Figure 2.17 Air entrainment above an aerator (Chanson, 1989)

94 Pages·2013·4.74 MB·English

by  Kevin Franke

Investigation of the Complex Flow in High
Energy Spillways by Means of Computational
Modelling and Experiments

Kevin Franke

Faculty of Civil and Environmental
Engineering
University of Iceland
20XX

Investigation of the Complex Flow in High
Energy Spillways by Means of
Computational Modelling and Experiments

Kevin Franke

60 ECTS thesis submitted in partial fulfilment of a
Magister Scientiarum degree in Environmental Engineering

Advisors
Piroz Zamankhan
Sigurður Magnús Garðarsson

Faculty Representative
Andri Gunnarsson

Faculty of Civil and Environmental Engineering
School of Engineering and Natural Sciences
University of Iceland
Reykjavik, 18th of September, 2013
Investigation of the Complex Flow in High Energy Spillways by Means of Computational
Modelling and Experiments
Spillway Flow Simulation
60 ECTS thesis submitted in partial fulfillment of a Magister Scientiarum degree in
Environmental Engineering

Copyright © 2013 Kevin Franke
All rights reserved

Faculty of Civil and Environmental Engineering School of Engineering and Natural
Sciences
University of Iceland
Hjarðarhagi 2-6
107, Reykjavik
Iceland

Telephone: [phone]

Bibliographic information:
Kevin Franke, 2013, Investigation of the Complex Flow in High Energy Spillways by
Means of Computational Modelling and Experiments, Master’s thesis, Faculty of Civil and
Environmental Engineering School of Engineering and Natural Sciences, University of
Iceland, pp. XX.

ISBN XX

Printing: XX
Reykjavik, Iceland, XXmonth 20XX
Abstract
The hydrodynamics in open channel flows are most challenging and obey complex
physical laws. In order to investigate the cavitation potential and the functionality of a
spillway, time consuming and cost-intensive physical models are built in a smaller scale.
Froude scaling is used to compare the model to the prototype. A two-phase flow,
consisting out of air and water, is common in high energy spillways. Air entrainment and
air distribution in spillway flows are subjected to scaling effects and cannot be obtained
from a model and transferred to a prototype. For an accurate determination the evolvement
of an aerated flow depending on bubble sizes and their distribution, suspended particles
and aeration rate on the bottom of the spillway have to be taken into account in respect to
the cavitation potential. In this work, experiments and simulations are carried out to
understand the complexity of high-energy spillway flows. The simulations are based on
numerical modelling, which is a combined large-eddy simulation technique (LES) and
discrete element method. Three-dimensional simulations of an aerator are performed on a
graphics-processing unit (GPU). The results are in agreement with the experiments and
confirm prior findings from physical models such as formation of bubble size, bubble
coherence and separation and air concentration profiles. This promising effort in GPU
computing could pave the way for developing advanced simulation techniques for the
study of waterways and ports, as well as coastal and ocean engineering in the future.
Útdráttur
Straumfræði opinna farvega eru fræðilega krefjandi og fylgja flóknum eðlisfræðilegum
lögmálum. Til að rannsaka slittæringu (e. cavitation) og virkni yfirfalla, eru tíma- og
kostnaðarfrek líkön byggð í smáum skala. Froudeskölun er notuð til að bera saman líkanið
við raunverulega mannvirkið. Tveggja fasa rennsli, sem samanstendur af lofti og vatni, er
algengt í orkuríkum yfirföllum. Loftblöndun og loftdreifing í yfirfallsrennsli sæta
kvörðunaráhrifum og er því ekki hægt að yfirfæra frá líkantilraunum. Nákvæm ákvörðun á
þróun loftblandaðs rennsli veltur á stærð og dreifingu loftbóla, svifagna, og loftunar við
botn yfirfallsins sem hefur svo áhrif á mat á mögulegri slittæringu. Í þessu verkefni eru
tilraunir og hermanir gerðar til að skilja flókið rennsli orkuríks yfirfalls. Hermanirnar eru
byggðar á tölulegum líkönum, sem eru gerðar með iðu hermunartækni og bútareikningi.
Þrívíðar hermanir af loftblöndunarinntaki eru gerðar á grafík-vinnslu einingu (GPU).
Niðurstöðurnar passa við tilraunir og staðfesta fyrri niðurstöður líkana með tilliti til
loftbólu stærða, loftbólu samloðunar og loftstyrkssniða. Þessar góðu niðurstöður með
GPU gefa tilefni til að þróa áfram slíkar aðferðir fyrir farvegi og einnig fyrir strand- og
hafverkfræði í framtíðinni.

Dedication
Für meine Eltern, die immer für mich da sind.

Table of Contents
List of Figures ................................................................................................................... viii
List of Tables ...................................................................................................................... xii
Acknowledgements ........................................................................................................... xiii
1 Introduction ..................................................................................................................... 1
1.1 Motivation ............................................................................................................... 1
1.2 Conceptual formulation ........................................................................................... 1
1.3 Organization of the Thesis ...................................................................................... 5
2 Literature review ............................................................................................................ 6
2.1 Cavitation ................................................................................................................ 6
2.1.1 Cavitation Damage....................................................................................... 12
2.2 Air entrainment on chutes ..................................................................................... 15
2.2.1 Introduction .................................................................................................. 15
2.2.2 Free surface aeration .................................................................................... 15
2.2.3 Local aeration............................................................................................... 25
2.2.4 Rising velocity of air bubbles in still water ................................................. 29
2.2.5 Turbulent flow ............................................................................................. 33
2.2.6 Single bubble in turbulent flow.................................................................... 34
2.3 Focus of the present project................................................................................... 36
2.3.1 Summary of the literature review ................................................................ 36
2.3.2 Focus of the current research study ............................................................. 36
3 Experiments and Simulations ...................................................................................... 37
3.1 Set 1: Flow characteristics in a turbulent flow ...................................................... 37
3.1.1 Aerated turbulent flow in a glass tube ......................................................... 38
3.1.2 Mixing bucket .............................................................................................. 42
3.1.3 Mathematical model and simulation results ................................................ 46
3.2 Set 2: Cavitating flow and air distribution in a spillway ....................................... 53
3.2.1 Sheet cavitation in a tube ............................................................................. 53
3.2.2 Cavitation in an open channel ...................................................................... 61
3.3 Summary ............................................................................................................... 68
4 Conclusion ..................................................................................................................... 69
References........................................................................................................................... 71
Appendix A ......................................................................................................................... 77

vii
List of Figures
Figure 1.1 Aerial view of Kárahnjukar spillway with bottom aerator, eastern Iceland
(Tomasson et al., 2009) ...................................................................................... 1
Figure 1.2 Retained water behind Kárahnjukar dam. Inset: A hydrometer is used to
estimate the relative density with respect to water of the sample, which is
1.08. .................................................................................................................... 2
Figure 1.3 Cavitation indices at different discharges on a physical model of the
Kárahnjukar spillway (VAW, 2006). Blue diamonds: 200 m3/s; red
squares: 400 m3/s; green triangle: 800 m3/s; blue squares: 950 m3/s;
yellow square with green star: 1350 m3/s; orange dot: 2250 m3/s. ................... 3
Figure 2.1 Development of cavitation (Falvey, 1990) ......................................................... 7
Figure 2.2 Equilibrium conditions for vapour bubbles containing air (Daily and
Johnson, 1956) .................................................................................................... 9
Figure 2.3 Collapse mechanisms of a bubble (Falvey, 1980) ............................................ 10
Figure 2.4 Interaction of bubble collapse mechanisms (Falvey, 1980) ............................. 11
Figure 2.5 Spillway of the Karun Dam, Iran (Kramer, 2009) ........................................... 12
Figure 2.6 Hoover Dam, USA, (Warnock, 1945) .............................................................. 13
Figure 2.7 Axial views from the inlet of the cavitation and cavitation damage on the
hub or base plate of a centrifugal pump impeller (Soyama et al., 1992) .......... 13
Figure 2.8 Breaking wave from below (Oceanwide Images, 2002-2013) ......................... 15
Figure 2.9 Critical turbulent velocity v´ for air entrainment (Falvey, 1987). .................... 17
Figure 2.10 Air entrainment process from the free surface including turbulent
structures (Volkart, 1980) ................................................................................. 18
Figure 2.11 Development of flow characteristics and boundary layer on a flat plate
(Cortana Corporation) ...................................................................................... 18
Figure 2.12 View from upstream of the Split Rock dam spillway on 6 Sept. 1998. The
Split Rock dam is a rockfill embankment (66-m high, 469-m long)
completed in 1987 near Tamworth, Australia (Chanson,1988) ....................... 19
Figure 2.13 Self-aeration on chute spillway (Chanson, 1993) ............................................ 20
Figure 2.14 Air concentration distribution over the non-dimensional flow depth z/z90
in the uniform flow region for various chute angles a (Wood 1985) ............... 23
viii