Study on free-surface aeration with high- velocity air ...1150561/FULLTEXT01.pdf · Study on...

Study on free-surface aeration with high-

velocity air-water flows in open-channels

Belkiz Hasan

Paulo Monsalve

Master of Science Thesis

KTH School of Industrial Engineering and Management

Department of Energy Technology EGI_2017-0044-MSC EKV1190

Division of Heat and Power Technology

SE-100 44 STOCKHOLM

Master of Science Thesis EGI_2017-0044-MSC

EKV1190

Study on free-surface aeration with

high-velocity air-water flows in open-

channels

Belkiz Hasan

Paulo Monsalve

Approved

2017-06-13

Examiner

Björn Laumert

Supervisor

James Yang

Commissioner

Energiforsk AB & Vattenfall AB

Contact person

James Yang

Abstract

China’s biggest source of the renewable energy is hydropower, with a share of 85 %, in 2013, of

the total renewable power generation. For the tenth sequential year, China has maintained the

country’s leading role in global hydropower development by installing more hydropower plants

than the rest of the world combined. There are some important issues when constructing

hydropower plants and designing spillways and chute sidewalls. One of these issues is considered

to be the presence of air, which can be entrained in large amounts through the free surface into the

water within high-velocity flows and leads to the bulk of the flow to increase.

This project aims to describe the relationship between free-surface entrapped deformation and air

entrainment (entrained air in the flow) by studying uniform self-aerated flows in open-channels.

The performed experiments have been carried out in a physical scaled model at the State key

laboratory of Hydraulics and Mountain River Engineering at Sichuan University in Chengdu,

China. A literature study has been done in order to examine the self-aerated flows in open-channels

and used as the basis for the experiments in this project.

The software, Free Video to JPG Converter, AUTOCAD, Photoshop, OriginPro and Motion

Studio have been utilized for the evaluation of free-surface deformation curve and the process of

surface deformation and air entrainment. After analysing images taken by a camera during the

experiments, the result has been divided in two parts, namely, to describe the air-entrainment

phenomenon using the relevant curve type and fitting the obtained curves into the known curves,

and to obtain the critical radius of curvature for the air-entrainment affected by flow mean velocity

and water depth.

Based on the experimental data from the image analysis and one sample t-test which has been

utilized to obtain a confidence interval of the adjusted R-square in order to evaluate how good

fitting the relevant curves have, the Gaussian-curve type have been decided to describe the

phenomenon. After the image analysis of the free-surface deformation curve type has been done,

the process of surface deformation and air entrainment has been evaluated. For this evaluation,

various processes with various durations have been observed. As a result, it is found that the surface

achieves closure at a relatively low position at a range of 7 to 19 milliseconds and the free-surface

deformation occurs when the air bubble is entrained into the flow, varies between 8 and 19,5

milliseconds for different observation. The results of evaluating the radius of curvature with respect

to the time of occurrence indicate that the free-surface deformation intensity in the experiments

exceeds the critical condition of curvature radius when the surface instability occurs. The results of

the radius of curvature reveal that that the radius of curvature has a “bell-shape” behaviour. It is

shown that the critical radius of curvature varies for different processes and it occurs after the

maximum value is reached, the critical radius of curvature has a range between 0,53 and 2,97 mm

for all the processes.

The results show that the experiments have a good potential for evaluating the process of free-

surface deformation and air entrainment. To make final conclusions, further studies and

experiments in self-aerated open-channel flows should be done including non-intrusive

measurements for the entrained air bubble size and the relationship between the free-surface

deformation and bubble distributions.

Sammanfattning

Kinas största källa till förnybar energi är vattenkraft, med en andel på 85 %, år 2013, av den totala

förnybara kraftproduktionen. Tio år i rad har Kina behållit landets ledande roll i den globala

vattenkraftutvecklingen genom att installera fler vattenkraftverk än resten av världen kombinerat.

Det finns några viktiga frågor vid konstruktionen av vattenkraftverk och utformningen av

spillvägar och skuggade sidoväggar. Ett av dessa problem anses vara närvaro av luft, vilket kan

medföras i stora mängder genom den fria ytan i vattnet inom höghastighetsflöden och leder till att

huvuddelen av flödet ökar.

Detta projekt syftar till att beskriva sambandet mellan infångad deformation och luftintagning

(medbringad luft i flödet) genom att studera enhetliga, självluftade flöden i öppna kanaler. De

utförda experimenten har utförts i en fysisk skalad modell vid Institutionen för Hydraulik och

Bergflodteknik vid Sichuan Universitetet i Chengdu, Kina. En litteraturstudie har gjorts för att

undersöka de själv-luftade flödena i öppna kanaler och använts som grund för experimenten i detta

projekt.

Programvaran, Free Video to JPG Converter, AUTOCAD, Photoshop, OriginPro och Motion

Studio har använts för utvärdering av fri-deformationskurvan och processen för yta-deformation

och luftintagning. Efter att ha analyserat bilderna som tagits av en kamera under experimenten har

resultatet uppdelats i två delar, nämligen att beskriva luftintagningsfenomenet med den relevanta

kurvtypen och anpassa de erhållna kurvorna till de kända kurvorna samt att erhålla den kritiska

radien av krökning för luftintag som påverkas av flödesmedelhastighet och vattendjup.

Baserat på experimentella data från bildanalysen och ett prov t-test som har utnyttjats för att erhålla

ett konfidensintervall för den justerade R-kvadraten, vilket utvärderar de relevanta kurvorna

passning, har Gauss-kurvtypen bestämts för att beskriva fenomenet. Efter att bildanalysen av

deformationskurvan för fria-ytan har gjorts, har processen för yta-deformation och luftintagning

utvärderats. För denna utvärdering har olika processer med olika varaktighet observerats. Som ett

resultat är det konstaterat att ytan åstadkommer stängning vid ett förhållandevis lågt läge i

intervallet 7 till 19 millisekunder och fri-yta deformationen uppträder när luftbubblan medföljer

flödet varierar mellan 8 och 19,5 millisekunder för olika observationer. Resultaten av utvärdering

av krökningsradie med avseende på tidpunkten för förekomsten indikerar att intensiteten för fri-

yta deformationen i experimenten överstiger kretsens kritiska tillstånd när ytans instabilitet

uppträder. Resultatet av krökningsradien visar att krökningsradien har ett "klockformat" beteende.

Det visas att den kritiska krökningsradien varierar för olika processer och det inträffar efter att

maximivärdet har uppnåtts, den kritiska krökningsradien har ett intervall mellan 0,53 och 2,97 mm

för alla processer.

Resultaten visar att experimenten har en bra potential för utvärdering av processen med fri-yta

deformationen och luftintagningen. För att göra slutgiltiga slutsatser bör ytterligare studier och

experiment i självluftade öppna kanalflöden göras, inklusive icke-påträngande mätningar för den

medförde luftbubbelstorleken och förhållandet mellan deformation och bubbeldistributionen för

fria-ytan.

摘要

水电作为最主要的一种可再生能源利用形式，其在中国国内可再生能源利用总量中占

比达到 85%（2013 年），在近几十年中，中国作为世界范围内加强水电利用的主导国

家，引领着水利水电工程的建设。在水利水电工程建设过程中，面对高流速、大流量

条件下的水力运行，大型泄洪建筑物（如泄洪洞、溢洪道等）的泄水安全，直接关系

着整体水利水电工程的运行安全，其中一个重要的高速水力学问题为由于自由面卷吸

掺气引起的明渠高速掺气水流问题。

本项目旨在研究明渠水流自由面卷吸掺气过程形成机理进行研究，基于对自掺气水流

研究背景充分了解的基础上，在四川大学水力学与山区河流开发保护国家重点实验室

中采用明渠水槽进行自由面卷吸掺气观测试验研究，并采用高速摄像与图像分析技

术，整合利用多种分析软件，包括，Free Video to JPG Converter, AUTOCAD,

Photoshop, OriginPro 和 Motion Studio等，对自由面凹陷形态特征与卷吸掺气过程

进行分析。研究内容主要包括一下两部分：1）对明渠水流局部自由面水体凹陷形态进

行分析，确定描述自由面凹陷形态的曲线形式；2）对自由面凹陷卷吸掺气过程进行分

析，确定凹陷卷吸气泡过程中自由面形态变化规律及卷吸气泡的临界形态条件。

通过对试验观测的明渠水流局部自由面凹陷形态曲线采用拟合相关系数进行对比，并

进行定量分析以及 T-检验，表明自由面凹陷形态更符合高斯曲线形式，采用高斯曲线

顶点的曲率半径可以对自由面凹陷形态进行定量描述。在此基础上对自由面卷吸气泡

过程进行观测分析，结果表明，自由面闭合过程发生时间约为在观测到自由面凹陷起

7~19 ms，而对于不同观测情况，卷吸气泡过程所需时间约为 8~19,5 ms。通过对于自

由面凹陷变形并卷吸掺气过程的观测分析，验证了自由面凹陷卷吸掺气机理的理论分

析，即当自由面凹陷变形过程中当形态形变无法克服紊动作用时，超过临界条件时，

自由面发生凹陷失稳过程，并在此过程中由于凹陷两侧自由面闭合形成卷吸气泡。试

验观测的卷吸气泡过程中凹陷形态曲率半径随时间变化过程类似“钟形”，过程存在一

个临界峰值位置，在此之后曲率半径迅速减小，对于不同掺气过程，曲率半径峰值位

置变化范围约为 0,53 mm~2,97 mm。

本项目研究表明了采用试验对于明渠自由面形态演变及卷吸掺气机理的研究是可行

的，在今后进一步的研究过程中，应当发掘采用非接触式的试验测量方式对明渠水气

二相流进行直观的研究，并进一步研究自由面凹陷形态特征与卷吸气泡尺寸之间的定

量关系，全面揭示明渠高速水流自掺气形成机理。

Acknowledgement

We would like to express our greatest gratitude towards every one of whom directly and indirectly

have guided us and supported us throughout the project.

Special thanks to Dr. James Yang from KTH/Vattenfall AB whom enabled the chance to perform

this field study, without you we would not have met all the wonderful people and visited all the

beautiful places in China. Furthermore, we thank Energiforsk AB that funded the project.

We would also like to thank Dr. Wangru Wei, you were not only our supervisor, but also has been

a great friend and the memories we have shared will always be cherished. He provided us the right

equipment for the experiments and has always been there for our help during our stay. We are very

grateful for the guidance given by Professor Jun Deng at the Department of Hydraulics and

Mountain River Engineering at Sichuan University. Thanks to Dr. Ruidiscu Bai for helping us upon

our arrival to Chengdu and guiding us during our stay.

We would like to express our gratitude to Ms. Hera Shi and Ms. Flore Verkest, who made our stay

in Chengdu truly memorable. Thanks for your kindness and for showing us all the amazing places

in Sichuan province, but specially for having the patience to help us with everything we needed,

because when you do not speak Chinese, even the simplest things become very difficult.

We also owe special thanks to our examiner, Associate Professor Björn Laumert at Royal Institute

of Technology (KTH) for reviewing this Master’s thesis and providing all the necessary

arrangements at KTH for us.

Belkiz and Paulo from Chengdu, China. 2017-05-30

Table of Content

Abstract ............................................................................................................................................................

Sammanfattning ..............................................................................................................................................

摘要 ................................................................................................................................................................

Acknowledgement ..........................................................................................................................................

List of Figures .................................................................................................................................................

List of Tables ..................................................................................................................................................

Acronyms and abbreviations ........................................................................................................................

Nomenclature .................................................................................................................................................

1 Introduction .......................................................................................................................................... 1

1.1 Country overview ........................................................................................................................ 1

1.2 Electricity Generation Today and in Future ............................................................................ 2

1.3 Hydraulic Engineering ................................................................................................................ 3

1.4 Hydroelectric power .................................................................................................................... 4

1.5 Hydropower Capacity and Development in China ................................................................ 6

2 Problem Description ........................................................................................................................... 8

2.1 Objectives ..................................................................................................................................... 8

2.2 Process of study ........................................................................................................................... 9

2.3 Delimitations ................................................................................................................................ 9

3 Literature study ................................................................................................................................... 11

3.1 Open Channel Flow .................................................................................................................. 11

3.2 Spillways ...................................................................................................................................... 12

3.3 Key aspects in high-speed open-channel flows ..................................................................... 13

3.3.1 Energy dissipation ............................................................................................................. 13

3.3.2 Cavitation in Chutes and Spillways ................................................................................. 15

3.3.3 Vibration ............................................................................................................................. 16

3.3.4 Atomization ........................................................................................................................ 17

3.3.5 Aeration (Free-Surface Aeration and Aerator-Aeration) ............................................. 17

3.4 High-Velocity Air-Water Flows in The Open-Channel ....................................................... 21

3.5 Process of Free-Surface Deformation .................................................................................... 22

4 Methodology ....................................................................................................................................... 25

4.1 Experimental Setup ................................................................................................................... 25

4.2 Relevant Curve Types ............................................................................................................... 26

4.3 Image Analysis Method for Evaluating Free-Surface Deformation Curve ....................... 28

4.4 Method for Evaluating the Process of Surface Deformation and Air Entrainment ....... 30

5 Result from Experiments .................................................................................................................. 32

5.1 Analysis of The Free-Surface Deformation Curve Type ..................................................... 32

5.2 Results of The Process of Surface Deformation and Air Entrainment............................. 37

6 Improvements for Experiments ...................................................................................................... 47

7 Discussion ........................................................................................................................................... 48

8 Conclusion and Future work ............................................................................................................ 50

9 Bibliography ........................................................................................................................................ 51

Appendix A. ................................................................................................................................................ 54

Appendix B. ................................................................................................................................................ 55

Appendix C. ................................................................................................................................................ 56

List of Figures

Figure 1. The country overview of China and its neighbour countries (Central Intelligence Agency,

2017). .............................................................................................................................................................. 1

Figure 2. Electricity generation share of the total installed generating capacity in 2014. .................. 2

Figure 3. Growth of the total primary energy supply in China between the years of 1990-2030 (The

International Renewable Energy Agency (IRENA), 2014). ................................................................... 3

Figure 4. Typical "Low Head" hydropower plant schematic (How Stuff Works Science, 2017). .... 5

Figure 5. China's top ten provinces of hydropower (China National Renewable Energy Centre,

2012). .............................................................................................................................................................. 7

Figure 6. The process of the study shown in step by step. .................................................................... 9

Figure 7. Spillway design (FWEE, 2017). ............................................................................................... 12

Figure 8. Different phases during an energy dissipation process in a surface spillway with a stilling

basin (Indian Institute of Technology Kharagpur, 2017). .................................................................... 14

Figure 9. Cavitation damages in a chute spillway and a tunnel spillway (Teng, 2017). .................... 16

Figure 10. Atomization ranges of Baihetan hydropower station in China where (a) is from the

physical model, (b) is calculated in no-wind condition and (c) is calculated in constantly wind

condition (Jijian Lian, 2014). ..................................................................................................................... 17

Figure 11. Free-Surface Aeration in open-channel flows (Chanson, 2013). ...................................... 18

Figure 12. Self-Aeration on Chute Spillway (Chanson, 1993). ............................................................ 19

Figure 13. An aerator device shown with its principles (Teng, 2017). ............................................... 20

Figure 14. Air-water free-surface region in high-velocity flows (Chanson, 1996). ........................... 22

Figure 15. The two-dimensional model of the free-surface entrapped deformation process

(WangRu Wei, 2016). ................................................................................................................................. 24

Figure 16. The schematic figure of the experimental setup. ................................................................ 25

Figure 17. The Gauss curve distribution. ................................................................................................ 27

Figure 18. The Sine curve distribution. ................................................................................................... 27

Figure 19. A picture of the free-surface deformation curve. ............................................................... 28

Figure 20. Treated picture in Photoshop. ............................................................................................... 28

Figure 21. Snapshot of the image treatment in Autocad. ..................................................................... 29

Figure 22. Deformation curve and fitted known curves. ..................................................................... 29

Figure 23. Frames of the process of surface deformation and air entrainment. ............................... 30

Figure 24. Photoshop treatment. ............................................................................................................. 31

Figure 25. Measurement process in Autocad. ........................................................................................ 31

Figure 26. Plot of one frame in the process of surface deformation and air entrainment. ............. 31

Figure 27. Deformation curve shape, Observation 1, Video 1, Curve 3............................................ 32

Figure 28. Deformation curve shape, Observation 1, Video 2, Curve 10. ........................................ 32

Figure 29. Deformation curve shape, Observation 2, Video 1, Curve 8............................................ 33




Figure 33. Gauss Adj. R-Square coefficient............................................................................................ 35

Figure 34. Sine Adj. R-Square coefficient. .............................................................................................. 35

Figure 35. Adj. R-Square difference between Gauss and Sine fitting. ................................................ 35

Figure 36. Gauss vs. Sine box-plot. ......................................................................................................... 37

Figure 37. Process of surface deformation and air entrainment, Process 1. ..................................... 39





Figure 42. Radius of Curvature vs T/To for all the 5 Free-Surface Entrapped Deformation and Air

Entrainment Processes. ............................................................................................................................. 45

Figure A. Pictures from experimental setup and the department of hydraulic engineering............ 54

Figure B. The velocity measurement device. .......................................................................................... 55

Figure C. The adjusted R-squared coefficient. ....................................................................................... 60

List of Tables

Table 1. Basic simplifications for analysis of high-velocity air-water flows. ...................................... 21

Table 2. Relevant variables shown with units for Observations 1-3. ................................................. 26

Table 3. Relevant variables shown with units for Observation 4. ....................................................... 26

Table 4. Image analysis process. ............................................................................................................... 28

Table 5. Evaluation of the Process of Surface Deformation and Air Entrainment. ........................ 30

Table 6. Summary of observations. ......................................................................................................... 34

Table 7. One sample t-test results for the difference between fittings. .............................................. 36

Table 8. Descriptive statistics and confidence intervals for mean. ..................................................... 36

Table 9. Summary of observation. ........................................................................................................... 37

Table 10. Critical radius of curvature for all processes ......................................................................... 46

Acronyms and abbreviations

PRC People’s Republic of China

GDP Gross Domestic Product

PPP Purchasing Power Parity

GHG Greenhouse Gases

kW Kilowatt

kWh Kilowatt-hour

TWh Terawatt-hour

GW Gigawatt

AC Alternating Current

RVF Rapidly Varied Flow

GVF Gradually Varied Flow

CFD Computational Fluid Dynamics

LED Light Emitting Diode

Nomenclature

Re Reynolds number [-]

ρ Density [𝑘𝑔/𝑚3]

V Average velocity [𝑚/𝑠]

𝑅ℎ Hydraulic radius [𝑚]

μ Dynamic viscosity [𝑘𝑔

𝑚.𝑠]

𝑣 Kinematic viscosity [𝑚2

𝑠]

𝐹𝑟 Froude number [-]

𝑔 Gravity [𝑚

𝑠2]

𝐿𝑐 Characteristics length [𝑚]

𝑣′ The turbulent velocity [𝑚/𝑠]

𝜎 Surface tension [𝐽

𝑚2]

𝑑𝑏 Bubble diameter [𝑚]

𝑢𝑟 Bubble rise velocity [𝑚/𝑠]

𝛼 Spillway slope [°]

𝜎𝑐𝑎𝑣 Cavitation number [-]

𝑝0 Reference pressure [Pa]

𝑝𝑣 Vapor pressure [Pa]

𝑉0 Reference flow velocity [𝑚/𝑠]

𝑑 Equivalent clear water depth [𝑚]

𝑊 Chute width [𝑚]

𝐶 Air concentration in water flows [%]

𝑄𝑤 Unit flow discharge [𝑚3

𝑠]

𝑄𝑎 Air flow rate [𝑚3

𝑠]

𝐷0 Hydraulic diameter of the initial water flow in the chute [𝑚]

∆𝑝 Air pressure drop [Pa]

𝐶0 Summation of loss coefficients [-]

𝐾 Cavity pressure coefficient

ℎ0 Water depth of the approach flow [𝑚]

𝐸𝑘 Kinetic energy of the eddy [𝐽]

𝐸𝜎 Surface energy [𝐽]

𝐷 Characteristic size of the turbulent eddy [𝑚]

𝑣∗ Local velocity [𝑚/𝑠]

𝑣𝑓 Bed friction velocity [𝑚/𝑠]

𝑟𝑐 Radius of curvature [𝑚]

𝑟𝑎𝑏 Actual local radius [𝑚]

1

1 Introduction

In this chapter, a comprehensive introduction to the project will be presented including China's

country overview, China's electricity infrastructure, hydraulic engineering, and a description of

hydropower and lastly China's hydropower development.

1.1 Country overview

China, officially the People's republic of China (PRC), is located in the Eastern Asia bordering the

East China Sea, Korea Bay, Yellow Sea, and South China Sea, between North Korea and Vietnam

shown in Figure 1. Covering approximately 9 390 784 square kilometres, China is the world´s

fourth-largest by total area and the largest country situated entirely in Asia. With a population of

over 1,382 billion (July 2016), China is the world's most populated country and the capital city of

the country is Beijing. The country has an authority over 22 provinces, five self-governing regions,

four direct-controlled municipalities (Beijing, Tianjin, Shanghai, and Chongqing) and two

independent regions (Hong Kong and Macau) and claims sovereignty over Taiwan (Central

Intelligence Agency, 2017).

Figure 1. The country overview of China and its neighbour countries (Central Intelligence Agency, 2017).

Since initiating market reforms in 1978, China has moved from being a centrally-planned country

to a market-based one and has experienced rapid economic and social development. This economic

development has contributed to nearly 10 % of Gross domestic product (GDP) growth a year since

1978, and it has helped more than 800 million people to lift out of the poverty. Measuring the

purchasing power parity (PPP), China stood as the largest economy in the world in 2015 and is

increasingly playing an important role in the global economy. Still, China remains as a developing

country (China’s per capita income is below the world average) and its market reforms are

2

incomplete. Additionally, China is the world's largest exporter and the second-largest importer of

goods (The World Bank, 2016).

Agriculture, industries and services can be counted as the country's main sources of income. China

is the world leader in gross value of agricultural output such as rice, wheat, potatoes, corn and

industrial output such as mining and ore processing, iron, steel, aluminium, coal, petroleum,

cement, chemicals, fertilizers, machine building, textiles and apparel (Central Intelligence Agency,

2017).

1.2 Electricity Generation Today and in Future

China is the world's most developing country in terms of economically and technologically

expansions as well as population expansion. This kind of developments and expansions cause more

energy demand and the country should meet the requirement of energy demand by producing the

electricity and the heat itself or importing by other countries. By 2014, China has become the

world's largest exceeding the United States in terms of total electric power generation capacity with

5,388 trillion kWh and an installed generating capacity of 1,505 billion kW. Furthermore, the

electricity consumption in China is considerably high with 5,523 trillion kWh counted as the world's

leader electrical consumer (Central Intelligence Agency, 2017).

In 2014, the fossil fuels have still weighed the electricity generation in China with a share of 67,3 %

of its installed capacity while hydroelectric plants have had a share of 22,2 %. China is blessed with

abundant resources of the renewable energy sources and merely a small portion of these sources

are used today. Other renewable sources such as wind on-grid, solar PV, biomass, geothermal &

ocean share merely 9 % of the total installed capacity in the year of 2014. Figure 2 shows the share

of different fuel types of the total installed generating capacity for the year of 2014 (Central

Intelligence Agency, 2017), (The International Renewable Energy Agency (IRENA), 2014).

Figure 2. Electricity generation share of the total installed generating capacity in 2014.

China has the enormous coal reserves which is combusted in coal-fired power plants and ensures

that the coal combustion is the most available and cheapest alternative to generate electricity. The

reliance on coal combustion has great impact on the levels of harmful emissions. The emissions of

67%2%

22%

9%

Electricity Generation Share of Total Installed Capacity in 2014

Fossil

Nuclear

Hydroelectric

Other renewable

3

greenhouse gases from energy supply by combusting as much coal to generate electricity, China

causes an increase to the greenhouse gases emissions (GHG) with a share of 28 % of the world's

CO2 emissions (The International Energy Agency (IEA), 2013).

China's power generation capacity is expected to increase more than double by 2030 or even before.

A considerable share in this increase will be provided by renewable energy projects to eliminate the

fossil fuel and the coal usage as much as possible.

According to the Reference Case renewable energy trends in China between the years 2010 - 2030,

coal consumption is expected to flatten until the year 2030 and instead utilizing more natural gas,

followed by oil and nuclear power. Other renewable sources (solar, wind), hydro and bioenergy

will significantly contribute to this increase. In the Reference Case, the power generation is

expected to increase more than double from 4 200 TWh/year in 2010 to approximately

9 300 TWh/year by 2030 as it can be seen in Figure 3 below. By 2030, hydroelectricity generation

will totally be 1 600 TWh followed by wind with 650 TWh, solar PV with 200 TWh and biomass

with 190 TWh. A significant part of hydroelectricity with an additional 200 TWh is related to the

increased use of electricity-efficient technologies in end-use sectors resourcing electricity demand

from the renewable power sources according to the Reference Case, for example heat pumps and

electro instability (The International Renewable Energy Agency (IRENA), 2014), (U.S. Energy

Information Administration (EIA), 2016).

Figure 3. Growth of the total primary energy supply in China between the years of 1990-2030 (The International Renewable Energy Agency (IRENA), 2014).

1.3 Hydraulic Engineering

Hydraulics is an engineering discipline that overlooks the mechanical properties of fluids and the

discipline of fluid power in a useful way. Fluid mechanics provides the theoretical basis for the

engineering use of fluid properties for hydraulics. Hydraulic engineers have always played an

important role for the technical development of the hydraulic engineering. However, the challenges

have been enormous considering the different levels of complexity and variety of water systems

such as that the broad range of relevant time and length scales, the variability of river flows from

4

droughts to gigantic floods, the difficulty of fluid mechanics with non-linear governing equations,

natural fluid imbalances, interactions between water, solid, air and biological life, and more

importantly human life’s total dependence upon water (Chanson, 2007).

The dependence of water has introduced the need of the innovative solutions of hydraulic

engineering. Hydraulic structures should be designed to facilitate the dissipation of the kinetic

energy of the flow. By innovative solutions and excellence in hydraulic research, the construction

cost as well as the impact on environment and habitants would be decreased.

1.4 Hydroelectric power

Harnessing the potential energy accumulated in water to generate electricity is a classic way to

obtain renewable energy, since it is based on the water cycle and it has been in used since the end

of the nineteenth century (German Energy Agency (DENA), 2017). About 20 % of the world’s

electricity comes from this source (United Nations Educational, Scientific and Cultural

Organization (UNESCO), 2016).

Hydropower is the most flexible energy source available and can easily respond in minutes to

demand fluctuations which arise with weather-dependent solar and wind energy. Because of this

flexibility, hydropower is an ideal complement to other renewable energy sources. Furthermore, it

is the only large-scale and cost-effective storage technology available nowadays and relatively

effective (The International Renewable Energy Agency (IRENA), 2012). From the environmental

point of view, hydroelectric power is one of the cleanest and it is relatively cheap, although this

does not mean that it is totally harmless. The dams, needed to create water reservoirs have severely

consequences in the ecosystems, it could be harmful for both animal and human populations.

Additionally, the construction phase of hydropower plants causes substantial emissions, from the

construction of the dam but also from the production and transportation of the materials needed

(Worldwatch Institute, 2013).

The hydroelectric power plants produce electrical energy from the potential or gravitational energy

(mass at a certain height) contained in the water flowing in a river with a certain vertical fall or

head. The concept is relatively simple, it converts the potential energy into electrical energy by

hydraulic turbines coupled to electric generators (The International Renewable Energy Agency

(IRENA), 2012). The main components of a conventional hydropower plant are shown in Figure

4 below.

5

Figure 4. Typical "Low Head" hydropower plant schematic (How Stuff Works Science, 2017).

• Dam: Most hydropower plants rely on a dam that holds back water, creating a large water

reservoir that can be used as storage. There may also be a de-silter to cope with sediment

build-up behind the dam.

• Intake, penstock and surge chamber: Gates on the dam open and gravity conducts the

water through the penstock (a cavity o pipeline) to the turbine. There is sometimes a head

race before the penstock. A surge chamber or tank is used to reduce surges in water

pressure that could potentially damage or lead to increased stresses on the turbine.

• Turbine: The water strikes the turbine blades and turns the turbine, which is attached to a

generator by a shaft. There is a range of configurations possible with the generator above

or next to the turbine. The most common type of turbine for hydropower plants in use

today is the Francis Turbine, which allows a side-by-side configuration with the generator.

• Generators: As the turbine blades turn, the rotor inside the generator also turns and electric

current is produced as magnets rotate inside the fixed-coil generator to produce alternating

current (AC). Transformer: The transformer inside the powerhouse takes the AC voltage

and converts it into higher-voltage current for more efficient (lower losses) long-distance

transport.

• Transmission lines: Send the electricity generated to a grid-connection point, or to a large

industrial consumer directly, where the electricity is converted back to a lower voltage

current and fed into the distribution network. In remote areas, new transmission lines can

represent a considerable planning hurdle and expense.

• Outflow: Finally, the used water is carried out through pipelines, called tailraces, and re-

enters the river downstream. The outflow system may also include “spillways” which allow

the water to bypass the generation system and be “spilled” in times of flood or very high

inflows and reservoir levels.

6

1.5 Hydropower Capacity and Development in China

The biggest source of renewable energy in China is hydropower, it accounts for 85 %, in 2013, of

the total renewable power generation. For the tenth sequential year, China has maintained the

country’s leading role in global hydropower development by installing more hydropower plants

than the rest of the world combined. In 2015, China has added 19 370 MW including 1 230 MW

of pumped storage, of new hydropower capacity bringing the China’s total installed hydropower

capacity to 320 GW. Furthermore, China remains as the world leader regarding other renewable

energy utilization and this increase of other renewable sources have led a decrease in the

hydropower share (International Hydropower Association (IHA), 2016). Pumped-storage

hydropower has rapidly been developed in the country to complement the increasing nuclear power

capacity. Pumped-storage hydropower is used to store energy in the form of water during periods

when there is a surplus of electricity in the grid. When the electricity demand is high, power is

generated by releasing the stored water from the upper reservoir through turbines which can act as

both pumps and turbines. During low electricity demand periods, usually nights and weekends then

the electricity cost is low, the upper reservoir is recharged by utilizing lower-cost electricity from

the grid to pump the water back to the upper reservoir. Pumped-storage hydropower can provide

energy-balancing, stability in terms of meet the peak electricity demand, high round-trip efficiencies

reaching greater than 80 %, storage capacity, and auxiliary grid services (Energy Storage

Association, 2017). However, the pumped-storage hydropower plants have not reached a rate as

the conventional hydropower plants as expected. Installed pumped-storage capacity reached 23

GW in 2015, which is far from the plan’s 41 GW target. By 2017, China’s target for the total

installed capacity is 330 GW (International Hydropower Association (IHA), 2016).

More than 70 % of the total electricity production from hydropower comes from 10 provinces, see

Figure 5, and about 25 % of the population relies on small scale hydroelectric facilities (China

National Renewable Energy Centre, 2012), One of the notable capacity additions in 2015 contains

the addition of the first two 650 MW turbines at the Dagangshan hydropower plant on the Dadu

River in Sichuan. The total planned installed capacity was 2 600 MW when fully commissioned in

2016. The Guanyinyan project on the Jinsha River with a total installed capacity of 3 000 MW has

added three more turbines with a capacity of 600 MW in 2015. In the Tibet Region, the 510 MW

run-of-river Zangmu station was fully authorized, containing added its first two 85 MW turbines

in 2014 is planned to be the largest hydropower station in this region. The Niyang stations also

located in the Tibet Region with a capacity of 120 MW was fully commissioned. Another large

hydropower station called Mamaya hydropower station located on the Beipangjiang River in

Guizhou province, with a capacity of 558 MW was connected to the grid. It is planned to supply

power through newly constructed transmission lines to Guangdong provinces (International

Hydropower Association (IHA), 2016).

7

Figure 5. China's top ten provinces of hydropower (China National Renewable Energy Centre, 2012).

Although, China has the largest installed hydropower capacity in the world (World Energy Council,

2017), it only accounts for about 40 % of the technical potential, which is a lot less the average

than in other developed countries. The goal is that by 2020 the installed capacity will reach 420

GW. In order to achieve this goal, it will be necessary to construct 50 large-scale dams on the

Jinsha, Yalong, Dadu, Lancang and Yarlung Tsangpo rivers (The International Renewable Energy

Agency (IRENA), 2014).

8

2 Problem Description

The hydroelectric power plants produce electrical energy from the potential or gravitational energy

(mass at a certain height) contained in the water flowing in a river with a certain vertical fall or

head. Hydroelectric power is produced as water passes through a dam and thereafter into a river.

Dams are structures built across the river and used to control river flow, improve navigation and

regulate flooding. There are several points that needs to be considered when designing a

hydroelectric dam, for example the available head, the geographical position suited to construct a

dam. To obtain a flow duration curve for the water flow distribution throughout a year, a

comprehensive study is needed to be done because the quantity of water flow in a river is unsteady.

Based on this kind of study, different dam designs could be considered and the most appropriate

solution for its conditions could be chosen (German Energy Agency (DENA), 2017).

Another important point is that the design of flood discharge structures, such as spillways, sidewalls

etc. The majority of dam safety lacks identified consists of inadequate spillway capacity for passage

of new design floods up to the possible maximum flood. Because of the passage of water flow

through spillways is enormous, it can easily destroy the dam due to the undersized spillways, and

can result in both economic losses and threat to life (International Commission on Large Dams

(ICOLD), 1992).

When designing spillways and chute sidewall, one important aspect to consider, is the presence of

air, which can be entrained in large amounts through the free surface into the water in high-velocity

flows and leads to the bulk of the flow to increase (WangRu Wei, 2016).

This is important since the present of air in the boundary layer leads to lower shear stress, which

in turn leads to an increase of momentum that must be taken in account when designing a ski jump

downstream of a spillway (Chanson, 1993). The air entrainment process is described as the

occurrence after many ejected droplets fall into the flow disrupting the free-surface and causing an

entrainment of air in the form of bubbles. The reasons behind the formation mechanism of air

entrainment in self-aerated open-channel or chute flows has been investigated under a long period.

Different studies have been conducted and different results have been presented regarding the

relationship between free-surface deformation and air entrainment, nevertheless, the key aspect has

not been understood yet. Another significant reason for the key aspects not being fully understood,

is the lack of information about the characteristic features of such flows.

Another important aspect regarding dam safety is the cavitation phenomena which can be

prevented or reduce by the present of air in high-velocity flows (Jansen, 1988).

2.1 Objectives

The aims and objectives are to study uniform self-aerated flows and describe the relationship

between free-surface entrapped deformation and air entrainment. This will be achieved by an

empirical analysis of a simple two-dimensional model of free-surface deformation, based on

dynamic and energy transitions.

The objectives are presented shortly below;

9

STAGE 1

INITIATION

Establish a vision

Purpose

Schedule

STAGE 2

IDEAS

Literature study

Local advisory

Experiments

STAGE 3

RESULTS

Theoretically

Experimentally

STAGE 4

REVIEW

Discussions

Conclusions and

Future Work

Improvements for

Experiments

• The process of free-surface entrapped deformation and air entrainment will be analysed

based on a simple two-dimensional model of free-surface deformation in order to find the

reasons behind the formation mechanism of air entrainment.

• To perform a number of experiment and observe the results of the experiments and

comparing the results with earlier experimental data and published work.

• To describe the whole process of free surface entrapment using the performed experiments

and the earlier works.

2.2 Process of study

The layout of this thesis has been organized into different sections in order to enable both readers

and authors to follow the structure in a proper way. The thesis will be planned accordingly;

• Planning and structuring

• Performing experiments

• Analysis of experiments and interpretation

• Securing and evaluation of the quality

• Writing of report

The steps of the study are shown in Figure 5 below. To begin with the study, a vision should be

established and a schedule based on the vision should be created. When the vision of study has

been established, the aims and objectives can be decided and the schedule including all processes

can be created. For the next step, a comprehensive literature study is needed as the basis for

understanding all experiments. During the field study, information will be gathered through

experiments, observations, measurements and advisory with responsible personal. The results will

be provided both theoretically and experimentally based on the gathered information and data from

experiments and measurements. As the last stage, discussions, conclusions and future work will be

done based on the all gathered data from the performed experiments and information from the

earlier stages. Afterwards, some useful suggestions to improve the experiments will be provided.

Figure 6. The process of the study shown in step by step.

2.3 Delimitations

The selection of appropriate measurement technique(s) for any experimental investigation is most

important to ensure reliable experimental data. In the present study, the most suitable and

appropriate measurement technique for experiments is chosen and a few important limitations are

considered while performing experiments and analysing the result of the experiments. The

limitations are described accordingly;

10

• The velocity difference between the centre of the flow and sidewalls will be neglected due

to the friction between the flow and sidewalls is negligible.

• It is assumed that the uniform flow conditions are achieved along the chute because the

watercourse is relatively long.

• The interactions between entrained air bubbles and turbulent length-scales of air-water

flow is assumed to be scaled properly.

11

3 Literature study

Self-aerated open channel flows have been studied relatively and investigations have been

performed based on laboratory models. All experimental investigations revealed the complexity of

the free-surface aeration process. Some major contributions have been done to develop the basic

principles of self-aerated flow by describing the uniform air-water flow properties, the air content

and mean velocity distributions, and the gradually-varied air-water flow properties. However, there

is little information on the characteristics of air-water flows down small-slope chutes and in

partially-filled conduits.

A literature study has been done regarding spillway designs, key aspects in high-speed open-

channel, air-water flows characteristics and process of free-surface deformation based on the

available literature and earlier researches. In this section, a summary of these earlier studies will be

presented in order to provide the reader information about the aforementioned titles.

3.1 Open-Channel Flow

A flow that has the presence of a liquid–gas interface (free-surface) and flows due to gravity is

called an open-channel flow, the slope of the channel drives the flow rather than the pressure.

Flows in pipes could also fall in this category if the pipe is not full (has a free surface). In an open-

channel the velocity is zero at the walls and bottom due to the no-slip condition (the fluid velocity

at all fluid–solid boundaries are equal to that of the solid boundary (Weisstein, 2017)). The

maximum velocity is at the midplane of the free surface but often the velocity changes in the

stream-wise direction (Yunus A. Çengel, 2014).

The flow in the channel can be classified as:

• Steady and Unsteady flow: a steady flow is defined as a flow in which conditions (flow rate,

velocity, depth, etc.) are constant with respect to time, on the other side, the conditions for

an unsteady flow varies with time.

• Uniform and Non-uniform flow: a uniform flow is defined as a flow where depth and slope

of the channel, the cross section and velocity are constant along the channel, while in a

non-uniform these features change along the channel.

The presence of obstructions or barriers along the channel leads to variation in flow depth, the

flow could be, rapidly varied flow (RVF), which means that the variation happens over a short

distance close to the obstruction. Furthermore, the flow could also be, gradually varied flow (GVF),

when the variation occurs over large distances. A GVF frequently connects RVF and uniform flow.

Depending on the value of the Reynolds number (Re), see Eq. 1, the flow could be laminar (𝑅𝑒 <

500), transitional (500 < 𝑅𝑒 < 1 000) or turbulent (𝑅𝑒 > 1 000) (Yunus A. Çengel, 2014);

𝑅𝑒 =ρ ∙ V ∙ 𝑅ℎ

μ=

𝑉 ∙ 𝑅ℎ

𝑣 (1)

where,

• 𝜌 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

• 𝜇 = 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦

• 𝑣 = 𝑘𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦

12

• 𝑉 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

• 𝑅ℎ = ℎ𝑦𝑑𝑟𝑎𝑢𝑖𝑙𝑖𝑐 𝑟𝑎𝑑𝑖𝑢𝑠 = 𝐴𝑐 𝑝⁄ ; 𝐴𝑐 = 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 ; 𝑝 = 𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟

In free-surface flows, gravity effects are mostly important and therefore laboratory studies must be

based on a Froude similitude. This classification for open-channel flow is given by the Froude

number (Fr), see Eq. 2. The flow in an open-channel could be subcritical (𝐹𝑟 < 1), critical (𝐹𝑟 =

1) or supercritical (𝐹𝑟 > 1) (Yunus A. Çengel, 2014);

𝐹𝑟 =V

√𝑔 ∙ 𝐿𝑐

(2)

where,

• 𝑉 = 𝑓𝑙𝑜𝑤 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

• 𝑔 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑦

• 𝐿𝑐 = 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑙𝑒𝑛𝑔𝑡ℎ

3.2 Spillways

Spillways are structures used in a hydropower plant to provide a controlled release of flows from

the dam into the downstream area when the reservoir becomes full. A controlled spillway has

mechanical structures or gates to regulate the flow rate, therefore it is important to design these

spillways in a proper way to dissipate the energy in the water to avoid scour. For smaller dams,

water can be carried around the dam through water channels back to the adjacent river or lake

while for larger dams containing several millions cubic meters of water, the excess water needs to

be released more controlled and direct methods. Poorly designed and constructed spillways can

create major problems to the foundation of the dam leading to costly reparations and maintenance

work, or destroy the dam (International Commission on Large Dams (ICOLD), 1992). In Figure

7 below, spillway design in a high dam is shown in order to dissipate the energy in the water.

Figure 7. Spillway design (FWEE, 2017).

When designing spillways or chute sidewalls, the increasing bulk effect of the flow with incoming

air in open channels should be considered. The presence of air within the boundary layer causing

13

a reduction of shear stress and the resulting increase of momentum should further be considered

when designing spillways (Chanson, 1993).

Hydraulic structures under turbulent flow conditions regularly involve free-surface flow and

interactions between air and water. This can be observed in different kind of structures and

spillways, e.g. smooth chute spillways, stepped spillways, side-channel spillways, shaft spillways,

siphon spillways etc. The design and the most appropriate choice of spillway type depends on the

energy dissipation (Indian Institute of Technology Kharagpur, 2017).

The stepped spillways are overall spillway structures followed by steps on the spillway face with

the purpose of decreasing the energy dissipation in the spillway surface. In a side-channel spillway,

the water from the reservoir flows in from the side of the channel. The water after flowing over a

crest enters a side channel which is nearly parallel to the crest. When the side of the channel facing

the reservoir, is enough steep and deep then this design can be considered as an appropriate

structure for the energy dissipation. Side-channel spillways are located just upstream and to the side

of the dam in types of earth and rockfill dams. Shaft spillways utilize a crest circular in plan, water

enters a horizontal crest, drops through a vertical shaft and then flows to the downstream river

channel trough a horizontal conduit or tunnel. The shaft spillway has a using advantage when

maximum spillway discharge is not likely to be exceeded. Siphon spillways are structured as closed

conduits shaped with the shape of an inverted U of unequal legs. By using these types of spillways,

the specific flow rate can be increased (Indian Institute of Technology Kharagpur, 2017).

In this study, smooth chute spillways will be considered as the basis of the experiments and further

literature studies will be done based on this type. In a smooth chute spillway, the spillway discharge

flows in an open-channel right from the reservoir to the left downstream river. The smooth chute

should be designed in order to keep the channel bed in excavation and its side slopes in a stable

position with sufficient margin of safety. The simplest design of a smooth chute spillway is an

open-channel with straight centre line and constant width. However, this design can be suited

according to the geography of the site and the axis of either the channel entrance or the discharge

channel can be curved. The flow condition differs from subcritical upstream of the controlling

crest to critical at the crest and supercritical in the discharge channel. The chute spillway is adapted

mostly in earth-fill dams because of the simplicity of their design and construction (Chanson, 2013).

3.3 Key aspects in high-speed open-channel flows

Most high dams constructed in the hydraulic engineering field in China during recent decades have

features of high water head, large flow capacity, a deep narrow valley and large flood discharge

power. There are some important issues that should be considered in high-speed open-channel

flows such as energy dissipation, vibration control of a hydraulic structure, vapor atomization

protection, cavitation and aeration for cavitation protection.

3.3.1 Energy dissipation

The main purpose of energy dissipation at dam sites is to transport the downstream water flow of

the dam to the same condition as in the upstream reservoir in as short distance as possible. Energy

dissipation is an important matter of dam safety and this matter should be considered when

evaluating and choosing the most appropriate solution in order to avoid the impact of downstream

14

scour of the dam. Especially for large dams, the energy dissipation of downstream water flow is

important since large volumes of water of high pressure are transported in these types of dams.

Several different ways can be used to dissipate the energy for dam outlets. Energy dissipators often

included in the spillway are structural elements that has a function of dissipating the energy in the

flow before released to the downstream area. The types of energy dissipators are many and may be

used along with a spillway, alone or in combination of more than one depending on the dam type,

the energy to be dissipated, location and flow regime and erosion control required downstream of

a dam. Generally, the energy dissipators are categorized accordingly – Stilling basins or Bucket

Type (Indian Institute of Technology Kharagpur, 2017). The stilling basin that extends directly at

the end of the spillway, a hydraulic jump can be created. The structure created a sudden turbulent

transition and causes a hydraulic jump, effectively reducing the stress on the downstream ground.

This type of energy dissipators are effective in dams where the toe of the spillway reaches the water

level of the downstream area, as the downstream water depth is required to create the hydraulic

jump. Bucket type energy dissipators are more often used for spillways located at a certain height

above the downstream water level in order to increase the energy dissipation of the jet leaving the

spillway. The jet of a ski jump spillway leaves horizontally whereas the jest of a flip bucket is

deflected upwards to stimulate dispersion in the air. The energy can be dissipated by friction forces

within the jet and between the water jets. The flow coming down the spillway is thrown away from

toe of the dam to a considerable distance downstream as a free discharging upturned jet which falls

into the channel directly, thereby avoiding excessive scour immediately downstream of the spillway.

This is the main purpose of designing the bucket type energy dissipators which results in the force

of the jet landing at a safe distance away from the dam and by that minimizing the possible channel

bed erosion close to the downstream toe of the dam (Indian Institute of Technology Kharagpur,

2017).

Figure 8. Different phases during an energy dissipation process in a surface spillway with a stilling basin (Indian Institute of Technology Kharagpur, 2017).

15

In Figure 8, an energy dissipation process in a surface spillway with a stilling basin is shown in five

different steps.

1. The spillway surface

2. The free-falling jet

3. The inception point

4. The stilling basin

5. The outflow back to the river

3.3.2 Cavitation in Chutes and Spillways

Cavitation is described as the formation of a bubble or void within a liquid. The formation of

bubble or void is not to a change in temperature, however to a change of pressure. Cavitation will

occur when the local pressure in flowing water drops below vapor pressure. When the pressure

drops below vapor pressure, depending on the liquid properties, the dissolved air is released and

the liquid vaporizes in local areas. The vapor structures are frequently unsteady and when the region

of increased pressure has been reached, they collapse strongly since the internal pressure hardly

varies and remains close to the vapor pressure (Jean-Pierre Franc, 2004). In hydraulic structures,

the most common sources of cavitation are irregularities in the flow surface. Another reason for

the creation of cavitation can be shear flows. The submerged jet is an example of a shear flow. The

shear is generated between the high velocity jet and the relative quiescent fluid adjacent the jet

(Falvey, 1990).

There are some damaging effects of cavitation in hydraulics accordingly;

• Reduced capacity to evacuate water in spillways, energy dissipation,

• Appearances of additional forces not designed for on the solid structures,

• Production of noise and vibrations,

• Wall erosion if the velocity difference between the liquid and the solid wall is high

enough when the cavitation is developed.

In spillways, cavitation regarding pressure decrease occurs most commonly at sudden curvatures

and where gate establishes or similar structures interrupt the smooth flow along a boundary. Such

failures create abrupt micro-cracks in the surface and with time, prolonged holes are created. Figure

9 shows the cavitation effects in two different structures, in a) chute spillway and b) tunnel spillway.

To decrease these damaging effects of the cavitation in spillways, the strength of surface material

and entraining air into the flows can be increased (Teng, 2017).

16

Figure 9. Cavitation damages in a chute spillway and a tunnel spillway (Teng, 2017).

The grade of cavitation as well as to see whether cavitation occurs or not can be described and

calculated by the cavitation number, 𝜎𝑐𝑎𝑣. Eq. 3 for the cavitation number is shown below.

𝜎𝑐𝑎𝑣 =𝑝0 − 𝑝𝑣

12 ∙ 𝜌 ∙ 𝑉0

2 (3)

The reference pressure, 𝑝0 is the local pressure at any given location. The atmospheric pressure is

also included in the reference pressure since the water in the tunnel is affected by that. Normally,

the gauge pressure is obtained from the experiments and after that, the atmospheric pressure is

added. The vapor pressure, 𝑝𝑣 is dependent on the temperature. For the experiments, the water

temperature is set to 20°C which has the vapor pressure of 2,3 kPa (Laboratory, 2015).

The water density is shown with 𝜌 and 𝑉0 stands for the reference flow velocity. The lower values

of the cavitation number indicate that the more likely cavitation occurs. For negative values, it is

totally expected that the cavitation occurs (Falvey, 1990).

3.3.3 Vibration

Vibration controls of hydraulic structure have been investigated several times before. However,

the underlying mechanism is not fully understood because of the physical situations leading to gate

vibrations are usually very various and complex in practice. As it is stated in different review papers

before, one of the most regular sources of gate vibrations is dynamic loads due to unstable flow

separation and reattachment at the gate cross section. This condition can be applied to vertical-lift

gates with flow below as well as to certain submersible gates with flow over the top. Generally, it

occurs whenever flow is separated from an upstream edge and wavers near remaining part of the

gate profile under submerged-flow conditions, considerable vibrations may develop (Thang, 1990).

According to the result of performed experiments and calculations from these earlier studies, the

vibration tendency can be increased by the presence of a free-water surface submerging the gate

bottom on the downstream side of a conduit gate compared to the condition of full-conduit

discharge. When the critical gate-opening range concerning potential gate, vibrations is known,

appropriate solutions can be considered, e.g. reshaping the inlet section or adding mechanical

damping (Thang, 1990).

17

3.3.4 Atomization

Flood discharge atomization is an inevitable phenomenon for high dams with ski-jump energy

dissipation which may cause heavy rainfall and diffuse clouds around the dam-site area. There are

some harmful effects of this phenomenon, such as disturbing the normal operation of the buildings

and the transportation, disturbing the power transmission system, causing landslides and slope

variability, affecting the ecological environment and the residents’ life conditions. To minimize

these effects of the flood discharge atomization, a prediction method has been developed based

on prototype observation, physical model and mathematical model. The prediction method is used

to determine the rainfall intensity and coverage area of the flood discharge atomization. The

mathematical model including differential equations of the jet, the splashing as the jet impacting at

the downstream water surface and random splashing of the water droplets combined with the large-

scale physical model has been verified as the most appropriate way to predict the atomization of a

hydropower station (Jijian Lian, 2014). As it is shown in Figure 10 below, the atomization rainfall

intensities and coverage area near to the Baihetan dam differ along the various distances due to

different wind conditions and the physical model.

Figure 10. Atomization ranges of Baihetan hydropower station in China where (a) is from the physical model, (b) is calculated in no-wind condition and (c) is calculated in constantly wind condition (Jijian Lian, 2014).

3.3.5 Aeration (Free-Surface Aeration and Aerator-Aeration)

Aeration is the process by which air is circulated through, mixed or dissolved in the water flow. Air

in the form of small bubbles entrains in the water flow and allows a portion of the oxygen content

of the air to be moved to the water flow as dissolved oxygen. Aerated flow may occur naturally in

open channels of steep slope having high velocity flow and an accompanying high degree of

turbulence. When open-channel flow is exposed to aeration, there is a significant increase in the

flow retardance as a direct result of the aeration. Aeration process can be performed in two

different ways, namely, free-surface aeration and aerator-aeration.

• Free-Surface Self-Aeration

The flow conditions that cause air to enter, or in other words, the transport of air through the free

surface of water, is called self-aeration. This results in the free surface aeration, or natural aeration.

18

In some flows, the air inlet takes place on the entire surface of the water and in others, the air inlet

occurs locally on a discontinuity in the surface (Jansen, 1988).

In open channels with high flow velocity, as in spillways or discharge channels, the turbulent flow

gives rise to disturbances on the surface, which lead to the entrance of air. Several studies have

shown that air may be entrained by breaking waves at the free surface if conditions satisfy 𝐹𝑟 <

1,5 (Keulegan, 1940), but also that air is entrained by the water droplets that are projected above

the surface of the water and then fall back into the flow, these drops penetrate the surface of the

water carrying air (Volkart, 1980).

For air to be entrained the flow should be turbulent enough to overcome surface tension and

gravity effects. This occurs when (Ervine, 1987);

• The turbulent velocity (𝑣′) overcome the surface tension (σ) pressure of the entrained

bubble shown in Eq. 4 below;

𝑣′ > √8 ∙ 𝜎

𝜌𝑤 ∙ 𝑑𝑏 (4)

• When 𝑣′ is bigger than the bubble rise velocity component for the bubble to be carried

away shown in Eq. 5 below;

𝑣′ > 𝑢𝑟 ∙ cos 𝛼 (5)

where,

• 𝜎 = 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑛𝑠𝑖𝑜𝑛

• 𝜌𝑤 = 𝑤𝑎𝑡𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

• 𝑑𝑏 = 𝑏𝑢𝑏𝑏𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

• 𝑢𝑟 = 𝑏𝑢𝑏𝑏𝑙𝑒 𝑟𝑖𝑠𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦

• 𝛼 = 𝑠𝑝𝑖𝑙𝑙𝑤𝑎𝑦 𝑠𝑙𝑜𝑝𝑒

In an open channel, free-surface aeration occurs downstream of the inception point. The inception

point of air entrainment is defined as the point of apparition of “white waters” or free-surface

aeration. At the channel intake, the flow free-surface is smooth and glassy. Next to the bottom,

turbulence is generated and a boundary layer grows. See Figure 11 bellow.

Figure 11. Free-surface aeration in open-channel flows (Chanson, 2013).

19

It is generally accepted that the inception point occurs when the outer edge of the turbulent

boundary layer reaches the surface. Downstream of the point of inception, a layer containing a

mixture of both air and water extends gradually through the fluid. The rate of growth of the layer

is small and the air concentration distribution varies gradually with distance. Self-aeration is an

interfacial aeration process, with an uncontrolled supply of air. Next to the free-surface, the

entrained air is adverted in region of low shear. Figure 12, shows a schematic of the self-aeration

process on chute spillway.

Figure 12. Self-aeration on chute spillway (Chanson, 1993).

Self-aeration flows in spillways, chutes and storm waterways have been studied because of

entrained air on the thickness of the water flow. For air-water flows in a rectangular open channel,

the equivalent clear water depth, 𝑑 is defines in Eq. 6 accordingly;

𝑑 = ∫ (1 − 𝐶) ∙ 𝑑𝑦

𝑌90

0

(6)

where, 𝑌90 characterizes the air-water flow thickness when the air concentration is 𝐶 = 0,9. This

method for the fully-developed uniform flow region is utilized in order to explain the air

concentration distribution and the water level variation in different regions. In previously studies

this interface is defined with the air concentration line 𝐶 = 0,9 (i.e 𝑦 = 𝑌90), (Chanson, 1996)

since high-velocity air-water flows act as a homogeneous mix when 𝐶 < 0,9 (CAIN, 1978)

(Chanson, 1988), (Wood, 1991). On the other hand, for 𝐶 > 0,9 water droplets are ejected and

behave as free-fall particles. The depth averaged mean air concentration 𝐶𝑚𝑒𝑎𝑛 is defined as the

integration of the local values 𝐶(𝑦) over the water depth between the chute bottom at 𝑌 = 0 and

the free-surface 𝑌 = 𝑌90 as it is shown in Eq. 7 below (Wangru Wei, 2016).

𝐶𝑚𝑒𝑎𝑛 =1

𝑌90∫ 𝐶(𝑦) ∙ 𝑑𝑦

𝑌90

0 (7)

20

Approach flows with variable initial depths, 𝑑0 , velocities 𝑈0, relative Reynolds number, 𝑅𝑒0, and

relative Froude numbers, 𝐹𝑟0, are usually generated in the intake connected to the chute. The

hydraulic diameter of the initial water flow in the chute, 𝐷0 is defined in Eq. 8 accordingly (Wangru

Wei, 2016);

𝐷0 =𝑊 ∙ 𝑑0

𝑊 + 2 ∙ 𝑑0 (8)

where, 𝑊 is the chute width. The initial average water velocity, 𝑈0 defines as it is shown in Eq. 9;

𝑈0 =𝑄𝑤

𝑑0 (9)

where, 𝑄𝑤 is the unit flow discharge and 𝑑0 is the initial water depth (Wangru Wei, 2016).

• Aerator-aeration

When there is a risk of damage due to cavitation and the free-surface aeration is not sufficient,

artificial aeration has been one of the most widely used solutions to protect the dam from the

cavitation and for the water quality enhancements. This is done by designing aerators to distort

high velocity flow away from the chute surface. Aerators have basically a shape of a ramp, an offset

and a groove (air duct) and are usually constructed down the length of the chute to suck the air

and provide into the flow. See Figure 13 below. A combination of these basic shape principles

provides the most appropriate design; the ramp controls the operation at small discharges, the

groove provides area for air supply, and the offset expands the jet trajectory at higher discharges

and enlarges the air cavity. In the previous studies, it has been recognized that air bubbles are

redistributed downstream of an aeration device as in free-surface self-aerated flows and there is

similarity between the flow downstream of an aerator and self-aerated flows. An aerator device is

considered as the most cost-effective solution to entrain air into the flow (Chanson, 2016).

Figure 13. An aerator device shown with its principles (Teng, 2017).

Due to the complexity of the air entrainment process, investigation of the characteristics of aerator

flows has likewise been difficult. After utilizing both hydraulic model tests and prototype aerators,

some relevant parameters governing the capacity of an aerator have been defined, namely, the

geometrical layout, air pressure drop in the cavity and air supply and entrainment. An air pressure

21

drop (∆𝑝) may be caused in the aerator by transporting away air in the cavity formed downstream

of an aerator (Teng, 2017). This pressure drop can be defined according to Eq. 10 below;

∆𝑝 =𝜌𝑎 ∙ (1 + 𝐶0) ∙ 𝑄𝑎

2

2 ∙ 𝐴2 (10)

where, 𝐴 is the cross-sectional area of the air passage, 𝜌𝑎 is the air density, 𝐶0 is the summation of

loss coefficients along the air passage, 𝑄𝑎 is the air flow rate. When the geometrical layout is

known, the pressure drop can be defined instead in Eq. 11 below;

∆𝑝 = 𝐾 ∙ 𝜌𝑤 ∙ 𝑔 ∙ ℎ0 (11)

where, K is the cavity pressure coefficient, 𝜌𝑤 is the water density, 𝑔 is the acceleration of gravity

and ℎ0 is the water depth of the approach flow (Teng, 2017).

The air supply and entrainment process can be defined by an air entrainment rate, 𝛽 = 𝑄𝑎/𝑄𝑤,

where 𝑄𝑤 is the water flow rate (Teng, 2017). There are different ways that have been tried to

evaluate values of 𝛽. Due to the objectives of the present study, further considerations about the

aerator-aeration have not been done in this report.

3.4 High-Velocity Air-Water Flows in The Open-Channel

In order to make analytical and numerical models of air-water flow, which consists of two phases,

continuity equations for each phase must be taken into account (momentum and energy for each

phase). Furthermore, gas-liquid transfer equations require consideration. Air-water flows are

typically portrayed by a high gas-bubble velocity, which is caused by small gas inertial forces, some

level of compressibility, surface tension impacts and buoyancy. Additional mass force when

bubbles accelerate, fluid acceleration because of variations in the bubble’s shape and volume, are

factors that must be considered when there is an interaction between the fluid and air bubbles. All

these considerations lead to complex calculation and many governing equations, making impossible

to make satisfactory models without the need of simplifications, see Table 1 bellow (Chanson,

1996).

Table 1. Basic simplifications for analysis of high-velocity air-water flows.

1 Slow gas transfer rate, can be neglected. Water and air are assumed to be immiscible.

2 Air-water flow is assumed to be incompressible. Eq. 12 approximates the local density

of the air-water flow mixture,

𝝆𝒘 ∙ (𝟏 − 𝑪)

𝝆𝒘 = 𝒘𝒂𝒕𝒆𝒓 𝒅𝒆𝒏𝒔𝒊𝒕𝒚, 𝑪 = 𝒂𝒊𝒓 𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏.

(12)

3 No-slip condition is a practical approximation since the bubble rise velocity component

in the flow direction is often significantly less than the mean flow velocity.

4 Two-dimensional flow motion.

22

5 The air-water flow behaves as the homogenous mixture and uniform.

The structure of high-velocity air-water flow is studied by using a high-speed camera to capture

every moment and further to analyse it. The results of such studies show two air-water flow

patterns. Through this interface, air is uninterruptedly trapped and released. Interfacial aeration

consists of both entrainment of air bubbles and formation of water droplets. Consequently, the

exact location of the interface becomes uncertain, and the free-surface or air-water interface area

becomes the cumulative surface area of all air-water particles. The flow shows a highly-aerated

region for C higher than 0,3 to 0,4 and a bubbly region for low air content. These regions can be

observed in Figure 14 below (Chanson, 1996).

Figure 14. Air-water free-surface region in high-velocity flows (Chanson, 1996).

When the air concentration is high, the flow mix shows a complex structure. The mix consist of

air-water projections and foam. These projections are sporadically ejected in a normal direction to

the mean flow and are highly-aerated. The foam or emulsified region consist of big air cluster

separated by film interfaces, the bubbles’ shape is often pentagonal or decahedron and the size

increases with increasing air content. Nevertheless, when the air content is low, often less than 0,3

to 0,4, the flow mix consist of asymmetrical individual air bubbles, air bubbles clusters and air

packets (Chanson, 1996).

The water quality has some important impact on the air entrainment process. The presence of

contaminants, particles, chemicals changes the physical properties of air and water, e.g. surface

tension, viscosity. Dissolved oxygen content might affect the air entrainment process also by

affecting the bubble cavitation inception and even the inception of air entrainment in the same

manner. However, there is no evident result of studying this manner yet (Wood, 1991).

3.5 Process of Free-Surface Deformation

The air entrainment process is described as the occurrence after many ejected droplets fall into the

flow disrupting the free-surface and causing an entrainment of air in the form of bubbles. In a

turbulent and horizontal open-channel flow, the process of entrapped air deformation on a free

23

surface can be explained by a characterized eddy with the abrupt vertical velocity fluctuation

𝑣′shown with a two-dimensional model in Figure 15. The process can further be described by

means of energy equations. When the kinetic energy of the eddy, 𝐸𝑘 becomes larger than the

surface energy, 𝐸𝜎 , the free-surface deformation develops. A disordered and asymmetrical water

flow develops along the channel and during the surface enclosure process, the entrapped deformed

free surface can move diagonally under horizontal fluctuation velocities, 𝑣1′ and 𝑣2

′ and can be

described by different free-surface roughness (𝐿𝜎, 𝐿𝐶 , 𝐿0) in the same direction. Lastly, the air

bubble entrainment occurs and the self-aeration generates in the open-channel flow when the air

reaches the bottom of the channel and the air concentration remains variable with depth. The

critical condition for the air entrainment process can be set by an energy balance according to Eq.

13 (WangRu Wei, 2016);

𝐸𝑘 = 𝐸𝜎 (13)

there, the kinetic energy and the surface energy can be obtained by Eq. 14 followingly;

𝐸𝑘 =1

2∙ 𝜌𝑤 ∙

4

3∙ 𝜋 ∙ (

𝐷

2)

3

∙ 𝑣′2

𝐸𝜎 = 𝜋 ∙ 𝑟𝑐2 ∙ 𝜎

(14)

where, 𝜌𝑤 is the water density, 𝐷 is the characteristic size of the turbulent eddy, 𝑣′ is the

fluctuation turbulent velocity in the y-direction, 𝜎 is the surface tension. The characteristic size of

the turbulent eddy is analysed in the previous studies in terms of the effect of disturbing the free-

surface with the energy of surface deformation. The local velocity, 𝑣∗ is described as the sum of

gravity (0,13 ∙ 𝑔 ∙ 𝐷) and the surface tension effects (1,57. 𝜎/ 𝜌. 𝐷) in the same study in Eq. 15

accordingly (WangRu Wei, 2016).

𝑣∗2 = 0,13 ∙ 𝑔 ∙ 𝐷 +1,57 ∙ 𝜎

𝜌 ∙ 𝐷 (15)

The surface tension effect on the abrupt turbulent eddy size can be neglected before the surface

entrapped deformation occurs and the local velocity equation can be re-written as 𝑣∗2 = 0,13 ∙

𝑔 ∙ 𝐷. The local velocity can be characterized by the bed friction velocity, 𝑣𝑓 which is used to

describe the turbulence in an open-channel and approximately constant in the region near to a wall.

See Eq. 16 below.

𝑣∗ = 𝑣𝑓 (16)

The radius of curvature, 𝑟𝑐 at the chest of the deformed free-surface profile is used to describe the

intensity of surface deformation. Based on the analysis of the air entrainment caused by entrapped

surface deformation above, a critical condition for the radius of curvature can be set up according

to Eq. 17.

24

𝑟𝑐 = 𝑟𝑎𝑏 (17)

When the critical radius of curvature, 𝑟𝑐 is smaller than the actual local radius, 𝑟𝑎𝑏 of the free-

surface entrapped deformation, the air entrainment will occur. The intensity of deformation

becomes greater and the turbulent level caused by the eddy is large enough to overcome surface

tension effects which provides an unstable free-surface. During this process, the free-surface can

achieve closure under the fluctuation effect and the air entrapped in the free-surface will be

entrained into the water flow in the form of individual bubbles. When the critical radius of

curvature is larger than the local radius, then the intensity of free-surface deformation will not be

high enough for the air to be entrained into the water. Hereby, the entrapped air will not be

entrained into the water flow. In summary, the actual surface deformation caused by the turbulent

eddy has a significant effect on the air entrainment.

Figure 15. The two-dimensional model of the free-surface entrapped deformation process (WangRu Wei, 2016).

Laboratory studies of air-water flows require the selection of an adequate similitude. According to

the earlier experimental studies about the free-surface deformation and air entrainment process,

the free-surface entrapped deformation and the critical radius of curvature can be approximated

by Eq. 18 with 𝑟𝑐 given accordingly;

𝑟𝑐 =𝐿2

8 ∙ 𝑦 (18)

where, 𝐿 is the width of the curve, and 𝑦 is the maximum deflection as it is shown in Figure 15

above (WangRu Wei, 2016).

25

4 Methodology

In this chapter, the methodology of the study will be described. Empirical data from experiments

of a physical scaled model at the Department of Hydraulics and Mountain River Engineering,

Sichuan University will be obtained and further analysed in order to provide a relationship between

the air entrainment (entrained air in the flow) and the free surface. The relationship between the

air entrainment and the free-surface deformation will be investigated by considering the shape of

creation in terms width and height using the free surface entrapped creation’s curve type.

4.1 Experimental Setup

The free-surface deformation and the air entrainment process in high-speed open-channel flows

will be examined by using a video system to capture associated events in detail. Experiments were

conducted at the state key laboratory of Hydraulics and Mountain River Engineering Department,

Sichuan University in China in a flat chute of 8,6 m length and 0,4 m width and has an open channel

with a chute slope of α=36°. The test section is made of planed glass boards with glass sidewalls

of 0,4 m height and the bottom side of the test section is made of acrylic. The water flow rate is

supplied by a pump controlled electronically, enabling an accurate discharge adjustment in a closed-

circuit system. This closed-circuit system includes a watercourse, large tank below the chute (for

the water supply and return) and pressure head tank as it is shown in Figure 16 below.

Figure 16. The schematic figure of the experimental setup.

The water flow visualizations, especially these occurrences, are conducted with a digital video-

camera and high-speed photographs. The system includes a video camera (Canon EOS 70D), a

Canon lens (EF-S 18-200 mm IS), with a resolution ratio of 5 472*3 648 and auto focus. The

cinematic results are obtained by capturing 24 frame/s. The recording position is decided to be

close to the glass sidewalls, approximately 0,35 m away with a recording scope of 40 x 12 cm2. The

lens is adjusted to the same elevation as the free surface of water flow and controlled perpendicular

to the sidewall of the watercourse. A set of LED lights lay opposite beside the flume as a

supplement light source to improve the image definition. During the recording period, the focusing

plane is placed at the central longitudinal plane to reduce the sidewall effect, and the surface

deformation is mainly considered as the result of water turbulence (WangRu Wei, 2016). To

26

measure the water velocity, the water flow has been adjusted several times in order to obtain a

uniform water flow. The water velocity at the recording location is obtained to be an average value

after the measurements at six different locations with 0,05 m distance from each other, and the

mean flow depth at the recording location has slightly varied between the average values. The

velocity measurement principle is shown in Appendix B. below.

As it is shown in Table 2 below, totally three observations have been made with different water

flow rates, water depths and water flow velocities. The result of the analysis of these observations

will be presented in Chapter 5 Result from Experiments.

Table 2. Relevant variables shown with units for Observations 1-3.

OBSERVATION FLOW RATE

(𝒎𝟑

𝒔)

WATER DEPTH

(𝒎)

FLOW VELOCITY

(𝒎

𝒔)

1 0,048 0,18 0,28

2 0,015 0,14 0,15

3 0,013 0,13 0,21

For the consideration of the shape of bubble creation, another observation has been done using a

high-speed camera due to the high flow velocity. The high-speed camera system is used to

investigate surface roughness characteristics because the free-surface deformation and air

entrainment occur very rapidly, in the order of 15,5 milliseconds. High-speed cinematic results are

obtained by capturing 2000 frame /s with an exposure time of 0,5 milliseconds. The water flow

rate, water depth and water flow velocity of this observation is shown in Table 3 below.

Table 3. Relevant variables shown with units for Observation 4.

OBSERVATION FLOW RATE

(𝒎𝟑

𝒔)

WATER DEPTH

(𝒎)

FLOW VELOCITY

(𝒎

𝒔)

4 0,080 0,08 2,66

4.2 Relevant Curve Types

When analysing the relationship between the air entrainment and the free-surface deformation,

several curve types could be examined in order to find the most appropriate curve type explaining

this phenomenon. In order to do that, curve fitting process could be used which is the process of

constructing a curve that has the best fit to a series of data points. Different types of curve fitting

are available, however most commonly functions of the form (𝑦 = 𝑓(𝑥)) are used to fit data points.

A relevant topic is regression analysis which focuses on present uncertainties in a curve that is fit

to data observed with random errors. Fitted curves can be used to visualize data (University, 2017).

The coefficient of determination, called 𝑅2, is the proportion of variability in a data set and used

to show how well data points fit a curve. The term “variability” is defined as the sum of squares.

The value of this coefficient is significant when analysing curves and will provide information about

the goodness of fit of a model. An 𝑅2 of 1.0 indicates that the regression line perfectly fits the data.

Adjusted 𝑅2 also indicates how well data points fit a curve, however, adjusts for the number of

terms in a model. 𝑅2 always increases when a new term is added to a model while adjusted 𝑅2

27

increases only with new term improving the model or decreases with new term that is useless

(University, 2017).

There are several curve types that can be used as an aid to explain the relationship between the air

entrainment (entrained air in the flow) and the free-surface. The Gaussian (or normal) distribution

is one of the most commonly used probability distributions for applications. This type of curve,

also known as bell-shaped curve, shows a particular distribution of probability over the values of a

random variable. The equation for Gaussian curve type is shown in Eq. 19 accordingly;

𝑦 = 𝑦0 +𝐴

𝑤 ∙ √𝜋/2∙ 𝑒

−2∙(𝑥−𝑥𝑐)2

𝑤2 (19)

where, 𝑦0 = 0 is offset point, 𝐴 is area under the bell-shaped curve, 𝑤 is width (𝑤 =𝐹𝑊𝐻𝑀

√ln (4)), and

𝑥𝑐 = 0 is center point. In Figure 17, the Gauss curve distribution is shown for this equation with

all variables and points.

Figure 17. The Gauss curve distribution.

A sine curve is a mathematical curve that describes a smooth repetitive oscillation. The sine curve

is important in applications because it retains its wave shape when added to another sine wave of

the same frequency. The equation for sine curve is shown in Eq. 20 below;

𝑦 = 𝑦0 + 𝐴 ∙ sin (𝜋 ∙𝑥 − 𝑥𝑐

𝑤) , 𝐴 > 0 (20)

where, the variables are shown with relevant values in Figure 18 below.

Figure 18. The Sine curve distribution.

28

4.3 Image Analysis Method for Evaluating Free-Surface

Deformation Curve

In order to understand the phenomenon of air entrainment, the free-surface deformation needs to

be understood. This is achieved by analysing images of the water flow, where the deformation in

the free surface is clear and observe if the deformation can be mathematically explained by fitting

a known curve to the free-surface deformation curve.

The image analysis has been done according to the following steps in Table 4:

Table 4. Image analysis process.

1. All the frames from the videos taken during the different observations are extracted,

using the free software “Free Video to JPG Converter”.

2. All the frames are examined and those containing the free-surface deformation curvature

are separated. Figure 19. A picture of the free-surface deformation curve. below shows

an example of one of the pictures that contains the deformation curve.

Figure 19. A picture of the free-surface deformation curve.

3. The software “Photoshop” is used to crop and straighten the pictures. Using the ruler

in the pictures as reference, all the pictures are 10 cm wide, and the ruler have an

inclination of 0 degrees. Figure 20 shows the result of this step.

Figure 20. Treated picture in Photoshop.

29

4. Using the software Autocad, the treated images are placed in a coordinate system using

a scale of 1:100. The deformation curve can be traced on the image, and moved to the

origin. Using functions in the software Autocad, the curve can be converted to a polyline

and all the coordinates can be extracted. Figure 21 shows this step.

Figure 21. Snapshot of the image treatment in Autocad.

5. Using the extracted coordinates, the curve can be plotted in the software OriginPro. This

software is also used to fit a known curve (Gauss & Sine curves) to the deformation

curve. The results from this step gives data about the goodness of the fit. Figure 22

shows the results of this step.

Figure 22. Deformation curve and fitted known curves.

6. The results from all the curves are later stored in excel, a graph of curve number vs.

curve fitting is made to analyse the results and a one sample T-test is performed to obtain

a confidence interval of the adjusted R-square to evaluate how good the fitting is.

30

4.4 Method for Evaluating the Process of Surface Deformation and

Air Entrainment

For evaluating the process of surface deformation and air entrainment, a similar process to the

previously mentioned in Chapter 4.3 is performed. Table 5 below, shows the steps of this process.

Table 5. Evaluation of the Process of Surface Deformation and Air Entrainment.

1. Using the free software Motion Studio, the video is analysed frame by frame. Using the

same software, all the frames where the process of surface deformation and air

entrainment observed are extracted. Figure 23 shows an example of this process.

0 ms

0,5 ms

1 ms

1,5 ms

2 ms

2,5 ms

3 ms

3,5 ms

4 ms

4,5 ms

5 ms

5,5 ms

6 ms

6,5 ms

7 ms

7,5 ms

Figure 23. Frames of the process of surface deformation and air entrainment.

2. Since the quality of the pictures is not the best, all pictures are treated in the software

Photoshop to make the contour easier to see and handle. Figure 24 below shows the

result of the treatment.

31

Figure 24. Photoshop treatment.

3. Using the software Autocad, the treated images are placed in a coordinate system using

a scale of 1:185. The deformation curve can be traced on the image, and moved to the

origin. Using functions in the software Autocad, the curve can be converted to a polyline

and all the coordinates can be extracted. The width, 𝐿 (mm) and the depth, 𝑌 (mm) are

also measured in Autocad. Figure 25 below shows this step.

Figure 25. Measurement process in Autocad.

4. Using the extracted coordinates, the process of surface deformation and air entrainment

can be plotted in the software OriginPro. Figure 26 shows the results of this step.

Figure 26. Plot of one frame in the process of surface deformation and air entrainment.

5. The coordinates, 𝐿 and 𝑌 for all the frames are stored in excel. The radius of curvature

is calculated for all the frames using equation Eq. 18 in Chapter 3.5. The radius of

curvature is later plotted for each process as s function of 𝑇 𝑇𝑜⁄ , where 𝑇 is the frame

time in milliseconds and 𝑇𝑜 is the total time of the process in milliseconds.

32

5 Result from Experiments

The results of the study are presented in two different parts below. In the first part, the results of

the image analysis method for evaluating free-surface deformation curve (Chapter 4.3) are

presented. Totally, 3 observations were performed for this part. In the second part, the results of

the evaluation of the radius of curvature in the process of surface deformation and air entrainment

(Chapter 4.4) are presented. One observation was performed for this part.

5.1 Analysis of The Free-Surface Deformation Curve Type

After performing the image analysis, 200 images containing the free-surface deformation curve are

founded. The image analysis reveals that the deformation curve takes many different shapes and

sizes. Differences in depth, width or skewness (curve symmetry) can be observed. Figure 27 to

Figure 32 below shows these differences in the original picture and the curve placed in a coordinate

system.

Figure 27. Deformation curve shape, Observation 1, Video 1, Curve 3.


33




34


The steps in Table 4 above leads to 400 fitting curves, namely, 200 for the Gauss curve and 200

for the Sine curve.

Table 6 below summarizes the duration of the videos in each observation, the number of frames

and the number of frames containing the free-surface deformation curve.

Table 6. Summary of observations.

Observation Video Duration

(seconds)

Total frames Free-surface

deformation

frames

1

1 19 500 28

2 22 569 29

3 23 587 31

4 20 515 32

5 20 509 26

2 1 30 761 14

3

1 57 1 500 21

2 21 536 9

3 25 641 10

The curve fitting process results in 2 lists of the adjusted R-Square coefficient for all the 200

deformation curves that are discovered in the observations, one list for the Gauss fitting and one

for the Sine fitting. Figure 33 below shows the results for the Gauss fitting.

35

Figure 33. Gauss Adj. R-Square coefficient.

Figure 34 shows the results of the Sine fitting for all the 200 deformation curves.

Figure 34. Sine Adj. R-Square coefficient.

Both fittings are compared in order to show the difference in Adjusted R-Square coefficient

between Gauss and Sine fitting for each deformation curve. The result of this comparison is shown

in Figure 35 below.

Figure 35. Adj. R-Square difference between Gauss and Sine fitting.

0,660,680,700,720,740,760,780,800,820,840,860,880,900,920,940,960,981,00

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Ad

j. R

-Squar

e

Curve Number

0,60

0,65

0,70

0,75

0,80

0,85

0,90

0,95

1,00

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Ad

j. R

-Squar

e

Curve Number

-0,03

-0,01

0,01

0,03

0,05

0,07

0,09

0,11

0,13

0,15

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Ad

j. R

-Squar

e d

iffe

ren

ce (

Gau

ss -

Sin

e)

Curve Number

Difference

36

A one sample t-test is an analysis of two populations means using statistical examination. The t-

test is utilized to test the difference between the samples when the variances of two normal

distributions are unknown. A t-test contains the t-distribution and degrees of freedom, DF, to

determine the probability of difference between populations. Analysis of the difference of these

samples, the Gauss fitting and the Sine fitting reveals that the first named is the best choice, since

the adjusted R-Square coefficient is greater most of the time. At a confidence level of 0,05, the

difference is significantly greater than zero. Table 7 shows the results of the one sample t-test.

Table 7. One sample t-test results for the difference between fittings.

t-Statistic DF Prob > t

10,63163 199 1,70159E-21

Null Hypothesis: Mean <=0

Alternative Hypothesis: Mean >0

At the 0,05 level, the population mean is significantly greater than the test mean (0)

A confidence interval for levels of confidence of 90, 95 and 99 percent can be used because it

generates a lower and upper limit for the mean. The interval estimate provides an indication of

how much uncertainty there is in the estimate of the true mean. When the interval is narrower,

then the estimate is more precise. It is shown that the lower limit is higher than zero for all three

levels in Table 8 below, where N is the sample size, SD is the standard deviation, SEM is the

standard error of the mean.

Table 8. Descriptive statistics and confidence intervals for mean.

N Sample

Mean SD SEM

Confidence level (%) Lower Limits

90 95 99

200 0,02086 0,02775 0,00196 0,01834 0,01762 0,01626

It can similarly be observed in Figure 36 below, which is a box plot that displays the variation in

the Adjusted R-Square coefficient that the degree of dispersion (spread) is smaller for the gauss

fitting than for the Sine fitting. The plot also shows the outliers.

37

Figure 36. Gauss vs. Sine box-plot.

5.2 Results of The Process of Surface Deformation and Air

Entrainment

One observation is performed to evaluate the process of surface deformation and air entrainment.

The observation consists in a 2,5 seconds video, containing a total of 5 000 frames. An analysis of

the video is done and resulted in 5 various processes of surface deformation and air entrainment,

Table 9 below summarizes the video analysis.

Table 9. Summary of observation.

Observation Duration

(seconds)

Total

frames

Processes Process

duration

(milliseconds)

1 2,5 5 000

1 15,5

2 19,5

3 19

4 7,5

5 8

The first process is found between the frames 779 and 809, which corresponds to a total time of

15 ms. The free-surface entrapped deformation and air entrainment processes are schematically

shown in Figure 37 below. It can be clearly observed that the entrapped air goes deeper with time,

from approximately 1 mm to 2 mm, until it becomes unstable, after 9 ms. It can also be observed

that after reaching instability, the width 𝐿 becomes smaller with time, after 15 ms the free surface

reaches closure and an air bubble is entrained into the flow.

39

Figure 37. Process of surface deformation and air entrainment, Process 1.

The second process is found between the frames 915 and 955, corresponding to a total time of

19,5 ms. The process is shown in Figure 38 below. For this process, the depth of the entrapped air

varies more randomly, it increases and decreases with time. The process becomes unstable, after

7,5 ms. It can be observed that after reaching instability, the width 𝐿 increases for one frame and

later decreases until the free surface reaches closure and an air bubble is entrained into the flow

after 19 ms.

40


The third process is shown in Figure 39, it is found between the frames 2 167 and 2 205,

corresponding to a total time of 19 ms. In this process, as in the second process, the depth of the

entrapped air varies randomly, it increases and decreases with time. The process becomes unstable,

after 8 ms. The free surface reaches closure and an air bubble is entrained into the flow after 18,5

ms.

42


The fourth process is in Figure 40, it is found between the frames 2 921 and 2 937, which is

considerably shorter than the previously processes, the total time was 7,5 ms. In this process, the

depth of the entrapped air increases from approximately 0,5 mm to 1,25 mm until it becomes

unstable, after 2 ms. The free surface reaches closure and an air bubble is entrained into the flow

after 7 ms.

43


The fifth process is also short, compared to the first three. It is found between the frames 3 241

and 3 257, with a total time of 8 ms. It can be observed in Figure 41 below that the depth increases

and decreases until instability, before 4 ms. The free surface reaches closure and an air bubble is

entrained into the flow after 7,5 ms.

44


The parameters 𝐿 and 𝑌 are measured for all the frames in all the processes. These parameters are

later used to calculate the radius of curvature (see Eq. 18) in every frame. The results are plotted

and showed in Figure 42 below.

The X-axis in the plots, is the time where the parameter is measured, divided by the total time of

the process. This provides an axis that ranges from 0 to 1 for all the 5 processes. The results reveal

that the radius of curvature varies for a short period of time, it increases and decreases, until the

process becomes unstable. The instability of the process leads to a rapidly decrease or increase in

the radius of curvature and later an air bubble being entrained into the flow.

The results show that for the first process, the radius of curvature becomes critical after 60 % of

the process time, where the size of the radius of curvature decreases quickly. The radius of

curvature which is shown in Y-axis (mm) ranges between 1,5 and 3 mm for the first process. For

the second process, the instability arises after 35 % of the process time and the radius of curvature

ranges between 1,4 and 2 mm. There, the radius of curvature increases very rapidly and after 60 %

of the time, it drops. The third process becomes unstable after 40 % of the time, there the radius

of curvature peaks and later drops very rapidly, and has a range of 1,5 to 2 mm. The fourth process

behaves different, there the radius of curvature peaks almost directly, after 10 % of the time, and

later drops. The radius of curvature for this process varies between 0,5 and 1 mm. For the last

process, the radius of curvature peaks after 20 % of the time and later drops after 30 % of the time,

the radius of curvature has a range of 1,5 to 3 mm for this process.

The figures below show that radius of curvature has a “bell-shape” behaviour through the whole

process. However, they also reveal that the time chosen as origin is not the true origin. This can be

easily observed in the process 1 and 4, here the process starts with a peak in the radius of curvature.

For the other processes, the shape is clearer. In process 2, 3 and 5 the radius of curvature increases,

it reaches a peak and then it drops.

The radius of curvature becomes critical after the peak in the process, it decreases very rapidly, it

get some stability and later the air bubble is entrained into the flow.

45

Figure 42. Radius of Curvature vs T/To for all the 5 Free-Surface Entrapped Deformation and Air Entrainment Processes.

In Table 10 below, an average of the values of the radius of curvature is calculated for all five

processes. This gives an awareness of the value of the critical radius of curvature. The average is

calculated for the values of the radius of curvature from the peak value until it stabilizes.

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,2 0,4 0,6 0,8 1

Rad

ius

of

Curv

ature

(m

m)

T/To

Process 1

0

0,5

1

1,5

2

0 0,2 0,4 0,6 0,8 1

Rad

ius

of

Curv

ature

(m

m)

T/To

Process 2

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

0 0,2 0,4 0,6 0,8 1

Rad

ius

of

Curv

ature

(m

m)

T/To

Process 3

0

0,5

1

1,5

0 0,2 0,4 0,6 0,8 1

Rad

ius

of

Curv

ature

(m

m)

T/To

Process 4

0

0,5

1

1,5

2

2,5

3

3,5

4

0 0,2 0,4 0,6 0,8 1

Rad

ius

of

Curv

ature

(m

m)

T/To

Process 5

46

Table 10.Critical radius of curvature for all processes.

Process Critical Radius of Curvature (mm)

1 2,9658501

2 1,402605001

3 1,92201647

4 0,528200791

5 2,660480161

47

6 Improvements for Experiments

Considering the experimental setup and performed observations, there are some improvements

that could be done in order to impact the outcome of the results. For laboratory studies, there are

constantly several issues that should be considered and seen for any kind of possibilities for the

improvement. One of these improvements can be done by changing the light condition by using a

type of thin-surface light source above the water flow instead of opposite beside the flume. By that,

these points that provide more information about the free-surface deformation and air entrainment

process could be considered.

The sidewalls conditions could be changed from glass to for example wood or another material

and observations could be done based on it and see how the result of the process of free-surface

deformation would be affected. By that, several models could be considered to investigate the

various air entrainment processes and compare the results from these.

Changing some parameters, e.g. the water flow velocity or slope of the open-channel would affect

the result of the turbulent layer thickness. The turbulent layer thickness is directly affected by both

the open-channel slope and wall roughness. The free-surface deformation and air-entrainment

process could possibly be changed due to the changes of the turbulent layer thickness and wall

roughness. Retaining all parameters same and using another chute type instead of smooth chute

type could similarly affect the result of the free-surface deformation and air entrainment process.

For example, in stepped or rocked chute types compared to the smooth-surface chute, the free-

surface deformation would be more intensive based on the higher local turbulence intensity.

Videos and pictures used for the image analysis to evaluate the free-surface deformation curve

could be improved by using a high-speed camera for all observations and direct connection with a

computer system. The result by improving that would be obtained more accurate and quicker.

Another improvement could be done by increasing the number of observations in order to increase

the probability of obtaining the Gauss curve type.

The numerical modelling using CFD or another software of this open-channel flow could be done

as a complement in order to provide more rapid and accurate information. The numerical

modelling could be done by creating an open-channel and the water flow with all physical

properties and changing its properties in order to obtain different results and compare these. Most

numerical models of self-aerated flows have been created based on the physical properties, however

a solid validation and verification can be lacked. For example, most validations are shown in terms

of flow depth and depth-averaged velocity, sometimes including a limited comparison of void

fraction and time-averaged velocity distributions. An appropriate validation of CFD modelling

results should be based upon the distributions of void fractions, velocity, turbulence intensity, and

bubble-droplet chord sizes.

48

7 Discussion

The present study has been performed to examine the self-aerated flows and to show the

mechanism of free-surface air entrainment. It could be described as air that will be entrained into

the water when the free-surface deformation exceeded the critical form condition and created the

free-surface instability. The free-surface is not a fixed boundary and it fluctuates to accommodate

the expansion of the flow bulk. Additionally, the flow characteristics, e.g. dissolved oxygen into the

water could affect the air entrainment process.

After the experimental observations and image analysis have been made, it has been found that the

free-surface entrapped deformation can be approximated by a Gaussian-curve type deformation

rather than a Sine-curve type. This result has been obtained by performing a one sample t-test for

both curve types and comparing the adjusted R-square values. The one sample t-test for the Gauss

adjusted R-square reveals that the mean is higher than 0,9 with 95 % confidence level. Both curves

are good representatives of explaining the real process of free-surface deformation, however, the

Gauss-curve type is slightly better as it is shown in the result part. Furthermore, the results show

that the differences between Gauss- and Sine-curves are relatively small in many cases. In a few

cases where the Sine-curve has a better fitting, the difference between Sine- and Gauss-curves can

be neglected. In many cases where the Gauss-curve has a better fitting, the difference is

considerably high.

The results from the process of free-surface deformation and air entrainment show that there are

various process durations for these observed processes. The surface achieves closure at a relatively

low position at a range of 7 to 19 milliseconds and the free-surface deformation occurs when the

air bubble is entrained into the flow, varies between 8 and 19,5 milliseconds for different

observations. As it is mentioned in Chapter 3.5, the air entrainment will occur when the critical

radius of curvature is smaller than the actual local radius of the free-surface entrapped deformation.

The results of evaluating the radius of curvature with respect to the time of occurrence indicate

that the free-surface deformation intensity in the experiments exceeds the critical condition of

curvature radius when the surface instability occurs. The results of the radius of curvature reveal

that the radius of curvature has a “bell-shape” behaviour. However, it fluctuates under the

increasing and decreasing period. It is also very important to discuss that the time chosen as the

origin of the process, is not the true origin. This is because of the way the experiment and the data

analysis is performed, the origin of the process is chosen from the time the free-surface

deformation is observable in the pictures, but it does not necessary mean that it is the origin of the

process. The radius of curvature becomes critical after reaching the maximum value and has a range

of 0,53 to 2,97 mm for all the processes, as it can clearly be seen in Table 10 above. A comparison

between the processes could not be done directly because all the processes occur separately and

independent from each other.

For the creation of self-aerated air-water flows, the free-surface roughness plays an important role

in order to understand the reasons behind this creation. The result of the development of bubbles

and the free-surface entrapped deformation show that the bubble size distributions occur

significantly different in different points throughout the open-channel. Smaller bubble sizes are

obtained at the edges compared to the bubbles in the centre of the focus area due to the higher

shear stress in the centre. Higher bottom roughness provides the faster development of boundary

49

layer thickness. Furthermore, the higher bed friction velocity could affect the result of bubble

creation by means of increasing the shear stress and which in turn providing more intensive free-

surface deformation.

50

8 Conclusion and Future work

Our skills have been improved about the hydraulic engineering and flood discharge structures

during the literature study and performed experiments. By doing the literature study regarding

spillway designs, key aspects in high-speed open-channel, air-water flows characteristics and

process of free-surface deformation, and performing experiments based on the gathered

information have opened a new sight for us to study further on this area.

The Gaussian-curve type has been decided to approximate and explain the process of free-surface

entrapped deformation with a better confidence level of 95 % and adjusted R-square value of

higher than 0,9.

The air entrainment mechanism through free-surface entrapped deformation has been examined

and described during this study. When the severity of Gauss-type free-surface deformation exceeds

the critical condition, the local radius of curve is smaller than the critical radius of curve and the

entrapped free-surface encounters closure in the unstable deformation movement process,

resulting in air-entrainment. It is shown that the critical radius of curvature varies for different

processes and it occurs after the maximum value is reached, the critical radius of curvature has a

range between 0,53 and 2,97 mm for all the processes.

Based on the present study about the free surface air entrainment observation, the future research

on self-aerated open channel flows will be to present a simple two-dimensional model of free-

surface deformation based on dynamic and energy transitions, with the aim to describe the

relationship between free-surface entrapped deformation and air entrainment. A microscopic

sufficient condition for surface air entrainment is developed, which is different to the previous

reorganization on the “water droplet impact” air-entrainment mechanism. The theoretical model-

based analysis should be applicable to the visual process of air entrainment caused by free-surface

turbulent movement. This will give further insight into the structure of free-surface turbulence in

high-speed velocity flows.

Moreover, the experimental study on high-speed open-channel flows should include the

measurement of free-surface deformation and air entrainment process. Non-intrusive

measurement for the entrained air bubble size is required and the relationship between free-surface

deformation and bubble distributions should be further studied experimentally. Additional

experiments should be conducted on spillways and high-speed chute to verify and support the

concept and analysis done in this study.

Regarding air-water mixture flows in open-channel, further experiments are needed in order to

study the air bubble movement and the relationship between turbulence and the two-multiphase

flow mass transfer properties. Furthermore, it is helpful to verify the calculation of air-water

mixture and gas transfer efficiency.

The difference in free-surface deformation between the sidewalls and the centre region is not clear,

as the turbulent-intensive and interaction with the flow is still unknown. The 3D effect on self-

aeration formation and development should be studied both theoretically and experimentally in the

future.

51

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54

Appendix A.

Several pictures are shown from the experimental setup below in Figure A.

Figure A. Pictures from experimental setup and the department of hydraulic engineering.

55

Appendix B.

The velocity of flow has been measured with a device (LGY- II) with a sensor diameter (φ) of 15

mm and with high electroplate to make sure the signal process is enough in the flows. The device

is shown in Figure B below. Velocity calculation principle is shown in Eq. 21 accordingly;

𝑉 = 𝐴 ∙ (𝐾 ∙ 𝑁

𝑇 + 𝐶) (21)

where, 𝑉 is the velocity of flow (𝑐𝑚/𝑠), 𝐴 is velocity scale (𝐴 = 1), 𝐾 and 𝐶 are sensor calibrate

coefficients (𝐾 = 2,88 and 𝐶 = 1,00), 𝑇 is sampling period (𝑠) and 𝑁 is impeller revolutions in

the sampling period.

Figure B. The velocity measurement device.

56

Appendix C.

The value adjusted R-square coefficient is shown for all observations and from different videos.

See Figure C below.

0,750,760,770,780,790,800,810,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

AD

J. R

-SQ

UA

RE

CURVE NUMBER

Video 1, Observation 1Gauss Sine

0,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

AD

J. R

-SQ

UA

RE

CURVE NUMBER


57

0,830,840,850,860,870,880,89

0,90,910,920,930,940,950,960,970,980,99

1

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

AD

J. R

-SQ

UA

RE

CURVE NUMBER


0,810,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

AD

J. R

-SQ

UA

RE

CURVE NUMBER


58

0,720,730,740,750,760,770,780,790,800,810,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10 12 14 16 18 20 22 24 26

AD

J. R

-SQ

UA

RE

CURVE NUMBER

Video 5, Observation 1GAUSS SINE

0,750,760,770,780,790,800,810,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10 12 14

AD

J. R

-SQ

UA

RE

CURVE NUMBER


59

0,680,700,720,740,760,780,800,820,840,860,880,900,920,940,960,981,00

0 2 4 6 8 10 12 14 16 18 20

AD

J. R

-SQ

UA

RE

CURVE NUMBER


0,630,650,670,690,710,730,750,770,790,810,830,850,870,890,910,930,950,970,99

0 2 4 6 8

AD

J. R

.SQ

UA

RE

CURVE NUMBER


60

Figure C. The adjusted R-squared coefficient.

0,810,820,830,840,850,860,870,880,890,900,910,920,930,940,950,960,970,980,991,00

0 2 4 6 8 10

AD

J. R

-QU

AR

E

CURVE NUMBER


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