joseph lawson dissertation

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University of Brighton Joseph Lawson 10808671 1 Faculty of Science & Engineering School of Environment & Technology Final Year Individual Project in part fulfilment of requirements for the degree of MEng (Hons) in Civil Engineering Investigating the use of Converging Ski-Jump Spillways and their effects on the characteristics of Hydraulic Jump and Energy Dissipation. By: Joseph Lawson 10808671 Supervised by: Dr. Heidi Burgess 7 th May 2014

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Page 1: Joseph Lawson Dissertation

University of Brighton Joseph Lawson 10808671

1

Faculty of Science & Engineering

School of Environment & Technology

Final Year Individual Project

in part fulfilment of requirements for the degree of

MEng (Hons) in Civil Engineering

Investigating the use of Converging Ski-Jump Spillways and their effects on the

characteristics of Hydraulic Jump and Energy Dissipation.

By: Joseph Lawson

10808671

Supervised by: Dr. Heidi Burgess

7th

May 2014

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Declaration

I Joseph Lawson, confirm that this work submitted for assessment is my own and is

expressed in my own words. Any uses made within it of the works of other authors in

any form (e.g. ideas, equations, figures, text, tables, programmes) are properly

acknowledged at the point of their use.

I also confirm that I have fully acknowledged by name all of those individuals and

organisations that have contributed to the research for this dissertation.

A full list of the references employed has been included.

Signed: …………………………….

Date: ……………………………….

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Acknowledgements

Throughout the course of this dissertation, I have gained help and guidance from

many University of Brighton lecturers, help from my friends, and continued support

from family.

I would like to express my utmost gratitude in particular, to my dissertation

supervisor, Dr. Heidi Burgess, for all her help, guidance, patience and enthusiasm

throughout this project. I would also like to express my gratitude to all the laboratory

technicians, in particular, Dominic Ryan, who continually supported me though all

laboratory experiments.

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1.0 Abstract

A spillway is a structure constructed on the face of a dam. Ski-jump spillways are the

only hydraulic structures which can efficiently dissipate energy where take-off

velocities exceed 15-20m/s. The design of the ski-jump spillways forms a jet which

causes large amounts of scour around the point of impact, which can be avoided by

converging jets. This research project aims to investigate the use of converging ski-

jump spillways. Modelling both horizontal and vertical converging spillways, across

a range of discharges of flood capacity and analysing the data recorded. Based on the

experiments conducted, the following parameters were analysed: (1) the energy

dissipation in phases two and three; (2) the energy dissipation in phases four and

five; (3) the length of hydraulic jump and length of spilling basin; (4) the

downstream water depth; (5) the characteristics of jet disintegration and air

entrainment; and (6) the effects of cavitation . The majority of the results presented

larger amounts of energy dissipation in phases two and three, and therefore less

scour/erosion would occur on the stilling basin and downstream. The results also

showed that the stilling basin length could be reduced. Although cavitation was

observed on the models with higher energy dissipation.

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Table of Contents

Acknowledgements ...................................................................................................... 3

1.0 Abstract .................................................................................................................. 4

2.0 Introduction ............................................................................................................ 6

3.0 Literature review .................................................................................................... 8

3.1 Energy Dissipation ............................................................................................. 8

3.2 Hydraulic Jump and Froude Number ............................................................... 11

3.3 Measurement of the Length of Hydraulic Jump .............................................. 14

3.4 Cavitation ......................................................................................................... 15

4.0 Methodology and Design ..................................................................................... 20

5.0 Results .................................................................................................................. 28

6.0 Analysis of Results and Discussion ..................................................................... 41

7.0 Conclusions and Future Work .............................................................................. 51

8.0 References ............................................................................................................ 53

9.0 Appendices ........................................................................................................... 57

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2.0 Introduction

This research project is focused within the area of hydraulics. In particular, this

project aims to analyse hydraulic structures and the variation of energy dissipation

across spillways and stilling basins.

A spillway is a structure which is constructed on the face of a dam. It facilitates the

control of downstream water flow, including removing the risk of flood waters

exceeding reservoir capacities. The most common types of spillways are; the ogee,

overfall and breast-wall (Azmathullah & Deo, 2005), however, for energy dissipation

purposes these are relatively in-efficient; therefore trajectory, or ski-jump spillways

tend to be used. A ski-jump spillway is the only type of structure which can

efficiently dissipate water energy from a dam, where take-off velocities exceed 15-

20m/s (Heller, Hager & Minor, 2005). Ski-jump spillways are widely used,

particularly in areas which experience high levels of flood water. This is due to the

design of the hydraulic structure, in which water can be transferred in a hydraulically

safe manor, and it’s energy dissipated, without affecting the integrity of the structure

(Heller, Hager & Minor, 2005). A ski-jump spillway transfers water by throwing a

water jet away from the spillway edge, through the air, and into a plunge pool or

stilling basin, downstream and dissipating energy as it’s released, (Azmatullah &

Deo, 2005). The design of a ski-jump spillway encourages a high-velocity water jet

to impact on the stilling basin below. This causes a large amount of scour, both

upstream and downstream of the site of impact of that jet (Schmocker et al., 2008).

The impinging water jet produces a breaking hydrodynamic pressure fluctuation on

the downstream rock bed. This can trigger a hydraulic jacking action, in which small

pieces of rock mass can be broken apart and swept downstream, (Azmathullah &

Deo, 2005). This process is known as erosion and can have significant

geomorphological implications to the river basin over long periods of time, (Kehew,

1982).

‘After a full analysis of the current literature that has been published on spillways

and hydraulic structures to date, it is apparent that there is a need to design a more

efficient structure that is less disruptive to the surrounding habitats. In this

investigation, it is necessary to design and test a number of new structures that may

provide a more successful solution than is currently available.’

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This research project aims to investigate the use of converging ski-jump spillways.

More specifically, this project will test both horizontal and vertical converging

designs and analyse their effects on water energy dissipation compared with non-

converging structures. The convergence of two or more jets of water, from ski-jump

spillways, reduces the embodied energy within the jets of water, to the atmosphere,

therefore reducing the effects of erosion to the stilling basin where the water is

transferred, (Steiner et al., 2008). Studies have shown that energy losses that take

place in the period immediately after the ski-jump, when the water is travelling

through the air, directly affect the amount of erosion that takes place within the

plunge pool area, (Nov k & C belka, 1981).Thus having less environmental and

ecological disruptions to the habitats below, (Graff, 2006).

This research project included practical experimental testing of converging and non-

converging ski-jump spillways, within a controlled flume. A hydraulic jump is

formed and energy dissipations were calculated from the raw data collected. The

Hydraulic jump phenomenon occurs during the flow transition from a supercritical

flow to subcritical flow. Large energy losses occur during a hydraulic jump due to

the high turbulent intensity (Chadwick & Morfett, 2013). The energy dissipations of

each spillway were modelled and the results were tabulated. Analytical testing was

carried out and a full examination of the information has been concluded to compare

for a range of hydraulic discharges.

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3.0 Literature review

3.1 Energy Dissipation

The classic overflow spillway, i.e ogee or overfall are smooth and have a streamlined

surface and overflow transitional section into the stilling basin. Therefore

comparatively, only a small percentage of energy can be dissipated on the spillway

surface, where an accelerated movement of water passes. Consequently the majority

of the energy dissipation will take place in the hydraulic jump. This high localised

energy dissipation produces large forces on the stilling basin and requires one with

significantly large dimensions, and high construction and upkeep cost.

To lessen these forces, alterations to the spillway, and different overflow design

solutions have been investigated, providing energy dissipation at various phases

during the passage of discharge ov bel a, . For example baffles can

be used on the spillway surface and a ski-jump to the end of the spillway. These

produce an intensive energy dissipation in the phases during and before the impact

with the stilling basin. As a result the forces acting upon the stilling basin, are now

just residual energy which can be dissipated in a much smaller and inexpensive

stilling basin. ov and bel a (1981) had produced research and concluded that

if a ski-jump spillway was designed where the overflow jet was projected far enough

away from the edge of the jump, aided by a particular spillway surface, and the jet

falls upon a firm rock bed, then it could be possible to not have a stilling basin at all.

The Froude law of similarity (Avery & Novak, 1978) can be used to most efficiently

model the energy dissipation over a spillway for the most economical and

technological designs. The Froude law is explained in more detail in section 3.2.

Formalised by ov and bel a (1981), there are different phases of the passage

of discharge over a spillway and stilling basin, which incorporate a ski-jump and

baffles. The five phases are:

1. The phase where the water flows down the spillway, from the crest down

to the edge of the spillway.

2. The phase where the water takes off from the edge of the spillway, travels

through the air and hits the surface of downstream water.

3. The phase of impact with the stilling basin pool.

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4. The phase of the hydraulic jump in the stilling basin pool.

5. The phase of transition from hydraulic jump and into conventional river

flow.

Energy Dissipation in the Second Phase

During the second phase where the water takes off from the edge of the spillway,

travels through the air and hits the surface of downstream water, there are three main

types of energy dissipation. These are air resistance, internal friction and in

particular, the collision of different separated overflow jets and the water particles

within.

The ski-jump spillway together with a combination of the three main types of energy

dissipation, disperses and aerates the overflow jet in supercritical flow. The

effectiveness of this energy dissipation is increased by the compression of entrained

air bubbles as part of a colliding jet mixture, ( ov bel a, . hese ets

apply much less stress on the stilling basin then an unaerated compact jet.

However the dispersed and aerated overflow jet does not substantially increase the

energy dissipation during phase two (the fall); the energy dissipation is around 12%,

as discovered by Horeni (1956). Although the dispersed and aerated overflow jet

does contribute greatly to energy dissipation upon impact with the stilling basin pool,

phase three. What does produce the high energy dissipation in phase two are the

multiple colliding jets themselves.

The collision of these jets is a highly complicated hydraulic problem, but by treating

it as a vertical sum of momentum problem, with the two jets being symbolised as

solid colliding bodies, on a two-dimensional plane, an approximation of the specific

energy loss can be calculated. Faktorovich (1952) derived such an equation, which is

expressed in equation 3.1.1 below:

(eq. 3.1.1)

Where k2 is the specific energy loss, qI and qII are specific discharges relating to jets

I and II, and vI and vII are the jets mean velocities during collision.

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The above equation has been used for many years, by such people as Komora (1969)

and has proven to produce an adequate approximation for specific energy loss.

However the actual energy loss for this hydraulic jet collision problem is actually

larger than Faktorovich's equation estimates. This is due to volumetric alterations in

the entrained air bubbles of the aerated jets. The rapid compression when the jets

collide contributes an additional energy loss ov and bel a, .

Many engineers such as Faktorovich (1952) and Roberts (1980) have produced a

variety of overflow spillway designs involving the jet collision principle to dissipate

energy intensively. Some of Faktorovich's (1952) designs incorporated the use of

bottom outlets combining with the spillway flow. Whereas many of Roberts (1980)

designs incorporated a few baffles along the spillway surface and a ski-jump beneath.

In 1934 Roberts design was used to construct the Vaalbank and Loscop dams in

South Africa. Figure 3.1.1 below depicts two of Skoupy's designs, figure 3.1.1a

shows a design using deflectors and figure 3.1.1b shows a design combining

deflectors and baffles at various locations on the spillway. This design in figure

3.1.1b can significantly increase the energy dissipated in phase 1 and 2.

Figures 3.1.1 - Spillways with baffles and deflectors (Horsky, 1961)

Energy Dissipation in the Third Phase

During the third phase the water impacts with the stilling basin pool. The energy

dissipation in this phase is due to the water mass colliding with the downstream

stilling basin pool. It is also due to the compression of entrained air bubbles within

the overflow jet undergoing rapid pressure increase at the point of impact. The

energy dissipation increases with greater aeration and dispersion of the overflow jet.

It is therefore logical to aim to achieve an overflow jet which maximises the aeration

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and dispersion during phase two. However in phase three these energy losses can

only be achieved if the downstream pool is sufficiently deep at point of impact.

3.2 Hydraulic Jump and Froude Number

The Hydraulic jump phenomenon occurs during the flow transition from a

supercritical flow to subcritical flow. Large energy losses occur during a hydraulic

jump due to the high turbulent intensity. It is not possible to use the specific energy

method for this phenomenon, therefore the momentum and continuity equations are

used to establish a relationship between upstream depth y1 and downstream depth y2,

which also incorporates the Froude Number, Fr (Chadwick & Morfett, 2013). A

Reference diagram for the momentum and continuity equations is shown in figure

3.2.1 below:

Figure 3.2.1 - Reference diagram for the momentum and continuity equations (Nalluri and

Featherstone, 2001).

The Froude Number in its simplest form is shown in equation 3.2.1 below:

√ (eq. 3.2.1)

Where V is the flow velocity, g is the acceleration due to gravity and L is a

characteristic dimension. For the experiments carried out in this investigation the

characteristic dimension was expressed as yi which was the depth at a location i in

the channel. This produced the equation 3.2.2 below:

√ (eq. 3.2.2)

The basic principle of the Froude Number was that it classifies the regime of flow.

The Froude Number has become one of the most important figures in Hydraulic

Jump and many other hydraulic structure analyses (Mahmodinia et al., 2012). The

main reason for the Froude Number being so important is it can directly classify the

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regime of flow, and can produce a link between upstream and downstream

dimensional properties. There are three classifications of the Froude Number which

are Subcritical flow, Critical flow and Supercritical flow.

Subcritical flow is when the flow velocity V is less than the critical flow

velocity Vc. This is when Fr < 1, and downstream control effects upstream

water level.

Critical flow is when the flow velocity V is equal to the critical flow

velocity Vc. This is when Fr = 1, and undular standing waves are created by

unstable flow.

Supercritical flow is when the flow velocity V is greater than the critical

flow velocity Vc. This is when Fr > 1, and downstream control do not effect

upstream water level, since flow disturbances travel downstream only, due

to the water velocity being greater than the wave velocity. This is different

to subcritical flow, where flow disturbances travel downstream and

upstream.

The United States Bureau of Reclamation (USBR), produced a table which clearly

classifies the type of hydraulic jump, in respect to its upstream Froude Number and

presents approximate energy dissipations for each type. This table is shown in figure

3.2.2:

Hydraulic Jump Classification (USBR, 1955)

Type of Jump Froude Number, Fr Energy Dissipation

Undular Jump 1.0 - 1.7 < 5%

Week Jump 1.7 - 2.5 5 - 15%

Oscillating Jump 2.5 - 4.5 15 - 45%

Steady Jump 4.5 - 9.0 45 - 70%

Strong Jump > 9.0 70 - 85%

Figure 3.2.2 - Hydraulic Jump Classification and Energy Dissipations (USBR, 1955)

As stated above a relationship can be established between upstream depth y1 and

downstream depth y2, using the momentum equation. The resulting equation for y2 in

terms of y1 is shown in the equation 3.2.3 below (Streeter and Wylie, 1981):

(

) (√

) (eq. 3.2.3)

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and y1 can also be found in terms of y2 as shown in the equation 3.2.4 below:

(

) (√

) (eq. 3.2.4)

The equations 3.2.3 and 3.2.4 above are true for rectangular horizontal channels with

constant channel width and assuming all wall and bed friction are negligible

(Chanson,1995).

The energy loss through the hydraulic jump can be determined by evaluating

equation 3.2.3 in terms of y1. Therefore an equation for the change in energy or

energy dissipation is shown in equation 3.2.5 below:

(

) (

) (eq. 3.2.5)

By substituting in discharge, , an energy dissipation equation can be found in

terms of q and y, shown in equation 3.2.6 below:

(

) (eq. 3.2.6)

Equation 3.2.3 can be rewritten with Fr12 as the subject, shown in equation 3.2.7

below:

(

) (eq. 3.2.7)

and equation 3.2.7 can be found in terms of q and y, shown in equation 3.2.8 below:

(eq. 3.2.8)

By substituting in equation 3.2.7 and equation 3.2.8, an energy dissipation equation

can be found in terms of y1 and y2 only, shown in equation 3.2.9 below:

(eq. 3.2.9)

For investigation and experimental purposes it is very useful to have equation 3.2.9

to calculate the energy dissipation purely in terms of the flow depth parameters. It

can be seen in equation 3.2.9 that the relative height of the jump, y2-y1 cubed, that

with increased relative height of the jump, the energy dissipation is sharply

increased. Therefore if the aim in an investigation is to produce a large energy

dissipation, it is also an aim to achieve an increased relative height of the jump.

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The efficiency of the hydraulic jump can be calculated using the energy upstream, E1

(calculated using equation 3.2.11) and the energy downstream, E2 (calculated using

equation 3.2.11). The efficiency of the hydraulic jump, η is shown in equation 3.2.10

below:

(eq. 3.2.10)

(eq. 3.2.11)

(eq. 3.2.12)

3.3 Measurement of the Length of Hydraulic Jump

The length of the hydraulic jump has typically been difficult to measure. The

definition of this length is the horizontal distance Lj from the start of the roller

upstream, in supercritical flow, to the downstream section where the mean surface

water achieves an approximate maximum flow depth, and is reasonably level, in

subcritical flow (Ead & Rajaratnam, 2002). Consequently a sizable human error is

usually introduced with the determination of this measurement, since investigating

engineers determine the end of the jump in different locations. To normalise the

length of hydraulic jump, equations have been produced to match the values from

experimentation. Chaudhry (2008) produced such an equation to approximate the

length of jump, shown in equation 3.3.1 below:

[

] (eq. 3.3.1)

Due to the difficulties in determining the length of jump, involving residual

turbulence and surface waves at the end of the hydraulic jump, studies have been

produced to find an improved and easier parameter to determine a hydraulic jump

length characteristic measurement. Many studies including Carollo and Ferro (2007),

Ead and Rajaratnam (2002) and Rutschmann and Hager (1990) support this need for

an improved measurement and all state that the 'length of roller' would be easier to

measure. This is due to the end of the roller being easy to observe, particularly in

steady flow conditions. The definition of the length of roller is the horizontal

distance Lrj from the start of the roller upstream, in supercritical flow, to the

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downstream point of surface stagnation (Carollo & Ferro, 2012). This is represented

graphically in figure 3.3.1 below:

Figure 3.3.1 - Graphical depiction of Jump Length and Roller Length (Ead & Rajaratnam, 2002).

The length of roller Lrj can be calculated by equations 3.3.2, 3.3.3 and 3.3.4. The

applicability of the relationships are verified by Carollo (2007).

(

) (eq. 3.3.2)

(

) (eq. 3.3.3)

( ) (eq. 3.3.4)

Where is a coefficient equal to 4.616, 0 is a coefficient equal to 2.244, and b0

depends on the ratio between surface roughness ks and h1. The coefficients and 0

were found through experimentation by Carollo (2007). In this research project a

negligible surface roughness ks was assumed in all experiments, therefore these

equations were not valid in this project.

3.4 Cavitation

Cavitation Background

Many hydraulic structures including spillways are affected by cavitation, involving

several mechanisms of damage. The process of cavitation is where a void or bubble

forms within a liquid. Falvey (1990) explained cavitation as the change of state from

a liquid to a vapour, by reducing the local pressure, whilst keeping a constant

temperature. The reduction in local pressure can be from vortices or turbulence in

flowing water.

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Within a hydraulic structure, the water flow can contain impurities and air bubbles of

various types and sizes, ranging from microscopic to a few centimetres. These

microscopic impurities and air bubbles are essential to initiate cavitation, and are part

of what causes the damage to hydraulic structures.

The occurrence is a property which can also be used to describe cavitation. For

instance, increases in the flow velocity, decrease the flowing water pressure. A

critical condition is achieved here, at the point where cavitation begins, which is

called incipient cavitation. Likewise if flowing water pressure increases and flow

velocity decreases then another critical condition is achieved called desinent

cavitation, (Falvey, 1990). In practical purposes the distinction between these two

conditions is not relevant; however in laboratory investigations it becomes more

significant. There is also a third critical condition known as supercavitation,

developed flow or cavity flow, which is when individual cavitation bubbles rapidly

transition into large cavitation voids.

Due to the critical nature of cavitation and the occurrence of cavitation to occur and

to supercavitate, a parameter was defined to explain the cavitation in a system,

known as the cavitation index, σ. The Bernoulli equation for steady flow between

two points is used to derive the equation for the cavitation index, and the full

derivation can be found in the ‘ avitation of hutes and Spillways’ Falvey, 0 .

Therefore the cavitation index is given in equation 3.4.1 below:

(eq. 3.4.1)

Where E0 is the potential energy at a reference point, Z is the elevation vertical, ρ is

the fluid density, g is the acceleration due to gravity, Pv is the fluid vapour pressure

and V0 is the fluid velocity at a reference point. If Z is equal to Z0 then the equation

above can be refined as the following equation below:

(eq. 3.4.2)

Where P0 is the pressure at a reference point.

Evaluation of both equations 3.4.1 and 3.4.2 show that with an increase in fluid

vapour pressure Pv, the cavitation index decreases, therefore increasing the changes

of cavitation and supercavitation.

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For streamline smooth bodies, the peak negative pressure materialises at the

boundary, and pressure measurements made at the surface can be used to estimate

the cavitation index. However for non-streamlined bodies, the peak negative pressure

will materialise within the flow, due to the flow separating from the body (Falvey,

1990).

Figure 3.4.1 depicts the development of cavitation, and their respective cavitation

indexes. The figure therefore shows that cavitation will not occur for a cavitation

index of larger than 1.8, and supercavitation will only occur for a cavitation index of

less than 0.3.

Figure 3.4.1 - Development stages of cavitation (Falvey, 1990).

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Damage from Cavitation

Cavitation can cause a large amount of damage to hydraulic structures, including

spillways. An example of damage to a spillway would be where cavitation forms on

an irregular surface. The damage will occur on the downstream end of the collapsing

cavitation bubble cloud. After some time, a crack or hole will form on the surface of

the concrete and over more time this will increase in size due to the increased

pressure and flow velocity impinging on the downstream edge of the hole. Therefore

bits of aggregate or small chunks will likely start to erode away (Falvey, 1990). The

damage can be substantially increased if the spillway includes reinforcement bars.

This is due to, if the erosion exposed the bars to the high flow velocity, the bars

could start to vibrate; leading to what could be significant breach in the dam

structure, or a catastrophic mechanical failure. In 1983 the Bureau's Glen Canyon

Dam had this happen to its spillways, causing a substantial amount of damage.

It is important to know the factors which effect cavitation damage in order to be able

to design against them. Falvey (1990) outlined some of the main factors as follows:

Cause of cavitation

Location of cavitation damage

Intensity of cavitation

Flow velocity magnitude

Flow air content

Surface resistance to damage

Time of exposure to the cavitation

Damage from cavitation can occur in different locations depending on the shape of

the hydraulic structure surface and its roughness properties. The surface roughness

can be categorised into two main categories, singular roughness and uniformly

distributed roughness. A singular roughness involves a surface which has protruding

irregularities which are smaller than the singular roughness irregularities itself.

Whereas a uniformly distributed roughness does not have singular roughness’s

(Falvey, 1990).

Singular roughness’s are sometimes known as local asperities, of which some

hydraulic structure examples include:

Offset into the flow (figure 3.4.2a)

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Offset away from the flow (figure 3.4.2b)

Abrupt curvature away from flow (figure 3.4.2c)

Voids and transverse grooves (figure 3.4.2e)

Protruding joints(figure 3.4.2g)

The figure below shows graphically some isolated roughness elements:

Figure 3.4.2 - Typical Isolated roughness elements located on hydraulic structures (Falvey, 1990)

The spillways in this investigation are based around dissipating high amounts of

energy. When utilising converging jets in ski-jump spillway design, high amounts of

aeration occurs (see section 3.1). It is known that aerated flows prevent cavitation

damage to some degree, where used with hydraulic structures (Bradley, 1945).

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4.0 Methodology and Design

Methodology

For this research project, experiments were conducted within a scaled flume located

at the University of Brighton. The parameters of the flume were; length (L) equal to

5m, width (b) equal to 300mm, and height (h) equal to 475mm. The discharge

pumped though the flume was part of a hydraulic circuit to provide a steady

discharge recirculation. The flume had a maximum discharge, Qmax equal to 118.8

m3/h, or 0.033 m

3/s, and was measured by an electro-magnetic flow meter, with a

maximum error to the order of 0.2%.

The flow depths (yi) were measured using manometers, with a zero reference at the

base of the flume. The accuracy of the manometers was to the order of 0.5mm and

the pressure heads were read taken to the closest millimetre, due to a fluctuation

turbulent flow. The longitudinal distance i.e. to measure the length of jump/roller,

was measured using a scale along the base of the flume, with a zero reference at the

take-off edge of the ski-jump spillway. The accuracy of this scale was to the order of

1mm. The experiments were all conducted for classic hydraulic jumps, therefore the

inclination angle (α) was equal to 0o.

In the experiment a pre-fabricated ski-jump spillway was utilised, and tested on its

own, to achieve a base energy dissipation result which would act as a comparator for

alternative designs. The dimensions of the spillway are; height of the peak (P) equal

to 310mm and width 300mm, with a flip-bucket with deflection angle (β) and of

radius (R). Deflectors were added to the pre-fabricated ski-jump spillway, to achieve

predicted increased energy dissipation. One model aimed to vertically collide the

overflow jets, and another to horizontally collide the overflow jets.

The flow approaching the spillways was non-aerated, known as "black water". The

jet cavity was naturally aerated to atmospheric pressure. These experiments were

restricted to a horizontal flow channel approach, which kept in unison with bottom

outlet investigations, as such avoiding complications with steeply sloping chute

flows. herefore the data is not li ely to give a true representation of all field

applications with high bed slope angles, although does give a good estimation and

comparative data to other laboratory investigations (Juon & Hager, 2000). Heller,

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Hager & Minor, (2005) considered this sufficient in their studies of ski-jump

spillway hydraulic parameters.

Part of the limitations of using a flume in this project is that sidewall effects may

occur. These sidewall effects may have a negative influence on the results within this

research project. This is due to the narrow flume width, where the water is deflected

by the edges of the flume, causing manufactured results (Chiang et al., 2000). The

impact of this has been ignored for the purposes of this dissertation research project,

however, the impacts of the sidewalls remained constant throughout the experiments,

thus keeping consistency in the data analysed. The effects of the sidewalls were

minimised by the manometers being arranged centrally in the flume width. It was

also noted that the surface roughness was not a variable in this investigation, due to

the bed roughness not being a variable parameter in the hydraulic flume.

The experiments were tested for a scaled design discharge (Q) of 33m3/h

(0.00917m3/s) which was approximately similar to the 1:50 scaled discharge of a

large dam spillway under high flood conditions. The experiments were therefore

tested for 15 discharge increments ranging between 26-40m3/h (0.00722-

0.01111m3/s).

The raw data measured in the experiments were; upstream depth (y0), supercritical

depth (y1) and downstream depth (y2), (see figure 4.1). The downstream gate height

(Hg) was measured for reference purposes to understand the downstream flow depth

required for a hydraulic jump to occur in the required location. The length of jump

(Lj) and length of roller (Lr) were also recorded in order to compare between the

calculated and measured jump/roller lengths.

Figure 4.1 - Depiction of the dimensions y0, y1 and y2 measured by manometers.

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Design

There are two main types of shapes of bucket deflectors in current use worldwide;

the circular-shaped buc et deflector and the triangular-shaped buc et deflector,

(Steiner et al., 2008). The triangular deflector usually produces greater throwing

distances, which can be advantageous in many applications. However for this

investigation it was preferable to have shorter throwing distances, therefore the

circular-shaped deflector design was used. In a full scale model, these shorted

throwing distances usually decrease the dimensions of the stilling basin, which likely

reduces construction costs. A circular-shaped deflector design was also preferable

due to the easier construction when testing, and therefore more reliable data as the

equipment is more robust.

As stated in the methodology a pre-fabricated ski-jump spillway was used as the non-

converging spillway, with moulded plasticine being secured to the pre-fabricated

spillway to form the horizontal and vertical converging aspects of the second and

third spillway models. Figure 4.2 depicts 3D illustrations of the three spillway

models. The models in figure 4.2 were initial designs, which were altered after

preliminary testing of each model at a design discharge (Q) of 33m3/h (0.00917m

3/s).

Alterations were quick and cost effective to model due to the ductility of the

plasticine. However in the full scale model these would be constructed from

concrete. The vertical converging spillway design took aspects from those produced

by ov and bel a , and aimed to achieve 50% of the water flow over the

main bucket deflector, and 50% of the water flow over the additional deflectors.

From the literature reviewed for this project, the horizontal converging spillway

design is new concept. The three different models were tested against each other to

determine the most efficient design for water dissipation.

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Figure 4.2 – 3D illustrations of the three spillway models; Non-Converging, Horizontal Converging

and Vertical Converging respectfully.

This research project was split into two phases. The first phase consisted of the

testing of three different types of spillways.

1. Non-converging spillway – pre-fabricated spillway

2. Horizontally-converging spillways – concept created as an alternative to

current designs from previous literature

3. Vertically-converging spillways – designed from the use of previous studies

ov k & bel a,

The second phase of this research project, was to use a calculated method to design

an efficient model for water dissipation. The calculation chosen for this project is the

‘vertical sum of momentum problem’ formula. his can be found in equation 3. . .

After initial testing of the three different designs, the vertically-converging model

produced the most efficient water dissipation results. herefore, the ‘vertical sum of

momentum problem’ equation was applied to produce a final model for the

vertically-converging spillway concept. This fourth design is known as the modified

vertically-converging spillway for the purposes of this dissertation.

Final technical-design, or as-built, drawings of the three spillway models are shown

in figures 4.3, 4.4 and 4.5 respectfully. The fourth model, and as-built technical-

design drawing, created using the ‘vertical sum of momentum problem’ formula, can

be found in figure 4.6. All dimensions shown are in millimetres (mm).

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Figure 4.3 – Non-Converging Ski-Jump Spillway Design, Technical drawing; Side view and front

view (dimensions in mm)

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Figure 4.4 – Horizontal Converging Ski-Jump Spillway Design, Technical drawing; Side view and

front view (dimensions in mm)

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Figure 4.5 –Vertical Converging Ski-Jump Spillway Design, Technical drawing; Side view and front

view (dimensions in mm)

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Figure 4.6 – Modified Vertical Converging Ski-Jump Spillway Design, Technical drawing; Side view

and front view (dimensions in mm)

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5.0 Results

The experiments of this investigation were undertaken in three laboratory sessions. The three spillway models, the non-converging, horizontally-

converging and vertically-converging ski-jump spillways were all tested in a flume with a discharge (Q) ranging between 26-40m3/h (0.00722-

0.01111m3/s) passing over them, which the raw data for each are summarized respectively in figures 5.1, 5.2 and 5.3.

The raw data which was measured from experiments are upstream depth (y0), supercritical depth (y1) and downstream depth (y2), which can be

seen in figure 4.1. The downstream gate height (Hg) Length of jump (Lj) and length of roller (Lr) were also recorded. All other data was

calculated from the raw data measured, and using the equations shown in the literature review of this report, section 3.0.

Figure 5.1 - Experimental results for the Non-Converging Ski-Jump Spillway

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Figure 5.2 - Experimental results for the Horizontally-Converging Ski-Jump Spillway

Figure 5.3 - Experimental results for the Vertically-Converging Ski-Jump Spillway

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Figure 5.4 shows all the supercritical Froude numbers (Fr1) of each spillway, with

their relevant hydraulic jump classifications, based upon the United States Bureau of

Reclamation, USBR hydraulic jump classification table is shown in figure 3.2.2.

Discharge

(M3/s)

Non-Converging Horizontal Converging Vertical Converging

Froude

Number

(Fr1)

Hydraulic

Jump

Classification

Froude

Number

(Fr1)

Hydraulic

Jump

Classification

Froude

Number

(Fr1)

Hydraulic

Jump

Classification

0.00722 3.0801 Oscillating 5.0183 Steady 2.8402 Oscillating

0.00750 3.1986 Oscillating 5.2113 Steady 2.7310 Oscillating

0.00778 2.8321 Oscillating 5.4044 Steady 2.6323 Oscillating

0.00806 2.7263 Oscillating 5.0085 Steady 2.3785 Weak

0.00833 2.6302 Oscillating 5.1812 Steady 2.0472 Weak

0.00861 2.7179 Oscillating 5.3539 Steady 1.9990 Weak

0.00889 2.6246 Oscillating 5.5266 Steady 2.0635 Weak

0.00917 2.7066 Oscillating 5.6993 Steady 2.0150 Weak

0.00944 2.7886 Oscillating 5.8720 Steady 1.9696 Weak

0.00972 2.8706 Oscillating 6.0447 Steady 2.0276 Weak

0.01000 2.9527 Oscillating 6.2174 Steady 2.0855 Weak

0.01028 3.0347 Oscillating 6.3901 Steady 2.0371 Weak

0.01056 2.9239 Oscillating 6.5629 Steady 1.9918 Weak

0.01083 3.4193 Oscillating 6.7356 Steady 2.0442 Weak

0.01111 3.7604 Oscillating 6.9083 Steady 1.9991 Weak

Figure 5.4 - Classification of Hydraulic Jump (Tabulated)

Figure 5.5 shows a graphical interpretation of the data in figure 5.4. It shows an

increase in sequent depth ratio for increased discharge for the non-converging and

horizontal converging spillways, a decrease in sequent depth ratio for increased

discharge for the vertical converging spillway.

Figure 5.5 - Graphical depiction of the Classification of Hydraulic Jump

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The following graphs in figures 5.6 - 5.15 show graphical results of the experimental

raw data and subsequent calculated data taken directly from figures 5.1, 5.2 and 5.3.

The energy dissipations in the graphs were all within the hydraulic jump, not in

phases 2 and 3 of the passage of water (unless stated).

Figure 5.6 - Graphical depiction of Supercritical Froude Number (Fr1) against Energy Dissipation

(ΔE)

Figure 5.6 shows that the energy dissipation across the jump increased for all

spillways with an increase in supercritical Froude number. Figure 5.7 shows that the

energy dissipation increases for the non-converging and horizontal converging

spillways as discharge increases, and energy dissipation decreases for increased

discharge for the vertical converging spillway.

Figure 5.7 - Graphical depiction of Energy Dissipation (ΔE) against Discharge (Q)

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Figure 5.8 - Graphical depiction of Relative energy loss against Supercritical Froude number (Fr1)

Figure 5.8 shows that the relative energy loss increased for all spillways with an

increase in supercritical Froude number. Figure 5.9 shows that the supercritical

Froude number increased for the non-converging and horizontal converging

spillways as discharge increased. Thus supercritical Froude number decreased for

increased discharge for the vertical converging spillway.

Figure 5.9 - Graphical depiction of Supercritical Froude number (Fr1) against Discharge (Q)

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Figure 5.10 - Graphical depiction of Downstream depth (y2) against Discharge (Q)

Figure 5.10 shows that the downstream depth (y2) increased for all spillways with an

increase in discharge. Figure 5.11 shows that the length of jump ratio increased for

all spillways with an increase in supercritical Froude number.

Figure 5.11 - Graphical depiction of Length of jump ratio (Lj/y1) against Supercritical Froude number

(Fr1)

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Figure 5.12 - Graphical depiction of Discharge (Q) against Length of jump (Lj)

Figure 5.12 shows that the length of jump increased for the non-converging and

horizontal converging spillways as discharge increased. For the vertical converging

spillway the length of jump decreased slightly, and then increased back to the same

value for increasing discharge.

Figure 5.13 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Non-

Converging Spillways

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Figure 5.14 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Horizontal

Converging Spillways

Figures 5.13, 5.14 and 5.15 show a more detailed graphical interpretation of figure

5.12. They all show that the measured jump/roller length for each was greater than

the calculated equivalent length, and that the length of jump was greater than the

length of roller.

Figure 5.15 - Graphical depiction of Discharge (Q) against Length of Jump/Roller for Vertical

Converging Spillways

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Figure 5.16 - Graphical depiction of Discharge (Q) against Energy Dissipation (Phases 2 and 3 only)

Figures 5.16 and 5.17 show the energy dissipation against discharge for phases 2 and

3 (phases from take-off from the spillway edge to the impact with the downstream

pool), and the same for phases 4 and 5 (phase of hydraulic jump and transition to

conventional river flow) respectfully.

Figure 5.17 - Graphical depiction of Discharge (Q) against Energy Dissipation (Phases 4 and 5 only)

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The experiments show raw data relating to three scale models of spillway designs.

To assess how this raw data would compare to a full scale dam spillway under flood

conditions, dimensional analysis was necessary. A 1:50 scale was chosen to represent

an average full scale model. The derived scale factors are:

; √

and

(eq. 5.1)

The following graphs in figures 5.18, 5.19, 5.20 and 5.21 are scaled up models of the

raw data produced from the experiments.

Figure 5.18 - Graphical depiction of Discharge (Q) against Length of jump (Lj) (Full Scale)

Figure 5.18 shows the length of jump against discharge for a full scale model. This

shows that the length of jump ranged between 16-19m for the vertical converging

spillway, and the non-converging spillway ranged between 20-35m.

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Figure 5.19 - Graphical depiction of Discharge (Q) against Energy Dissipation (Phases 2 and 3 only)

(Full Scale)

Figures 5.19 and 5.20 show the energy dissipation against discharge for phases 2 and

3, and the same for phases 4 and 5 respectfully for a full scale model, scaled up by a

factor of 50.

Figure 5.20 - Graphical depiction of Discharge (Q) against Energy Dissipation (Phases 2 and 3 only)

(Full Scale)

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Figure 5.21 - Graphical depiction of Downstream depth (y2) against Discharge (Q) (Full Scale)

Figure 5.21 shows the downstream depth against discharge for a full scale model.

This shows that the downstream depths ranged between 3.1-3.7m for the vertical

converging spillway, and the non-converging spillway ranged between 3.4-5.0m.

A modified vertical converging ski-jump spillway was tested in the same flume,

under the same conditions. The raw data for this experiment is summarized in figure

5.22.

Figure 5.22 - Experimental results for the Modified Vertically-Converging Ski-Jump Spillway

The supercritical depth of the modified vertically-converging spillway could not be

recorded in this experiment, due to the hydraulic jump occurring immediately at the

toe of the spillway, therefore limited graphs and conclusions could be drawn from

this data. Figures 5.23 and 5.24 show graphs of the data recorded.

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Figure 5.23 - Graphical depiction of Discharge (Q) against Total Energy Dissipation (Full Scale)

Figure 5.23 shows the total energy dissipation across the length of the whole system

against discharge for a full scale model. It was noted that the modified vertical

converging spillway produced the largest energy dissipations across all discharges

tested. Figure 5.24 shows the downstream depth against discharge for a full scale

model. This shows that the downstream depths ranged between 2.4-3.3m for the

modified vertical converging spillway (shorter than the other two spillways).

Figure 5.24 - Graphical depiction of Downstream depth (y2) against Discharge (Q) (Full Scale)

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6.0 Analysis of Results and Discussion

The results in section 5.0 show that altering the spillway structure has the potential to

increase energy dissipation and reduce subsequent erosion downstream. This will be

discussed in more detail.

Analysis of Results

The main objective of this research project was to investigate, through practical

experimentation, if larger energy dissipation could be achieved by converging jets as

part of a ski-jump spillway. The experiments show that the horizontal converging

ski-jump spillway decreased the energy dissipation in phases 2 and 3 (see section

3.1) of the passage of discharge over a spillway and stilling basin, compared to a

non-converging ski-jump spillway. However the vertical converging ski-jump

spillway substantially increased the energy dissipation in phases 2 and 3.

The classifications of the jumps ranged between steady and weak (see section 3.2).

Reviewing the non-converging and vertically-converging spillways, the vertically-

converging spillway decreased from an oscillating to weak jump at around a sequent

depth ratio of 3.00, whereas the non-converging spillway remained as an oscillating

jump, increasing slightly.

The vertically-converging spillway dissipated the least energy in the hydraulic jump

(phases 4 and 5) and therefore dissipated the most energy in phases 2 and 3. Figures

5.6 and 5.7 shows this in terms of energy dissipation against supercritical Froude

number and against discharge respectfully. Figures 5.16 and 5.17 also show the

energy dissipation against discharge, for phases 2 and 3, and also for phases 4 and 5

separately.

The downstream water depth is lowest for the vertically-converging spillway, where

the non-converging and horizontally-converging spillways were considerably higher

(see figure 5.10).

The length of jump ratio increased for increasing supercritical Froude number for all

spillways, with the non-converging spillway having a larger length of jump ratio than

the vertically-converging spillway.

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The length of jump for the non-converging spillway increased noticeably with

increased discharge and was much larger than that of the vertically-converging

spillway, which remained at a reasonably constant length across all discharges tested.

The experimentally measured hydraulic length of jump/roller was, for all spillways,

overestimated compared to the calculated values of each. All related measured and

calculated length of hydraulic jumps and rollers demonstrated a similar correlation,

(the hydraulic length of jump/roller are explained in more detail in section 3.3).

Cavitation was observed for all three spillways, particularly for the converging

spillways, with moderate to severe cavitation occurring on the jump edge of the

vertically-converging spillway.

Discussion

As previously stated, the horizontally-converging ski-jump spillway does not present

increased energy dissipation in phases 2 and 3, compared to the non-converging ski-

jump spillway, this could be due to a number of factors. The most rational reason

would be that the angle of colliding jets was not large enough; therefore the act of

colliding the jets together was not achieving the air entrainment and dispersion

required for energy dissipation in these earlier phases (discussed in more detail in

section 3.1).

Figure 6.1 – Experimental testing of the horizontal converging spillway

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In fact the jets were converging smoothly enough to form a uniform single jet with

increased velocity and throwing the jet further from the spillway edge (which can be

seen in figure 6.1), therefore decreasing the energy dissipation in phases 2 and 3, and

increasing the classification of the hydraulic jump to a steady jump (see figures 5.4

and 5.5). This can also be seen in figures 5.6, and 5.7, which show the relationships

between energy dissipation and supercritical Froude number and with discharge

respectfully, and figure 5.8 shows the relationship between relative energy loss and

supercritical Froude number. All three figures show that the horizontally-converging

ski-jump spillway increased energy dissipation the most within the hydraulic jump,

therefore the least in phases 2 and 3. The horizontally-converging spillway did not

achieve the level of energy dissipation anticipated in the early phases, therefore

further investigation could be undertaken to design a model which converged the

horizontal jets at a larger angle. The collisions at larger angles are likely to achieve

the collision forces required for air entrainment and dispersion, therefore high energy

dissipation (see section 3.1).

This compares to the vertically-converging spillway, in which a large proportion of

the energy was dissipated within phases 2 and 3. This can be seen in figure 5.5,

where the classification of the jump decreased from an oscillating jump to a weak

jump at around a sequent depth ratio of 3.00. Figure 5.16, shows the energy

dissipation during phases 2 and 3 are higher for the vertically-converging spillway,

than the non-converging spillway. As discussed in section 3.1, the energy dissipation

in phases 2 and 3 were greatly increased by achieving a dispersed and highly air

entrained jet, ov & bel a, 1981). Since more energy is dissipated in the

earlier phases, less energy is required to be lost in the hydraulic jump to achieve

subcritical conventional river flow (see figures 5.16 and 5.17).

The energy dissipation also stays relatively constant for the vertically-converging

spillway compared to the non-converging spillway (see figure 5.16). This is more

desirable as a design solution for a large dam spillway under a fluctuating flood

discharge. Therefore the downstream river channel will be less affected by a more

constant flood river flow. The non-converging spillway varies significantly in energy

dissipation between different discharges and phases, therefore has a greater effect on

downstream river flow.

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The experiments in this investigation showed raw data relating to four scale models

of spillway designs. To assess how this raw data compared to a full scale dam

spillway under flood conditions, dimensional analysis was necessary. A 1:50 scale

was chosen to represent an average full scale model. The results of which can be

seen in figures 5.18, 5.19, 5.20 and 5.21.

Figures 5.19 and 5.20 show full scale interpretations of figures 5.16 and 5.17, these

demonstrate the relationship between energy dissipation and discharge, for phases 2

and 3, and also for phases 4 and 5 separately. The energy dissipations of the full

scale models are a factor of 50 larger than the scaled models due to the units of

energy dissipation being in metres head. Although the discharge is a factor of 17678

larger, due to scale effects. It is important to note that the energy dissipation of the

vertically-converging spillway has a much smaller full scale range of 13.0-14.5m

head compared to the non-converging spillway which has a full scale range of 10.0-

13.5m head. Therefore the energy dissipation is not only much larger in the phases 2

and 3, but the range of energy dissipation is also 2.33 times smaller than the non-

converging spillway. The results indicate that the dimensions of the stilling basin

could be reduced, potentially leading to cost savings in the construction process

(Toso & Bowers, 1988).

The downstream water depth was lowest for the vertically-converging spillway,

where the non-converging spillway is considerably higher (see figure 5.10). Figure

5.21 shows a full scale interpretation of figure 5.10, which demonstrates the

relationship between downstream water depths and discharge. The downstream water

depths range between 3.1-3.7m for the vertically-converging spillway, and the non-

converging spillway range between 3.4-5.0m. Therefore the downstream depths are

not only much shallower for the vertically-converging spillway, but the range of

depths was also around 2.67 times smaller. The relevance of this does depend on

what is required downstream of the spillway, due to the habitats and biological

communities within a river varies with water depth, distance from the coastline and

with environmental seasonal changes, (Wetzel, 2001). For many river systems a

varied flow depth is favourable to mimic a natural ecosystem, if designed correctly,

(Gehrke et al., 1995).

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To show the relationship between the length of hydraulic jump and discharge, the

measured length of jump was used in its graphical representation, rather than the

measured length of roller, or calculated versions of each. This length was used due to

it being more common in similar previous studies, and allows an easier comparison

between this and other studies (Li et al., 2012; Wu et al., 2012).

The length of jump is lowest for the vertically-converging spillway, where the non-

converging spillway is considerably higher (see figure 5.12). Figure 5.18 shows a full

scale interpretation of figure 5.12, which shows the relationship between the length

of jump and discharge. This shows that the length of jump ranged between 16-19m

for the vertically-converging spillway, and the non-converging spillway ranged

between 20-35m. Therefore the lengths of jumps are not only much shorter for the

vertically-converging spillway, but the range of lengths are also around 5.00 times

shorter. With the length of jump range vastly smaller, this allows for the construction

of a stilling basin, in which the hydraulic jump occurs over the majority of it across

most discharges. This compared to the non-converging spillway, in which the full

usage of the stilling basin would only be used for the highest of discharges. A much

shorter stilling basin could also be constructed, due to the length of jump having

decreased, therefore the area of erosion is smaller. The shorted stilling basin length is

likely to lower construction costs.

It is useful to evaluate the length of jump/roller relative to supercritical depth; this is

common practice in many other studies (Gupta et al., 2013; Hager, 1989). Therefore

the relative length of the jump Lj/Y1 is plotted against the supercritical Froude

number, providing a relative comparison between the three spillway models tested.

The relative length of jump/roller is a dimensionless measurement; hence clearer

conclusions can be derived using data from a larger discharge range, and

comparisons with previous and future work can be made without using the same

discharges or scaling.

The resulting graph in figure 5.11 shows that the non-converging spillway has a

larger relative length of jump and supercritical Froude number than the vertically-

converging jump, for supercritical Froude numbers ranging between 1.9 and 3.9

(weak and oscillating jumps). For the experiments carried out on spillways (above)

the figure shows an increase in relative length of jump, with increased supercritical

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Froude number. The data for the non-converging spillway shows a sizable deviation

in data points, which may be due to the inaccuracy in determination of the correct

location of the start and end of the length of jump. To correct this inaccuracy

duplicates of the experiments could have been undertaken, therefore an average of

the readings could be taken, providing a more accurate measurement.

The measured and calculated lengths of jump/roller of all three spillways are

presented in figures 5.13, 5.14 and 5.15 respectfully. These results present a good

correlation between different methods of producing the measurements. They

demonstrate a similarity between what was measured experimentally and what was

calculated from the raw data (Carollo & Ferro, 2012). The measured lengths appear

to be larger than the calculated results for almost all data points, resulting in an

average discrepancy of 21%, 8% and 14% respectfully. To achieve a higher accuracy

experimental repeats could be undertaken. The variation in the experimental results

shows that it is good practice to take measured and calculated parameters. This helps

to clarify that both measured and calculated results may not be the most accurate

measurement in scale modelling, and a new method may be required. Furthermore

the figures also show a correlation between length of jump and length of roller. This

is clarified by Hager (1989), who also establishes an equivalent relationship in his

study, and large scattering of measured data for the length of jump/roller. This

demonstrates that other authors have found discrepancies in measuring the lengths of

jump/roller.

Following analysis of the three models tested, it became apparent that the vertically-

converging spillway was the most efficient and dispersing energy. This lead to the

vertically-converging design being selected and further modelling was carried out

using the ‘vertical sum of momentum problem’ formula this can be found in

equation 3.1.1). The results from the equation showed an increase in energy

dissipation and therefore the design was constructed and tested. This further testing

was carried out in order to confirm if further efficiencies could be reached. The

modifications, identified from the calculations from the formula, included an

increase in the height of the two small ski-jumps further up the pre-fabricated

spillway. This was done with the aim of altering the angle of collision to something

closer to 90o, therefore increasing the collision forces between the water jets and

increasing air entrainment and dispersion ov & bel a’s, 1981).

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The experiments for this model presented results which behaved differently to the

other three models. The hydraulic jump for the modified vertically-converging

spillway occurred immediately at the toe of the spillway and therefore the

supercritical depth and length of jump/roller could not be measured, (using either

calculation or standard measurement). It is normal practice to measure a supercritical

depth for the calculation, which wasn't evident for this model. However the upstream

and downstream depths could be measured and therefore graphs of the total energy

dissipation could be plotted and compared. Figure 5.23 shows a graph of the total

energy dissipation against discharge. The figure demonstrates that the modified

vertically-converging spillway has the greatest total energy dissipation of all the

models tested. A calculated hydraulic jump classification was not possible to be

calculated for this model, however through observation it can be seen that the

hydraulic jump was undulating (see figure 6.2) and therefore was dissipating less

than 5% of the total energy in the hydraulic jump according to USBR (1955), shown

in figure 3.2.2. Therefore, a large proportion of energy is lost, during phases 2 and 3,

to achieve an undulating jump at such high discharges.

Figure 6.2 - Undular hydraulic jump, downstream of the modified vertical converging spillway

The full scale downstream water depth was lowest for the modified vertically-

converging spillway, where the non-converging spillway is considerably higher (see

figure 5.24). The downstream water depths ranged between 2.4-3.3m for the

modified vertically-converging spillway. However, the vertically-converging and

non-converging spillways ranged between 3.1-3.7m and 3.4-5.0m respectively.

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Therefore the downstream depths of the modified vertically-converging spillway

were even shallower than the other two models, which would be preferable in most

circumstances.

Although the length of the jump/roller could not be accurately measured for the

modified vertically-converging spillway, the length from the spillway toe to the end

of the hydraulic jump/roller was measured. This is the length which is used for

construction purposes of the stilling basin. It was noted that this length for the

modified vertically-converging spillway was around 61% of the average length of the

original vertically-converging spillway. This vastly reduced length, reduces stilling

basin dimensions and is likely to reduce construction costs. Both of the vertically-

converging spillways had an equally small range of spilling basin lengths for the

discharges tested, which was 38% of the non-converging stilling basin length. The

success of the modified vertically-converging ski-jump spillway design, with its

more efficient energy dissipation results, and cost-effective construction, shows that

it has the potential to be a leading design.

Figure 6.3 - Experimental testing of the modified vertical converging spillway

Cavitation appeared to be a large issue with the modified vertically-converging

spillway. When the water jets from the smaller deflectors converged with the main

water jet, a proportion of it collided with the main ski-jump toe. This collision

formed cavitation in the ski-jump bucket, which can be seen in figure 6.3. Through

observation, and detailed in figure 3.4.1, which shows the development stages of

cavitation, it can be seen that the cavitation formed in the bucket is classed as

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supercavitation, and therefore has a cavitation index σ of 0.3 or less (the highest form

of cavitation). Cavitation was also observed in the bucket of the original vertical

converging spillway, although not at the same high levels as the modified model. The

cavitation in the bucket of the original model was observed at a class of developed

cavitation, bordering on supercavitation, and therefore has a cavitation index σ of 0.3

to 1.8. Cavitation was not observed with the horizontal and non-converging

spillways.

Although the potential construction costs would be less with the vertically-

converging spillways, due to their shorter stilling basin lengths, the high cavitation

levels experienced increases the amount of potential erosion occurrence in the ski-

jump bucket and toe. These cavitation effects would also be greatly increased when

scaled up to full construction size. This will mean that the construction of the ski-

jump will have to be heavily engineered to resist cavitation erosion. The majority of

dam spillways are constructed from concrete; a material which is susceptible to

cavitation erosion. Therefore without prolonged scaled testing using concrete

models, it is unknown exactly how much cavitation would affect the structure of the

spillways.

Limitations

All the spillways were tested in the same hydraulic flume, under the same conditions

and variables; therefore they can be scaled up to an average full size model and

compared. However the scaled laboratory experiments have many limitations, and it

will always be difficult to generalise findings, due to the results not being

ecologically valid (representative of real life) (Le Coarer, 2007). The laboratory

experiments were tested to a very narrow range in terms of many parameters, which

are generally not issues in full scale prototype testing. For example the relatively

narrow width of the channel meant that scale wall effects altered the trajectory of the

water jets, producing an uncharacteristic flow. This would not be the case in a full

scale construction.

Other limitations included bed slope angle, surface roughness and air entrainment.

The bed slope angle was set at zero degrees for all experiments, which kept in unison

with bottom outlet investigations, as such avoiding complications with steeply

sloping chute flows. herefore the data is not likely to give a true representation of

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all field applications with high bed slope angles, although does give a good

estimation and comparative data to other laboratory investigations (Juon & Hager,

2000). The surface roughness in the experiments was very low due to the metal bed

and glass walls. When compared to the surface roughness of concrete, which would

most likely be used in a full scale prototype model, which is likely to produce an

altered outcome, slowing the water and an anticipated increase in the hydraulic jump.

The air entrainment observed in large quantities in this investigation could only be

commented in terms of the scaled models, due to scaling limitations and the

equipment used for measuring air entrainment not being available (Juon & Hager,

2000).

Human error is a limitation within these experiments. It is impossible to establish an

exact measurement for many parameters within the field of hydraulics, particularly

when it is difficult to accurately determine a parameter such as the length of

hydraulic jump/roller. Downstream of the hydraulic jump undulations were observed,

particularly with lower classification jumps. Therefore the manometer readings of the

downstream depth often fluctuated, resulting in an average reading being recorded.

The duration of time spent undertaking laboratory experiments was limited, therefore

narrowing the range of experiments which could be undertaken within the time-

frame. Additional experiments could have provided opportunities for further

modifications to the designs tested. Repetitions of experiments would have provided

more reliable and resilient data that could further support the analysis of this report.

The supercritical depth could not be recorded for the experiments of the modified

vertically converging spillway, due to the hydraulic jump occurring immediately at

the toe of the spillway, therefore limited graphs and conclusions could be drawn

from this data. Although the data that was recorded presented some very positive

conclustions.

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7.0 Conclusions and Future Work

The experiments of both of the vertically-colliding spillway produced positive

results, which confirm ov bel a’s (1981) concept of producing a greater

energy dissipation when converging multiple jets as part of a ski-jump spillway.

Further testing using more modifications of the vertically-converging design would

be recommended to produce the potential of further increases in energy dissipation.

The horizontally-converging spillway did not produce an increase in energy

dissipation, due to a small angle of colliding jets. However further testing would be

recommended, with a design with a greater angle of collision and possibly the

combination of both horizontal and vertical colliding jets, adopting the concept by

ov bel a’s (1981), of the greater the number of colliding jets the greater the

capacity of energy dissipation. However, cavitation erosion would need to be taken

into consideration to understand the consequences of increasing jet collision.

There are many benefits to having the energy dissipation occur during the second and

third phases of the passage of water over a spillway, including a reduction in stilling

basin length, less erosion of the stilling basin and downstream river, and a greater

energy dissipation capacity. Cavitation appears to be a key aspect which needs to be

considered with any proposed designs. This is due to the apparent conclusion that the

designs which produce higher energy dissipations also produce higher levels of

cavitation. The modified vertically-colliding spillway produced greatest energy

dissipations, but also the highest levels of cavitation. Further study could be

undertaken to review whether higher cavitation is always an outcome of high energy

dissipations. If so then comprehensive study into cavitation effects to vertically-

converging spillway designs and how different materials degrade with prolonged

cavitation, could prove valuable. Due to the unknown effects of concrete cavitation

erosion, further studies would need to be undertaken, and a full cost exercise

executed, in order to confirm that cost-savings in reduced energy-dissipation designs,

outweigh the potential increases in costs that cavitation may produce.

Furthermore it can be drawn from this study that hydraulic jump energy dissipation

increases with increased supercritical Froude number, as stated by Chadwick &

Morfett (2013). The sequent depth ratio and length of jump are decreased by multiple

converging ets, as stated by ov bel a (1981). Also the spillway designs

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with high energy dissipations help prevent erosion downstream of the spillway and

aid the preservation of the conventional river environment downstream.

With the continued reporting of flooding, occurring both nationally and

internationally, and the predicted rate of these events set to increase in the future, it

may be prudent to extend on this project, new high energy dissipation designs for

large scale spillways (Driessen & Van Ledden, 2013).

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8.0 References

Avery, S. T. and Novak, P. (1978) ‘Oxygen transfer at hydraulic structures’, Journal

of the Hydraulics Division, Vol. 104, No. 11, pp. 1521 – 1540.

Azmathullah, H. M., Deo, M. and Deolalikar, P. (2005) ‘Neural networks for

estimation of scour downstream of a ski- ump buc et’, Journal of Hydraulic

Engineering, Vol.131, No. 10, pp. 898 – 908.

Bradley, J., (1945) ‘Study of air in ection into the flow in the Boulder Dam spillway

tunnels, Boulder Canyon Project’, Bureau of Reclamation, Hydraulic

Laboratory Report, 186.

Carollo, F. G., Ferro, V. and Pampalone, V. (2007) ‘Hydraulic jumps on rough

beds’, Journal of Hydraulic Engineering, Vol. 133, No. 9, pp. 989 – 999.

Carollo, F. G., Ferro, V. and Pampalone, V. (2012) ‘New Expression of the

Hydraulic Jump Roller Length’, Journal of Hydraulic Engineering, Vol. 138,

No. 11, pp. 995 – 999.

Chadwick, A., Morfett, J. C. and Borthwick, M. (2013) Hydraulics in civil and

environmental engineering, Boca Raton, Fla. [u.a.]: CRC Press.

Chanson, H. and Montes, J. (1995) ‘ haracteristics of undular hydraulic umps:

Comparison with Near-Critical Flows’, Journal of hydraulic engineering, Vol.

121, No. 2, pp.129 – 144.

Chiang, T., Sheu, . and Wang, S. 2000 ‘Side wall effects on the structure of

laminar flow over a plane-symmetric sudden expansion’, Computers & fluids,

Vol. 29, No. 5, pp.467 – 492.

Driessen, T. and Van Ledden, M., (2013) ‘The large-scale impact of climate change

to Mississippi flood hazard in New Orleans’, Drinking Water Engineering \&

Science, Vol. 6, No. 2.

Ead, S. and Rajaratnam, N. (2002) ‘Hydraulic jumps on corrugated beds’, Journal of

Hydraulic Engineering, Vol. 128, No. 7, pp. 656 – 663.

Faktorovick, M. E. (1952) Energy Dissipation at Jet Collision, (in Russian),

Gidrotechnicheskoje strojitelstvo, No. 8, pp. 43 – 44.

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Falvey, H. T. (1990) ‘Cavitation in chutes and spillways’, A water resources

technical publication. Engineering monograph, No. 42

Gandhi, S. and Yadav, V. (2013) ‘Characteristics of supercritical flow in rectangular

channel’, International Journal of Physical Sciences, Vol. 8, No. 40, pp. 1934 –

1943. Available at:

http://www.academicjournals.org/article/article1384763242_Gandhi%20and%2

0Yadav.pdf [Accessed: 11th Feb 2014].

Gehrke, P., Brown, P., Schiller, C., Moffatt, D. and Bruce, A. 5 ‘River

regulation and fish communities in the Murray-Darling river system,

Australia’, Regulated Rivers: Research & Management, Vol. 11, No. 3-4, pp.363

– 375.

Graff, W. (2006) ‘Downstream hydrologic and geomorphic effects of large dams on

American rivers’, 37th Binghampton Geomorphology Symposium – The Human

Role in Changing Fluval Systems. Vol. 79. No. 3-4. pp. 336 – 360.

Gupta, S., Mehta, R. and Dwivedi, V. (2013) ‘Modeling of relative length and

relative energy loss of free hydraulic jump in horizontal prismatic

channel’, Procedia Engineering, Vol. 51, pp.529 – 537.

Hager, W. (1989) ‘Hydraulic jump in U-shaped channel’, Journal of Hydraulic

Engineering, Vol. 115, No. 5, pp.667 – 675.

Heller, V., Hager, W. and Minor, H. (2005) ‘S i ump hydraulics’, Journal of

Hydraulic Engineering, Vol. 131, No. 5, pp.347 – 355.

Horeni, p. (1956) Disintegration of a Free Jet in Air, (in Czech), Prace a studie No.

93, VUV, Prague

Juon, R. and Hager, W. (2000) ‘Flip buc et without and with deflectors’, Journal of

Hydraulic Engineering, Vol. 126, No. 11, pp.837 – 845.

Kehew, A. (1982) ‘Catastrophic flood hypothesis for the origin of the Souris

spillway, Saskatchewan and North Dakota’, Geological Society of America

Bulletin, Vol. 93, No. 10, pp.1051 – 1058.

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Komora, Y. (1969) ‘Spillway design using jet collision for energy

dissipation’, Power Technology and Engineering (formerly Hydrotechnical

Construction), Vol. 3, No. 4, pp. 363 – 364.

Le Coarer, Y. (2007) ‘Hydraulic signatures for ecological modelling at different

scales’, Aquatic ecology, Vol. 41, No. 3, pp.451 – 459.

Li, N., Liu, C., Deng, J. and Zhang, X., (2012) ‘Theoretical and experimental studies

of the flaring gate pier on the surface spillway in a high-arch dam’, Journal of

Hydrodynamics, Ser. B, Vol. 24, No. 4, pp.496 – 505.

Mahmodinia, S., Javan, M. and Eghbalzadeh, A. (2012) ‘The Effects of the Upstream

Froude Number on the Free Surface Flow over the Side Weirs’, Procedia

Engineering, Vol. 28, pp.644 – 647.

Nalluri, C. and Featherstone, R. E. (2001) Civil Engineering Hydraulics. 4th ed.

Oxford: Wiley-Blackwell.

ov , . and bel a, J. (1981) Models in hydraulic engineering. Boston: Pitman.

Roberts, C. (1980) ‘Hydraulic Design of Dams’, RSA Department of Water

Affairs,Forestry and Environmental Conservation, Division of Special Tasks,

July.

Rutschmann, P. and Hager, W. H. (1990) ‘Air entrainment by spillway

aerators’, Journal of Hydraulic Engineering, Vol. 116, No. 6, pp. 765 – 782.

Schmocker, L., Pfister, M., Hager, W. and Minor, H. (2008) ‘Aeration characteristics

of ski jump jets’, Journal of Hydraulic Engineering, Vol. 134, No. 1, pp.90 – 97.

Steiner, R., Heller, V., Hager, W. and Minor, H., (2008) ‘Deflector ski jump

hydraulics’, Journal of Hydraulic Engineering, Vol. 134, No. 5, pp.562 – 571.

Streeter, V. L. and Wylie, E. B. (1981) Fluid mechanics. 2nd ed. New York:

McGraw-Hill.

Toso, J. and Bowers, C. (1988) ‘Extreme pressures in hydraulic-jump stilling

basins’, Journal of Hydraulic Engineering, Vol. 114, No. 8, pp.829 – 843.

Wetzel, R. (2001) Limnology. 3rd ed. London: Academic Press.

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Wu, J., Ma, F. and Yao, L., (2012) ‘Hydraulic characteristics of slit-type energy

dissipaters’, Journal of Hydrodynamics, Ser. B, Vol. 24, No. 6, pp.883 – 887.

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9.0 Appendices

Ethics Checklist

Name of student: Joseph Lawson

Name of supervisor: Heidi Burgess

Title of project (no more than 20 words):

Investigating the use of Converging Ski-Jump Spillways and their effects on the

characteristics of Hydraulic Jump and Energy Dissipation.

Outline of the research (1-2 sentences):

This research aims to determine the differences in energy dissipation between

converging ski-jump spillways and the effect this has on the characteristics of a

hydraulic jump.

Timescale and date of completion: 7th

May 2014

Location of research: University of Brighton, Hydraulics Laboratory

Course module code for which research is undertaken: CNM30

Email address: [email protected]

Contact address: 30 Newmarket rd, Brighton, East Sussex, BN2 3QF

Telephone number: 07949822829

Please tick the appropriate box Yes No

1. Is this research likely to have significant negative impacts on

the environment? (For example, the release of dangerous

substances or damaging intrusions into protected habitats.)

x

2. Does the study involve participants who might be considered vulnerable due to age or

to a social, psychological or medical condition? (Examples include

children, people with learning disabilities or mental health

problems, but participants who may be considered vulnerable are

not confined to these groups.)

x

3. Does the study require the co-operation of an individual to gain access to the

participants? (e.g. a teacher at a school or a manager of sheltered

housing)

x 4. Will the participants be asked to discuss what might be perceived as

sensitive topics? (e.g. sexual behaviour, drug use, religious belief, detailed financial

matters)

x 5. Will individual participants be involved in repetitive or prolonged

testing? x

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6. Could participants experience psychological stress, anxiety or other

negative consequences (beyond what would be expected to be encountered in

normal life)?

x 7. Will any participants be likely to undergo vigorous physical

activity, pain, or exposure to dangerous situations, environments or materials as part of the

research?

x 8. Will photographic or video recordings of research participants

be collected as part of the research? x

9. Will any participants receive financial reimbursement for

their time? (excluding reasonable expenses to cover travel

and other costs)

x 10. Will members of the public be indirectly involved in the research without their

knowledge at the time? (e.g. covert observation of people in non-

public places, the use of methods that will affect privacy)

x 11. Does this research include secondary data that may carry

personal or sensitive organisational information? (Secondary data

refers to any data you plan to use that you

did not collect yourself. Examples of sensitive secondary data

include datasets held by organisations, patient records,

confidential minutes of meetings, personal diary entries. These are only examples and not an exhaustive list).

x 12. Are there any other ethical concerns associated with the research that are not covered

in the questions above?

x

All Undergraduate and Masters level projects or dissertations in the School of

Environment and Technology must adhere to the following procedures on data

storage and confidentiality:

Once a mark for the project or dissertation has been published, all data must be

removed from personal computers, and original questionnaires and consent forms

should be destroyed unless the research is likely to be published or data re-used.

Please sign below to confirm that you have completed the Ethics Checklist and will

adhere to these procedures on data storage and confidentiality. Then give this form

to your supervisor to complete their checklist.

Signed (Student):

Date: 11/02/2014

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Risk Assessment

School / Department: Environment & Technology Date of assessment: 11/02/2014

Activity / area: Hydraulics Laboratory Next review date:

Assessed by: Dominic Ryan RA Ref No:

No.

What are

the

hazards?

Who

might be

harmed

and how?

What controls do you

already have in place?

Risk

(H/M/L)

What further

action is

necessary to

reduce the risk

to Low?

Action by

whom?

Action by

when?

Done

1 Working at Heights User Hold the hand rail of step

ladder when working at

height

L N/A User Before start

of work

Yes

2 Lone Working User Notify a technician of all

works

L N/A User Before start

of work

Yes

3 Slips, trips and falls User Be aware of all obstacles,

clean up water spillages

immediately. Where correct

clothing and PPE

L N/A User Before start

of work

Yes

Assessor signature/date: Head of School signature/date: