Nr. 66 Mitteilungen der Versuchsanstalt fOr Wasserbau, Hydrologie und Glaziologie

an der Eidgenossischen Technischen Hochschule Zurich Herausgegeben von Prof. Dr. D. Vischer

Air Slots for Flow Aeration

Determination of shape, size and spacing of air slots for the San Roque Dam Spillway

Peter'Volkart

Zurich, 1983

- 3 -

PREFACE

Over the past few years there has been a trend worldwide for the con­

struction of larger and more daring spillways from artificial reservoirs.

With a high spillway chute, large flow velocities resulting from high

specific discharges can cause extensive damage due to cavitation erosion

if no special protective measures are taken. However, recently the in­

troduction of air to the flow at the bottom of the chute has given good

results in terms of preventing cavitation erosion. Special devices

facilitate the introduction of this air. Providing answers to the ques­

tions as to the best way to introduce the air into the water and the

subsequent behaviour of the entrained air were the main aims behind a

model investigation performed at the Laboratory on behalf of Electro­

consult {Milan). ~ese problems were studied specially for the spillway

of the planned San Roque project in the Philippines.

Due to the willingness of Electroconsult it is now possible for the

final report on this project {May, 1981) to be published as a communi­

cation of the Laboratory. ~e kind agreement of Electroconsult to this

endeavour is acknowledged with thanks.

Oipl.-Ing. A. Chervet

- 5 -

ABSTRACT

The Laboratory of Hydraulics, Hydrology and Glaciology

of the Swiss Federal Institute of Technology, Zurich, was

commissioned by Electroconsult, Milan , Italy, to carry out

model tests for the San Roque Dam Project in the Philippi­

nes. With a 1:25 scale hydraulic model , air- slots for flow

aeration were investigated with the aim to prevent cavita­

tion erosion of the dam spillway.

GROOVE

I

-8 Different shapes of ai r -slots were tested: deflectors (A) ,

offsets (C) , deflectors with offsets (B) an.d a groove with

offsets (D) . After comparison of general behavior and air de­

mand of the slots for specific discharges between 20 m3/s ·m

and 120 m3/s ·m, a 0.75m high offset with a 0.50m high de­

flector was selected.

With the selected air-slot, air concentration measurements

were made which resulted in an air-slot spacing diagram. The

results are compared with those of projects already in opera­

tion.

Finally, model-prototype conformity is considered and

substantiated with trials to show the effect of scale on air

demand .

- 6 -

List of Contents

List of Symbols

List of Figures

References

l . INTRODUCTION

l. l Commiss ion and Project Description

l .2 Cavitation and Methods of Controlling it

1.3 Scope of Investigations

2. HYDRAULIC MODEL

2. l Model Construction

2.2 Measuring Instruments

2. 2. l Measurement of Flow

2.2.2 Measurement of Water Levels

2.2.3 ~leasurement of Pressure Heads

2. 2.4 Measurement of Velocities

2.2.5 Measurement of Air Demand

2.2.6 Measurement of Local Air Concentration

2.3 Simi la rity Problem

2. 3.1 Froude-Analogy

2. 3.2 Influence of Air

2.3.3 Influence of Surface Roughness

2.3.4 Influence of Channel Width

2.3.5 Inf luence of Air Supply System

2. 3.6 Scale Effect on Air Demand

page

4

6

7

8

8

9

9

10

10

10

10

13

14

14

14

14

17

17

18

19

21

23

24

- 7 -page

3. DETERMINATION OF SHAPE AND SIZE OF THE AIR-SLOT 29

3.1 Background 29

3. 1.1 Outline of Possible Shapes 29

3.1. 2 Genera 1 Outline of Investigations 30

3. 2 Deflectors 31

3.2 . 1 General Behavior 31

3.2.2 Main Parameters 33

3.3 Groove 37

3. 3.1 Initial Design 37

3.3.2 Drainage of the Groove 39

3.3.3 Side Deflectors 40

3 .4 Offsets 43

3.5 Selection of Air-Slot 47

4. SPACING OF THE AIR-SLOTS 49

4.1 Air Concentration Measurements 49

4.1 . 1 Conditions Upstream of the Air-Slot 49

4.1 .2 Selected Cross Sections 49

4.1 .3 Concentration Profiles along the Channel Bottom 54

4.2 Criterion against Cavitation 56

4.3 Determination of Air-Slot Spacing 58

4.3.1 Applying Anti-Cavitation Criterion to the Measure- 58 ments

4.3.2 Additional Considerations 59

4.3.3 Results from other Sp illways 61

5. SUMMARY AND CONCLUSIONS 63

- 8 -

List of Symbo l s

Symbol Di mension Defintion --------------------------------------

A [m2] area

a=f (e:) [ - ] friction parameter

b [mm] ~1i dth of the model chute

c

C*

D

Fr

[ % l

[ % l

[m]

[ - ]

[ - ]

air concentrati on:

air content:

Oa C =-­

Oa + o~~

c* = .9E_ Ow

distance between air slots

correction factors for air demand

Froude-number : Fr = __ v __ /gL

= _£__ l + C*

9

h

acceleration due to gravity: g 9.81 m;s2

k

K

L

p

q

[m] flowdepth

[m] deflector heigh t

[m] offset height

[r:1113;s] Strickler coefficient

[ -] constant

[m] cha r acteri stic length

[m water] pressure as static ~1ater head: lm = 9.8l · l03Pa(N/m2)

[m3/s · m] specifi c discharge

[m3/s ·m) water f l ov1 in the drainage system, per meter channel width

Q [m3;s , R./s] discharge

Re [ - ]

[ - ]

u [m/s]

Reynold ' s number : Re = _v_· L_ \)

Reynold ' s number : Rex 2g ·V-Sl n Cl

velocity outside of bounda ry layer

Symbol

V

We

x,y,z

E

\l

\)

p

0

Indices

Dimension

[m/s]

[m/s]

lm/s I

[-)

[m]

[degree]

[m]

[m]

[ lllll}

[-]

[ -J [m2/s]

[kg/m2J

[N/m]

a

m

mix

M

p

tot

w

- 9 -

Definition

velocity

absorption velocity

characteristic ve locity = velocity 25 cm above bottom

p·L Weber- number: We= v (-) g·o

coordinates: x =a 1 ong the axis y =transverse z =vertical

slope, angle to the horizontal

boundary layer thickness

displacement thickness

equivalent roughness height

friction factor (Darcy- Weisbach)

geometric model scale

kinematic viscos i ty, v = 1 .3·10-6 m2;s

density: water 103kg/m3, air = 1. 293 kg/m3

surface tension: oair-water = 74.2 · 10-3 N/m

air

mean

mixture

model

prototype

total

water

- 11 -

1 . INTRODUCTION

1. 1 Commission and Project Desc ri ption

The Laboratory of Hydraulics, Hydrology and Glaciology of the S~liss Fe­

deral Institute of Technology in Zurich was commissioned by Electroconsult

Consulting Engineers, 11ilan, Italy (by letter dated ~1ay 2, 1980), on behalf

of the National P01•1er Corporation, 11anila, Philippines, to carry out model

tests for the spillway and the low level outlet of the San Roque Dam Project .

The project concerns a gravel fill dam on the Agno River . The dam's ma­

ximum height \~ill be 210 m, its fill volume 43 million m3 . It ~1ill create

a reservoir with a gross storage volume of 990 million m3 and active stora­

ge of 670 million m3 .

As a multipurpose project, the dam wil l be used for the production of

hydroelectric energy, irrigation and flood protection. The power instal ­

l ations will consist of 3 vertical Francis turbines with a maximum head

of 190 m and a max . discharge of 306 m3;s .

The spi llway is of the gated open chute type, designed for a flood of

12'800 m3;s . The width of the chute is about lOO m, its length 550 ~- ~ith

a slope of 1: 4, maximum water veloci ties will be up to 40 m/s. At the down­

stream end energy will be dissipated by a ski-jump into a stilling basin.

During the construction stage, the river wil l be diverted through two

rectangular tunnels, each ~1i th a capacity of 1950 m3;s, and one circu l ar

tunnel with a capacity of 380 m3;s. This latter one will al so be used as

the downstream section of the S-shaped low level outlet .

The hydraulic problems related to the low level outlet were investigated

by computer-simulation and hydraulic model tests at the Laboratory of Hyd­

raulics, Hydrology and Glaciology, Zurich (reports Nr. 774 and 777). The

spillway was investigated with a 1 :lOO scale model at the National Hydrau­

lic Research Center, Philippines. Additional studies concerning cavitation

problems of the spillway were made 1·1ith a l :25 scale model at the Zurich

laboratory and are described in this report (776).

- 12 -

1.2 Cavitation and Methods of Controlling it

A surface irregularity in a hydraulic structure tends to deflect the

stream away from the surface and, consequently, to form a low pressure zone

just downstream from the irregularity. It the pressure falls to the vapour

pressure of water, vapour bubbles appear then suddenly collapse when they

reach a region of higher pressure. If they collapse against a solid boun­

dary, serious cavitation erosion may occur. From damage to existing spill­

ways and low-level-outlets, it is known that within a relatively short time,

erosion can reach a depth of l .5 to 2 m and remove tens of cubic meters of

high-strength concrete.

There are two traditional methods for preventing cavitation erosion,

firstly by finish -specifications for concrete surfaces (Ball, 1976) and se­

condly by using high strength material, such as epoxy concretes, epoxy mor­

tars, fibrous concretes or steel-lining . The first method defines objectio­

nable irregularities . However, the standards are difficult to obtain, espe­

cially with velocities higher than 20 or 25 m/s. Furthermore, the method i s

relatively uncertain because of defects that can occur on the surface con­

crete as a result of atmospheric, climatic or chemi·cal agents. The second

method is safer, however being expensive, is reserved for small areas such

as near outlet gates , or for repairing damaged surfaces.

More recently, a new method, which is proposed for the San Roque dam

spillway, has been developed to protect the surface by _aeration devices.

Devices on the spillway bottom (air- slots) produce a local subpressure by

which air is sucked into the flow. The compressibility of the air-water­

mixture reduces the pressures of collapsing vapour bubbles and thus protects

the surface concrete from cavitation erosion.

l .3 Scope of Investigations

The following investigations were made with the. l :25 scale hydraulic model

by representing a 3 m wide section of the prototype with a single air slot :

Determination of shape and size for the air slot by comparing the over­all air demand of three different types of various sizes (deflectors, grooves, offsets and combinations of these types)

- Studying of scale-effects by varying the scale between 1:18.75 and 1:30

Determination of the optimum spacing of the air-slots by measuring air concentration along the bottom and at some selected cross -sections .

- 13 -

2. HYDRAULIC t~ODEL

2.1 Model Construction (Fig. 1, 2)

The 1:25 scale hydraulic model consists of a chute with a slope of 1 :4, (14-•; a total length of 8.50 m and a width of 120 mm, representing a section of

3 m width in the prototype. The chute is made of smooth PVC and fixed on

two rolled steel bars, so that no significant deformation should occur.

The whol e chute is div ided in t o three sections (see Fig.l). While the

upper section is f i xed, the lower one is movable so that its elevation re­

lative to the upper section can be varied, according to the step height of

an offset-type air-slot . The intermediate section contains the air-slot

connected with the air-supply system in the back wall. The front wall is

made of plexi glass and is removable so the different types of air-slots

can be easily interchanged.

The chute is supplied with water from the laboratory's high pressure

tank through a 250 mm steel pipe.

To reduce disturbances, the flow passes through a parallel-fl ow section

after the adapter and has a flap t o smooth the surface. Since the distance

to the air-slot is too short to establish uniform flow conditions, the

dep th of flow and thus the velocity at t he ai r-slot, can be varied by the

f lap at the beginning of the chute . In such a way it i s possible to vary

the velociti es between 5 m/s (25 m/s in the prototype) and 7 m/s (35 m/s) .

2.2 Measuring Instruments

2.2 .1 Measurement of Fl ow

Discharge is measured by an inductive flow-measurement gauge installed

in the 250 mm steel pipe . The principle of the measurement i s that the water,

being slightly conductive, induces a potential difference by flowing through

a magnetic field. This voltage is measured and can be related to the medium

flow velocity or the discharge, respectively. Assuming that the pipe is full

of water, the accuracy of measurements including potential difference mea­

surement error, ranges f rom 5 % to 2 % depending on the discharge. The accu­

r acy increases for hi gher discharges.

- 14 -

'··· .. ·······

~,,lf:J .. ······

~-..... . ·····

"· ......... .

- 15 -

Photo l Over-all viev1 of the model (water fl01·1ing from right to left)

Photo 2 Intermediate secti on with (from left) concentra­tion gauge, air slot (offset plus deflector) , gasometer and differential manometers (water flowi ng from right to left)

- 16 -

I I I

lt 0 50 IOOmm

Movablr

1-­

~------~~~rn~--------~.~~ C:,

measuring dev1ce ....... ..... .

11 y

, : I .fl ;

---JT"- ________ l..L.i. --~::t---t ~_-_--:.[~--[J - --_-_ -t= -.-

m: lt i :

I . rolled ~tee/

'····· piezometer

: PVC reinforcing rib

Fi g. 2 Cross- section of the chute

2.2 . 2 Measurement of Water Leve ls

Section A-A

70 ·7 PVC- chute

120 mm

Water levels in the chute are measured with a point gauge mounted on

an angle st eel profile. This steel profile can be fixed at any place

on the chute and serves as a movable measuring device for all the gauges

used.

Because the water is aerated by surface air entrainment even upstream

of the air-slot, the water surface is not plane but curved near the

walls. Furthermore , i t is difficult to exactly define the surface because

there is a continuous transition from water flow mixed with air bubbles

to free air with randomly ejected water drops . Compari son with the air

concentration profile showed that at the measured mean flow depth hm,

the air- concentraion was between 90 and 95 %.

- 17 -

2.2.3 Measurement of Pressure Heads

Piezometers along the chute axis downstream of the air-slot were used

for the investigation of pressure head. Each piezometer comprised a l mm

diameter hole perpendicular to the bottom of the chute. The piezometers

were connected to a battery of glass piezometer tubes. The water levels in

the glass tubes indicate the required pressure heads relative to the level

of the piezometer position. The precision of this set-up was l mm for the

model which is equivalent to 2.5 cm in the prototype.

2.2.4 r-teasurement of Ve locities

Local velocities upstream of the air slot were measured by a Pitot-tube

with 6 mm diameter, connected to a mercury differential manometer register­

ing the velocity head v2;2g. As long as air concentration is less than 10 %,

the accuracy of the measurement is very high, with a standard error of less

than l %.

With air concentrations higher than 10 %, velocities cannot be accurately

measured by the pitot tube. Velocities in the aerated layer upstream of the

air slot-slot were, therefore, extrapolated from the measured velocity pro­

file. Downstream of the air-slot no velocity measurements were made.

2. 2.5 t-teas urement of Air Demand

Air is supplied to the air-slot through an opening in the back wall,

connected by a 30 mm diameter plastic tube to a gasometer. The air supply

can be varied with a valve. Because head losses in the gasometer are rela­

tively high, additional measurements were made with a Venturi-pipe instead

of the gasometer. The Venturi pipe was connected to a differential manometer.

2.2.6 Measurement of Local Air Concentration

The local air concentration is defined as follows:

C(x,y,z) dQa(x,y,z)

dQa(x,y,z) +dQw(x,y,z)

The indices w and a stand for water and air, respectively. The measuring

- 18 -

principle which was applied is based on thedifference in electrical conduc­

tivity between water and air. While normal drinking water conducts electric

current, air bubbles act partically as an insulator. By placing two electric

conductors in the flowing water-air mixture, the local concentration can

be obtained as a function of the resistance of the unaerated water part of

the flow.

The 8 mm diameter gauge used had two pointed wire sensors of diameter

0.5 mm. The two transmitter wires, each of l,ength 8 mm with an interdistance

of 2 mm, were placed in the flow mixture parallel to the chute axis.

For accurate concentration measurements, calibration is very elaborate.

For calibration, a sampling method was used (see Volkart, 1978) employing

the actual flew mixture because air bubble size and the turbulence of the

flow is of great importance. The mixture was absorbed for long periods at

several points . on the cross section and separated into volumetric portions

of water and air. The absorption velocity must equal the mean flow velocity

(vm) of the mixture (Fig. 3) .

The mean air concentration over the area A is defined as follows:

C(x) Oa(x)

ff dQa(x,y,z) A

; ff ( dQ a ( x, y, z ) + dOw ( x, y, z ) ) ;

ff dQa(x,y,z) A

ff dOtot(x,y,z) A

As a first approximation, air and velocity distributions can be considered

as two-dimensional. Thus local discharges can be written as:

dOtot(x,z) v(x,z) · b · dz

dOa(x,z) C(x,z) · dOtot(x,z) C(x,z) · v(x,z) · b · dz

Thus, the equation for Cm(x) reduces to

h J C(x,z)·v(x,z)·b·dz h

1 J v(x,z) .::.o_ ...,.h ______ = h C( x, z). -v-m(_x_) ·dz

f v(x,z) ·b·dz o 0

As the above equation indicates, knowledge of the air and velocity

distributions is necessary for the calculation of mean air concentration.

0.6 1"""""'-o ..

I<J u 0!::

0,, I<J Q:: ... 1<1"-.._..., .._o _::.. 0 ....

0.2 ...,:::.

~ .... 0!:: I<J .... 0

0 11.

0

12 .. ..... ~

10 E .... ~

),.

8 !::: u 0 -.J I<J

1

I ::..

0!:: ~ 6 0 ;:::

11. Q:: 0

"' CO

' "{ I

I 2

- 19 -

....... ........ loo.. ......... ~~

~\.. \

.. , "~

' 20 60 80

A IR CONCENTRATION C c•/.} 1>

I

I 1 I V

I I r /' j V

V

/

20

kr- - --

/ / l / ~ I

I

I

: 60 80

AIR CONCENTRATION C C •/. 1 1> I I I

, .... a) 100

-- --ACTUAL FLOW VELOCITY

b) 100

CORRECT VALUE

Fig. 3 Cal ibration of the air concentration gauge

a) Calibration curve: Concentration versus measured voltage

b) Influence of the absorption velocity vA

- 20 -

For this reason mean air concentrations Cm were only calculated for the

section upstream of the air slot.

The air content is defined as C* = Oa/Qw . This definition is only mentioned

here because some other authors use it and comparison of resu l ts often leads

to confusion. The relation between air concentration C and air content is:

C = C* I ( 1 +C*) .

2.3 Similarity Problem

2.3. 1 Froude Analogy

Froude's law of similarity in its general form, was the base for the pre­

sent hydraulic 'model tests. This law is based on the equality of the ratio

of forces due to acceleration and gravity in the model and prototype. The '

scale ratios for relating dimensions from model to prototype are given in

Table 1.

Physical Dimension Formulae Scale

Length [mJ }!f_ Pp = - = \.1 25

Pressure [m wate r J tM PM

Velocity [m/s] }~ Vp 1/2 = - = \.1 5 Time [s] tM VM

Discharge [m3 /s] Qp

= \.15/2 3125 liM

Specific Discharge [m3 /S ·m] qp

= \.13/2 125 ""CIM

Srickler's friction [m113;s] } kp -1/6 0.585 coefficient KM = ,\.I

Frequency [Hz=s-1] fp

= ~.~-v2 0.20 "fi

Tab 1 e 1 Scale ratios between prototype and model

General remark : Unless otherwise indicated, all va lues given henceforth in this report refer to the prototype.

- 21 -

Under the conditions that completely turbulent flow exists in the hyd­

raulic model as well as in the prototype, the Strickler friction coeffi­

cients are constant and that the ratio kp/kM = \l-V6 = 0 . 585 holds, good

results for mean values (of flow depth, velocity etc.) will be obtained.

Further considerations regarding the velocity distribution and the influ­

ences of air entrainment, surface tension (scale effects) and differences

in the physical model (only a section of the spillway was modelled) are

made in the following subchapters .

2.3 . 2 Influence of Air

Relations between prototype and model, according to Froude's law, are

only valid for pure water flow. Transformations from model to prototype

are always based on the data for pure water and the influence of air must

be considered in addition .

Air entrainment is always connected with energy losses so that the

mean flow depth increases and the mean ve locity decreases . The exact re­

lations are:

Ow = Water discharge

Omi x Vmi x · b · hmi x Oa Ai r discharge

( 1 - Cm) · Omi x Omix = Ow+ Oa

Exper iments have shown (Volkart , 1978) that

~ l-c2 hmix 1 1 and therefore -- - · --

hw - (l -c2) (1-C)

t~asurements showed that the mean air concentraion Cm upstream of the air­

slot was between 7 and 10 % in the model and therefore the ratios become

Vmix Vw

hmix 0 . 995 to 0 .990 and --- 1.08 to 1.12 hw -

In the diverse formulae for surface air entrainment in spillways , the

mean air concentration is always a function of the Froude number (see e .g.

Volkart, 1978). These formulae are only valid for the range of data which

- 22 -

they were actually developed from , namely for prototypes. Exact modell ing

is only possible if the effect of surface tension is negligible. This is

approximately full filled if the geometric scale is 11 <4. For scales 11 >4,

air entrainment in the model is less than in the prototype. This also af­

fects the air concentration and velocity distribution. In the model there

is less air in the near-bottom layers than in the prototype, while the

velocity distribution is more uniform.

Scale effects on air demand at the air slot will be discussed in sub­

chapter 2. 3.6 .

2.3.3 Influence of Surface Roughness

As mentioned in chapter 2.3. 1, the Strickler-coefficients should be

of the ratio .· kp/kM = ~~-V6 = 0.585 . Assuming a Strickler-coefficient of

kp = 75 mV3;s for the prototype, the model should have a coefficient

kM= 128 mV3;s. As a consequence, PVC was used for model construction.

t~asurements of water level s, considering the Moody- diagram, showed that

kM was between 110-1 28 mV3;s which is satisfactory. This condition is only

valid, however, for "mean-considerations" and may not give accurate results

for the velocity distribution and air concentration.

To study the effect of surface roughness, expressed by the equivalent

roughness height £(mm), Kaveshnikov and Lentyaev investigated different

surfaces (plexiglas s, sand, gravel) in model tests for the Sayano-Shushens­

koe dam spi llway . Comparison of the average air content as well the air

content 10 mm (13 cm in prototype) above the bottom for different flow re­

gimes showed that the influence of surface roughness, especially for air

concentrations near the bottom, is considerable ~·

Knauss (1981 ) gives some indications about transformation of the equi­

valent roughness height £. His considerations ar~ based on the assumptions

that the friction factor A and the boundary layer development are equal in

the model and prototype, the differences in velocity distribution are neg­

ligible and that Froude's law of similarity is fullfilled. Extensive measu­

rements of Bormann (1968) for steep chutes resulted in the following for­

mula for the local friction factor:

-1 19 fi= /a·( logRex) · and

- 23 -

EFFECT OF SURFACE ROUGHNESS ON AIR ENTRAINMENT

0 1.0 2.0 3.0 1..0 E [mm] •

c*·/. 15

• 10

5

0

0 1.0 2.0 3.0 1..0 E {mm] •

Fig. 4 Change in average air content in the fl01·1 (left diagram) and air content 10 mm (13 cm in prototype) above the bottom (right diagram) for different test conditions (according to Kaveshnikov and Lent­yaev, 1980)

The definition of the Reynold's number Rex and the test results a= f(E)

are given in~ With A =>-(a(E), Re) the flow is in the transitional

region of the t~oody-Di a gram.

Boundary 1 ayer thickness

61 Displacement thickness

V

Velocity outside of boundary layer

u3 Rex= 2gv·sina with

a Slope

fi • .la·(log·Rex)-1 ·19

Friction factor

a

0.8

0.7

0.6

0. 5

0. 1,

0.319

0 2 3 E lmml

EQUIVALENT ROUGHNESS H£/GHT

Fig. 5 Friction parameter "a" as a function of equivalent roughness height E (according to Knauss, 1981)

From these results Knauss developed the follm~ing similarity condition:

( )

+2.38 ap log Rex,P

a;:; = 1 og Rex,P -1 og 1J3/2

a f(E) ace. to Fig. 5

lJ geometric scale

- 24 -

The velocity U may lie between 25 and 40 m/s. Thus the ratio becomes

1.75 < ap/aM < 1 .82. The equivalent roughness height of the PVC-chute is

estimated as e: =0.1 mm . Thus the paramett>r a becomes aM =0.39 in the

model and ap = 0.68 to 0. 71 in the prototype. The according equivalent

roughness height in the prototype must be between e: = 1.1 and 1. 4 mm. This

gives sufficient conformity between model and prototype. The influence

of a different roughness height is shown in Fig. 4.

2.3.4 Influence of Channel Width

Because of the capacity of the pumps in the laboratory, only a section

of 3 m width (120 mm in the model) cou ld be investigated , however the pro­

totype consists of three sections each of 33 m width. The influence of

channel width.on the velocity distribution is discussed in this chapter

while the influence of width on air demand will be discussed in the next

chapter .

Extensive velocity measurements were made in connection with the in­

vest igations of scale effect on air demand. With four different scales,

between 11 = 18. 75 and 11 = 30, a constant 2. 25 m wide section of the pro­

totype was modelled by varying the width of the model chute between b =120rrm

and b=75rrm. For specific discharges q=40, 60 and 80 m3/s·m the velo­

city was regulated so that 25 cm (prototype) above the bottom the velocities

were the same for each scale.

The results of the measurements on the chute axis upstream of the air­

slot are represented in~ There is no significant difference in the

velocity profiles for the scales between 11 =18.75 and 11 =25, i.e. for chute

widths between b = 120 mm and b = 90 mm, respectively. For the sea 1 e 11 = 30

(b = 75 mm), ve locities are slightly smaller and the f low depth is higher .

The same can be seen by analysing· the horizontal velocity profile over

a cross section. The ratio between mean velocity at a constant level,

Vm(Z = const) and the maximum velocity at the same level, Vmax(z = const), is

given in the following Table:

11(Model Scale) 18.75 21.429 25 30

Vm(Z = const) 0.924 0.916 0.902 0.800 Vmax(z = const)

0 0

"' E ~--.;,

' "'E 0 Cl)

i Q I

I

E E E E E E E E

...... 0 ...... 0

" 0) 0 .....

" " " ,,

.Q .Q .Q .Q

0) ~

"' ..... ...... -..1 0 0 ~ " <{

c:i lli -: ~ u

"' ..... ..... "' " "

,, "

-..1

"' :::1. :::1. :::1. :::1.

Q 0 ~

I

- 25 -

"4h lcml

0 0 .....

- --:=.r .---~ ... ~·~ ~.-

E n

., ......... E 0 <o

" Q

E -"'· .,

' !i "'E 0 ~

Q

0 0 .....

..._-

;::=

0 0

~-.· :~::: "'-:.-.,. """"';::; ~

:;;;--6,..:. ......... _ .... ~:... '':"..:...- ::;... ... ~

0 0 -

<4 h lcml

Fig . 6 Influence of channel width on velocity distribution

0

g ~ •

.... ~

., ' E ..... ::..

£!

0

"' ~-

'• 0 .....

£!

0

- 26 -

Thus it can be concluded that the influence of the chute width is only

significant if the width becomes smaller than go mm. In particular, with

the chosen scale of 1 :25 and a chute width of 120 mm the influence of the

sidewalls can be neglected. Thus the model gives a good analogy of the na­

tural flow behavior. Only the side wall region of the prototype spillway

is not exactly represented, which is not important for the flow.

2.3.5 Influence of Air Supply System

For the following reasons it was not possible to simulate the air supply

system of the prototype:

difference in width of channel between model and prototype

air demand measurements in the model were always connected with energy head losses

the design 'of the air supply system in the prototype will be based on the results of the model tests.

Because the air demand of an air-slot is a function of the hydraulic pa­

rameters and the air supply system, the model air supply had to be varied.

This was achieved with a valve and, as a result, the pressure in the air

space under the free nappe was varied. By measuring this pressure and the

air demand, the characteristic of the air-slot can be obtained. The point

of intersection between the characteristics of air-slot and supply system

in the prototype, gives the actual air demand and pressure in the prototype

(Fig. 7). Thus, the influence of the air supply system can be overcome.

.d p

CHARACrER/Srte OF rH£ SUPPLY·SYSrEM

Fig. 7 Calculation of the actual air demand in the prototype (principle)

- 27 -

2.3 .6 Scale Effect on Air Demand

As mentioned in chapter 2.3 .2, air entrainment occurs against the resi­

stance of surface tension o. For exact ~odelling, the equality of both

the Froude-nuntbP.r, Fr = v/ /9L and the l.Jeber-number We= v (PL/g ·o) 1~ould

be necessary . Since this is not possible, additional scale tests of the

effect of surface tension were made.

The scale ~tas varied between \l = 18.75 and \l =30 , simulating a con­

stant channel width of 2.25 m and a deflector with a height of 0.75 m.

Therefore, it was necessary to vary the 1~i dth of the chute bet~teen b = 120 mm

and b = 75 nlll with a movab 1 e 1~a 1 I p 1 aced in the chute . The range of possi b 1 e

scales was given by

- maximum possible discharge (upper limit of \l

maximum possible velocity (lower l imit of \l

Photo 3

18.75)

30)

Ch ute with movable side wall

b 75 nlll,

\l = 30

The investigations were made 1·1ith specific discharges qw=40 , 60 and

80 m3/s ·m and ve l ocities between 25 and 30 mjs (for velocity profiles see

Fig. 6) . The measured characteri stics transformed by Froude analogy are

represented in Fig. 8. As expected, the air demand is smaller for smaller

scales. To make a quantitative comparison, however, the same air supply

system must be used for al l investigations. Principally the supply system

has a characteristic of the form

0 -I

-2

-3

i -4

~ E

-5

-6

-7

-0

-I

-2

~ -

3

0 ~

E -4

-5

-6

-7

0 0

2

/~ l.-

::"-

!....

.,

HP

-

r I I I I

2

.I .. "

Fig

. 8

3 3

,. 5

. Q

Air

0

0 (m

Vs-

m)

-I

q =

40

m'/s

·m

-2

---

I"

=

18.7

5

----

I" =

21

.429

--·-

I" =

2

5.0

-3

-···

····

··--

I" =

3

0.0

~

-4

i E

-5

-6

-7

,. 5

. O

Air

0

(~/s

·m)

0

q =

8

0 m

'ls·m

---I"=

18.

75

----

I" =

21

.429

-·-·-

I" -

. 25

.0

-·--

-·-·

-I"

= 30

.0

~ •

-I

-2

-3

0 _,

. • E

-5

-6

-7

2 3

,. 5

QA

,.

(mo/

s-m

) ,....

...--::;:

~~ ~

//:/

/I

'I

q =

60

m'/

s-m

I --

J"

=1

8.7

5

----

I" =

21.

429

l -·

-·-

I" =

2

5.0

··

···-

·-··

···

I"=

30

0

---

/

2 5

QA

ir

· 3 /

s-m

) 3

,. -

-(n

~ :::

::::---

-~ ~ ~

~ KID

A

ssum

ed

Air

-su

pp

ly

""'@

Ch

ara

cte

rist

ics

qAir

W

·K

CU

RV

E

A :

K

=

4.08

2

B:

K =

3.3

33

C

:

K

=

2.88

7

Sca

le e

ffect

on

ch

ara

cte

rist

ics

of

a d

efle

cto

r (h

eig

ht

ho

=0

.75

m)

N

(X)

- 29 -

K =constant, representing geometry and head losses of the supply system.

To evaluate the scale effect, three characteristics were assumed:

Curve A B c

K 4.082 3. 333 2.887

The air demand thus obtained is listed in Table 2 including the ratio f 1 of air demand at a certain scale, qa(f.l), to the air demand at scale lJ= 25 ,

qa(25), under the same conditions (discharge, veloci ty, supply- syst em). As

can be seen , nine values of f1 could be obtai ned for each sca le. Mean and

extreme values of f1 are represented in Fig. 9 A as a function of scale,

including three possible extrapol ations. In Fig. 9 B the same curves are

standardized on the prototype by the transformation

f1 (Prot .) f2 =

fl (lJ)

This means that the air demand in the prototype, measured in a model

with scale lJ and transformed by the Froude analogy, has to be multiplied

by the factor f2. For the scale 1:25 , f2 is between l .05 and 1.45.

Measurements of prototype ai r demand by other authors gave the following

f actors f 2:

Barragem Foz da Are1a , model sca le l :50: sl ightly decreas i ng with i ncreas i ng water discharge

f2 3 to 4,

Nurek dam spillway, m0de l scale 1:35: f2 4 to 5

Sayano Shushenskoe dam, model sca le 1:13: f2 1.0

- Barragem Foz do Areia, model scale 1:8: f.., = <.

1.0

While the l ast two results confirm Fig . 9 B, the first one gives much

smaller values of f 2. It is not known whether the influence of the air

supply system was taken into account.

Finally it is proposed to multiply the air demand by the factor 1 .5 for

dimensioning of the supply system and to use the measured values for the

spacing of the air sl ots. Thus , the results should be on the safe side.

For al l diagrams in th i s report, air discharges are only transformed by

Froude analogy .

- 30 -

q = 40 m3/s ·r.: I IJ = 30 IJ = 25 IJ = 21 .429 IJ = 18.75

l. 84 2.28 2.48 - * A

0.807 1.00 1.088 - **

1.68 2.10 2.13 2.27 * 8

0 .800 1.00 1.014 1.081 **

l. 58 1.88 1.82 2.06 * c

0 .840 1.00 0.968 1.096 **

q = 60 m3/s·m I IJ = 30 IJ = 25 IJ = 21.429 IJ = 18. 75

2.74 3.36 3.68 3.58 * A

0 .815 1. 00 1.095 1.065 **

2.53 2.85 3.28 3.26 * B

0 .888 1.00 l. 151 1.144 **

2.38 2.62 3.03 3.03 * c

0.908 1.00 1.156 1 .156 **

q = 80 m3;s ·m I IJ = 30 IJ = 25 IJ = 21 . 429 IJ = 18.75

2.70 3.98 4.44 - * A

0.678 1.00 l. 116 - **

2.59 3.53 4.06 3.90 B

0.734 1.00 1.150 1.105

* * qa[m3/s·m]

**

2.53 3.34 3.78 3.61 c

* **~ qa(25)

0.757 1.00 1. 132 1.081 **

Table 2 Actual air demand for different scales

- 31 -

I A : Measured Factors f 1 Standardized on }J- = 25 I f = Qa ·( f'-)

F·~: I"'""'" 1 Qa · (f'-= 25) • factors

fmin

2

0 5 -cm-rr---t:----

1.

·-~· ·-@ ~ "·--·~ ...

i'." ~"\' 1\ \ ' 0

0 10 20 25 30 35 40 18.75 21.429

8 : Transformation of the Curves from A I Standardized on Prototype

f = f 1 ( prot l q0 ( prot l 2 f1(f'-) = Qa (}'-)

2 (!) @

I /' //@ --:£ ./· ---~---

I fz (fL= 25) I 1 : f,= 1.45

][ : f,= 1.20 I m : t,=Loo 0

0 10 20 25 35 40

Fig. 9 Froude-anal ogy correction f actors f or specific air demand

- 32 -

3. DETERMINATION OF SHAPE AND SIZE OF THE AIR-SLOT

3.1 Background

3.1 .1 Outline of Possible Shapes

An air slot has to serve two purposes. It must produce a local sub­

pressure so that air will be sucked into the flow and it must supply the

flow with air so that aeration over the whole width of t he channel is

guaranteed.

Three basic types of air-slots and some combinations are represented

in Fig. 10. They can be characterized as follows:

-~ (Fig.lOF) : This is often used in tunnels and after gates. The

idea arose from the necessity to aerate the slot of high pressure gates.

The advantage of this method is that the supply of air through a groove

is very easy. Its disadvantage is that the nappe is less exposed to the

air than with the other types. Usually, the groove is combined with a

deflector and/or an offset (Fig. 100/E). The depth of the groove is nor­

mally between l and 2.5 m.

-Deflector (Fig. lOA): In its pure form, this type is used in the Soviet

Union and fabricated from steel. Usually, however, a deflector is used

in combination with a groove or an offset (Fig. 10 B/D) since it helps to

produce higher sub-pressure. The height is about 0.50 m but when used

in combination with other types it is less, with a minimum of about O.lOm.

-~ (Fig. 10 C): If the need for air-s 1 ots is foreseen from the begin­

ning of design, offsets can be used resulting in a step-like spillway

surface. The advantage is that an offset produces less disturbances

(shock-waves) in the water profile than a deflector. The overall height

varies between 1 and 2 m.

Air is normally supplied from the side, either by special air vents or

by a free air space produced by side deflectors or by grooves in the side walls. For the San Roque Dam spillway it is planned to supply the air

through valves in the side and dividing walls.

DEFLECTOR

A*

F

GROOVE

- 33 -

OFFSET C*

Fig. 10 Some shapes of air slots (* investigated types)

3.1.2 General Outline of Investigations

In the hydraulic model tests the following types of air-slots were

investigated:

- Groove (type 0) as was planned in the initial design by Electroconsult .

- Deflectors of varying height to study the influence on air demand of

height of deflector, flow velocity and specific discharge (or flow depth).

- Offset of type Band C to include the most commonly used types.

Because it is difficult to accurately measure the flow depth

(see 2.2.2) and precise reproduction of the trials must be possible, fur­

thermore because the velocity near the bottom is of importance and not

the mean velocity, the characteristic velocity v0 was measured 25 cm

(1 cm in the model) above the bottom.

- 34 -

The air demand was measured as a function of the flow parameters and

of the sub-pressure in the air space under the nappe (see 2. 2.5 and 2.3.5).

The diagrams thus obtained (specific air demand versus sub-pressure under

the nappe) are cal led the characteristi c of an air slot.

In addition, static pressures were measured along the bottom to a

distance of 37.5 m from the air-slot. Although pressure fluctuations were

quite pronounced at the place of impact of the jet, only the n1ean static

pressure is indicated in the diagrams.

3. 2 Deflectors

3.2 . 1 General Behavior

Four deflectors with the heights varying between 0. 25 m ~ ho ~ 1.00 m

we re investigated. All deflectors were of the same shape but dimensions

were scaled i n accordance with ho (see ,Eis:...l.J.) . Measurements were made with:

- The same hydraulic conditions (q = 80m3/s·m, v0 =23 m/s) for all deflectors

varying hydraulic conditions (specific discharge, velocity) for a deflec­tor with optimal height (ho=750 mm) .

Photos 4 to 7 show the deflector with height ho = 0. 75 m, specific dis­

charge q =80 m3/s·m and velocity v0 = 23m/s for different rates of air

supply. The zone of aeration can be seen as a white layer. Before the

Fig. 11

1• : h X sing,_, . 0 0 sin 9.6•

10 : 10 · cos "·o· Hoight of d•fleclor ho varyi•d b•tw••n 0 . 25 m and I.OOm

Geometry of deflectors

- 35 -

Deflector ho = 0. 75 m, Air Supply Varied

q =80 m3fs ·m v0 =23m/s

Photo4 qAir=2.77Qm3;s .m Photo 5 qAir = 2. 55 7 m3fs ·m

Photo 6 qAi r = 1. 444 m3;s ·m Photo 7 qAi r = 0

impact a roller of water forms along the bottom under the aerated layer.

The greater the air supp ly, the longer is the distance from the deflector

to the impact of the free nappe. Or, alternatively , the more the nappe is

exposed to the air, the higher the air demand . With i nsufficient air

supply (Photos 6 and 7), the jet is clinging to the bottom and the surface

layer tends to deflect from the nappe.

- 36 -

The static pressure on the channel bottom along the axis is illustra­

ted in Figures 12 and 13. In the air space under the nappe there is a con­stant or slightly decreasing sub-pres~ur~ of about-1 m static water head.

At the impact zone there is a peak in the pressure distribution, due to

deflection of the jet. The smaller the air demand the bigger the angle of

impact of the jet and, consequently, the pressure peak is higher with

maximum of around 8 m static water head. With decreasing air supply the

sub-pressure after the deflector increases rapidly to a maximum of around

- lOm static water head. However, since the aim of an air-slot is to

aerate the water , these conditions are not of practical importance and

were not investigated further.

3.2.2 Main Parameter s

The characteristics of the different deflectors are represented in~·

The main parameters influencing air demand are deflector height hp and the

hydraulic parameters (specific discharge, velocity and flow depth).

Fig. 14A shm~s the influence of deflector height hp with constant hydrau­

lic conditions. For heights smaller than hp= 75011111, the air demand in­

creases with increasing deflector height. For heights bigger than hp = 750 11111

the air demand remains approximately constant. Thus the optimal height for

these specific flow conditions is hp= 750 mm.

Fig. 14 B shows the behavior with varying hydraulic conditions and con­

stant deflector height hp=75011111. With a specific discharge q=80m3/s·m

and velocity v0 =26mfs, the air demand is almost the same with

q=l20m3/s·m and v0 =25m/s. With q=80m3fs·m and v0 =23m/s , however,

air demand is significantly lower. The air demand is obviously a function

of the flow velocity and not of specific discharge or Froude-number.

It should be noted that the characteristic in the range of practical

importance (tlp ~ - lm) is very flat. This means that a small change in the

sub-pressure gives a big change in the air demand. The design of the air

supply system is ~fore of great importance with regard to the eff_i ci_:

ency of the aeration.

9

- 37 -

0 3.5 85 13.5 25.6 3 7.5

1.0 6.0 11.0 Distance From Dtfftctor in Mtttrs

0 3.5 8.5 13.5 25.6 37.5

10 6.0 11.0 Dlstancr From Otflrctor in Mdrrs

20 ....

~ t 15 f, .. -s 10 .,-

o E

5 ~~

"E "o .. _ ,._ 0 '-0

Q.Q)

20

15

/0

5

0

20

15

10

5

0

.. " 15 ~

i5 10 ~

~.'~~ ..... ~f.!(!_ , q0 • I . 225 rr?/s·m

Air11J oprn, q0 = 1.116m'ls ·m

Air closed . q0 :: 0

Air oprn,

~;~·~; -~-~~-~-. --------Air!IJ oprn,

q0

• 2.01.Brl/s·m

q0

• 1.938 nlls·m

q., • 7. 189m31s·m

q.,• 0

~f-~---~~-~?.: q0 • 3 .09~,!/s.m ~!.;j~o~~'!....: q0 = 2.836nlls·m

Air},oprn

~!:·~ .... ?.'!.~'!. · q0 z 2.8Btrrf/s-m

~~~J-~_!~ q0 • 2.665rrlls·m

~~~~-~·~ q0 • T.mnf;s.m

Aircloscd , C1g= 0

Fig . 12 Pressure distr ibution at specific discharge q 80 m3/s·m v0 = 23 m/s

- 38 -

Seal• I : 500

0 35 8.5 13.5 25.6 37.5m

1.0 6.0 11.0 Distance trom Dtlf~ctor in Mett rs

20

15

10

5

0

20

15

10

5

0

0 3.5 8.5 13.5 25.6 Distance from Deflector in Meters

1.0 6.0 11.0

q • '0 m1/s m

•o= 22m/s

Air closed, qa : 0

q = 80 mls ·m

vo~2Jm/s

Air open, ............... q0

r 2.770 m3/s -m

2.557d/sm

I. 320 rr?/s·m ~~J!~e.'!!' qo z

~~~!.. .o.!.'.!!: qtl :

Air closed , q0

: 0

q = 80 m'ls·m

•o=26m/s

~~~- ... ~f.~ ~~ qtl : 3.09' rrfls ·m

~~~!~e.!~ q0 = 2.836m'ls-m

~~r_~!_~~~!!....· q0 = '·''' m31s-m

Air closrd q0 z 0

q = 120rrf/s·m vo z 25 m/s

~(~_ .. ~f.~.~~ q 0 = 3.352 nlls·m

~~.!!.~e!.~ q0 = 3.117 m3/s·m

Air~J open, qa = 1.,93 m3/s -m

Fig. 13 Pressure distribution downstream from deflector

ho = 750 mm

- 40 -

3 . 3 Groove ~

3.3.1 Initial Design

The geometry of the groove as was proposed in t he initial design by

Electroconsult, is represented in Fig. 15. It consists of a deflector with

height ho=0:308m and a groove with a cross section of 2.50xl .80 m for

the air supply .

The characteristic of the groove .(Fig. 16) shows a slightly higher air

demand than for the deflector with height ho = 250 mm under the same hydrau ­

lic conditions (Fig . 14A). This is to be expected for the aeration is only

produced by the deflector while the groove serves to provide enough space

I I r

I

I I

I 1-I I I

Section A- A

S ection B-B

Q++

~- '-

I' 0 1 m

I I ,/

I

I ~

1 I! l I I

0 T I r ti e I

c c

~_j ..; --- - - -

I I I

Fig . 15 Geometry of groove with side-deflectors (Sea 1 e 1 : 100)

- 41 -

J qAir(m/sm)

I GROOVE I J

· ------+-

q • 1.0 mJ/s ·m "o• .. 12 mls

q • 10 m1/s m ~o ·-23 m/s

q ; 110 m3/s m ~o ... zs m/s

Fig. 16 Pressure as a function of air supply

- I

- 2

- J ~

- < -e ...

- 5

- 6

_,

for a generous air supply. However, within a relatively short time the

groove started to fill with water from falling droplets and from water

adhering to the side walls and trickling into the groove.

On the other hand, bubbles rising from the air supply system carry water

drops with them. Thus, at a certain water level in the groove , near the

vertex of the air supply conduit, equilibrium exists between water flowing

into the groove and the drops thrown out by air bubbles.

Water in the groove does not affect its characteristic but it does

affect the air supply system since the air has to overcome the resistance

of the water in the groove. Furthermore, it is uneconomical t o build a

groove which will only be filled with water. Two counter-measures against

filling of the groove are discussed in the following, namely

drainage of the groove,

side deflectors .

- 42 -

3.3.2 Drainage of the Groove

The groove was drained by one of the l mm diameter piezometer holes ,

connected to a 4 mm brass tu be (model dimensions). The effect of the drai­

nage is ill us tra ted in photos 8 and l 0. Photo 8 sho~1s the groove with dry

side walls and with drdinage, photo 9 without drainage. In the first case

the groove is empty but it is half filled with water in the second. As a

consequence , the air supply reduced from Qa = 2 . 2 m3/s·m to qa = 1.4 m3js · m.

The measured ~1aximum water fl01~ in the drainage system was about q0 =3£/s

Groove

Photo 8 Dry s i de walls, 1~i th drainage, qa = 2 . 2 m3;s ·m.

q l 20m3/s ·m

v0 25 m/s

Photo 9 Dry si de 1~a ll s , no drainage , 9a = 1.4 m3;s ·m.

Photo 10 Wet side walls. Although t here is drainage, groove does not empty because water adhering to the walls runs into the groove .

- 43 -

per meter channel width. The pressure distribution on the bottom and the

amount of air supplied is illustrated in Figure 17 for different dischar­

ges with and without the drainage system.

Starting with t he groove empty , dr ainage was sufficient, however, star­

ting with the groove f ill ed wi th water, the drainage system was not ab le

to empty the groove (photo 10). The main reason was that water was adhering

to the walls and f lowing into the groove while with dry side walls only a

few drops fell into the groove. To guarantee an empty groove under all con­

ditions, an extensive drainage system would be necessary. For this reason

this design was not investigated further.

3.3. 3 Side Deflectors

To prevent the adhesion of water to the walls, side deflectors were

investigated. The side-deflectors were 100 mm high with geometry as shown

in Fig. 15.

At t he discharge q = 40 m3/s·m , the nappe separated comp lete ly from the

wall and there was enough space to aerate the nappe from all sides. The

sub-pressure was so weak that no air was entrained through the air supply

system. The groove was filled with water but not used for air supply since

air was supplied between t he nappe and the side wall. Compared to the con­

dition without side deflectors, the trajectory of the jet was longer and

the shock-waves were substantially higher (photos 11 and 12).

Around the discharge q =80m3/s ·m , t he air demand became too high for

the air to be supplied by the space between nappe and si de wall. The jet

touched the wall and the air-slot worked as if there were no side-deflec­

tors (photos 13 and 14). Since the mode l simulates only a 3m width of the

prototype, the total air demand (specific air demand multiplied by channel

width) wi ll be higher i n the prototype than in the model . Therf ore, i t must

be expected that the positive effect of the side-deflectors will be lost

at even lower discharges than q=80m3/s·m. Higher deflectors, on the

other hand, also produce higher shock-waves which should be avoided. There­

fore, the design with side-defl ectors was not inves t igated f urther.

- 44 -

Scalt 1, 500

"' 8.225 ~ 27. 265 . "!

0.9 ~ 5.80 ::: ~ 15.5

~ ~ Distonct from

38.78' m

Deflector in Meters

0 Cb~ 8 .115 ~ -~ ~

0.9~ 5.80 ::: ~

~ ~

27.265

15.5

Dis toner From ~tire tor in Mttrrs

20

15

10

5

0

20

15

10

5

0

.. c:: c::

" .c:: 0 .. ~ c::~

o E .. ~ ~E "" ::::: .. 0 ... .,

q • 'Onlls ·m ~a· 22mls

Air open , q0

: I. 781 m3/s ·m

Drainage

Air optn , q0

• 1.086 m3/s.m

no Drainag~

q • 80 m3/s ·m

~a·22 m - s

A ir open , q0 # 1.830 m3/s ·m

Drainage

1.0 23 nlls·m no Dra inage

Air closed, q0 z 0

q • 120 mls ·n

vaz25m·s

2 .176 nlls ·m Drainage

Air open , q0 • I . '-'2 rJ/s ·m no Dra inage

Air ~oprn , q0 :: I . -'89 rJ/ s ·m

Fig . 17 Pressure Distribution: groove, ini t ial design

- 45 -

Groove

Photo 11 Groove 1~ithout si de­deflectors

Groove

Photo 13 The jet i s aerated from the sides, no air entrainment t hrough t he groove

q 40 m3/s·m

v0 26 m/s

Photo 12 Groove with si de­deflectors

Photo 14 The jet touches the side walls and starts entraining ai r through the groove

- 46 -

3.4 ,Offsets

Based on the results of the deflector t.es~s, offsets with height hoff =0. 75 m

and 1.00 m were investigated . In addition, they were combined with deflec­

tors with heights varying between 0.25m ~ ho ~ 0.75m (Fig. 18).

H•ighl of Off sot : h011 = 0.75 m and I. OOm

H•ight of O.fl•ctor Vary i ng b•tw .. n 0.25m o; ho o;o.7Sm

Fig. 18 Geometry of offsets

As the characteristics show (Fig. 19 ), the air demand of offsets with­

out deflectors was very sma ll. With a deflector only 0. 25 m high, the air

demand increased about three times, however, with the deflector 0.50 m

hi gh the air demand increased only a little more than with the smaller

deflector.

As can be seen from the pressure distribution (Fig. 20), the offset

without deflector produces only a very small sub-pressure . Furthermore,

the exposure of the nappe to the air is very sma ll. A deflector produces

not only a higher sub-pressure, but also the trajectory of the nappe be­

comes much longer (photos 15 to 20). These are the two main reasons for

the increase in air demand .

- 47 -

I OFFSET

E

h : 0. 75 m ~-- • 5

<>.

1------+----...,."""'--~--"'--+----1-------~...1-- - 6 <l

.• ~ •. 1 ~:gr~ -=-: : 'I 0

0

1.0

+ Dofloctor h

a Deflectorh

Qa• (m31s·m) 2.0

Air -Supply -

• 0. SO m, q :/20 nlls ·rn

- 9

-10

3.0

3 I 3 3 q= t.Om/s-m, v0 = 22m/s q=80 m/s-m, v0

= 23mlsjq=120m/s-m, v0

= 25m/s

Dflsol 1.00 ml-• q 120 m'ls·m

Delltclor h = 0. 25m, q = ' 0 m'ls·m Dtllrc tor h = 0. 25m,Q = 120 nll3·m

0 Dtffector h = 0. SOm,q = 120 nlls·m

1.0 Qa• ( rr!1s-m) 2 .0 3 .0

Air-Supply -

Fig . 19 Pressure as a function of air- supply

- ' - 5

E

<>. <l

:[~

Q

- 48 -

0 2.16 us 12.3

0.60 5.03 9.87 ".72 Distanc• in M•lors from Offs•l

20

15

10

20

15

TO

5

r0 -:-22m/s

~-i-~ .. ~P.~~.. q. • 0. 812 nf/s .m

Air 11J op•n. q. = 0.607 m3/s·m

Air tlosrd , q0 0

Offset h = 0 . 75 m

II

q 80 rrlAm

=- 23m/s

Air open

I ll J q 120m/s·m •o :-25m/s

Air open q0 : I. 096 rrl/s·m

Air 1/J open, q0 = 0.769rtfls·m 0 -·-· - · - ·-

0 2.16 us 12.3

.. ~

IS ~ t

10 ~ -~

0.60 5.03 9.87 14.72 Distance in Mdrrs From Offsrt with Drflrctor _.

Air closed , q 0 = 0

IV q

•o = 120 nlls·m

:-25m/s

01/s•t h :0.75m with d•fl•ctor h= 0. 50 m

Air open , qa = 3.605m3/s.m

Air 1 /3 optn. Q0 I. J65n?/s·m

A 1r closed . q0 0

Fig. 20 Pressure distribution downstream from offset, h = 0. 75 m

.... 0 ...., u <11

;;::: <11 "0

0 c

E 0 U"l

Cl .c.

- 49 -

Offset combined with Deflectors, q = 120 m3/s · m

hoffset = 0 . 75 m hoffset = 1.00 m

Photol5 qAir=l.Ol m3/s ·m

Photo 17 qAir = 3 . 04 m3;s · m

Photo 19

Photol6 qAir=l.51 m3js · rn

Photo 18 qAi r = 3 . 37 m3;s · m

Photo 20 3 qAir=3.77 m js·m

- 50 -

3.5. Selection of Air-Slot

To summari se the preceding chapters , deflectors alone and offsets combi­

ned with deflectors give the best resubt!. The air demand of the groove is

determined by the deflector, while the groove provides space for the air

supply . Because filling of a groove with water can not be prevented by rea­

sonable means , thi s type of air-slot was not further considered. The offset

without deflector showed too l ittle air demand because not enough sub-pres­

sure was produced and the exposure of t he nappe to the air was not suffi ­

cient.

The remaining types of air slot , a deflector with the optimal height

ho=0.75 m and offsets 0.75 m and 1.00 m high, combined with deflectors,

showed similar air demand . To get further information, the air demand as a

function of discharge was studied (Fig . 21) . The characteristic ve locity v0

was varied between 22 m/s and 29 m/s , according to the specific discharge.

The air supply system was not varied and was the same as used for t he air

concentration measurements . The representation in Fig . 21 is usually used

to indicate the efficiency of an air s lot. Comparing this with other re­

sults care must be taken for:

- the influence of the air supply system cannot be seen,

- the main parameter is not the specific discharge but the characteristic

(or mean) velocity of flow .

As Fig. 21 shows, _the optimal he i ght of the deflector is dependent _Qn..

the f l ow depth. For small discharges, offsets with the deflector height

0.25 m show the highest air demand while for higher discharges the optimal

height of the deflector also increases. _Obviously the combination of an

offset with a small deflector is opt imal. The deflector dominates opera­

tion at smal l discharges while the offset provides space for the air supply

and enlarges the trajectory of the jet at high discharges . For further in­

vestigations, the 0.75 m high offset with a 0.50 m high deflector was

selected because this type is closest to the envelope showing maximum air

demand over the whole range of discharges.

t E

t ~ Vl .....

M E

- 51 -

4.0

3.0

2.0

1.0

0

0 50

Offset h: 1.00 m w ith deflector

ho= 0.50 m ------ho= 0.25m

4.0

3.0

2.0

1.0

0

0 50

Offset h = 0. 75 m w ith Deflector

ho= 0.75 m

ho= 0.50 m

ho= o:25 m Envelope

... ... •••• ••• ••••• ,...--:;.-:i

.... ·· ······ - ,... .... --; ..... · . -~ ..... ..... .... ·· ........ ...... __.

100 ____._ qw(m3/s·m)

Deflector w ithout offset

h0 : 0.75m - · -·- · -

E nvelope

100 ____._ q1~(m3;s ·m}

Fig . 21 Air demand as a function of discharge

- 52 -

4. SPACING OF THE AIR-SLOTS

4. l Air Concentration Measurement

4. 1.1 Conditions Upstream of the Air-Slot

With the selected air-slot, i.e . a 0.75 m high offset, combined with a

0.5 m high deflector, extended veloci ty and concentration measurements were

made . Discharges of 40 and 60 m3/s ·m with three different ve locities each

and 80 m3/s·m with one velocity,were investigated.

Air concentration and veloci ty profiles upstream of the air-slot are

represented in Fig . 22. For all discharges the aerated layer is relatively

small and there is no air in the lower layers of the flow. The velocity

distribution is typical of a turbulent flow, being relatively uniform. The

decreasing limb is more pronounced at conditions with higher mean air con­

centration or with higher velocity or Froude-number. \~hile the model mean

air concentration is between 7 % and 10 %, due to surface entrainment

a mean air concentration of between 15 % and 20 % has to be expected in

the prototype.

A selection of measurements made by other authors are illustrated in

-~. The "Ehrenbergermode 11", 1·/i th the same range of velocity and di s­

charge as in the preliminary tests, gives the same air concentration and

velocity di stribution. The other diagrams, with sl ope (a = 15°) equal to

the San Roque dam spillway, but with higher discharges and velocities than

in the model, are significantly different . Aeration is more developed, the

air reaches down to the bottom, and the velocity profile is much less uni­

form. (The less uniform the velocity distribution, the higher is the ratio

between near-bottom velocity and mean velocity).

4. 1.2 Selected Cross Sections

To study the development of ai r concentration downstream of the air­

slot, axia l concentration profiles were measured for the specific discharge

q = 40 m3/s·m with maximum and minimum ve locity. The results are represen­

ted in Fig. 24 and Fi g. 25 .

[ q =

'0

mJ/s

·m~

A1r

cone~ntrot1on

m~1.

0 ;.~

-0

.2

0

v~locity V

m I

-0.

8 I

V m

=

1'

8m

/s

hm =

167

.Sem

0.6

; vm

:

1?.3

mls

.I1.0m

O,

, hm

=

IS1

5cm

0.1

I

0 -

-I

m! I!

M V

m

= 1&

.Jm

/s

h,.

=

U1.

Scm

0 2

0

<0

60

8

0

100

0 2

' 6

8 10

11

> VH

(

m/s

]

I I

I I

I I

I I

I I

I I

• c

("/,}

I

0 10

2

0

30

<

0 SO

11

> V

plm

/sJ

I

E=60

nl/

s m

I A

ir c

on

ctn

tro

tto

n

Vd

oc

1ty

Wl10

~ ±~~

I I I!

I I

I

V m

RI\:B

H

I~~-0

20

<O

6

0

80

10

0 0

2 '

6 8

10

•

I I

I I

I I

I I

I I

I I

• c

t•/.

J

0 10

2

0

30

<O

so

•

Fig

. 22

V

eloc

ity

and

air

con

cent

rati

on p

rofi

les

upst

ream

of

the

air

slo

t

V m

= 1

6.0

m/s

h,

= Z

I.O

Ocm

V'"

= 1

9'

m/s

h,

= 1

11

.5 c

m

Vm

=

31 1

m/s

h'"

= 1

91

S c

m

v,.,

l m

/si

Vp

{m/s

J

(J1

w

12

10

- 54 -

12 16 20 V [mls] V [mls]-

0 2 0 4 06 0 8 1 0 w 0 5 w 1.0

G1ZELDON CHUTE EHRENBERGERMODELL

WATER CONTENT w • 1- C

MEASURED AIR CONCENTRATION MEASURED VELOCITIES

.1. • 15° z r-

Zmax r r 0 8

0 6

0 •

02 0.4 0 6 OB 10 c

MEASURED AIR CONCENTRATION

I· I 1 f , ,

f Ow • 1 Smls

- I z Z mu

0 6

0 6

0 4

r 0 2

02 0 8 1 0

25 30

Ow • 360 1/s

280 Ifs 190 Ifs

50

MEASURED VELOCITIES

25 30 35 40 V [Ills)

I l a • fli:J

22. 5. 30• 37.5• 45.

Fig . 23 Velocity and air concentration profiles in steep chutes ~1ith surface air entrainment (diagrams by various authors, accor­ding to Volkart, 1978)

• Z

(mJ

H

JO

1.5

10

" 1.0

05

V

L

V

V

/ I Xz

".1

25

m

" "

\ 1\ If

/ v

·<I'

0 1

0

(0

tiiJ

10

10

0

[vm =m~ I

m

._,,.'0:

<~~~~!J

J:S~~;:====

io.so

m

9~~~

~~~!

~t0.7

Sm

lL

V

V

\ x. 1

7.87

5m

" r--- 1\

if

l/

V

~=20

.375m

.. " '0

J 1/

I

./

" 11

[\

1/

I

Q<

I~

I I

I I

I ~ :J

S.:

K12

5m

I 1

1

I""

.J I

I/ I

I I

01

0l0

60

10

10

0

0 1

0

lO

60

«J

tO

O

c (

0 /ol

..

10

0

0 1

0

lO

60

ID

10

0 0104D~IOIOO

Fig.

24

Air

con

cent

rati

on p

rofi

les

at s

elec

ted

cros

s se

ctio

ns

x =

dis

tanc

e fr

om t

he o

ffse

t

q =

40

m3/s

·m

lP'

V

1/ ./

II

X=

UI2

5m

010U1~alll00 1

.0 "

U1

U

1

.. 1

0 z

llff}

05

.. Z

(m

J <.0

JS

I 11

I

~19.125m

1.0

2.S

2.0

I.S

l

"'\

10

1\ 1

V

os

o---r-

-

0 1

0

lO

60

10

10

0

1 If

X•2

V2

5m

X:2

9.1

25m

lL

1 V

.... ~

1

J

.. Z

tm

J

2.S

2.0

IS .. os

lv, • 2

8 J

mfs

J --~

I·"·

W....

~ ~~

0

.75

m

' '~

. ~

-

l1 If X.J'-125~

r-;-

r-

./_

.L

1/

• ./

0 1

0

'0

60

1

0 IO

D 0

10

lO

60

10

10

0 c

("/.

) ...

100

0 10

lO

6

0

10

10

0 0

10

10

6

0

so 1

00

Fig

. 25

A

ir c

on

cen

trat

ion

pro

file

s at

sele

cted

cro

ss s

ecti

on

s

x =

dist

ance

fro

m

the

off

set

q =

40 m

3;s·

m

ll ./

]/

1-1 c!

-

X·6

02

5m

I rT ~ 0 1

0

"'

60

80

10

0

1.0

IS

<.n

en

• ID

Z I

m/

os

- 57 -

The first cross section is at the place of impact of the jet. The free

nappe is aerated from above and underneath so that there are two maximums

in the concentration profile with air concentration C almost equal to lOO %.

Because the nappe is not aerated over its whole depth, there is still a

core of almost pure water. At the bottom there is s roller of water up­

stream of the impact which causes the concentration to decrease almost

to zero near the bottom.

As a result of the turbulent effects, the air concentration increases

first at the bottom,in the direction of flow. The surplus air in the lower

layers rises because of buoyancy, and the lower maximum in the concentra­

tion profile disappears. Further down in the direction of flow, the con­

centration gradient near the bottom becomes steeper and the aerated layer

near the surface gets smaller but even at a distance of 65 m from the air­

slot there is still more air in the flow than upstream of the slot .

With the lm~er velocity , some irregularities were observed. The con­

centration does not decrease continuously in the direction of flow. This

not only occurs near the bottom, but the mean air concentration also pro­

duces wave- like fluctuations along the axis. This may be explained by

shock wave air induction and by horizontal air diffusion.

4. 1.3 Concentration Profiles along the Channel Bottom

Air concentration near the channel bottom is of main importance for

cavitation protection. Therefore, the distribution of air concentration

along the bottom was measured as closely as possible to the bottom (4 mm,

equivalent to 10 cm in the prototype). Profiles were measured along the

axis and at a distance of 20 mm (0.50 m in prototype) from the side wall .

The conditions upstream of the air-slot were the same as in the two prece­

ding chapters. Results are illustrated in Fig. 26 .

Distribution of air concentration along the axis: At the place of impact

the air concentration (C) is very lo1~, sometimes even less than 10 %. This

occurs at the place where the unaerated core of the nappe reaches the bot­

tom . Because impact pressures on the bottom are very high due to deflection

I q = '0

m3 /s:J

Z

= ID

em I'

mm

) A

BO

VE

B

OT

TO

M

X

: D

IST

AN

CE

F

RO

M

THE

O

FF

SE

T

AX

IS

50

cm

(20

mm

) F

RO

M

SlO

E W

ALL

I q:6

0m'l

s·m~

10

0

~~

I \

-!~ ril

o

80

o

...

0:

80

.. l

\ 6

0

60

\\ . F·

·~

V.,

:: 2

,.8

m/s

\. \

Ym

= 2

6.0

m/s

F

r :

6.1

~

Fr

: 5

.,

'0

.. '0

\" I

···\

I .....

. \ ... ~~

20

'

--2

0

\,;

... _

I .L

/ ~-

.. ~

····

····

·~·· ···

·····

........

... 0

0 10

1

5

20

2

5

10

1

5

X (

mJ

.,.

10

15

20

2

5

30

1

5

I--I

MP

AC

T

ZO

NE

TOO

10

0

80

~

-··""

""···

·0-·

·<1.

...

\ A

~

\ •

:-.. \

80

I'..

V m

=

27.

3 m

/s

.. V

m

' 2

9.,

m/s

6

0

Fr

=

7.1

Fr

=

6.,

6

0

U"1

I \

~-

····\·

~·-;::

~

00

...

... c

{"/,}

'0

V

\ ~

I \I

"\

\ 'o

ct•

!.J

20

2

0

V

···:::::::

: -..

..._

I V

··.::

::: ~--.

0 ···

··+···

······

··· ··

···

······

·· 0

10

15

2

0

25

1

0

35

X

l m

J.,

. 1

0

15

20

2

5

10

1

5

lOO

10

0

80

""'

.·

' _P

"···

O..

, Q

_

80

o

.... ·o-

····"7'"

""" '·

~p

.....

Vm

= 2

8.3

m/s

o.

... o

. .. -

o-··

·o ·

·•••

· Vm

=

31

.7m

/s

60

\ ~

Fr

= 7

.'

\ F

r '

7.2

60

'0

\._J

.. \

/ \..

._

'0

20

... ,

20

·~. __

......__

___ ~

"-- f

o-d

·o

....

... ;

::- ~

0 ·o

.... o

. ...

• g..

0

10

15

20

2

5

30

15

X

C

ml

... 10

15

2

0

25

10

1

5

Fig

. 26

A

ir c

once

ntr

ati

on a

long

the

bot

tom

- 59 -

of the jet, there is no danger of cavitation even though the air concent­

ration is low. After the impact, concentration increases rapidly because

of the mixing effect at the impact. In the further course of flow, air con­

centration decreases continuously, due to the surplus air rising to the

surface.

Distribution of air concentration along the side wall: For low water ve­

locities or Frounde-numbers, the wall air concentration profile follows

more or less the same profile as along the axis. Because of adhesion to

the side wall and lower velocities, the jet first reaches the bottom near

the wall and then at the axis of the chute. Therefore, the place of impact

and the maximum air concentration after mixing, are a little nearer to

the offset than they are on the channel axis. In the decreasing limb, the

air concentrations are slightly lower than along the channel axis.

For Froude -numbers higher than about Fr- 7, the nappe separates from

the side walls due to shock-waves from the deflector (conditions similar

to that with side deflectors, see 3.3.3) . For this reason, the air con­

centration is at first very high because the nappe is aerated also from

the sides. However, this has no significant consequences f~rther down­

stream. In the decreasing limb, the concentrations are again slightly

smaller than along the axis.

4.2 Criterion against Cavitation

The criterion for aeration to prevent cavitation erosion is based on

the results of Peterka (1955). Tests of concrete specimens were made in a

Venturi-type cavitation apparatus , with and without air injection. The

test period was 2 hours and the velocity through the throat of the Venturi

section was over 30 m/s. The weight losses of the specimens were plotted

against the percent (in volume) of air entrained in the flow (Fig. 27 A).

For 7.4 percent of entrained air there was no measurable weight loss;

the losses were greatly reduced for a value of air concentration higher

than 2 percent.

Additional investigations, also by Russian researchers, show that the

needed air concentration is also a function of concrete strength and the

8

7

6

• c: .. lJ

~ Q. .....

" lJ

2

0

•

\ ·' ~ r-........

~

0 0.1 0. 2

w [ kgl •

- 60 -

0

t 0 5 10 15 20 25 • m/s

B: Relation between all owable veloci­ties of a cavitation flow, the con­crete strength and the air content C* =OAiriOwater (according to Gal'­perin, R.S. et al., 1971)

-A: Air content versus cavitation 0. 3 weight loss of concrete specimens

(according to Pete rka, A. J ., 1955)

Fig. 27 Effect of entrained air on cavitation - protection .

velocity of flow (Fig. 27B). The investigations by Ball (1976) show fur­

ther, that the maximum allowable velocity of cavitation free flow depends

on the size and shape of surface irregularities.

Because knowledge of the relations between necessary air concentration,

allowable velocity, concrete strength and surface irregularities is only

very rudimentary, at present the criterion of a minimum air concentration

of .between 6 and 8 % near the channel bottom is appl ied. However, it is

not exactly defined as to what "near the bottom" means.

In the model tests for the Sayano-Shushenskoe dam spillway (Kaveshni­

kov, A. T. and Lentyaev, L.D. , 1980) the authors defined the near-bottom

zone in a 1:13 model as 10 rt111 (13 cm in prototype) from the bottom. In pro­

totype measurements at Bratsk dam spillway, the air concentration was al­

most the same at elevations of 2 cm and 7 cm and slightly higher at an

elevation of 15 cm from the bottom (Fig. 28). In the model tests the mea­

surements were made as close to the bottom as possible (limited by size

of gauge), i .e. 4mm or lOcm in the prototype.

~

~~,

' ....... .....__ + -"'

- 61 -

100

80 •

60 ....

~ 40 .... 20 t 0

"-"-

"-... ....... "K

I~ -._:i--~ - -""W

0 10 20 30 0 10 20 30

----- q [m3;s -m]

• 2 cm above the spi lll~ay surface

+ 7 cm above the spi lll~ay surface

~ 15 cm above the spi lll~ay surface

Fig . 28 Volumetric air content in water C* (percent) , of Bratsk spillway versus specific discharge q [m3/s·m] (according to Semenkov, 1973)

4.3 Determination of Air-Slot Spacing

4.3 . 1 Applying P.nti-Cavitation Criterion to the Measurements

According to the preceding chapter, new aeration is necessary if the

air concentration near the bottom becom!:' le~than~ t~. Applying

this criterion to the measurements (see 4.1.3), gave the slot spacing

diagram of Fig. 29.

Obviously, the distanceD between two air-slots depends directly on the

mean flow velocity vm and not on the specific discharge (although, of cour­

se, low discharges are connected with low velocities). After deciding the

maximum alowable velocity 1~ithout aeration, 1~hich depends on surface flo~1

aeration, concrete strength and concrete surface irregularities, the dis­

tance between air-slots can be read from its diagram . For a velocity of

e .g. V m = 25 m/s, D is between 23 m amd 29 m a 1 ong the axis and between

20 and 24 m near the wall . For higher ve l ocities D becomes longer so the

minimum allowable velocity l'lill determine the air-slot spacing.

When applying this diagram to the prototype, the different conditions

between model and prototype have to be considered. Rather than giving exact

design criteria , the diagram gives a first estimation for the spacing bet­~leen a i r s 1 ots .

- 62 -

4.3.2 Additional Considerations

Gradient of air concentration near the bottom: As mentioned in chapter

4.2, it is not precisely defined as to ~1hat "near the bottom" means. The

criterion of 6 to 8% air at a distance of l0cm(4mm) from the bottom,

is rather arbitrary. Hence, the air concentration 25 cm (10 nun) above the

bottom was also looked at to study the influence of the definition of the

"near bottom zone". Table 3 sh01~s the results for the specific discharge

q = 40 m3/s·m.

q V m D x = 29 m x = 34 m

40 m3/s·m 28.3 m/s 27 + 33 m c = 19 % c = 14 %

40 m3/s·m 24.8 m/s 23 + 29 m c = 4 % c = 10 %

Table3 Air concentration (percent) 25cm above the bottom D: Spacing between air-slots according to Fig. 29 .

While the air concentration gradient is high for vm = 28.3 m/s, the

criterion of 6 to 8 % air 25 cm above the bottom (instead of only 10 cm)

would not give a much longer inter-slot distance for vm=24.8m/s.

Differences between mode l and prototype:

- Air demand in the prototype is a little higher than expected according

to the Froude analogy. The correction factor f2 is between 1.0 and l .5

(see 2.3.6).

- Surface air entrainment is more developed in the prototype than in the

model (see 4.1. 1). In the prototype more air will be in the near bottom

zone than in the model. This will of course also lengthen the inter­

distance between air-slots.

The distribution of air concentration is dominated by the effects of

turbulence and buoyancy. Since the size and uplift velocity of the air

bubbles is almost the same in model and prototype, the ratio between

uplift velocity and flow velocity is higher in the model than in the prototype. Therefore the air losses are higher in the model than in the prototype.

- The surface roughness, expressed by the equivalent roughness height

e(mm), has some influence on the turbulent boundary layer and there-

1.0

..... 36 E ..... 32 Cl

A 28

21.

20

1.0

36 ..... E

...... 32 Cl

28 A

21.

20

- 63 -

0 CONCENTRATION ALONG AXIS

I .-c .6· ·.~-·- . _.-. I

f----t-----t---1-l .- I ! -·- . .:... .-· t l -·--· -··~--· -· ·- .-22 21. 26 28 30 32 31.

Vm(m/s) ....

* q = 40 m3/s ·m

... q = 60 m31s·m

"' q = 80 m31s·m

® CONCENTRATION NEAR SIDE- WALL ( 0. 50 m 2cm IN THE MODEL}

-· 22 21. 26 28 30 32 31.

V m { m/s ....

Fig . 29 Air-s 1 ot spacing di agramm

Criterium: C [%] > 6 - 8 %, 10 cm above the bottom

- 64 -

fore on the air concentration (see 2.3.3). The model corresponds to a

prototype with an equi va 1 ent roughness height of 1 . 0 ~ e: ~ 1 . 5 mm. For

a rougher spillway surface the air concentration along the bottom would

be higher. Estimates can be made with the diagrams of chapter 2.3 .3 .

(Note: a rougher surface need not be advantageous, because it also in­

creases the danger of cavitation) .

Other aspects :

After a distance D from the air-slot, there is still significantly more

air in the flow than upstream of the first air-slot. This means that

for successive aerations there is an excess of air in the flow.

Flow aeration is always connected with energy losses due to energy dis­

sipation in the impact zone and air entrainment . The test results showed

that after a distance D from the air-slot, the mean velocity is lower

than upstream from it. Therefore, consecutive aerations will be less

effective than the first one, an effect that is also reported in the

literature (see Quintely, 1980) . For this reason, the distance between

two air-slots should not be under-·estimated for this will lead to an

uneconomic design without increasing security.

4.3.3 Results from other Spillways

Barragem Foz do Areia (Brasil): With a slope of 1:4 and maximum specific

discharges higher than q = 100 m3;s-m, the conditions of the spillway

are equivalent to those of San Roque dam. The air-slots are of the offset

type with an over-all height of 1.80 m. The distance between the first and

the second air-slot is 72 m, between the second and the third one is go m

(Pinto, N.L., 1979) .

Bratsk dam spillway: The spillway is very steep with a slope of 1: O.B.

The air- slots are deflectors with a height of 0.45. The distances between

the air-slots are 41.4 m and 33.7 m.

Nurek dam spillway_: TI1e spillway has a convex curvature with a s 1 ope con­

tinuously increasing from 1 :5.5 (lOO) to 1:2 (26°). The distance bet-

- 65 -

ween air-slots (grooves) increases from 10 m to 15 m.

Although the distance 0 between air-slots varies in these examples

from 10 m to 90 m, it can be seen t hat the distance D i ne reases in the

direction of flow. The large differences in spacing may be for the fol-

1 m~i ng reasons:

different sl opes of the spillways

- different effectiveness of the air-slots

differences in modelling technique (scale effects, roughness effects

etc.)

uncertainity of the anti-cavi tat ion cri terion and diffe rent ways of

a pp lying of it.

In comparing these test results with those of the Barragem Foz do

Areia, the considerations of t he preceding chapter are confirmed, i . e .

the slot spaci ng di agram (Fig.29) gives rather conservative estimates.

- 66 -

5. SUMMARY AND CONCLUSIONS

The Laboratory of Hydraulics, Hydrology and Glaciology of the Swiss

Federal Institute of Technology, Zurich, was commissioned by Electrocon­

sult , Milan, Italy, to carry out model tests for the San Roque Dam Project,

Philippines. With a l :25 scale hydraulic model, air-s l ots for flow aera­

tion were investigated with the aim to prevent cavitation erosion of the

dam spillway. Based on the hydraulic model tests and an extensive litera­

ture study, conclusions can be made concerning:

the main parameters affecting air demand of an air-slot

a comparison of air-slots with different shapes

the optimal shape and size for the air-slot of the San Roque dam

spillway

the principles and diagrams to determine air-slot spacing

the differences between model and prototype

the influence of an air-slot on the water flow (shock-waves, trajec­

tory of the nappe after the ski - jump and

the equipement and strategy for measurement of the performance of the

prototype.

Main parameters affecting air demand: To correctly estimate the air de­

mand of an air-slot, the sub-pressure in the air space under the nappe

must be considered . This sub-pressure is strongly influenced by the~

supply system. Different air supply systems produce different sub-pressu­

res and thus different air demands.

The main hydraulic parameter is the velocity upstream of the air-slot

and not specific discharge . Air demand increases with incr easing velocity,

independent of specific discharge.

For deflectors there exists an optimal height, i.e . for deflectors

higher than the optimum, air demand does not increase further. This height

depends on the flow depth, so the .significant parameter is the ratio of

deflector height to flow depth.

- 67 -

Determination of shape and size of the air-slot: The different types of

air-slots investigated can be characterized as follows:

A Deflector

C Offset

B Offset with deflector

-8 0 groove with deflector

GROOY£

Air demand of a groove is determined by the deflector, while the groove

provides space for the air supply . However, the groove fi l ls with water

from falling droplets and from water adhering to the side walls and trick­

ling into the groove. Because water filling can not be prevented by reason­

able means, this type of air slot should be avoided .

The offset without a deflector resulted in an .air demand which was too

~because not enough sub-pressure was produced and the exposure of the

nappe to the air was not sufficient .

The deflector and offset combined with deflector showed similar air de­

mands f or high discharges. Over the whole range of discharges the combina­

tion offset with def lector gave superior results . The deflector dominates

during operation at small discharges. The offset provides space for the

air supply and enlarges the trajectory of the jet at high discharges . The

selected combination was a 0.75 m high offset with a 0.50 m high deflector.

Air-slot spacing : Results of the tests and the criterion that air concent­

ration near the bottom (10 cm above spillway surface) must not drop below

6 % to 8 %, gave the slot spacing diagram of Fig. 29. The distance 0 bet­

ween two air-slots depends directly on the mean flow velocity vm. After

deciding the maximum allowable velocity without aeration (which depends on

surface flow aeration,·concrete strength and concrete surface irregulari­

ties), the distance between air-slots can be read fom this diagram.

- 68 -

Differences between model and prototype: The hydraulic model tests were

based on the Froude analogy. When considering air-slot spacing, additional

aspects must be taken into account . The5e .are:

- surface air entrainment is more extensive in the prototype

- air demand in the prototype is between l .0 and 1.5 times higher than

in the model

- the model roughness corresponds to a prototype with an equivalent rough­

ness height of 1.0 ~ £ ~ l .5 mm. For a rougher spillway surface the

air concentration along t he bottom would be higher

the ratio of flow velocity to uplift velocity is higher in the proto­

type than in the model.

Al l these aspects will l engthen the required inter-distance between

air-slots, i.e . the slot spacing diagram gives a first, rather conserva­

tive estimate .

Influence of the air-slot on f l ow conditions :

- Shock waves caused by the deflector, have to be expected . The exact

pattern in the prototype can not be predicted by the hydraulic model

tests because of the difference in channel width. Maximum wave height

occurs along the channel axis and not at t he side walls . For a specific

discharge q = 120 m3/s·m, the maximum elevation of the nappe (i nc luding

maximum shock wave height) was 5.6 m above the spillway bottom just

downstream of the offset.

- The trajectory of the nappe after the spillway ski - jump is also influ­

enced by the air slots because of the energy losses connected with

aeration. Under unfavourable conditions, the flight distance of the nappe

to the lower pool may decrease (Semenkov, V.f~. and Lentyaev, L.D., 1973).

Equipment and program for measurements in the prototype: Because knowledge

of model prototype conformity is rather rudimentary with regard to air-slot

design, some measurements in the prototype are suggested. The following

parameters shou ld be investigated:

- 69 -

specific discharge

air demand and sub-pressure under the nappe and

air concentrations near the bottom.

Specific discharge can be determined from the water level in the basin

and the operating configuration of the gates. Air demand can be estimated

by measurement of the velocities in the air vent. Measurement of the air

demand must be connected with measurement of the sub -presure in the air

space under the nappe. The sub-pressure can easily be measured with piezo­

meter holes constructed in the spillway bottom. Air concentration can best

be measured by sampling the air-water mixture and separating it into two

volumetric portions. Sampling can be achieved with a gauge similar to a

Pitot tube (without an opening for the static water head) and small suction

pump (see Volkart, 1978). Because the sample intake velocity must equal

the flow velocity, the flow velocity must also be measured . This can be

done by the absorption gauge which connected to a piezometer tube without

the pump, indicates the energy head.

Aknowledgement

The presented report is a revised copy of the VAW report 776

from may 1981.

* Model Tests and Report A. Siegentha1er, Eng.

Editing Dr. G.M. Smart

Drawings V. Suter

Supervision Dr .P.Vo1 kart

*

- 70 -

References

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Beichley, G.L.: "Cavitation Control by Aeration of High Velocity Jets". Proceedings ASCE, Vol.lOl, No. Hy7, July 1975.

V Bormann, K.: "Der Abfluss in Schussrinnen unter BerUcksichtigung der Luftaufnahme". Beri cht Nr. 13 der Versuchsansta lt fur Wasserbau, Obe rnach , 1968.

Gal' perin, R.S. et al.: "Cavitation in Elements of Hydraulic Structures and Methods of Controlling it". Hydrotechnical Construction, August 1971.

Kaveshnikov, A.T. and Lentyaev, L. D.: "Flow Aeration of the Operating Spillway at the Sayano- Shushenskoe Hydroelectric Station". Hydro­technical Construction, January 1980.

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Peterka, A.J.: "Effect of Entrained Air on Cavitation Pitting". Procee­dings Minnesota International Hydraulics Convention, USA, 1955.

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Vouintela , A.C.: "Flow Aeration to Prevent Cavitation Erosion". !~ater Power & Dam Construction, January 1980.

Semenkov, V.M. and Lentyaev, L.D.: "Spillway with Nappe Aeration". Hydroelectrical Construction, t~ay 1973.

'"'Volkart, P.: "Hydraulische Bemessung steiler Kanalisationaleitungen unter Berucksichtigung der Luftaufnahme". Mitteilung Nr. 30 der Versuchs­anstalt fUr Wasserbau, Hydrologie und Glaziologie (VAW) an der ETH-Zurich, 1978 .

IAHR: Proceedings of the Fourteenth Congress, Vol. 5, Paris, 1971.

!COLD: Proceedings of the Thirteenth Congress, Vol. 3, New Delhi, 1979.

- 71 -

V Eccher L., Siegenthaler A.: "Spillway Aeration of the San Roque Project". Water Power and Dam Construction, London, September 1982.

/ Vischer D. , Volkart P. , Siegenthaler A.: "Hydraulic Modelling of Air Slots in Open Chute Spillways". Int. Conf. on the Hydraulic Modelling of Civil Eng. Structures, BHRA Fluid Engineering, Coventry, England, September 1982.

-/volkart P.U.: "Self Aerated Flow in Steep, Partially Filled Pipes". Journal Hydraulic Division ASCE, Vol. 108, September 1982.