Development of Aerated Chute Flow

220 Pages·2008·9.06 MB·English

Versuchsanstalt für Wasserbau
Hydrologie und Glaziologie
der Eidgenössischen
Technischen Hochschule Zürich
Mitteilungen 183
Development of Aerated Chute Flow
Kristian Kramer
Zürich, 2004
Herausgeber: Prof. Dr.-Ing. H.-E. Minor
Herausgeber:
Prof.Dr.--Ing.Hans--ErwinMinor
ImEigenverlagder
VersuchsanstaltfürWasserbau,
HydrologieundGlaziologie
ETH--Zentrum
CH--8092Zürich
Tel.: +41 -- 1 -- 6324091
Fax: +41 -- 1 -- 6321192
e--mail: [email protected]
Zürich,2004
ISSN 0374--0056
Development of Aerated Chute Flow
P
REFACE
It has been known for decades that spillway chutes or tailrace channels of
bottom outlets may suffer from cavitation damage if flow velocities are high or
if abrupt changes in flow direction occur. With flow velocities above 30 m/s,
small unavoidable surface imperfections are sufficient to trigger such damage.
The technically most simple and most economic method to avoid cavitation
damage in such conditions is air supply at the contact surface between the
concrete and the water flow. In 1953, Peterka demonstrated with simple tests
that the mass carried away from a test surface is reduced considerably, if 5% –
8% air is added to the water. His indications are based on average air
concentration values.
It took until the early eighties of the last century and it needed the large
damage of the spillway chute of the 200m high Karun arch dam in Iran until
bottom aerators were systematically developed for highly charged spillways.
VAW of ETH Zürich was one of the institutes to develop the design criteria. In
the Western world the focus was air entrainment. Bottom aerators were
optimised to entrain as much air as possible into the high-speed flow.
Concerning air detrainment, everybody relied on poorly documented
publications (which had a lot to do with the language) of Russian authors who
stated that the average air concentration is reduced by 0.4% – 0.5% per meter
chute length, due to the air bubble rise. The projects built on the basis of this
assumption, e.g. Foz do Areia in Brazil or Alicura in Argentina, showed that
more air was present in the spillway chute than anticipated. For some projects,
aeration devices were partly closed on purpose, therefore.
Simple analyses of average air concentration along prototype chutes led to
an air detrainment of 0.15 % –0.20% per meter chute length. The influences of
parameters like the Froude number or the bottom slope remained unknown.
Here, Kristian Kramer started with his work: He studied the development of
air concentration distribution over the water depth in a straight model flume. Its
slope was adjustable between 0% and 50% and, therefore, allowed to study the
influence of the bottom slope. These detailed studies were possible mainly
because novel measuring techniques were available. Kristian Kramer used the
i
fiber optic measuring system that was previously employed for investigations
on stepped spillways. This system allows measuring the local air concentration,
the flow velocity, and the bubble size.
Kristian Kramer presents some astonishing results. The air entrainment at
the lower side of the jet downstream of a deflector was large, however, shortly
downstream of its point of impact most of the entrained air detrains. The
measured air concentrations at the chute bottom were much lower than those
stated by Peterka. But still we know that in these cases, no cavitation damage
occurred. Kristian Kramer shows also that the air entrainement mechanism
influences the detrainment process. Using his results fairly accurate estimates
can be made on the average air transport in a chute flow. The design procedure
is illustrated with an example.
The research project was funded to a large extent by the Swiss National
Science Foundation for which I am grateful. Furthermore, I owe thanks to
Prof.Dr. W.H.Hager who was guiding the work as co-examiner, as well as
Prof.Dr. H.Kobus, University of Stuttgart, who served as the external
co-examiner.
Zurich, March 2004 Prof. Dr.-Ing. H.-E. Minor
ii
Development of Aerated Chute Flow
A
CKNOWLEDGMENTS
This work was carried out during my time as a PhD student and assistant at the
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zürich. I
would like to thank all persons who supported me at VAW and contributed in
any form to my thesis, in particular:
Thank you to Prof. Dr.-Ing. H.-E. Minor, for supervising this project, for his
enormous interest and contribution using his wide practical experience. He
enabled this thesis and provided an excellent research environment.
My deepest thanks to Prof. Dr.W.H. Hager who initiated this project and
supported me during my time at VAW. I very much appreciated his advice and
corrections, far exceeding the self-evident.
I would also like to thank Prof.Dr.H.Kobus for thoroughly reviewing this
thesis and being the external co-examiner.
Further, I would like to thank my office companions and colleagues for
giving me a good time at VAW. Thank you for the motivation, support and
discussions in hydraulics and other fields of interest.
I am grateful to the VAW workshop, the electronics workshop, the drawers,
the photographer, the secretaries and my diploma students for supporting me
with all their means.
This thesis profited from suggestions and discussions with Dr.-
Ing.H. Falvey and Prof.Dr. A. Ervine.
Thank you to Silviana and Michael for reading the draft. This research
project was supported by the Swiss National Science Foundation (Project No.
2100-057081.99/1) and the Swiss Committee on Dams.
Very many thanks to my family and friends for their support, considerations
and patience during my time being a PhD student.
iii
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Development of Aerated Chute Flow
C
ONTENTS
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Kurzfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Chapter 1 Introduction 1
1.1 Problem outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Purpose and aim of present studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2 Literature review 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Cavitation on chutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Cavitation formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Cavitation damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Methods to reduce cavitation damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 General methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Effect of air content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Air entrainment on chutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Free surface aeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3 Local aeration – chute aerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Air detrainment process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.1 Single bubble in stagnant water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5.2 Single bubble in turbulent flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.6 Air detrainment from chute flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.1 Detrainment zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.2 Aerator spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Focus of the present project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7.1 Summary of previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7.2 Research gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.7.3 Focus of the present research study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter 3 Physical model 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
v
3.2.1 Water discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Aeration device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Automated data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Two-phase flow instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.1 Air concentration measuring systems for two-phase flows . . . . . . . . . 44
3.3.2 Probe used in the present project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Preliminary investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 Air supply system and velocity measurements . . . . . . . . . . . . . . . . . . . 51
3.4.2 RBI fiber-optical measuring system . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3 Channel roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5 Dimensional analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.1 Dimensional quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.2 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter 4 Experimental observations 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Definitions and methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Two-phase flow parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.1 Air concentration profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2 Air concentration contours and gradients . . . . . . . . . . . . . . . . . . . . . . . 69
4.3.3 Streamwise flow depth and Froude number . . . . . . . . . . . . . . . . . . . . . 70
4.3.4 Streamwise average and bottom air concentrations . . . . . . . . . . . . . . . 72
4.3.5 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.6 Bubble size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chapter 5 Pre-aerated flow 77
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Average air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 Typical air concentration development . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 Effect of Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.3 Air detrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2.4 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.5 Air detrainment per chute distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2.6 Minimum average air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.7 Effect of inflow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.8 Effect of inflow air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2.9 Air entrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 Bottom air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.1 Effect of Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.2 Air detrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.3 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3.4 Minimum bottom air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4 Development of air concentration isoline . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4.1 Effect of Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4.2 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Bubble rise velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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Development of Aerated Chute Flow
Chapter 6 Aerator flow 113
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2 Average air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.1 Aerator flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.2 Effect of Froude number on air detrainment . . . . . . . . . . . . . . . . . . . . 115
6.2.3 Air detrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.2.4 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.5 Air detrainment per chute distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.2.6 Minimum air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2.7 Effect of inflow depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2.8 Air entrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.3 Bottom air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3.1 Effect of Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3.2 Air detrainment region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.3.3 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.3.4 Minimum bottom air concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Air detrainment gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4.1 Effect of Froude number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4.2 Effect of chute slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.5 Bubble rise velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Chapter 7 Discussion of results 141
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2.1 Hydraulic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.2.2 Critical cavitation number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.2.3 Amount of air needed for cavitation protection . . . . . . . . . . . . . . . . . . 143
7.3 Verification of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.4 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.6 Design example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.6.1 General comment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.6.2 Design procedure – an example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Chapter 8 Conclusions 157
8.1 Limitations and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
161
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
1
Appendix A Air flow meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A – 1
Appendix B Velocity tests – Pitot tube versus propeller . . . . . . . . . . . . . . . . . . B – 1
vii
Appendix C RBI – probe quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C – 1
C.1 Influence of threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 1
C.2 Influence of acquisition time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 2
C.3 Influence of channel width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 5
C.4 Discharge measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 7
Appendix D Channel roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D – 1
Appendix E Air detrainment gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E – 1
E.1 Pre-aerated flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 1
E.2 Aerator flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 3
Appendix F Summary of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F – 1
F.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 1
F.2 Data CD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . – 5
Appendix G Curriculum vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G – 1
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