Dower input and satisfactory deaeration is possible up to 20-ft/sec by diverting some 5% of the main flow at exit

for the working section. Use of a tilting floor enables channels of this type to operate with a wave free surface over the whole

speed range'.

There is need for research to improve the roughness of water surfacewhich occurs with the use of an enclosed nozzle

possibly by some form of-boundary.layer control or by the

use of a sluice gate.

It is thought that. the small drawt-down at exit can be pre-vented or much reduced by suitable shaping of the floor contour at exit. Also the provision of a separate tank to deaerate the

dimensions small; places a limit on the contractionratio of about 4: land makes the use of large diffuser _{angle (7° - 8°)}

essential. This can lead to a slight non-uniform velocity

distri-bution through the depth of the working section and there _is

scope for research to find out how compact channels can be de-signed with good velocity distribution. _{Essentially the problem}

is one of obtaining a more uniform flow at the _{diffuser exit} and in reducing secondary flow.'

(c) _{Water channels for the .testing of orthodox ship models} must be large in order.that the Reynolds numbers _{are as large}

as possible and that the boundary layers are sufficiently thick ' for experimental investigations. On economic grouds it is _likely.

thatthese will be of the open stilling tank - sump design. with a natural draw-down through the Contraction nozzle. There appears

to be scope for improvement.in the surface flow by _reduction of the wavelets generated from the walls of the _{contraction..} This might be achieved by greater smoothness of the walls and

possibly the merits of contractions in the vertical plane _versus those in the horizontal plane should be investigated. A tilting

floor is necessary for wave free operation throughout the speed range. It would also be interesting to know whether a channel of this kind could operate satisfactorily.through _the

critical speed.

(d) _{Blade frequency vibration as well as whirl of the impeller} Shaft should be considered in the design

stage.--..(e). _{Fairing of instrument leads and holders needs special} consideration in channels of medium to large size when the instruments have to operate at deep immersions and at high

10.

Part II - The Liverpool Channel

10,1 Introduction

The initial design was based on a simple wind tunnel type of circuit with a contraction ratio of 4:1. This design was put,

into -a practical form by Dr. Remmers of Kempf and Remmers

(Hamburg), who incorporated his experience of dealing with the exit flow.

Initially, the working section dimensions were 15 ft long

x 5 ft wide x 3 ft deep and the top speed was to be about 18 ft/sec for an input of 100 h.p..It was then decided to in-corporate depressurisation and the extra cost of this was

partially met by an 8% reduction in overall dimensions, so that the working section is now 14 ftlong x 434 ft wide x 24 ft deep.

The question of smoothing screen was left open until the

com-pletion of model tests...

Fig.A shows an outline of the 'channel. It is seen. that the overall length (excluding motor) is 53 ft and the maximum height is 18.6 ft and width is 7.7 ft. The decision was made

to have those surfaces in contact with water. made of stainless steel, with the exception of the honeycomb (brass) and the

im-peller (phosphor bronze). The external stiffeners are of mild steel.

The uses to which the channel is to be put- demanded a speed range of (1 - -1-) max, and speed holding to 1% at any. selected

-200

speed. The electrical drive is of a standard Ward-Leonard-type, with automatic electronic speed control. .The impeller is driven

via pulleys and a toothed belt without gear box..

10.2. The model tests

These are described in reference [9]: The impeller was driven by a 6.b.h.p..motor to give a top speed of 6.m/s: The

scale model was 1/4.67 full scale.

The water surface .

The water surface could be controlled by the tilting floor

to be remarkably level and free from waves at all speeds. The surface roughness was slight below the critical speed but be-came pronounced at top speed.

The velocity distributions

The velocity distributions both across the channel and in , depth were remarkably good. These are extracted from ref.' [9J' and are shown in Fig. .9.

Depressurisation tests

Tests were also run at different free surface pressures

and from these it was deduced that the performance of the full scale channel should be satisfactory. Reference [9] gives details

of these tests and we have presented these in a .compact non

dimensional form in Fig. 16, based on analysis given in Appendix

Concluding remarks

The very good performance of the model has led to Kempf

. and Remmers offering it as a standard production for University

and Technical College teaching.

From our standpoint, the results meant that subject to

possible sdale, (Reynolds number). effects on velocity distri-bution we could have confidence in the full Scale performance.

The roughness of water surface is not expected to scale up, but will mainly be a function of

speed.-DEPTH IN CMS.

16 15 13 12 11 -10 9 8

Vinax 6.46 FT /SEC.

53.5 EM' FROM NOZZLE

Vmax 13.10 FT/SEC. .

.

DISTANCES ACROSS I CHANNEL CMS.

' 8 10 12 14 18 18 40 22 24 28 ,26 30

-

1.0 as

'

0 4. 2

Fig. 9 Kempf and Remti4ii model channel

Variation of velOCity with depth and,iariation aCo-aW at 6 cms , depth for different speeds and positions along working sections

1716 15 -.14 13 '12 ; 11 10

I

6 .1 0

-:17

I.

5 CM. FROM DISTANCES NOZZLE . V ma6 ACROSS, Vinal .13.12 CHANNEL 6.48 FI/SEC ki/SEC. CMS

-02 0 10 12 . 14 I 16 1820' 4 S '26 30. S. 1.0 09 08 07 as

10.3. The full scale channel tests

The water surface

Tests amply confirm the model results that a level wave free surface can be maintained over the whole speed range by.

operation of the adjustable floor. It has been found that there

is one angle of tilt which is approximately correct for all

speeds. This is 1 in 230 and is about that required to

compen-sate for boundary layer growth. At speeds of about 3 ft/sec small standing waves occur for this particular floor setting, but they can be removed by suitable adjustment of the floor. There is also a slight drawdown at exit at high speeds, which

can be corrected by readjustment of the floOr, operation of the flap controls and increasing the water content.

. The roughness of the water surface is very small at speeds

below the critical (9.4 ft/sec) and is barely noticeable ( +1/2)

ins), At 15 ft/sec it is quite small amounting to about .± 1/16

ins. However, at 18 ft/sec it has increased to 1/10 ins and

at top speed -- 21 ft/sec it is quite marked (± 1/8 ins) and is probably unacceptable for some tests...

Air entrainment

Up to 15 ft/sec, air entrainment in the form of small

bubbles

is

slight provided the channel has been run for some time after filling. Above this speed, bubbles of air become

very numerous and of larger size. Depressurisation is expected to reduce this somewhat.

The velocity distrioution

The velocity distribution in depth (on the centre line) and across the channel (1.0 ft depth) are in Figs. 10 and 11 for stations 1 ft, 6. ft and 12 ft downstream of nozzle and at

'2 rt FROM NOZZLE

ibex 4 136

F7,4EO.-max

rT/SCC:-max!S.çCu

gi 1 .Liverpool Channel

FT. FROM NOZZLE

L

DISTANCES ACROSS i CHANNEL CMS ' ;

70 60 50

-Le

_{"la': _20} 30 -41:1 50 10 . 09. , vi Q8,Y,0?".5 , -4.86F7F/SEC. FT( SEC.,-_ FT/SE.C::

11-Fig. 11 Liverpool channel

1_ ft,,,,depth..; Variat.ion of velocity: across_ chafin'el for different..

' ', speeds and positions in working.,7ire'ctiOri

, .. . .,,--J:...:.., _ -=:-.- - ... . ,yri,-4-,..-463 rrtsEc. .: '-' 12 FT, FROM NOZZLE - : : - ." - -: FT/SEC:.' .Vin.ij'i..,° 14.9 0 0 . ,.. -r ,

The distribution across the channel is very uniform (within 170) except in the boundary layer of the side walls (Fig. 11).

The distribution in depth is very uniform up to half the

maximum depth (Fig. 10). After the position the velocity slowly falls, so that at 0 75 of the maximum depth it has fallen by

3%.-There is a slight worsening with increase of speed and also

compared with the model results (Fig. 9). In other words there is some adverse scale effect,

which is

thought to be due to the

secondary flows becoming relatively stronger as the Reynolds

number increases.

-Our view is that the full scale distributions are

satis-factory for the testing of models of surface craft and that for

calibration of current meters and other oceanographic instru-ments the error will be small. However, we think that the

ob-served fall-off of velocity with increase of depth results from the effect of secondary flows on a non-symmetrical distribution

of velocity at the outlet from the diffuser. This gives rise

to a rather poor distribution of total pressure at the entrance to the nozzle. We think this can be rectified by a screen

(possi-bly graded) resting on the cascade immediately after the

dif-fuser_ This will even up the velocity distribution at the dif-fuser exit and reduce the secondary flows. Alternatively, vortex

generators in the diffuser might xtify the velocity

distri-Outiodwithout introducing addition/ losses (see reference [16]).

d) Impeller vibration

At impeller revolutions between 285 300 r.p.m. and with certain flap control settings, a mild vibration occurred. This was traced to resonance between fluctuations in the blade bend7 ing moment (due to non-uniform velocity distribution) and the-first natural bending frequency of the shaft. This is not serious audit can be avoidedtg suitable setting of the various controls.

.Tile metal tubes leading from the Pitot-static head are

streamlined by a fairing formed by hi-convex arcs. The whole is cantilevered from a support on the top of the channel. At medium,

to high speeds, depending on the depth, a critical speed is

reached at which 'divergence' in torsion and bending occurs.. This is because the centre of torsion is behind the centre of

pressure of the 'lift' forces on the _{As already mentioned}

in Part I; _{this divergence.was avoided by introducing a pivot}

axis ahead of the 'quarter-chord point, using weak rubber

sus-pension bearings.

10.4. Conclusions

This design of channel (with a contraction ratio of _4:1).

should be satisfactory, both in quality of free surface and in

velocity distribution up to 13 ft/sec. Also up to this speed

air entrainment is small.-The,adjustable floor is an essential

control. Model results for the

velocity

distribution in depth

tend to be optimistic.

11. Acknowledgements

TO Dr.-Norbury, who was chiefly responsible for Appendices I and II, and to Dr. Alexander who superintended the calibration of the channel.

To Dr. K. .Remmers of Kempf and Remmers for making available

his wide experience in the design of water channels _for per-mission to use results and photographs from his report on the :modal of the Liverpool channel and for permission to refer to

the-very high speed channel now.under

construction.-TO Mr,.Silverleaf, Superintendent of Ship Division,

Nation-al

Physical Laboratory, for permission to refer to the large National Physical Laboratory Channel which.has just cone into

To Dr. Benedini of the Istituto di Idraulica, University

of Padoua and Mr. Rossiter of Liverpool University who took most

of the observations of velocity distribution,

Appendix I (Dr. J.F. Norbury)

Design of free surface contractions by onedimensional theory

We use the onedimensional theory to obtain general ideas

about the form of a free surface contraction for a given Froude

number

in

the working section. The notation used is given in Fig. 12, with in addition

z = breadth of contraction. Z = breadth of working section

u = local velocity in contraction

A = local crosssectional area = z(H + h +

= u/U

h = h/H working section

z =

2/Z

_{Froude number,}

WITT

A=

A/HZ

2

The suffix zero refers to conditions at the entry.to the con-traction. Bernoulli' s equation gives 112 = U2 - 2gh, and the

equation of continuity is

= UHZ = Alz(H

4 h + c)

In-non-dimensional form this gives

Also and =

1

so that the contraction ratio,

A0

==---co

1 -

2

210

For given values of Ao and F. we can determine co and

E,.

Now if T1 is specified as a function of

xc

we can calculate 71(xc)

and A(x). This means that for a given surface profile the

longitudinal variation of area is fixed. The area variation can be obtained in one of three ways.:

i) the constant breadth contraction, with = L Then

_

-

-c =

A -

(1 + h)

"ii) the contraction with horizontal floor, so that c = 0. In

this case

A/ ( 1 +

iii) the more general case in which both Z and C vary with

xc.

Calculations have been carried out for values of F = 0.5,

1.0,

2.0

at a contraction ratio AO of A. The surface profile is taken to bean approximate hyperbolic tangent curve,