Aeration and Energy Dissipation over Stepped Gabion Spillways

THE UNIVERSITY OF QUEENSLAND

REPORT CH92/13

AUTHORS: Davide WUTHRICH and Hubert CHANSON

AERATION AND ENERGY DISSIPATION OVER STEPPED GABION SPILLWAYS: A PHYSICAL STUDY

SCHOOL OF CIVIL ENGINEERING

HYDRAULIC MODEL REPORTS This report is published by the School of Civil Engineering at the University of Queensland. Lists of recently-published titles of this series and of other publications are provided at the end of this report. Requests for copies of any of these documents should be addressed to the Civil Engineering Secretary. The interpretation and opinions expressed herein are solely those of the author(s). Considerable care has been taken to ensure accuracy of the material presented. Nevertheless, responsibility for the use of this material rests with the user. School of Civil Engineering The University of Queensland Brisbane QLD 4072 AUSTRALIA Telephone: (61 7) 3365 4163 Fax: (61 7) 3365 4599 URL: http://www.eng.uq.edu.au/civil/ First published in 2014 by School of Civil Engineering The University of Queensland, Brisbane QLD 4072, Australia © Wuthrich and Chanson This book is copyright ISBN No. 9781742720944 The University of Queensland, St Lucia QLD, Australia

Aeration and Energy Dissipation over Stepped Gabion Spillways: a Physical Study

by

Davide WUTHRICH

Visiting research fellow, The University of Queensland, School of Civil Engineering, Brisbane

QLD 4072, Australia

Masters student, Ecole Polytechique Fédérale de Lausanne, Lausanne, Switzerland

and

Hubert CHANSON

Professor, The University of Queensland, School of Civil Engineering, Brisbane QLD 4072,

Australia, Email: [email protected]

REPORT No. CH92/13

ISBN 9781742720944

School of Civil Engineering, The University of Queensland

February 2014

Gabion stepped weir, Robina, Gold Coast (Australia)

ii

ABSTRACT

Stepped spillway structures have been used for more than 3,000 years. Recently the design of

stepped chutes regained some interest because of their suitability with roller compacted concrete

(RCC) construction methods and gabion placement. In this study, the hydraulic performances of

gabion stepped weirs were investigated experimentally in terms of the air-water flow properties,

energy dissipation and re-oxygenation rate. A physical study was performed in a relatively large

size facility with a 26.6° slope (1V:2H) and 0.10 m step height. Three gabion stepped

configurations were tested, as well as a flat impervious stepped configuration. For each

configuration, the detailed flow properties were investigated for a wide range of discharges. Some

visual observations highlighted the seepage flow through the gabions. The seepage flow motion

resulted into a modification of the cavity flow dynamics, as well as some air bubbles were

entrapped in the gabions. The air-water flow properties showed that the air concentration, bubble

count rate and turbulent intensity profiles presented lower quantitative values in the gabion stepped

configuration, compared to those on the impervious stepped chute. In skimming flows, higher

velocities were measured at the downstream end of the gabion stepped chute, associated with

smaller energy dissipation rates and lower friction factors. The aeration performances of the gabion

stepped configurations were lesser than on the impervious stepped chute, but for low discharges,

i.e., the nappe flow regime. For two configurations, some step capping was added, and the resulting

flow properties were close to those on the impervious stepped configuration.

Keywords: Stepped spillways, Gabion stepped weirs, Air entrainment, Energy dissipation, Re-

oxygenation, Physical modelling, Air-water flow properties, Seepage flow, Impervious step

capping.

iii

TABLE OF CONTENTS

Page

Abstract ii

Keywords ii

Table of contents iii

List of symbols v

1. Introduction 1

2. Experimental facility and instrumentation 4

2.1 Presentation

2.2 Experimental facility

2.3 Instrumentation

2.4 Experimental flow conditions

3. Flow patterns 11

3.1 Basic flow patterns

3.2 Air entrainment within the gabions

3.3 Inception point of free surface aeration

4. Air -water flow properties 20

4.1 Presentation

4.2 Flat and gabion stepped configuration

4.3 Capped and fully-capped stepped configurations

4.4 Discussion

5. Energy dissipation and flow resistance 36

5.1 Residual head and energy dissipation

5.2 Flow resistance

5.3 Discussion

6. Interfacial area and mass transfer rate 41

6.1 Presentation

6.2 Mass transfer rate

6.3 Discussion

7. Conclusion 46

iv

8. Acknowledgements 48

APPENDICES

Appendix A - Photographs of stepped spillways configuration and flow patterns A-1

Appendix B - Signal processing and sensitivity analysis B-1

Appendix C - Hydraulic conductivity tests C-1

Appendix D - Air-water flow properties on flat impervious stepped configuration D-1

Appendix E - Air-water flow properties on gabion stepped configuration E-1

Appendix F - Air-water flow properties on capped stepped configuration F-1

Appendix G - Air-water flow properties on fully-capped stepped configuration G-1

Appendix H - Longitudinal distribution of characteristic air-water properties H-1

Appendix I - Video movies of air bubble motion inside the gabions I-1

REFERENCES R-1

Bibliography R-5

Internet bibliography R-6

Bibliographic reference of the Report CH92/13 R-7

v

LIST OF SYMBOLS

The following symbols are used in this report:

A gas-liquid interface area (m2);

Aw flow cross-section area (m2);

a specific interface area, defined as the air-water surface area per unit volume of air and

water (m-1);

amax maximum value of specific interface area in a cross section (m-1);

amean mean specific interface area in a cross section (m-1):

90Y

0y90mean dya

Y

1a

b characteristic value of maximum variation of β;

C void fraction or air concentration, defined as the volume of air per unit volume;

CDS concentration of dissolved gas in the downstream cross-section (kg/m3);

CFmax void fraction for which F = Fmax;

Cgas concentration of the gas dissolved in water (kg/m3);

Cmean depth-averaged void fraction defined in terms of Y90: Cmean = 1-d/Y90;

CSAT gas saturation concentration in water (kg/m3);

CUS concentration of dissolved gas in the upstream cross-section (kg/m3);

DH hydraulic diameter (m) defined as DH = 4×Aw/Pw;

Dgas molecular diffusion coefficient of the gas in water (m2/s);

Do constant function of the mean void fraction in the advective diffusion equation

(skimming flow);

d equivalent clear water flow depth (m) defined as

90Y

0y

dy)C1(d

dc critical flow depth (m);

d50 median grain size (m);

E aeration efficiency, defined as:

USSAT

USDS

CC

CCE

F bubble count rate (Hz) defined as the number of detected air bubbles per unit time;

F* Froude number defined in terms of the step cavity roughness;

Fmax maximum value of bubble count rate in a cross section (Hz);

fe equivalent Darcy-Weisbach friction factor of the air-water flow;

g gravity constant (m/s2): g = 9.794 m/s2 in Brisbane (Australia);

H (a) total head (m);

(b) piezometric head (m);

Hdam weir height (m);

Hmax upstream total head (m): Hmax = Hdam + H1 Hdam + 3/2×dc;

vi

Hres residual head of the flow (m);

H0 height (m) of the vertical seepage face on the downstream face of the gabions;

H1 reservoir elevation (m) above the spillway crest;

h vertical step height (m);

i integer;

K hydraulic conductivity of a porous medium (m/s);

Ke modified hydraulic conductivity (m/s);

KL mass transfer coefficient or liquid film coefficient (m/s);

K' integration constant in the advective diffusion equation (skimming flow);

K" integration constant in the advective diffusion equation (transition flow);

ks cavity height perpendicular to the direction of the flow (m): ks = h×cos;

ks' step surface roughness height (m);

Lo length of the horizontal seepage above the first gabion (m);

Lb distance (m) between step edge 10 and the measurement location in the bottom channel;

Lcrest length of the broad-crested weir (m);

LI longitudinal distance (m) between the inception point of aeration and step edge 1;

(LI)cavity longitudinal distance (m) between the inception point of step cavity aeration and step

edge 1;

(LI)fs longitudinal distance (m) between the inception point of free-surface aeration and step

edge 1;

(LI)gabion longitudinal distance (m) between the inception point of gabion aeration and step edge

1;

l horizontal step length (m);

Mgas mass of dissolved gas (kg);

N power law exponent;

Po porosity;

Pw wetted perimeter (m);

Q water discharge (m3/s);

q water discharge per unit width (m2/s), defined as q = Q/W;

qw water discharge per unit width (m2/s) calculated from the integration of the void ratio

and velocity profiles:

90Y

0y

w dyV)C1(q

R normalised correlation coefficient;

rcrest radius of the upstream rounded corner of the broad-crested weir (m);

Re Reynolds number defined in terms of the hydraulic diameter: Re = w×V×DH/w;

ReP Reynolds number defined in terms of the seepage flow velocity: ReP = w×uD×d50/w;

Rxx normalised auto-correlation function;

Rxy normalised cross-correlation function;

vii

Sf friction slope defined as Sf = - ∂H/∂x;

T time (s) at which the cross correlation between the probe tip signals is maximum;

TK temperature (K);

T0.5 time (s) for which the auto-correlation function Rxx(T0.5) = 0.5;

Tu turbulent intensity: Tu = u'/V;

Tumax maximum turbulent intensity in a cross section;

t time (s);

Uw mean flow velocity (m/s) defined as Uw = q/d;

uD seepage velocity (m/s);

u' root mean square of velocity fluctuations (m/s);

V interfacial velocity (m/s);

V90 characteristic interfacial velocity (m/s) where C = 0.9;

Vc critical velocity of the flow (m/s) defined as: Vc = (g×dc)1/2;

W width of the stepped spillway (m);

x longitudinal distance (m) measured along the pseudo-bottom formed by the step edges;

Y90 characteristic depth (m) where C = 0.9;

y distance (m) measured perpendicular to the pseudo-bottom formed by the step edges;

z transverse distance from the channel centreline (m);

α correction factor, function of the local void ration and flow conditions;

β correction factor, function of the local void ration and flow conditions;

ΔH total energy loss (m) defined as ΔH = Hmax - Hres ;

Δx streamwise distance between the probe tips (m);

Δz transverse distance between the probe tips (m);

Δzo difference in height between the weir crest and calculated step edge (m);

κ intrinsic permeability (m2) of the porous medium;

ν kinematic viscosity of water (m2/s): = w/w.

θ chute slope: tan = h/l;

λ dimensionless function of the mean air concentration (transition flow);

λa characteristic air bubble chord (m);

λb characteristic water chord (m);

w dynamic viscosity of water (Pa.s);

w water density (kg/m3);

surface tension between air and water (N/m);

τo boundary shear stress (Pa);

τ0.5 time for which the cross-correlation function is half of its maximum value (s);

Ø diameter of the probe sensor (m);

Subscript

c critical flow conditions;

viii

DS downstream flow conditions;

US upstream flow conditions;

90 flow properties at the characteristic location where C = 0.90;

Abbreviations

NA nappe flow regime;

PR porous seepage flow regime;

SK skimming flow regime;

TRA transition flow regime.

1

1. INTRODUCTION

Stepped spillways and weirs have been used for more than 3,500 years (CHANSON 2000-2001).

The stepped chute design enhances the rate of energy dissipation on the spillway chute, thus

reducing the size and cost of the downstream stilling structure. During the last three decades,

research into the hydraulics of stepped spillways has been active with a focus on steep stepped

spillways for concrete gravity dams (CHANSON 1995a,2000,2001, OHTSU and YASUDA 1998,

MINOR and HAGER 2000). For a given concrete stepped chute, the spill flows as a nappe flow

regime for small discharges; for a range of intermediate discharges, a transition flow regime may be

observed; most prototype spillways operate in the skimming flow regime for large flow rates per

unit width (Fig. 1-1). In skimming flows, the waters skim as a coherent stream over the pseudo-

bottom formed by step edges and large form losses take place (RAJARATNAM 1990, CHANSON

et al. 2002).

Stepped spillway flows are characterised by some strong flow aeration, very-strong turbulence, and

interactions between entrained air and turbulence as illustrated in Figures 1-1 and 1-2 (CHANSON

and TOOMBES 2002a,b, OHTSU et al. 2004, GONZALEZ and CHANSON 2004). A few studies

studies investigated the effects of macro-roughness and turbulence manipulation on skimming flow

properties (ANDRE et al. 2004, KOKPINAR 2004, GONZALEZ and CHANSON 2008, FELDER

and CHANSON 2013, GUENTHER et al. 2013). The effects of step roughness on the flow

properties were specifically studied independently by GONZALEZ et al. (2008) and BUNG and

SCHLENKHOFF (2010) with similar counter-intuitive results: i.e., all data showed faster flow

motion and lesser energy dissipation on rough stepped chutes. PEYRAS et al. (1991,1992) studied

the flow patterns and energy dissipation of gabion stepped weirs. KELLS (1993,1995) discussed the

interactions between of seepage and free-surface flows on gabion weirs. CHANSON (1995a,2001)

reviewed the design of gabion stepped chutes.

It is the purpose of this study to study thoroughly the hydraulics of gabion stepped weirs and

spillways, including their air-water flow properties, rate of energy dissipation and re-oxygenation

performances. New measurements were conducted in a relatively large size facility (θ = 26.6º, h =

0.1 m) with four stepped conditions (flat impervious, gabion and gabion with cappings). Detailed

air-water flow properties were measured systematically for a range of discharges with a focus on

the transition and skimming flow regimes. The results provided a new understanding of the

combined effects of seepage and step surface roughness on the characteristics of overflows.

2

(A) Paradise dam stepped spillway (Australia) in operation on 5 March 2013 (shutter speed: 1/1,600

s) - Flow conditions: q = 7.4 m2/s, dc/h = 2.9, skimming flow - Spillway geometry: = 57.4, h =

0.62 m, RCC dam

(B) Hinze dam stepped spillway (Australia) in operation on 29 January 2013 (shutter speed: 1/8,000

s) - Flow conditions: q = 14 m2/s, dc/h = 2.3, skimming flow - Spillway geometry: = 51.3, h = 1.2

m, Rockfill dam wall with conventional concrete spillway

Fig. 1-1 - Photographs of concrete stepped spillways in operation

3

(A1) On 2 April 1997 shortly after completion (B2) On 25 April 2013

(A) Gabion stepped weir at Robina, Gold Coast (Australia) - h = 0.6 m, l = 1.1 to 2 m

(B) Diversion stepped channel at Duralie Coal project (Australia) on 23 March 2005 (Courtesy of

Tony MARSZALEK)

Fig. 1-2 - Photographs of gabion stepped weirs and spillways

4

2. EXPERIMENTAL FACILITY AND INSTRUMENTATION

2.1 PRESENTATION

Physical hydraulic models are commonly used during the design stages to optimise a spillway and

to ensure a safe operation of the structure. In a physical model, the flow conditions must be similar

to those in the prototype: that is, a similarity of form, of motion and of forces. In free-surface flows,

a Froude similitude is typically applied to scale the flow motion. In most applications, the physical

hydraulic model is a smaller-size representation of the prototype; thus scale effects might take

place.

For a rectangular gabion stepped weir, a simplified dimensional analysis leads to a number of

relationships between the air-water (over)flow properties, fluid properties, boundary conditions and

channel geometries:

,....Po,d

'k,,

d

W,

g,

DV,

h

d,

d

z,

d

y,

d

xF,...da,

V

dF,

V

'u,

V

V,C

c

s

c3

w

4w

w

Hw

c

ccc1c

c

c

cc

(2-1)

where C is the void fraction, V is the interfacial velocity, u' is a characteristic velocity fluctuation, F

is the bubble count rate, a is the specific interface area, dc and Vc are the critical flow depth and

velocity respectively, x, y, z are respectively the longitudinal, normal and transverse coordinates,

DH is the hydraulic diameter, W is the channel width, h and l are the step height and length

respectively, g is the gravity acceleration, θ is the chute slope, μw is the dynamic viscosity of water,

ρw is the water density, σ is the surface tension between air and water, ks' is the equivalent sand

roughness height of the step boundary surface, Po is the gabion porosity. Equation (2-1) expresses

the dimensionless air-water overflow properties at a location (x,y,z) as functions of the relevant

dimensionless parameters, including Froude, Reynolds and Morton numbers. Indeed the

dimensionless discharge dc/h is proportional to a Froude number defined in terms of the step height:

3/23c )hg/q(h/d where q is the water discharge per unit width. Note that the grain size and

mesh characteristics are implicitly accounted for by the equivalent sand roughness height ks'.

In the present study, the Morton number was an invariant because the same fluids were used in

model and prototype (WOOD 1991, CHANSON 2009, PFISTER and CHANSON 2012). Similarly,

the chute slope (tan = h/l) and the channel width W were kept constant during the experimental

study, while all the measurements were conducted on the channel centreline. Hence Equation (2-1)

may be simplified into:

,....Po,d

'k,

DV,

h

d,

d

y,

d

xF,...da,

V

dF,

V

'u,

V

V,C

c

s

w

Hw

c

cc2c

c

c

cc

(2-2)

Herein a Froude similitude was developed and the experiments were conducted in a large size

facility which operated at large Reynolds numbers (Table 2-1, column 4) with relatively large-size

5

gabion material. These conditions may correspond to a 1:3 to 1:6 scale study of the gabion stepped

weirs shown in Figure 1-2, thus ensuring that the extrapolation of the laboratory data to prototype

conditions is unlikely to be adversely affected by scale effects.

2.2 EXPERIMENTAL FACILITY

New experiments were conducted in a relatively large size stepped spillway model at the University

of Queensland. The facility was previously used by FELDER and CHANSON (2013a,b) and

GUENTHER et al. (2013). The test section consisted of a broad-crested weir followed by ten steps

with step height h = 0.1 m and step length l = 0.2 m. The chute was 0.52 m wide.

A pump controlled with an adjustable frequency AC motor drive delivered the flow rate, allowing

an accurate discharge adjustment in a closed-circuit system. The water flow was supplied by a large

upstream intake basin followed by a smooth sidewall convergent with a 4.23:1 contraction ratio. At

the upstream end of the chute, the flow was controlled by a broad-crested weir equipped with an

upstream rounded corner. The water discharge was deduced from the measured upstream head

above crest using the discharge calibration results of FELDER and CHANSON (2012):

3

1crest

1 H3

2g

L

H153.092.0

W

Q

(2-3)

where H1 is the upstream total head above the crest and Lcrest is length of the broad-crested weir

(Lcrest = 1.01 m). At the downstream end, the stepped chute was followed by a smooth horizontal

channel ending with an overfall. The flow was supercritical in this horizontal tailwater raceway for

all investigated flow conditions (Table 2-1).

Four stepped configurations were tested (Fig. 2-1). The flat impervious stepped configuration

consisted of smooth impervious steps made of marine ply. For the other three configurations, ten

identical gabions were installed above the smooth impervious steps. Each gabion was 0.3 m long,

0.1 high and 0.52 m wide, made of fine 12.7×12.7 mm2 galvanised metallic mesh and filled with

natural river pebbles (Fig. 2-2). The gravels (Cowra pearl) were sieved with 14 mm square sieve.

The density of the dry gravels was 1.6 tonnes/m3 corresponding to a porosity Po 0.35-0.4. The

hydraulic conductivity of the gabions was estimated to be K 10-1 m/s. Full details of the hydraulic

conductivity tests are presented in Appendix C. Note that the ratio of stone size to mesh size was

typical of construction practices for more economical cage filling and better adaptability of gabions

to deformation (AGOSTINI et al. 1987, CHANSON 2001).

The capped stepped configuration was obtained by installing 6 mm thick plexiglass plates on the

horizontal faces of steps 2 to 10. Each plexiglass plate was 0.195 m long and 0.51 m wide. All the

step edges were identically shaped, with the plate sharp edge ending 6-7 mm before the gabion

6

edge. The first horizontal step was not capped, allowing water to seep directly into the first gabion

(Fig. 2-1C). The fully-capped stepped configuration was identical to the capped one, but for the

addition of a plexiglass plate covering both the crest of the weir and first gabion (Fig. 2-1D).

Table 2-1 - Experimental investigations of air-water flow properties on stepped spillways

Reference θ (°) Geometry Flow conditions Instrumentation

(1) (2) (3) (4) (5)

Gabion steps (plain) Capped steps (layer cake) Upward steps

PEYRAS et. al (1991)

45 26.6 18.3

h = 0.2 m, l = 0.4 m W = 0.8 m

Pooled steps (End Sill)

Q = 0.05 - 0.2 m3/s Re = 2.5×105 - 1.0×106

Pitot tube array (copper pipe with inlet holes every 5 cm)

15.9 Flat steps: h = 0.1 m, l = 0.35 m W = 1 m

Q = 0.05 - 0.26 m3/s Re = 2.0×105 - 1.0×106

Double-tip conductivity probe (Ø = 0.025 mm).

CHANSON & TOOMBES (2002b) 21.8 Flat steps: h = 0.1 m, l = 0.25 m

W = 1 m Q = 0.04 - 0.18 m3/s Re = 1.6×105 - 7.2×105

Double-tip conductivity probe (Ø = 0.025 mm).

TOOMBES & CHANSON (2005)

3.4 Flat steps: h = 0.143 m, l = 2.4 m, W = 0.5 m Flat step: h = 0.143 m, W = 0.25 m

Q = 0.021 - 0.075 m3/s Re = 3×105 - 6×105

Single tip conductivity probe (Ø = 0.35 mm) Double tip conductivity probe (Ø = 0.025 mm)

A: rough step faces

B: rough vertical faces

C: rough horizontal faces

GONZALEZ et al. (2008)

21.8 h = 0.1 m l = 0.25 m W = 1 m

S: smooth steps

Q = 0.01 - 0.22 m3/s, Re = 5×104 - 7×105

Double tip conductivity probe (Ø = 0.025 mm)

TOOMBES & CHANSON (2008a,b)

3.4 Flat steps: h = 0.143 m, l = 2.4 m, W = 0.5 m Flat step: h = 0.143 m, W = 0.25 m

Q = 0.02 - 0.49 m3/s, Re = 1.6×105 - 1.5×106

Single tip conductivity probe (Ø = 0.35 mm) Double tip conductivity probe (Ø = 0.025 mm)

FELDER & CHANSON (2009)

21.8 Flat steps: h = 0.05 m, l = 0,125 m W = 1 m

Q = 0.04 - 0.18 m3/s Re = 1.7×105 - 7.2×105

Single-tip conductivity probe (Ø =0.35 mm) Double-tip conductivity probe (Ø =0.25 mm)

BUNG & SCHLENKHOFF (2010)

26.6 Flat steps: h = 0.06 m W = 0.30 m (1) Flat steps (2a) Rough horizontal faces (in row) (2b) Rough horizontal faces (shifted)

Q = 0.021, 0.027 & 0.33 m3/s Re = 2.7×105, 3.6×105, 4.4×105

Double-tip conductivity probe (Ø =0.13 mm, Δx = 5.1 mm, Δy = 1 mm)

FELDER & CHANSON (2013b)

26.6 Flat steps : h = 0.1 m, l = 0.2 m Pooled steps: h = 0.1 m, w = 3.1 cm Porous pooled steps: h = 0.1 m, w = 3.1 cm, Po = 5 % Porous pooled steps: h = 0.1 m, w = 3.1 cm, Po = 31 % W = 0.52 m

Q = 0.013 - 0.13 m3/s Re = 1.0×105 - 1.0×106

Double tip conductivity probe (Ø = 0.25 mm, Δx = 7.2 mm, Δz = 2.1 mm)

Flat and impervious

Gabion and porous

Capped and porous

Present Study 26.6 h = 0.1 m l = 0.2 m W = 0.52 m

Fully-capped and porous

Q = 0.02 - 0.11 m3/s, Re = 1.4×105 - 8.8×105

Double tip conductivity probe (Ø = 0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)

Notes: h: step height; l: step length; Q: water discharge, Re: Reynolds number defined in terms of

7

hydraulic diameter; W: width of channel; Ø: probe diameter; Δx: streamwise distance between

probe tips; Δy: vertical distance between probe tips; Δz: transverse distance between probe tips; θ:

chute slope.

(A) Flat impervious stepped configuration (dc/h = 1.3)

(B) Gabion stepped configuration (dc/h ~ 0.9)

8

(C, Left) Capped gabion configuration - Note the absence of capping on the first gabion

(D, Right) Fully-capped gabion configuration (dc/h = 0.5)

Fig. 2-1 - Photographs of the experimental configurations

Fig. 2-2 - Details of the gabion placement: view in elevation

2.3 AIR-WATER FLOW INSTRUMENTATION

The air-water flow measurements were conducted with a phase detection intrusive probe (Fig. 2-3).

The probe was manufactured with two identical tips based upon a needle tip design. The recordings

were performed at all step edges downstream of the inception point using the double-tip

9

conductivity probe which had an inner tip diameter Ø = 0.25 mm and a separation of probe tips Δx

= 6.2 mm in the longitudinal direction (Fig. 2-3) and Δz = 1.35 mm in the transverse direction. The

conductivity probe was mounted on a trolley and the elevation in the direction perpendicular to the

pseudo bottom formed by the step edges was controlled by a fine adjustment screw-drive

mechanism equipped with a MitutoyoTM digital ruler (accuracy < 0.1 mm). Similar double-tip

conductivity probes were previously used in a number of air-water flow studies at the University of

Queensland (CAROSI and CHANSON 2008, FELDER and CHANSON 2009, GUENTHER et al.

2013).

The probe was excited by an electronic air bubble detector with a response frequency greater than

100 kHz. The probe signal output was sampled at 20 kHz per sensor for 45 seconds. The selection

of the sampling rate and duration was derived from a sensitivity analysis (Appendix B). The signals

were processed with a Fortran code developed at the University of Queensland (FELDER 2013).

The main parameters derived from the signal processing were the void fraction C, bubble frequency

F, interfacial velocity V, turbulent intensity Tu and specific interfacial area a. Further details on the

signal post-processing were discussed in CHANSON and CAROSI (2007) and CHANSON

(2002,2013).

Fig. 2-3 - Details of the dual-tip phase detection probe (shutter speed: 1/25 s) - View in elevation

with flow direction from left to right

2.4 EXPERIMENTAL FLOW CONDITIONS

The experimental study was conducted on the four stepped spillway configurations. Flow

visualisations were carried out for all configurations for a wide range of discharges within 0.005 ≤

Q ≤ 0.114 m3/s. The air-water flow properties were recorded mostly in the transition and skimming

flow regimes, for a range of dimensionless discharges between 0.5 ≤ dc/h ≤ 1.7 corresponding to

Reynolds numbers between 1.40×105 and 8.78×105. The experimental flow conditions are

10

summarised and compared with previous air-water flow studies in Table 2-1. They are further

detailed in Table 2-2.

Table 2-2 - Experimental flow conditions for all stepped configurations (Present study, θ = 26.6°, h

= 0.10 m)

Configuration Q [m3/s]

dc/h [-]

Re [-]

Flow investigations

0.005 – 0.114

0.2 - 1.7 3.54104 – 8.78105

Flow observations, flow regimes

0.018 0.5 1.40×105 0.037 0.8 2.83×105 0.059 1.1 4.57×105 0.076 1.3 5.87×105 0.095 1.5 7.28×105

Flat stepped configuration (h = 0.10 m θ = 26.6°)

0.114 1.7 8.78×105

Measurements or air-water flow properties at all step edges

downstream of the inception point

0.005 – 0.114

0.2 - 1.7 3.54104 – 8.78105

Flow observations, flow regimes, inception point, dye study, string study

0.018 0.5 1.40×105 0.037 0.8 2.83×105 0.059 1.1 4.57×105 0.076 1.3 5.87×105 0.095 1.5 7.28×105

Gabion stepped configuration (h = 0.10 m θ = 26.6°)

0.114 1.7 8.78×105



0.005 – 0.114

0.2 - 1.7 3.54104 – 8.78105

Flow observations, flow regimes, inception point, dye study, string study

0.018 0.5 1.40×105 0.037 0.8 2.83×105 0.059 1.1 4.57×105 0.076 1.3 5.87×105 0.095 1.5 7.28×105

Capped stepped configuration (h = 0.10 m θ = 26.6°)

0.114 1.7 8.78×105



0.005 – 0.114

0.2 - 1.7 3.54104 – 8.78105

Flow observations, flow regimes, inception point, dye study

0.018 0.5 1.40×105 0.037 0.8 2.83×105 0.059 1.1 4.57×105 0.076 1.3 5.87×105 0.095 1.5 7.28×105

Fully-capped stepped

configuration (h = 0.10 m θ = 26.6°)

0.114 1.7 8.78×105



11

3. FLOW PATTERNS

3.1 PRESENTATION

Visual observations were carried out for all configurations for a wide range of dimensionless

discharges dc/h up to 1.7. For all stepped configurations, the 'classical' flow regimes were identified:

namely nappe, transition and skimming flows with increasing flow rates. In addition a porous flow

regime was observed on the gabion stepped configurations for very low discharges. A summary of

flow properties of the changes between flow regimes is reported in Table 3-1. A detailed review of

flow visualisations is presented in Appendix A.

On the flat impervious stepped chute, a nappe flow regime was observed for the smallest discharges

(dc/h < 0.5). The flow consisted of a succession of free falling nappes from a step to the following

one (CHAMANI and RAJARATNAM 1994, CHANSON 1994a, TOOMBES and CHANSON

2008a). Below each falling nappe, a recirculating pool of water was formed with an air cavity

above. A schematic representation of the cavity pattern can be found in Figure 3-1 (Bottom). For a

range of intermediate discharges (0.5 < dc/h < 0.9), the flow was characterised by strong

hydrodynamic instabilities associated with a well developed spray region and a large amount of

splashes. The step cavities were almost completely full, with a small air pocket under the step edge,

while for larger discharges the cavities became filled with water (CHANSON and TOOMBES

2004). For the larger discharges (dc/h > 0.9), the flow skimmed as a coherent stream above the

pseudo-bottom formed by the step edges. Substantial air entrainment occurred downstream of the

inception point of free surface aeration, and an energetic recirculation pattern was observed in the

step cavities (CHANSON 1994b, BOES 2000, GONZALEZ and CHANSON 2004, FELDER 2013)

(Fig. 3-2, Bottom). Overall the flow pattern observations and flow conditions for the changes

between flow regimes were in agreement with the literature (CHANSON and TOOMBES 2002b,

GONZALEZ 2005, FELDER and CHANSON 2009, FELDER and CHANSON 2011).

Table 3-1 - Summary of changes in stepped chute flow regimes on rough stepped chutes

Ref. h Configuration dc/h (°) (m) PR-NA NA-TRA TRA-SK

Present 26.6 0.10 Flat impervious N/A 0.5 0.9 study Gabion 0.3 0.6 0.9 Capped gabion 0.2 0.6 0.9 Fully-capped gabion N/A 0.5 0.9 GONZALEZ 21.8 0.10 S - Smooth steps N/A 0.64 0.97 et al. (2008) A - Rough steps N/A 0.64 0.97 B - Rough vertical step faces N/A 0.64 0.97 C = Rough horizontal step faces N/A 0.64 0.97

12

Fig. 3-1 - Nappe flow regime on gabion and impervious stepped configurations: definition sketches

- From top left in the clockwise direction: gabion steps, capped gabion steps, flat impervious steps

On the gabion stepped spillway, a porous seepage flow regime was observed for very small

discharges (dc/h < 0.3). In that flow regime, all the water seeped through the gabion materials. On

the first gabion box, some infiltration was observed as shown in Figure 3-3A. A short horizontal

seepage face was observed on each step and there was no overflow past the step edges. In the

porous material, the free-surface (i.e. water table) could be observed through the transparent

sidewalls. A relatively large amount of water (i.e. the total discharge) was seen coming out of the

10th gabion box to fulfil the conservation of mass. For the smallest discharges, some vertical

seepage was not observed through the step vertical face. With increasing discharge, some small

water jets came out of the gabions as shown in Figure 3-3B. The transition between porous and

nappe flow regimes occurred once some overflow took place at the first gabion. The nappe flow

(0.3 < dc/h < 0.6) appeared as a succession of free falling nappes from one step edge to the next one

(Fig. 3-1, Top left). The cavity behind the nappe was filled with a superposition of seepage jets

coming out of the upstream gabion (Fig. 3-1, Top Left). In the lower part of the cavity an oscillating

recirculation pool was observed. The recirculation motion in the cavity pool exhibited a different

13

flow pattern compared to that observed on flat impervious stepped spillways. This is illustrated in

Figure 3-1.

Fig. 3-2 - Skimming flow regime on gabion and impervious stepped configurations: definition

sketches - From top left in the clockwise direction: gabion steps, capped gabion steps, flat

impervious steps

(A) dc/h = 0.20, Q = 0.005 m3/s, Re = 3.5104 (B) dc/h = 0.25, Q = 0.006 m3/s, Re = 4.9104

First gabion box located at end of broad-crest Steps in the middle of the staircase chute

Fig. 3-3 - Porous flow regime on the gabion stepped configuration

14

Fig. 3-4 - Cavity flow pattern in a skimming flow on gabion stepped configuration - Flow

conditions: step cavity 7-8, Q = 0.068 m3/s, dc/h = 1.20, Re = 5.2105 - Note the clear water core in

the step cavity

A transition flow regime was observed for 0.6 < dc/h < 0.9. The hydrodynamic instabilities and

splashes appeared less intense than those observed on flat impervious stepped spillways. For the

largest discharges, a skimming flow was observed (dc/h > 0.90). The flow pattern was generally

similar to that observed on the flat stepped configuration. However a different streamline pattern

was seen next to the stagnation point on the horizontal step face (Fig. 3-2, Top left). Some bubbly

flow and air bubble entrainment into the gabions were observed, mostly in the upper corner of each

gabion box downstream of the inception point of free-surface aeration. Further differences were

found in terms of cavity flow motion as a result of seepage flow effect. Detailed string studies were

carried out to visualise the cavity flow. A vertical flow of air bubbles was observed close to the

vertical step face (Fig. 3-4). In the centre of the cavity a clear water core was seen in all cavities

downstream of the inception point for all discharges. The existence of a similar clear water core was

previously reported by GONZALEZ et al. (2008) for rough impervious steps. Visually the

recirculation motion appeared to be restricted by the existence of the clear-water core. In the gabion

stepped configuration, a continuous interaction between the cavity and the gabion was noted. The

behaviour of the flow inside the cavity is schematically sketched in Figure 3-2 (Top left).

On the capped gabion stepped chute, a porous regime was observed for dc/h < 0.20. For larger

discharges, a nappe flow regime was seen for 0.20 < dc/h < 0.60, a transition flow for 0.60 < dc/h <

0.90, and the skimming flow for dc/h > 0.90. In these flow regimes (nappe, transition and skimming

15

flows), the flow patterns were similar to those observed on the flat impervious stepped chute. Some

differences were noticed at cavity level as a consequence of the seepage flow through the gabions.

This is sketched in Figure 3-1 (Top right) and Figure 3-2 (Top right). The effect of the seepage flow

was mostly noticeable for the small discharges, i.e., for the porous and nappe flow regime. The

skimming flow did not appear to be much influenced by the seepage flow.

On the fully capped gabion stepped configurations, the flow patterns were generally close to those

observed on the flat impervious stepped chute and capped gabion stepped configuration, but for the

first step cavity. As illustrated in Figure 3-5, some seepage into the gabion took place through the

vertical step face beneath the first step edge.

(A) Q = 0.006 m3/s, dc/h = 0.25, Re = 4.9104 (B) Q = 0.018 m3/s, dc/h = 0.50, Re = 1.4105

Fig. 3-5 - Seepage flow visualisation on fully-capped gabion stepped configuration using dye

injection - Flow conditions in nappe flows, red dye injection (step cavity 1-2)

3.2 AIR ENTRAINMENT WITHIN THE GABIONS

A key difference between the flat impervious and gabion stepped chutes was the entrainment of air

bubbles inside the gabions. For all porous configurations, air bubbles were seen flowing through the

gravel (App. I). Appendix I regroups a series of digital video movies of bubbly flow motion in the

gabions. Visually, the bubbly flow in the gabions appeared to depend upon the water discharge,

flow regime, and step cavity location.

The largest amount of gabion bubble motion was observed in the gabion stepped structure for a

given (over)flow rate. (Lesser air entrainment in gabions was seen in the capped and fully-capped

stepped configurations for an identical flow rate.) With a nappe (over)flow regime, a large amount

of bubbles moved inside the top edge of the gabions (Fig 3-6). A majority of bubbles flowed

through the gabions and into the downstream step cavity. Some collided with gravel particles and

emerged into the cavity by buoyancy. A few bubbles flowed through the gravel into the downstream

gabion box. A sketch of the bubbly flow inside the gabions is presented in Figure 3-6. Figure 3-7

16

shows some photographs of the bubble motion in the gabions. With increasing discharges, the

upstream gabion boxes became water saturated and no bubble was observed. For the larger

discharges with transition and skimming (over)flows, an inception point of gabion aeration was

clearly observed. The location basically coincided with the apparition of air bubbles in the step

cavities. Downstream, bubbles were entrained into the gabions. In the skimming flow regime, a

modification of the streamlines impacting onto the horizontal step face was observed. It resulted in

some bubbly flow into the upper edge of the gabion as sketched in Figure 3-2 (Top left).

With both capped and fully-capped stepped configurations, some bubble motion inside the gabions

was also observed. Both configurations presented very similar patterns. For the nappe (over)flow

regime, the upper edge of each gabion box was unsaturated and a free surface was clearly identified

(Fig. 3-1, Top right). Some bubbles were seen flowing in the saturated gabion material. The amount

of entrained bubbles inside the gabions appeared to be reduced compared to the gabion stepped

configuration. In the skimming flow regime, a majority of gabion bubbles came from the cavity-

gabion interactions along the vertical step face (Fig. 3-2, Top right). The cavity recirculation motion

tended to push air bubbles inside the gabion. The gabion bubbles either moved up or down to the

downstream gabion box (Fig. 3-2, Top right). The latter bubbly motion tended to flow horizontally

beneath the capping and between the capping and metallic mesh wire. Differences between capped

and fully-capped stepped configurations were mostly seen in the first gabion box and first step

cavity.

Fig. 3-6 - Definition sketch of air bubble motion (red dotted lines) inside a gabion stepped structure

with nappe (over)flow regime

17

(A) dc/h = 0.45, nappe flow, gabion steps (B) dc/h = 0.85, transition flow, capped gabions

(C) dc/h = 0.5, nappe flow, capped gabions

Fig. 3-7 - Photographs of air bubble motion inside a gabion stepped structure - Flow direction from

top left to bottom right

3.3 INCEPTION POINT OF FREE SURFACE AERATION

The inception point of free surface aeration is defined as the location where the turbulence

overcomes surface tension and air is entrained within the flow. The position of the inception point

(LI)fs was measured for a wide range of discharges (0.6 < dc/h <1.7). The experimental data are

presented in Figure 3-8 in dimensionless form in the form of LI/ks as a function of the Froude

number F* defined in terms of the step cavity roughness:

3

s

*ksing

qF

(3-1)

with q the water discharge per unit width, g the gravity constant, θ the slope of the facility and ks

the cavity height perpendicular to the flow direction (ks = h×cos). The data are compared with two

empirical correlations for smooth impervious stepped spillways:

713.0*

0796.0

s

fsI Fsin719.9k

)L( 27°< θ < 53° (CHANSON 1994b) (3-2)

18

*s

fsI F11.505.1k

)L( =21.8°, 0.45 < dc/h < 1.6 (CAROSI and CHANSON 2008) (3-3)

The present results showed that the location of inception point of free surface aeration was close for

all stepped configurations.

F*

(LI)

fs/k

s

0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

Chanson (1994) ( = 26.6)Carosi & Chanson (2008) ( = 22)Impervious stepsGabionsCapped gabionsFully-capped gabions

Fig. 3-8 - Location of the inception point of free-surface aeration - Comparison with the correlations

of CHANSON (1994b) and CAROSI and CHANSON (2008) for smooth impervious stepped chutes

In addition, the locations of cavity aeration inception and gabion aeration inception were recorded

for the gabion stepped configuration. Herein, the inception of cavity flow aeration is defined as the

first step cavity in which substantial aeration across the whole cavity was observed through the

sidewalls, while the gabion inception point is defined as the first gabion box in which bubbles were

encountered. The findings are regrouped in Figure 3-9, and they are compared with the location of

the inception point of free-surface aeration. Overall the inception of step cavity aeration and gabion

aeration took place at the same location, namely one step cavity in average downstream of the

location of inception point of free-surface aeration (Fig. 3-9). Further the inception of cavity

aeration took place further upstream of the capped gabion stepped configuration: i.e., up to a step

cavity earlier typically.

Note that a few air bubbles were seen intermittently upstream, up to one to two step cavities

upstream of the inception point of free-surface aeration. But their numbers were small and their

appearance was irregular. Herein we selected a definition of cavity aeration which focused some

19

sustained aeration of the whole step cavity.

F*

(LI)

fs/k

s, (L

I)ca

vity

/ks,

(LI)

gabi

on/k

s

0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25 Free-surface aerationStep cavity aerationGabion aerationCarosi & Chanson (2008) ( = 22)

Fig. 3-9 - Location of the inception point of step cavity and gabion aeration for the gabion stepped

configuration - Comparison with the location of inception point of free-surface aeration

20

4. AIR-WATER FLOWPROPERTIES

4.1 PRESENTATION

The air-water flow properties were measured for all configurations for a range of dimensionless

discharges from dc/h = 0.5 to 1.7 corresponding to Reynolds numbers between 1.40×105 and

8.78×105. The experimental conditions are summarised in Table 4-1. The air-water flow

measurements were conducted at all step edges downstream of the inception point of free surface

aeration. For the porous stepped configurations, further sampling was conducted in the tailrace

channel immediately downstream of last step edge as sketched in Figure 4-1A. The measurements

were taken on the channel centreline between y = 0 and the upper spray region, where y is the

distance perpendicular to the pseudo bottom formed by the step edges as defined in Figure 4-1B.

Table 4-1 - Experimental program for the air-water properties investigation (θ = 26.6°, h = 0.10 m)

Configuration dc/h [-]

Q [m3/s]

Re [-]

Flow Regime

Measurement at Step Edge Position of the Inception Point

0.5 0.018 1.40×105 NA 3,4,5,6,7,8,9,10 step 2 0.8 0.037 2.83×105 TRA 4,5,6,7,8,9,10 step 3 to 4 1.1 0.059 4.57×105 SK 5,6,7,8,9,10 step 5 1.3 0.076 5.87×105 SK 5,6,7,8,9,10 step 5 to 6 1.5 0.095 7.28×105 SK 5,6,7,8,9,10 step 6 to 7

Flat stepped configuration (h = 0.10 m θ = 26.6°)

1.7 0.114 8.78×105 SK 6,7,8,9,10 step 7 to 8 0.5 0.018 1.40×105 NA 2,3,4,5,6,7,8,9,10, Bottom step 2 0.8 0.037 2.83×105 TRA 4,5,6,7,8,9,10, Bottom step 3 to 4 1.1 0.059 4.57×105 SK 5,6,7,8,9,10, Bottom step 5 1.3 0.076 5.87×105 SK 6,7,8,9,10, Bottom step 5 to 6 1.5 0.095 7.28×105 SK 8,9,10, Bottom step 7 to 8

Gabion stepped configuration (h = 0.10 m θ = 26.6°)

1.7 0.114 8.78×105 SK 8,9,10, Bottom step 8 to 9 0.5 0.018 1.40×105 NA 2,3,4,5,6,7,8,9,10, Bottom step 2 0.8 0.037 2.83×105 TRA 4,5,6,7,8,9,10, Bottom step 3 to 4 1.1 0.059 4.57×105 SK 5,6,7,8,9,10, Bottom step 5 1.3 0.076 5.87×105 SK 6,7,8,9,10, Bottom step 6 1.5 0.095 7.28×105 SK 7,8,9,10, Bottom step 6 to 7

Capped stepped configuration (h = 0.10 m θ = 26.6°)

1.7 0.114 8.78×105 SK 8,9,10, Bottom step 7 to 8 0.5 0.018 1.40×105 NA 5,6,7,8,9,10, Bottom(1) step 2 0.8 0.037 2.83×105 TRA 4,5,6,7,8,9,10, Bottom step 2 to 3 1.1 0.059 4.57×105 SK 5,6,7,8,9,10, Bottom step 5 1.3 0.076 5.87×105 SK 6,7,8,9,10, Bottom step 6 1.5 0.095 7.28×105 SK 7,8,9,10, Bottom step 7

Fully-capped stepped

configuration (h = 0.10 m θ = 26.6°)

1.7 0.114 8.78×105 SK 8,9,10, Bottom step 8 to 9

Notes: NA: nappe flow regime; SK: skimming flow regime; TRA: transition flow regime; (1):

Because of flow instabilities, measurements at step edges 2, 3 and 4 were conducted for dc/h = 0.5.

21

(A) General view of the stepped chute

(B1) Flat stepped configuration (B2) Gabion stepped configuration

(B3) Capped and fully-capped stepped configuration (B) Definition sketch of coordinate system for all stepped configurations, with the probe set at y = 0Fig. 4-1 - Definition sketch of the stepped chute sampling locations

A comparison between flat and gabion stepped configurations is presented in Section 4.2, in terms

of the air-water flow properties. In Section 4.3, the flow properties on both capped stepped

configurations are discussed and compared to those on flat and gabion stepped chutes. A short

discussion is developed in Section 4.4.

4.2 FLAT AND GABION STEPPED CONFIGURATIONS

4.2.1 Void fraction and bubble frequency distributions

The void fraction distributions for both flat and gabion stepped configurations exhibited shapes

which were comparable to previous observations on stepped spillways, including CHANSON and

22

TOOMBES (2002b), GONZALEZ (2005) and FELDER (2013). Some typical profiles are

presented in Figures 4-2 and 4-3, in which the flow depth is normalised in terms of the

characteristic air-water flow depth Y90 and critical flow depth dc.

The results for small discharges are presented in Figure 4-2. For the flat impervious stepped

configuration the discharge dc/h = 0.5 corresponded to the limit between nappe and transition flow,

whereas, for the gabion stepped configuration, the same discharge belonged to the nappe flow

regime (Table 3-3). All the void fraction profiles showed a substantial flow aeration in the nappe

flow regime. Overall the nappe flows over gabion steps were slightly less aerated than the flow on

the flat impervious stepped configuration. However the air concentration at y = 0 (i.e. at the gabion

edge) was non-zero because of the bubbly flow inside the gabions (Fig. 4-2). The void fraction

distributions were compared to the theoretical model (CHANSON and TOOMBES 2002b):

90Y

yexp1"KC (4-1)

where K" and λ are dimensionless functions of the mean air concentration Cmean:

exp1

9.0"K (4-2)

meanC"K

9.0

(4-3)

Equation (4-1) is compared with some experimental data in Figure 4-2 (Right). Altogether the

nappe flow data showed some similar results between all step edges, as seen in Figure 4-2A.

For the skimming flows, the void fraction data exhibited a S-profile (Fig. 4-1). The flow aeration

tended to be lesser on the gabion stepped chute than on the smooth impervious stepped chute. The

air concentration distributions were successfully compared with the advective diffusion equation

developed by CHANSON and TOOMBES (2002b):

0

3

90

0

902

D3

3

1

Y

y

D2

Y

y

'Ktanh1C (4-4)

where K' is an integration constant and Do is a function of the depth-averaged void fraction Cmean

00 D81

8

D2

10327.0'K

(4-5)

7622.0

C0434.1Ln

614.3

1D mean

0 (4-6)

Results showed a good self-similarity of the void fraction profiles (Fig. 4-3A) and little difference

between the two stepped configurations. Equation (4-4) is compared with data in Figure 4-3A.

23

C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5Flat Steps - Step edge 6Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10

Cy/

Y90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2 Flat Steps - Step edge 6Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10Theory step 10 - FlatTheory step 10 - Gabion

Fig. 4-2 - Comparison of void fraction distributions for flat and gabion stepped configurations,

nappe flow regime ( = 26.6°, h = 0.10 m) - dc/h = 0.5, Q = 0.018 m3/s, Re = 1.40×105

C

y/Y

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8 Flat steps - Step edge 7Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 7Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Theory step 10 - FlatTheory step 10 - Gabion

C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8 Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10

(A) dc/h = 1.3, Q = 0.076 m3/s, Re = 5.9×105 (B) dc/h = 1.5, Q = 0.095 m3/s, Re = 7.3×105

Fig. 4-3 - Comparison of void fraction distributions for flat and gabion stepped configurations,

skimming flow regime (θ = 26.6°, h = 0.10 m)

The bubble count rate distributions on both flat impervious and gabion stepped configurations

showed a marked maximum (Fig. 4-4 & 4-5), corresponding to a local void fraction between 0.4

and 0.5. The results were consistent with previous studies on stepped spillways with flat impervious

24

steps (TOOMBES 2002, CHANSON and TOOMBES 2002b, GONZALEZ 2005). In Figures 4-4

and 4-5, the results are presented in terms of the dimensionless bubble count rate Fdc/Vc where F

is the bubble count rate, and Vc is the critical flow velocity: cc dgV . For all discharges, the

bubble count rate was consistently smaller on the gabion stepped weir compared to the flat

impervious stepped chute. In the skimming flows, some difference was noted between smooth and

gabion stepped chutes in the lower part of the flow: namely, significantly less bubble count rates

were recorded in the gabion stepped configuration (Fig. 4-5). This finding is still not fully

understood and no further explanations can be given.

Fdc/Vc

y/Y

90

0 2 4 6 8 10 12 140

0.3

0.6

0.9

1.2

1.5

1.8

2.1 Flat Steps - Step edge 6Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10

Fdc/Vc

y/Y

90

0 2 4 6 8 10 12 140

0.3

0.6

0.9

1.2

1.5

1.8



Fig. 4-4 - Comparison of bubble count rate distributions for flat and gabion stepped configurations,

nappe and transition flow regimes (θ = 26.6°, h = 0.10 m)

25

Fdc/Vc

y/Y

90

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6 Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10

Fdc/Vcy/

d c

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7



Fig. 4-5 - Comparison of bubble count rate distributions for flat and gabion stepped configurations,

skimming flow regime (θ = 26.6°,h = 0.10 m)

The relationship between void fraction and bubble count rate was tested for all flow conditions at all

step edges. All the data indicated a pseudo-parabolic relationship close to (CHANSON 1997,

TOOMBES 2002, CHANSON & TOOMBES 2002b):

C1C4F

F

max

(4-7)

where Fmax is the maximum bubble rate in a cross-section. A more advanced theoretical model was

introduced by TOOMBES (2002) and TOOMBES and CHANSON (2008b):

2Fmax

maxC

C1C1

F

F

(4-8)

where and are two correction factors which are functions of the local void fraction and flow

conditions, and CFmax is the void fraction for which F = Fmax. The first correction parameter α

accounts for the different average sizes of air bubble chord size λa and water droplet chord size λw:

C11a

w

(4-9)

with the ratio λw/λa assumed to be constant within a cross-section and independent of the void

fraction. The second correction factor β takes into account the variation of λw and λa with the void

fraction:

4C21b1C (4-10)

26

where b is a characteristic value of the maximum variation of β: i.e., 1-b < β < 1 (TOOMBES and

CHANSON 2008b). Some typical results are presented in Figure 4-6 where Equations (4-7) and (4-

8) are compared with experimental data. Equation (4-8) compared favourable with the data on both

flat impervious and gabion stepped configurations. The best agreement was found for λw/λa = 2.4

and b = 0.55 for the flat impervious stepped configuration. and for λw/λa = 1.6 and b = 0.52 for the

gabion stepped configuration. The values were generally in agreement with the findings of

FELDER (2013) for the same chute slope.

C

Fd

c / V

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25 Flat steps - Step edge 7Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 7Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Parabolic - step 10 - FlatTheory (w/a=2.4, b=0.55)- step 10 - FlatTheory (w/a=1.6, b=0.52)- step 10 - Gabion

Fig. 4-6 - Relationship between void fraction and bubble count rate on flat impervious and gabion

stepped chute in skimming flow (θ = 26.6°)

4.2.2Velocity and turbulence intensity distributions

The velocity data were calculated based upon a cross-correlation analysis between the leading and

trailing tip signals. Typical velocity distributions are presented in dimensionless form as V/Vc and

V/V90 in Figures 4-7 and 4-8, where V90 is the interfacial velocity at y = Y90 (i.e. C = 0.9). The

velocity distributions showed some self-similar profiles which were compared with a power law for

y < Y90 and an uniform profile above:

N

1

9090 Y

y

V

V

1

Y

y0

90

(4-11A)

1V

V

90

1Y

y

90

(4-11B)

A comparison between Figures 4-7A and 4-8A showed some typical differences between the nappe

and skimming flow data. In the nappe flow regime (Fig. 4-7), the interfacial velocities were smaller

on the gabion steps for the same flow rate (Fig. 4-7A). Some typical results in the skimming flow

regime are presented in Figure 4-8A, illustrating that the gabion stepped chute flow exhibited faster

velocities than the smooth impervious stepped chute flow, for the same discharge at the same

location downstream of the inception point of free-surface aeration. Given the increased roughness

27

of the gabion steps, the finding was counter-intuitive, although a similar trend was previously

observed on rough impervious steps by GONZALEZ et al. (2008) and BUNG and

SCHLENKHOFF (2010). For completeness, the velocity data were comparable in transition flows

for both configurations in the present study.

V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5Flat Steps - Step edge 6Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10

V/V90

y/Y

90

0 0.2 0.4 0.6 0.8 1 1.20

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25Flat Steps - Step edge 6Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 101/10 power lawV/V90 = 1


Fig. 4-7 - Interfacial velocity distributions on flat impervious and gabion stepped configurations in

nappe flow regime (θ = 26.6°, h = 0.10 m)

V/Vc

y/d c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10

V/V90

y/Y

90

0 0.2 0.4 0.6 0.8 10

0.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 9Gabion Steps - Step edge 101/N power lawV/V90 = 1


Fig. 4-8 - Interfacial velocity distributions on flat impervious and gabion stepped configurations in

28

skimming flow regime (θ = 26.6°, h = 0.10 m)

Tu

y/d c

0 0.5 1 1.5 2 2.50

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25


Tu

y/Y

90

0 0.4 0.8 1.2 1.6 2 2.4 2.80

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4Flat Steps - Step edge 7Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10


Fig. 4-9 - Turbulence intensity distributions on flat impervious and gabion stepped configuration in

nappe and transition flow regimes (θ = 26.6°, h = 0.10 m)

Tu

y/Y

90

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Flat Steps - Step edge 8Flat Steps - Step edge 9Flat Steps - Step edge 10Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10

Tu

y/d c

0 0.4 0.8 1.2 1.6 2 2.4 2.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7



Fig. 4-10 - Turbulence intensity distributions on flat and gabion stepped configurations in skimming

flow regime (θ = 26.6°, h = 0.10 m)

Equation (4-11) is compared with some experimental data in Figure 4-7B and 4-8B, using a power

29

law exponent of 1/N = 1/10.

The turbulence intensity gave an indication of the turbulence level in the air-water flow. For all

configurations, a local maximum was observed at the location where the bubble count rate was

maximum. Typical results for all flow regimes are presented in Figure 4-9 in nappe and transition

flows, and in Figure 4-10 in skimming flows. Overall the level of turbulence was higher in the flat

impervious stepped configuration. The same self-similar shape was observed for both

configurations (Fig. 4-9B & 4-10A). The relationship between bubble count rate and turbulence

intensity showed a monotonic increasing trend for both flat impervious and gabion stepped

configurations (Fig. 4-11) (CHANSON and TOOMBES 2002b). Some data scatter together with

form of hysteresis was observed in both stepped chute data.

Fdc/Vc

Tu

0 2 4 6 8 10 12 14 16 180

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 100.25+0.55x0.5

0.25+0.25x0.7

Fig. 4-11 - Relationship between bubble count rate and turbulence intensity on flat impervious and

gabion stepped configurations in skimming flow regime (θ = 26.6°, h = 0.10 m)

4.2.3 Longitudinal distributions of characteristic air-water flow parameters

The longitudinal distributions of the main characteristic air-water properties are presented in this

section, including the characteristic flow depth Y90, the depth averaged void fraction Cmean, the

maximum bubble count rate Fmax, the characteristic air-water flow velocity V90 and the maximum

turbulence intensity Tumax. The results are plotted in dimensionless form in terms of the step edge in

Figure 4-12. Note that an additional measurement (location 11) was included. Location 11 was set

in the horizontal channel at the bottom of the stepped chute facility; the sampling location was

located at a distance Lb = 0.2 m downstream of step 10 edge (Fig. 4-1A) and the co-ordinate y was

measured vertically there.

30

Step edge

Y90

/dc

2 3 4 5 6 7 8 9 10 110

0.20.40.60.8

11.21.41.61.8

2

Step edge

Cm

ean

2 3 4 5 6 7 8 9 10 110

0.10.20.30.40.50.60.70.80.9

1

(A) Characteristic flow depth Y90/dc (B) Mean void fraction Cmean

Step edge

Fm

axd

c/V

c

2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

Step edge

V90

/Vc

2 3 4 5 6 7 8 9 10 110

0.51

1.52

2.53

3.54

4.55

(C) Characteristic maximum bubble count rate

Fmaxdc/Vc

(D) Characteristic interfacial velocity V90/Vc

Step edge

Tu m

ax

2 3 4 5 6 7 8 9 10 110

0.5

1

1.5

2

2.5

3

3.5

4

4.5 Flat steps - dc / h = 0.5Flat steps - dc / h = 0.8Flat steps - dc / h = 1.1Flat steps - dc / h = 1.3Flat steps - dc / h = 1.5Flat steps - dc / h = 1.7Gabion steps - dc / h = 0.5Gabion steps - dc / h = 0.8Gabion steps - dc / h = 1.1Gabion steps - dc / h = 1.3Gabion steps - dc / h = 1.5Gabion steps - dc / h = 1.7

(E) Maximum turbulence intensity Tumax

Fig. 4-12 - Longitudinal distributions of characteristic air-water flow parameters for flat and gabion

stepped configurations (θ = 26.6°, h = 0.10 m) - Same legend applies to all figures

31

Figure 4-12A presents the dimensionless characteristic flow depth Y90/dc. The results showed that

the air-water flow height was lower for all discharges on the gabion stepped configuration. The

largest differences between the two stepped configurations were seen with the nappe flow regime,

for which the gabion stepped chute flow presented an almost evenly distributed flow heights. The

depth-averaged void fraction data Cmean are presented in Figure 4-12B. The results highlighted a

lesser aeration of the flow on the gabion stepped configuration. At the step edge 10, the depth-

averaged void fraction was between 1.0 and 1.4 times larger on the flat impervious stepped chute

than on the gabion stepped chute, and the difference increased monotonically with an increasing

discharge (Fig. 4-12B). The maximum bubble count rate Fmax×dc/Vc increased monotonically with

the downstream direction for all discharges and all configurations. Smaller maximum bubble counts

were recorded on the gabion stepped chute for both nappe and skimming flows (Fig. 4-12C).

Figure 4-12D shows the characteristic air-water velocity V90/Vc as function of the longitudinal

distance. Although the step surface roughness was larger on the gabion steps, the data showed that,

in the skimming flow regime, the velocities on gabion steps were larger than those on the flat

smooth stepped configuration (Fig. 4-12D). Although counter-intuitive, these results were similar to

the findings of GONZALEZ et al. (2008) for rough impervious steps. On the other hand, for the

nappe flow regime, the air-water velocities were smaller on the gabion steps. The longitudinal

distributions of maximum turbulence intensity Tumax are presented in Figure 4-12E. At the

downstream end of the facility (step edge 10), Tumax ranged from 1.6 to 2.5 for all configurations.

However, for all discharges, the maximum turbulence intensity observed over the smooth

impervious stepped structure was on average 12% larger than that recorded on the gabion stepped

chute.

The porosity of gabion steps induced some seepage through the gabions, thus reducing the overflow

discharge above the steps. The overflow discharge per unit width above the gabions qw was

estimated based upon the equation of conservation of mass:

90Y

0

w dyVC1q (4-12)

The data are presented in Figure 4-13. The results showed that the proportion of seepage flow, that

is 1-qw/q, was a function of the flow regime and flow rate. In nappe flow conditions, the seepage

flow ratio was about 0.5 on average. In skimming flows, it was down to 0.05 to 0.15. Despite some

data scatter, the results gave a general estimate of the seepage magnitude through the gabions.

32

Step edge

q w/q

0 1 2 3 4 5 6 7 8 9 10 110

0.20.40.60.8

11.21.41.61.8

2

Flat steps - dc / h = 0.5Flat steps - dc / h = 0.8Flat steps - dc / h = 1.1Flat steps - dc / h = 1.3Flat steps - dc / h = 1.5Flat steps - dc / h = 1.7

Gabion steps - dc / h = 0.5Gabion steps - dc / h = 0.8Gabion steps - dc / h = 1.1Gabion steps - dc / h = 1.3Gabion steps - dc / h = 1.5Gabion steps - dc / h = 1.7

Fig. 4-13-Discharge ratio qw/q between the measured volume flux and the total discharge per unit

width

4.3 CAPPED AND FULLY-CAPPED STEPPED CONFIGURATIONS

4.3.1 Void fraction and bubble frequency distributions

For both capped gabion configurations, detailed air-water flow measurements were conducted.

Some typical void fraction profiles are presented in Figure 4-14. The data exhibited similar trends to

those obtained for both gabion and flat stepped configurations, as well as earlier stepped chute

studies with comparable slopes (CHANSON and TOOMBES 2002b, GONZALEZ 2005, FELDER

2013). Figure 4-14A shows some data for low discharges corresponding to a nappe flow regime.

Figure 4-14B presents some skimming flow data. Overall the behaviour of both capped and fully

capped gabion stepped configurations was in between the gabion and the flat stepped

configurations; the fully capped stepped configuration presenting results very similar to those on the

flat impervious stepped chute.

In terms of bubble count rate distributions, all stepped configurations presented a similar data shape

with a marked maximum corresponding at C 0.4-0.5 (Fig. 4-15). The capped and fully-capped

data yielded quantitative results which were generally similar to the flat stepped configuration data.

33

C

y/Y

90

0 0.2 0.4 0.6 0.8 10

0.3

0.6

0.9

1.2

1.5

1.8

2.1Step 10

Flat StepsGabion stepsCapped stepsFully-capped stepsTheory - CappedTheory - Fully-capped

C

y/Y

90

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6Step 10

Flat stepsGabion stepsCapped stepsFully-capped stepsTheory - Capped

(A, Left) Nappe flow regime, dc/h = 0.5, Q = 0.018 m3/s, Re = 1.40×105

(B, Right) Skimming flow regime, dc/h = 1.3, Q = 0.076 m3/s, Re = 5.9×105

Fig. 4-14 - Void fraction distributions on capped and fully-capped gabion stepped chutes (θ = 26.6°,

h = 0.10 m) - Comparison with flat impervious and gabion stepped chute data and theory

Fdc/Vc

y/Y

90

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Step 10Flat stepsGabion stepsCapped stepsFully-capped steps

Fig. 4-15 - Bubble count rate distributions on capped and fully-capped gabion stepped chutes (θ =

26.6°, h = 0.10 m) - Flow conditions: skimming flow regime: dc/h = 1.3, Q = 0.076 m3/s, Re =

5.9×105 - Comparison with flat impervious and gabion stepped chute data

34

4.3.2 Velocity and turbulence intensity distributions

Some typical velocity distributions are presented in dimensionless terms in Figure 4-16. The

velocity data presented a self-similar shape close to the flat impervious stepped chute data. For

small discharges, the velocity data on both capped configurations were between the gabion and flat

stepped chute data (Fig. 4-16A). The gabion stepped chute data presented the slowest velocities and

the flat impervious stepped chute data the largest. In the skimming flow regime the velocity

magnitude was similar for both capped configurations (Fig. 4-16B). The interfacial velocity data for

the capped configurations were between the flat impervious and gabion stepped chute data, with the

largest velocities being observed on the gabion stepped spillway and the smallest on the flat

impervious stepped weir. For all four configurations, the data showed a good correlation with a

1/10th power law.

Typical turbulence intensity data are presented in Figure 4-17 for a skimming flow. All the data

presented some local maxima corresponding to the location of maximum bubble count rate. For all

discharges and flow regimes, the turbulence intensity levels on the capped and fully capped stepped

chutes were generally smaller than those on the flat impervious stepped chute, for an identical flow

rate and measurement location.

V/Vc

y/d c

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5Step 10

Flat stepsGabion stepsCapped stepsFully-capped steps

V/Vc

y/d c

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Step 10


(A, Left) Nappe flow regime, dc/h = 0.5, Q = 0.018 m3/s, Re = 1.40×105

(B, Right) Skimming flow regime, dc/h = 1.3, Q = 0.076 m3/s, Re = 5.9×105

Fig. 4-16 - Interfacial velocity distributions on capped and fully-capped gabion stepped chutes (θ =

26.6°, h = 0.10 m) - Comparison with flat impervious and gabion stepped chute data

35

Tu

y/d c

0 0.5 1 1.5 2 2.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75Step 10


Fig. 4-17 - Turbulence intensity distributions on capped and fully-capped gabion stepped chutes (θ

= 26.6°, h = 0.10 m) - Flow conditions: skimming flow regime, dc/h = 1.7, Q = 0.114 m3/s, Re =

8.8×105 - Comparison with flat impervious and gabion stepped chute data

4.4 DISCUSSION

The detailed air-water flow properties were investigated on the channel. Some key differences were

observed between gabion and flat impervious stepped weirs. A proportion of the total discharge

flowed within the gabions and the percentage of seepage flow was a function of the head above

crest and stepped configuration. This ratio of seepage to total discharge varied from 0.5 in the nappe

flow regime down to 0.1-0.15 in the skimming flow regime. At large discharges and despite the

enhancement of the cavity roughness, the highest velocities were measured on the gabion stepped

weir. This counter-intuitive behaviour was in agreement with previous findings by GONZALEZ et

al. (2008) on rough impervious stepped weirs. For all gabion stepped configurations, the overall

turbulence of the flow was reduced compared to the flat impervious stepped chute.

36

5. ENERGY DISSIPATION AND FLOW RESISTANCE

5.1 RESIDUAL HEAD AND ENERGY DISSIPATION

For design purposes, the residual energy at the downstream end of the spillway chute is a key

parameter. The residual head was estimated from the air-water flow properties:

2Y

0

2Y

0

res90

90

dyC1g2

qcosdyC1H

(5-1A)

where C is the void fraction, y is the distance normal to the pseudo-bottom formed by the step

edges, Y90 is the characteristic height where C = 0.90, q is the water discharge per unit width, and g

is the gravity acceleration. Introducing the equivalent clear-water depth d and mean flow velocity

Uw = q/d, the residual head may be rewritten:

g2

UcosdH w

res (5-1B)

The energy loss was calculated as:

resmax HHH (5-2)

where Hmax is the upstream head above the sampling location. The rate of energy dissipation

∆H/Hmax expressed the percentage of total head loss above the stepped chute.

The results are presented in Figure 5-1 in terms of rate of energy dissipation at the downstream end

of the chute. Figure 5-1A shows the data at step edge 10 and Figure 5-1B the data in the

downstream tailrace channel. The data are presented as functions of the dimensionless drop in

elevation zo/dc between the broad crested weir and the sampling location. Note that the gabion

stepped data at step edge 10 were calculated using the overflow discharge estimate qw.

The experimental results showed that the gabion stepped weir was the least efficient in terms of

energy dissipation but for the smallest discharge. The three other stepped configurations (flat,

capped and fully-capped) yielded comparable results. For the smallest discharges (dc/h = 0.5), the

energy dissipation of the gabion stepped configuration was slightly larger than that on the flat

impervious stepped configuration. Between the step edge 10 and the tailrace channel, some

differences in terms of energy dissipation were seen for the gabion stepped chute which reflected

likely the large energy dissipation rate of the seepage flow component (STEPHENSON 1979).

37

z0/dc

H/H

max

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Flat steps - Step edge 10Gabion steps - Step edge 10Capped steps - Step edge 10Fully-capped steps - Step edge 10

z0/dc

H/H

max

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Gabion steps - BottomCapped steps - BottomFully-capped steps - Bottom

(A) Step edge 10 (B) Bottom (tailrace) channel

Fig. 5-1 - Rate of energy dissipation rate at the downstream end of flat impervious and gabion

stepped chutes (θ = 26.6°, h = 0.10 m)

dc/h

Hre

s/d c

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Flat steps - Step 10Gabion steps - Step 10Capped steps - Step 10Fully-capped steps - Step 10

dc/h

Hre

s/d c

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Gabion steps - BottomCapped steps - BottomFully-capped steps - Bottom

(A) Step edge 10 (B) Bottom (tailrace) channel

Fig. 5-2 - Residual head at the downstream end of flat impervious and gabion stepped chutes (θ =

26.6°, h = 0.10 m)

38

The residual head data are summarised in Figure 5-2. The results showed that the largest residual

head was achieved with the gabion stepped chute in skimming flows. In the nappe flow, on the

other hand, the gabion stepped chute flow presented the smallest residual head. Overall the flat

impervious, capped and fully capped gabion stepped chutes showed comparable performances in

terms of residual head.

5.2 FLOW RESISTANCE

The flow resistance is typically evaluated in terms of the Darcy-Weisbach friction factor

(RAJARATNAM 1990, CHANSON 2001), although CHANSON et al. (2002) pointed out that

neither the Darcy-Weisbach formula nor the Gauckler-Manning-Strickler formula should be used

when the form loss contribution is dominant, like on a stepped spillway. On the other hand, the

average shear stress between the skimming flow and the recirculating fluid in the step cavities may

be written in dimensionless form as:

2

ww

0e

U

8f

(5-3)

where fe may be considered as an equivalent Darcy-Weisbach friction factor. In the present study,

the flow was gradually-varied down the stepped chute and did not reach uniform equilibrium. Thus

the equivalent friction factor was calculated based upon the air-water flow properties and total head

line slope measurements:

2w

Y

0

f

eU

dyC1Sg8

f

90

(5-4)

The total head line slope Sf is also called the friction slope and defined as Sf = -∂H/∂x, where H is

the total head and x is the distance in flow direction (1). The present data are shown in Figure 5-3 as

a function of the dimensionless step roughness height ks/DH where ks = h×cos and DH is the

hydraulic diameter. The results indicated consistently that the smallest flow resistance was

experienced on the gabion stepped chute. On the flat impervious, capped and fully-capped gabion

stepped weirs, the flow resistance was on average two times larger than that on the gabion stepped

chute for the investigated flow conditions, and they were within commonly accepted values for

1 For the flat impervious stepped weir, all calculations were based upon the total discharge q

measured at the broad crest. For the gabion stepped chute, the flow resistance calculations were

performed using the overflow discharge qw.

39

stepped spillways (CHANSON 2001,2006). In the skimming flow regime, the average values of the

Darcy-Weisbach friction factor are summarised for each stepped chute configuration.

hcos/DH

f e

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.20.050.05

0.060.070.08

0.1

0.2

0.3

0.4

0.5Flat stepsGabion steps

Capped stepsFully-capped steps

Fig. 5-3 - Equivalent Darcy-Weisbach friction factor on flat impervious and gabion stepped chutes

(θ = 26.6°, h = 0.10 m)

Table 5-1 - Average equivalent Darcy-Weisbach friction factor fe on flat impervious and gabion

stepped chutes in the skimming flow regime (θ = 26.6°, h = 0.10 m)

Stepped chute configuration fe Flat stepped configuration θ = 26.6°, h = 0.10 m 0.23 Gabion stepped configuration θ = 26.6°, h = 0.10 m 0.11 Capped stepped configuration θ = 26.6°, h = 0.10 m 0.24 Fully-capped stepped configuration θ = 26.6°, h = 0.10 m 0.25

Note: calculations based upon air-water flow measurements downstream of the inception point of

free-surface aeration

5.3 DISCUSSION

Although the step faces were much rougher on the gabion stepped chute, the present results showed

that, in skimming flows, the gabion stepped weir was the least efficient in terms of energy

dissipation performances and flow resistance. The finding was counter-intuitive, but in agreement

with the results of GONZALEZ et al. (2008) and BUNG and SCHLENKHOFF (2010).

The present results for the gabion stepped configuration were further compared with the data of

40

PEYRAS et al. (1991,1992) for a same chute slope (Fig. 5-4). Some difference between the two

studies was observed, but it might derive from some differences in experimental configurations.

PEYRAS et al. (1991,1992) studied the performances of a flow above 3, 4 and 5 steps, in which the

skimming flow was not fully developed. Further the instrumentation only involved Pitot tubes and

no air-water flow measurement was conducted.

q2/(gHdam3)

H/H

dam

0.0001 0.0002 0.0005 0.001 0.002 0.003 0.005 0.010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Present study - Gabion steps - Step 10Peyras et al. (1991)

Fig. 5-4 - Comparison of energy dissipation rate on gabion stepped chutes between the present

study and the data of PEYRAS et al. (1991,1992) for θ = 26.6°

41

6. INTERFACIAL AREA AND MASS TRANSFER RATE

6.1 PRESENTATION

Aeration in stepped spillways is a key feature linked with the strong flow turbulence, free-

surface/turbulent interactions and air entrainment (NAKASONE 1987, TOOMBES and CHANSON

2005). For the treatment of drinking water, cascade aeration can be used to reduce the chlorine

content, offensive taste and odours (CORSI et al. 1992). Re-oxygenation cascades were also built

downstream of dam spillways, and along rivers and canals (GASPAROTTO 1992, HAUSER et al.

1992, GOSSE and GREGOIRE 1997). The physical process of mass transfer is described by the

Fick’s law stating that the mass transfer rate across an interface varies proportionally to a diffusion

coefficient times the gradient of gas concentration:

x

CAD

t

M gasgas

gas (6-1)

where Mgas is the mass of dissolved gas, t is the time, Dgas is the diffusion coefficient of the gas in

the liquid, A is the gas-liquid interfacial area, Cgas is the concentration of the dissolved gas and x is

the direction in which the diffusion occurs. The equation for gas transfer across an air-water

interface can be rearranged as

gasSATLgas CCaKt

C

(6-2)

where KL is the mass transfer coefficient or liquid film coefficient, a is the specific interface area

defined as the interface area per unit volume, and CSAT is the amount of gas dissolved in water at

equilibrium (GULLIVER 1990). The rate of mass transfer is directly proportional to the specific

air-water interface area of the flow and therefore enhanced in highly aerated, turbulent flows

(TOOMBES and CHANSON 2005).

The specific interface area represents the cumulative surface of air bubbles that is encountered per

unit volume. In a turbulent air-water flow, it may be estimated as (CHANSON 2002):

V

F4a

(6-3)

where F is the bubble count rate and V is the interfacial velocity. In the present study, the specific

interface area profiles were estimated for all four stepped chute configurations for a wide range of

discharges (0.05 < Q < 0.114 m3/s) at all step edges downstream of the inception point of free-

surface aeration. The depth-averaged specific interface area amean was calculated as

90Y

090mean dya

Y

1a (6-4)

Some typical vertical distributions of specific interface area are shown in Figure 6-1A. The data

42

showed systematically a marked maximum corresponding to the location of maximum bubble count

rate. Some typical longitudinal distributions of depth-averaged specific interface area are presented

in Figure 6-1B. The mean specific interface area increased monotonically with increasing distance

downstream of the inception point of free-surface aeration. Overall the interface area levels were

consistently smaller on the gabion stepped chute than on the flat impervious stepped weir (Fig. 6-1).

adc

y/d c

0 3 6 9 12 15 18 21 24 27 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Flat steps - Step edge 8Flat steps - Step edge 9Flat steps - Step edge 10Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10

Step edge

a mea

nd c

3 4 5 6 7 8 9 100

2.5

5

7.5

10

12.5

15

17.5

20

22.5

25

27.5

30Flat steps - dc/h = 0.8Flat steps - dc/h = 1.3Flat steps - dc/h = 1.5Gabion steps - dc/h = 0.8Gabion steps - dc/h = 1.3Gabion steps - dc/h = 1.5

(A, Left) Vertical distributions of specific interface area - Skimming flow regime, dc/h = 1.3, Q =

0.076 m3/s, Re = 5.9×105

(B, Right) Longitudinal distributions of depth-averaged specific interface area in skimming flows

Fig. 6-1 - Specific interface area on gabion and flat stepped chutes (θ = 26.6°, h = 0.10 m)

6.2 MASS TRANSFER RATE

Considering a stepped chute, the rate mass transfer process may be derived from Fick’s law (Eq. (6-

2)):

gasSATw

meanLgas CCU

aK

x

C

(6-5)

where Uw is the flow velocity defined as:

90Y

0

w

dyC1

q

d

qU Flat impervious stepped chute (6-6A)

43

90

90

Y

0

Y

0ww

dyC1

dyVC1

d

qU Gabion stepped chute (6-6B)

The coefficient of mass transfer KL was shown to be almost constant regardless of bubble size and

flow turbulence (KAWASE and MOO-YOUNG 1992):

3

6/1

w

wgasL gD47.0K

(6-7)

with μw the dynamic viscosity of water, w the density of water, g the gravity acceleration and Dgas

the molecular diffusivity. For oxygen, the molecular diffusivity may be approximated by

(FERRELL and HIMMELBLAU 1967):

3892.7K

272gas T1016793.1OD (6-8)

where TK is the temperature in Kelvin. Assuming TK = 293° K, the mass transfer coefficient KL

equals: KL = 4.3710-4 m/s.

The calculations were performed for both flat impervious and gabion stepped configurations for a

range of discharges. The results are presented below in terms of the aeration efficiency E of the

stepped weir defined as:

USSAT

USDS

CC

CCE

(6-9)

where CUS and CDS are respectively the upstream and downstream dissolved oxygen concentrations.

The results showed that the gabion stepped chute had a greater aeration efficiency for the lowest

discharges (dc/h = 0.5). Little difference between flat and gabion stepped weir were seen in the

transition flow (dc/h = 0.8). For the higher discharges corresponding to the skimming flow regime,

the re-oxygenation rate was substantially larger on the flat impervious stepped chute (Fig. 6-2).

Figure 6-3 shows the aeration efficiency per metre drop in invert elevation in terms of dissolved

oxygen at 20 Celsius, standard pressure and zero salinity as a function of the measured rate of

energy dissipation ΔH/Hmax. The data are compared with a number of air-water flow studies

(TOOMBES and CHANSON 2005, FELDER and CHANSON 2009) and with some dissolved

oxygen measurements on a flat stepped channel (θ= 3.4°, h = 0.143 m) by TOOMBES and

CHANSON 2005). Overall, the results compared well with the simple correlation proposed by

FELDER and CHANSON (2009):

6.2

max0 H

H15.0

z

E

(6-10)

where E is the total aeration efficiency in terms of dissolved oxygen, Δzo is the drop in elevation,

ΔH is the head loss and Hmax is the upstream total head. Equation (6-10) is compared with

44

experimental results in Figure 6-3. The results implied a monotonic increase in re-oxygenation rate

with increasing rate of energy dissipation on a stepped weir.

dc/h

E (

%)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

1

2

3

4

5

6

7Flat stepsGabion steps

Fig. 6-2 - Aeration efficiency of the flat impervious and gabion stepped weirs (θ = 26.6°, h = 0.10

m) - Calculations performed at step edge 10

H/Hmax

E/

z 0 (

m-1

)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.2526.6, h=0.10 m - Flat26.6, h=0.10 m - Gabion0.15 (H/Hmax)2.6

21.8, h=0.10 m - Flat3.4 , h=0.143 m - Flat3.4, h=0.143 m - DO data

Fig. 6-3- Aeration efficiency per metre drop in invert elevation E/Δz0 in terms of dissolved oxygen

at 20°C - Comparison with air-water flow data obtained from the integration of the mass transfer

45

equation (TOOMBES and CHANSON 2005, FELDER and CHANSON 2009) and dissolved

oxygen measurements (TOOMBES and CHANSON 2005)

6.3 DISCUSSION

Large specific interface areas were recorded with depth-averaged values up to 200 m-1. The

integration of Fick’s law based upon detailed air-water flow measurements allowed a comparison

between flat impervious and gabion stepped weirs in terms of aeration performances. The results

showed that, for a small discharge, the aeration efficiency was higher on the gabion stepped chute,

whereas, for large discharges, the flat impervious stepped weir was more efficient in terms of

aeration and mass transfer. The latter trend was consistent with the results of BUNG and

SCHLENKHOFF (2010).

A comparison with previous data showed a good agreement for stepped channels with slopes within

3.4° < θ < 26.6°, highlighting a monotonic increase in re-aeration with increasing rate of energy

dissipation.

46

7. CONCLUSION

The hydraulic performances of gabion stepped weirs were investigated experimentally through a

comprehensive physical study based upon a Froude similitude. Three gabion stepped chutes and a

flat impervious stepped chute were tested in a relatively large size facility with a chute slope of

26.6° (1V:2H) and step height of 0.1 m. The gabion stepped chutes consisted of 10 gabion boxes

filled with 14 mm sieved gravels, stacked above the flat impervious stepped chute. For two

configurations, some horizontal step cappings were added. The hydraulic conductivity of the

gabions was tested and the results yielded K 110-1 m/s. For all configurations, detailed

observations were performed on the chute centreline for a range of discharges corresponding to

Reynolds numbers between 3.8×104 and 8.7×105.

Some detailed visual observations were carried out for all stepped configurations. On the gabion

stepped chutes, a porous regime was observed for the smallest discharges: there was no overflow

and the water seeped through the gabions. For larger discharges, the main overflow regimes

included the nappe, transition and skimming flows with increasing discharges. The interactions

between seepage flow and overflow were functions of the discharge, gabion configuration and flow

regime. They resulted in a modification of the step cavity flow and recirculation patterns. On all

gabion stepped weirs, some strong interaction between the cavity flow and upstream gabion was

observed, as well some bubbly flow motion inside the gabions. The position of the inception point

of free-surface aeration was close on all four stepped configurations for a given discharge, although

slightly further downstream on the gabion and fully-capped stepped chutes.

Some detailed air-water flow measurements were conducted on all step edges downstream of the

inception point of free-surface aeration. The results showed comparable trends for all stepped weirs,

although with some quantitative differences. Overall the gabion stepped chute was less aerated and

the characteristic air-water flow height Y90 was lower than on all other stepped configurations for

an identical flow rate. The bubble count rate and turbulence intensity were also slightly lower on the

gabions stepped weir. In skimming flows, larger velocities were measured at the downstream end of

the gabion stepped chute. The air-water properties of the capped and fully-capped gabion stepped

weirs were typically between the flat impervious and gabion stepped chute flow properties.

The rate of energy dissipation, residual head and equivalent Darcy-Weisbach friction factor were

calculated based upon the air-water flow properties. For low discharges corresponding to nappe

flow regime, the gabion stepped configuration was the most efficient in terms of energy dissipation,

possibly because of the significant proportion of seepage flow rate. In skimming flows, on the other

hand, the energy dissipation rate on the gabion stepped weir was the lowest and the highest rate of

energy dissipation was observed on the flat impervious stepped chute. The Darcy-Weisbach friction

47

factor of the gabion stepped chute was consistently lower than that on the flat impervious stepped

weir. While the findings might appear counter-intuitive, they were consistent with previous

experimental results on rough impervious stepped chutes.

The aeration efficiency of gabion and flat stepped weirs was derived from the integration of Fick's

law based upon the specific interfacial area measurements. For low discharges, the aeration

performances of the gabion stepped configuration were enhanced. In skimming flows, the aeration

efficiency of the flat impervious stepped weir was larger than that of the gabion stepped chute.

In conclusion the present study focused on gabion stepped weirs with a 26.6° chute slope (1V:2H).

Using physical modelling based upon a Froude similitude, the observations showed the significant

interactions between the seepage and overflow. For large discharges, lower performances were

observed in terms of energy dissipation and aeration efficiency, in comparison to the performances

of flat impervious stepped chutes. This counter-intuitive result on the gabion stepped weir

highlighted the importance of sound physical modelling in the investigation of hydraulic structures.

48

8. ACKNOWLEDGEMENTS

The authors thank Professor Daniel BUNG (FH Aachen University of Applied Sciences, Germany)

for his expert review and inputs. The exchanges with Professor Jim KELLS (University of

Saskatchewan, Canada) are acknowledged

The authors acknowledge all the people who assisted with the large-scale experiments and the

technical staff of the School of Civil Engineering at the University of Queensland, in particular

JasonVAN DER GEVEL and Stewart MATTHEWS. The financial support of the Australian

Research Council (Grant DP120100481) is acknowledged.

A-1

APPENDIX A - PHOTOGRAPHS OF STEPPED SPILLWAYS CONFIGURATION AND FLOW PATTERNS

A.1 - PRESENTATION

Visual observations were carried out for all stepped configurations for a wide range of discharges

from 0.005 m3/s to 0.114 m3/s, corresponding to Reynolds numbers between 3.54104 and

8.78105. Table A-1 presents the experimental flow conditions that were investigated during the

project.

This appendix shows a detailed photographic documentation of the experiments. Paragraph A.2

shows the configurations of the stepped spillways facility. In section A.3 a photographic review of

the flow regimes is presented for each configuration and for a wide range of discharges. The flow

patterns observed for each configuration are presented in section A.4 for various discharges.

Table A-1 - Experimental conditions for visual observations of the flow patterns on the stepped

spillway model configurations (θ = 26.6°, h = 0.10 m)

Config. number

Description Q [m3/s]

dc/h [-]

Re [-]

1 Flat steps configuration

h = 0.10 m θ = 26.6°

0.005 - 0.114 0.2 - 1.7 3.54104 - 8.78105

2 Gabion steps configuration

h = 0.10 m θ = 26.6°

0.005 - 0.114 0.2 - 1.7 3.54104 - 8.78105

3 Capped steps configuration

h = 0.10 m θ = 26.6°

0.005 - 0.114 0.2 - 1.7 3.54104 - 8.78105

4 Fully-capped steps configuration

h = 0.10 m θ = 26.6°

0.005 - 0.114 0.2 - 1.7 3.54104 - 8.78105

Notes: dc: critical flow depth, h: step height, Q: water discharge, Re: Reynolds number defined in

terms of hydraulic diameter, θ: channel slope.

Abbreviations:

PR Porous regime (Seepage)

NA Nappe flow regime

TRA Transitions flow regime

SK Skimming flow regime

A-2

A.2 - STEPPED SPILLWAY CONFIGURATIONS

Fig. A-1 -Experimental facility for the flat stepped configuration. θ = 26.6°, h = 0.10 m, 10 steps.

A-3

Fig. A-2 - Experimental facility, gabions stepped configuration. θ = 26.6°, h = 0.10 m, 10 steps.

A-4

Fig. A-3 - Experimental facility, capped stepped configuration. θ = 26.6°, h = 0.10 m, 10 steps.

A-5

Fig. A-4 - Experimental facility, fully-capped steps configuration. θ = 26.6°, h = 0.10 m, 10 steps.

A-6

A.3 - FLOW REGIMES

A.3.1 - Flat stepped configuration

Fig. A-5 - Nappe flow regime on the flat stepped configuration (flow direction from left to right)


(C) dc/h = 0.50, Q = 0.018 m3/s, Re = 1.4105 (D) dc/h = 0.50, Q = 0.018 m3/s, Re = 1.4105

(E) dc/h = 0.50, Q = 0.018 m3/s, Re = 1.4105 (F) dc/h = 0.50, Q = 0.018 m3/s, Re = 1.4105

A-7

Fig. A-6 - Transition flow regime on the flat stepped configuration (flow direction from left to

right)




A-8

Fig. A-7 - Skimming flow regime on the flat stepped configuration (flow direction from left to

right)




A-9

Fig. A-8 - Skimming flow regime on the flat stepped configuration (flow direction from left to

right)




A-10

A.3.2 - Gabion stepped configuration

Fig. A-9 - Porous (Seepage) flow regime on the gabion stepped configuration




A-11

Fig. A-10 - Nappe flow regime on the gabion stepped configuration




A-12

Fig. A-11 - Transition flow regime on the gabion stepped configuration




A-13

Fig. A-12 - Skimming flow regime on the gabion stepped configuration




A-14

Fig. A-13 - Skimming flow regime on the gabion stepped configuration




A-15

A.3.3 - Capped stepped configuration

Fig. A-14 - Porous (Seepage) flow regime on the capped stepped configuration



A-16

Fig. A-15 - Nappe flow regime on the capped stepped configuration




A-17

Fig. A-16 - Transition flow regime on the capped stepped configuration




A-18

Fig. A-17 - Skimming flow regime on the capped stepped configuration




A-19

Fig. A-18 - Skimming flow regime on the capped stepped configuration




A-20

A.3.4 - Fully capped stepped configuration

Fig. A-19 - Nappe flow regime on the fully-capped stepped configuration




A-21

Fig. A-20 - Transition flow regime on the fully-capped stepped configuration




A-22

Fig. A-21 - Skimming flow regime on the fully-capped stepped configuration




A-23

Fig. A-22 - Skimming flow regime on the fully-capped stepped configuration




A-24

A.4 - DETAILED FLOW PATTERNS

A.4.1 - Flat stepped configuration

A.23 - Flow patterns in the nappe flow regime on the flat stepped configuration (step 7-8)


A.24 - Flow patterns in the transition flow regime on the flat stepped configuration (step 7-8)


A.25 - Flow patterns in the skimming flow regime on the flat step configuration (step 8-9)


A-25

A.4.2 - Gabion stepped configuration

A.26 - Flow patterns in the porous regime on the gabion stepped configuration




A-26

A.27 - Flow patterns in the nappe flow regime on the gabion stepped configuration




A-27

A.28 - Flow patterns in the transition flow regime on the gabion stepped configuration




A-28

A.29 - Flow patterns in the skimming flow regime on the gabion stepped configuration




A-29

A.4.3 - Capped stepped configuration

A.30 - Flow patterns in the porous regime on the capped stepped configuration


A.31 - Flow patterns in the nappe flow regime on the capped step configuration



A-30

A.32 - Flow patterns in the transition flow regime on the capped stepped configuration



(E) dc/h = 0.85, Q = 0.040 m3/s, Re = 3.1105 (E) dc/h = 0.90, Q = 0.044 m3/s, Re = 3.4105

A-31

A.33 - Flow patterns in the skimming flow regime on the capped stepped configuration




A-32

A.4.4 - Fully capped stepped configuration

A.34 - Flow patterns in the nappe flow regime on the fully-capped stepped configuration




A-33

A.35 - Flow patterns in the transition flow regime on the fully-capped stepped configuration




A-34

A.36 - Flow patterns in the skimming flow regime on the fully-capped stepped configuration




B-1

APPENDIX B - SIGNAL PROCESSING AND SENSITIVITY ANALYSIS

B.1 INTRODUCTION

The air water properties were recorded using a double tip conductivity probe. The conductivity

probe detected the difference in conductivity (or resistivity) between the two phases. Section B.2

shows how the main air-water properties were deduced from the raw probe signal. It is known that

the output values of the signal processing depend the sampling duration and frequency. Section B.3

presents a sensitivity analysis of the main signal acquisition parameters and their influence on the

air-water properties.

Notation

C air concentration, defined as the volume of air per unit volume; it is also called void

fraction;

dc critical depth of the flow (m);

F bubble frequency defined as the number of detected air bubbles per unit time; also

called bubble count rate (Hz);

h height of the steps (m);


R correlation function;

Re Reynolds number defined in terms of hydraulic diameter;

Rxx normalised auto-correlation function;

t time (s);

T time lag (s) for which the cross correlation between the signals is maximum;

T0.5 time lag (s) for which the auto correlation function Rxx(T0.5) = 0.5;

Tu turbulence intensity;


y distance measured perpendicular to the pseudo-bottom formed by the step edges (m);

Δx streamwise distance between the probe tips (m);

Δz transversal distance between the probe tips (m);

Ø diameter of the probe sensor (m);

τ0.5 time lag (s) for which the cross correlation function is half of its maximum value.

B-2

B.2 SIGNAL PROCESSING

The operation of conductivity needle probes is based upon the difference in conductivity between

the two phases (air and water) since the resistivity of water is much lower than that of air. A typical

raw signal is presented in Figure B-1.

Fig B-1 - Raw probe signal detected for dc /h = 1.3, Step 10, sampling frequency: 20 kHz, sampling

duration: 45 s.

(A) Raw signal recorded between t = 0 and t = 1 s.

Time

Vol

tage

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Leading tip Trailing tip

(B) Raw probe signal between t = 0.8 s and t = 0.85 s

Time

Vol

tage

0.8 0.805 0.81 0.815 0.82 0.825 0.83 0.835 0.84 0.845 0.85-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Leading tip Trailing tip

Theoretically the probe signal should be rectangular. But due to the finite size of the tips, the

B-3

wetting/drying time of the tip and the response time of the probe and the electronics, the signal is

not perfectly squared (CHANSON and GONZALEZ 2005). As a result, an air-water threshold is

introduced: e.g., if the value of the signal is greater than 50%, than it is considered water, otherwise

air (Fig. B-2).

Fig B-2 - Sketch of the effect of the air-water threshold in the signal processing analysis

(CHANSON 1995b)

In this study, the void fraction and bubble count rate data were processed using a single threshold

technique and the threshold was set to 50 % of the full air-water voltage range. A sensitivity

analysis was conducted with thresholds between 10 and 90% of the voltage range. The results

showed little effect of the threshold level on air-water flow properties (Appendix B.3). The void

fraction and bubble count rate are defined as:

Air concentration, or void fraction, C, is the proportion of time that the probe tip spent in

contact with air.

The bubble count rate, or bubble frequency, F, is the number of bubbles that the tip of the

probe encounters per second (Hz).

Further information may be obtained using a cross-correlation technique between the leading and

trailing tip signals (e.g. CAIN and WOOD 1981, CROWE et al. 1998). Namely the interfacial

velocity and the turbulence intensity. The time-averaged air-water velocity V is estimated as

T

xV

(B-1)

where Δx is the longitudinal distance between the leading and the trailing tips, and T is time lag for

B-4

which the cross-correlation function is maximum. The turbulence intensity Tu may be calculated

from the relative width of the cross-correlation function compared to the auto-correlation function

(CHANSON and TOOMBES 2002b):

T

T85.0Tu

25.0

25.0

(B-2)

where τ0.5 is the time lag for which the cross correlation function is half of its maximum value and

T0.5 is the time lag for which the auto correlation function Rxx(T0.5) = 0.5 (Fig. B-3). The turbulence

intensity is not a point measurement, but a spatial average between the probe sensors (CHANSON

and TOOMBES 2002b). FELDER and CHANSON (2014) discussed further the derivation of

Equation (B-2).

Fig. B-3 - Sketch of the cross-correlation function for a dual-tip phase-detection intrusive probe

B.3 SENSITIVITY ANALYSIS

A sensitivity analysis was carried out to assess the influence of the sampling duration, sampling rate

and air-water threshold on the air-water flow properties. The sensitivity analysis was conducted on

the flat impervious stepped configuration. For dc/h = 1.3 and at step 10, a minimum of 10 points

distributed between 0.05 < C < 0.95 were recorded.

B.3.1 Air-water threshold

With a sampling frequency and duration of 20 kHz per sensor and 45 s respectively, the effects of

the air-water threshold on the void fraction and bubble count rate were tested. The results are

presented in Figure B-4 showing little influence of the air-water threshold on the void fraction

distribution, for a threshold between 30 and 80 %, as previously reported (HERRINGE and DAVIS

1974, CHANSON and FELDER 2010). The bubble count rate data were more dependent on the

B-5

threshold level. Overall the present results justified the selection of a 50 % air-water threshold, as

shown by TOOMBES (2002) and FELDER (2013).

Fig. B-4 - Effect of the air-water threshold on the void fraction and bubble count rate. Sampling

duration 45 s, sampling frequency 20 kHz per sensor, dc/h = 1.3, step 10, Re = 5.87105, Q =

0.0763m3/s

(A) Void Fraction (B) Bubble frequency

Air-Water Threshold [%]

C

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm

Air-Water Threshold [%]

F [

Hz]

0 20 40 60 80 1000

20

40

60

80

100

120

140

160

180

200

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm

B.3.2 Effect of sampling duration

The raw signal was sampled for 180 s at 20 kHz. The data was analysed with a 50% air-water

threshold. Using smaller non-overlapping segments, the void fraction, bubble count rate, interfacial

velocity and turbulence intensity were calculated for each segment. The results showed that the

sampling duration had no effect on the vertical distributions of void fraction, bubble count rate and

time-averaged interfacial velocity for sampling durations equal to and greater than 20 s (Fig. B-5).

In terms of the turbulence intensity distributions, the sampling duration had to be at least 45 s (Fig.

B-5D). The results were generally in agreement with the results of CHANSON and FELDER

(2010) in skimming flows on a stepped spillway. Herein the selection of a 45 s sampling duration

was thus justified by the results.

B-6

Fig. B-5 -Effect of the sampling duration on the main air-water properties. Air-water threshold

50%, sampling frequency 20 kHz, dc/h = 1.3, step 10, Re = 5.87105, Q = 0.0763 m3/s

(A) Void Fraction (B) Bubble Frequency

Sampling Duration [s]

C

1 2 3 4 5 67 10 20 30 50 100 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm


F [

Hz]

1 2 3 4 5 67 10 20 30 50 100 2000

50

100

150

200

250

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm

(C) Velocity (D) Turbulent Intensity


V [

m/s

]

1 2 3 4 5 67 10 20 30 50 100 2000

1

2

3

4

5

6

7

8

9

10

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm


Tu

1 2 3 4 5 67 10 20 30 50 100 2000

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm

B.3.3 Effect of sampling frequency

The raw signal was sampled for 45 s for a range of sampling frequencies between 1 and 100 kHz

B-7

per sensor. The results are presented in Figure B-6 and showed no influence of the sampling

frequency on the void fraction data within the experimental conditions. The bubble count rate data

were adversely affected and more scattered for sampling frequencies less than 20 kHz. Overall the

results differed little in terms of void fraction and bubble count rate distributions with sampling

frequencies between 20 kHz and 100 kHz. The finding was consistent with the results of

CHANSON and FELDER (2010).

Fig. B-6 - Effect of the sampling frequency on the main air-water properties. Air-water threshold

50%, sampling duration 45 s, dc/h = 1.3, step 10, Re = 5.87105, Q = 0.0763m3/s

(A) Void Fraction (B) Bubble Frequency

Sampling Frequency [kHz]

C

1 2 3 4 5 6 78 10 20 30 50 70 1000

0.2

0.4

0.6

0.8

1

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm


F [

Hz]

1 2 3 4 5 678 10 20 30 50 70 10025

50

75

100

125

150

175

200

y = 22 mmy = 35 mmy = 48 mm

y = 58 mmy = 64 mmy = 74 mm

(C) Dimensionless bubble frequency (F/F100)


F/F

100

1 2 3 4 5 6 7 8 10 20 30 40 50 70 1000.4

0.480.560.640.72

0.80.880.96

y = 22 mmy = 35 mmy = 48 mmy = 58 mmy = 64 mmy = 74 mm

C-1

APPENDIX C - HYDRAULIC CONDUCTIVITY TESTS

C.1 INTRODUCTION

Some experimental tests were conducted to estimate the permeability and hydraulic conductivity of

the gabions. For an one-dimensional flow through the gabions, the seepage velocity uD is given by

the Darcy law for granular non-cohesive soils:

x

HKuD

(C-1a)

where K is the hydraulic conductivity (or coefficient of permeability), H is the piezometric head and

x is the longitudinal coordinate. New experiments were conducted for a range of discharge 0.0026

m3/s < Q < 0.0129 m3/s (Table C-1). The data showed that the hydraulic conductivity was about: K

10-1 m/s (Section C.5).

Notations

A flow area (m2) perpendicular to the main stream, A = WH;

a Forchheimer flow coefficient (s/m);

b Forchheimer flow coefficient (s2/m2);

d50 characteristic size (m) of the porous medium;

g gravity constant (m/s2);

H (a) piezometric head (m);

(b) height (m) of two stacked gabion weir;

H0 height (m) of the vertical seepage face on the downstream face of the gabions;

H1 upstream head (m) above crest;

Hds water height (m) downstream of the gabion weir;

Hus water height (m) upstream of the gabion weir;

K hydraulic conductivity (m/s) of the porous medium;

Ke modified hydraulic conductivity (m/s);

L length (m) of the gabion structure in the flow direction;

L0 length (m) of the horizontal seepage face above the gabions;

Lcrest length (m) of the broad crest of the stepped facility;


Re Reynolds number;

uD unit flux (m/s) through the pores of the gabion material, also called seepage velocity;

W channel width (m);

ΔH water height difference (m) between upstream and downstream, ΔH = Hus - Hds;

κ intrinsic permeability (m2) of the porous medium;

ν kinematic viscosity of water (m2/s).

C-2

C.2 SEEPAGE FLOW ANALYSIS

The unit flux uD through a porous medium is given as (DARCY 1856):

L

HK

A

QuD

(C-1b)

where Q is the discharge, A is the surface through which the water is flowing, and ΔH/L is the

hydraulic gradient. The hydraulic conductivity may be expressed as

g

K (C-2)

with κ the intrinsic permeability of the porous medium, ν the kinematic viscosity of the fluid and g

the gravity constant. Depending upon the pore velocity and porous medium properties, the seepage

flow may range from laminar (regime 1) to turbulent and unstable (regime 4). Let us define the pore

Reynolds number as (HORTON and POKRAJAC 2009):

50DP

duRe (C-3)

where d50 a characteristic size of the gabion material. The threshold between laminar and turbulent

flow occurred at ReP ~ 370.

Darcy law (Eq. (C-1) is a linear relationship applicable only to laminar steady porous flow. For non

laminar flows and unsteady flows, Darcy law may be modified in the form of a non-linear

relationship, for example the Forchheimer exponential relationship (JOY 1991):

2DD ubua

L

H

(C-4)

where a and b are the Forchheimer coefficients which are functions of the gabion properties.

Equation (C-4) includes a second non-linear term which characterises the inertia inside the porous

medium. With this relationship, the hydraulic conductivity may be estimated as K = 1/a (KELLS

1993). A different approach is used in finite elements modelling. The non-linearity of the flow is

taken into account by a modified hydraulic conductivity Ke (KRAHN at al. 1987). This modified

hydraulic conductivity is deduced by combining Equations (C-1b) and (C-4):

D

D2

e ub4

ub4aaK

(C-5)

C.3 EXPERIMENTAL SETUP

The experimental setup was installed downstream of the stepped facility. Some energy dissipation

system was installed downstream of step 10 to calm the water level upstream of the gabions. Two

identical gabions were stacked above each other, as shown in Figure C-1. Each gabion was

composed of an outer metallic mesh with squared opening of 10×10 mm2 filled with natural gravels

sieved at 14 mm. The characteristic size of the porous medium was selected as d50 0.01 m. The

C-3

dimensions of the gabion structure were W = 0.52 m, H = 0.215 m and L = 0.292 m. Preferential

flow through the sides was prevented by adding a layer of lanolin. Figure C-2 shows some

photographs of the experimental setup. For each discharge, the upstream and downstream water

levels were measured as well as a number of relevant characteristics shown in Figure C-1. The

water discharge was controlled with the broad crest of the stepped facility, whose calibration was

provided by FELDER and CHANSON (2012).

Fig. C-1 - Sketch of the experimental setup for the hydraulic conductivity tests

(A) Small discharge without overtopping

(B) Large discharge with partial overtopping and horizontal seepage face

C-4

Fig. C-2 - Photographs of the experimental setup

(A) View from downstream (B) View from upstream

C.4 RESULTS

The results are regrouped in Table C-1. The results are presented in Figure C-3A for the linear case

(Darcy) and in Figure C-3B for the non-linear case (Forchheimer). Below, only the experiments

without overtopping were analysed.

The Darcy equation gave a hydraulic conductivity K = 1.110-1 m/s. The Forchheimer relationship

gave the following values: a = 4.31 s/m, b = 48.32 s2/m2, K = 1/a = 2.310-1 m/s. The values of the

modified hydraulic conductivity (Eq. (C.5)) are summarised in Table C-2.

Table C-1 - Values measured during the hydraulic conductivity testing for different discharges

Flow condition

Q [m3/s]

Hus [mm]

Hds [mm]

L0 [mm]

H0 [mm]

uD = Q/A[m/s]

ΔH/L [-]

Re [-]

0.0026 60.0 15.0 - - 0.023 0.154 2.3102 0.0033 85.0 19.0 - - 0.030 0.226 3.0102 0.0039 105.0 24.0 - 29.0 0.035 0.277 3.5102 0.0051 131.0 29.0 - 49.0 0.046 0.349 4.6102 0.0063 156.0 35.0 - 77.0 0.057 0.414 5.7102 0.0076 187.0 17.5 - 87.5 0.068 0.580 6.8102

Wit

hout

ov

erto

ppin

g

0.0085 210.0 20.0 - 102.0 0.076 0.651 7.6102 0.0091 218.0 23.0 45.0 105.0 0.081 0.668 8.1102 0.0098 226.0 26.0 93.0 109.0 0.087 0.685 8.7102 0.0106 232.0 28.0 140.0 125.0 0.095 0.699 9.5102 0.0114 236.0 29.0 175.0 140.0 0.102 0.709 1.0103 0.0121 240.0 30.0 215.0 175.0 0.108 0.719 1.1103

Wit

h ov

erto

ppin

g

0.0129 242.0 30.0 245.0 180.0 0.115 0.726 1.2103

C-5

Table C-2 - Modified hydraulic conductivity values Ke

Q [m3/s]

uD = Q/A [m/s]

ΔH/L [-]

Ke

[m/s] 0.0026 0.023 0.154 1.8210-1 0.0033 0.030 0.226 1.6910-1 0.0039 0.035 0.277 1.6110-1 0.0051 0.046 0.349 1.5210-1 0.0063 0.057 0.414 1.4610-1 0.0076 0.068 0.580 1.3210-1 0.0085 0.076 0.651 1.2710-1

Fig. C-3 - Hydraulic conductivity test results

(A) Darcy linear relationship (B) Forchheimer exponential relationship

H/L

u D

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.02

0.04

0.06

0.08

0.1

0.12

Flow without overtoppingFlow with overtoppinguD = 0.11 H/L + 0.007

uD

H

/L

0 0.02 0.04 0.06 0.08 0.1 0.120

0.08

0.16

0.24

0.32

0.4

0.48

0.56

0.64

0.72

0.8

Flow without overtoppingFlow with overtoppingH/L = 48.32 uD

2 + 4.31 uD

C.5 DISCUSSION

The hydraulic conductivity data were consistent with typical gravel properties (RAUDKIVI and

CALLANDER 1976). There was little difference between the linear and non-linear data analyses.

The modified hydraulic conductivity ranged from 1.310-1 to 1.810-1 m/s with on average Ke =

1.5310-1 m/s. The intrinsic permeability of the porous medium was thus: κ = 1.110-8 m2.

In summary, the study gave an estimate of the hydraulic conductivity of the gabions. The Darcy

linear relationship represented a good estimate, even under non-Darcy flow conditions.

C-6

C.6 PHOTOGRAPHIC REVIEW

Fig. C-4 - Hydraulic conductivity testing without overtopping

(A) Q = 0.0033 m3/s (B) Q = 0.0033 m3/s

(C) Q = 0.0051 m3/s (D) Q = 0.0063 m3/s

(E) Q = 0.0076 m3/s (F) Q = 0.0085 m3/s

C-7

Fig. C-4 - Hydraulic conductivity testing with overtopping

(A) Q = 0.0098 m3/s (B) Q = 0.0098 m3/s

(C) Q = 0.0106 m3/s (D) Q = 0.0114 m3/s

(E) Q = 0.0121 m3/s (F) Q = 0.0129 m3/s

D-1

APPENDIX D - AIR-WATER FLOW PROPERTIES ON FLAT STEPS CONFIGURATION

The air-water flow measurements on the flat stepped configuration are presented in this section.

These included the void fraction C, bubble count rate F, interfacial velocity V, and turbulence

intensity Tu, as well as the relationship between bubble count rate and void fraction. The

measurements were conducted for a wide range of dimensionless discharges from dc/h = 0.5 to dc/h

= 1.7 (Table D-1).

Fig. D-1 - Definition sketch of the air-water flow down the stepped chute

D-2

Notation

C void fraction defined as the volume of air per unit volume;

Cmean depth averaged void fraction defined in terms of Y90: Cmean = 1 - d/Y90;



Fmax maximum bubble count rate (Hz) in a cross-section;



qw water discharge per unit width calculated from the integration of the measured void

fraction and velocity profiles:

90Y

0

w dyVC1q



Tumax maximum turbulence intensity in a cross section;


V90 interfacial velocity (m/s) at y = Y90;

y distance (m) perpendicular to the pseudo-bottom bottom formed by the step edges;

Y90 characteristic distance (m) where the void fraction equals 0.90;

Δx streamwise distance (m) between probe tips;

Δz transversal distance (m) between probe tips;

Ø diameter (m) of inner probe sensor;

θ chute slope;

Abbreviations


TRA transition flow regime;

SK skimming flow regime.

D-3

Fig. D-2 - Air-water flow properties on the flat stepped spillway (θ = 26.6°) as functions of y/dc -

NA: dc/h = 0.5, Q = 0.018 m3/s, Re = 1.40×105; step edges 3-10. Legend applies to all figures.

(A) Void fraction distribution (B) Bubble count rate distribution

C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

F x dc / Vc

y / d

c

0 2 4 6 8 10 12 140

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

(C) Velocity distribution (D) Turbulent intensity distribution

V / Vc

y / d

c

0 0.75 1.5 2.25 3 3.75 4.50

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

Tu

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

(E) Relationship between bubble count rate and void fraction

C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

Step edge 3Step edge 4Step edge 5Step edge 6Step edge 7Step edge 8Step edge 9Step edge 10

D-4


TRA: dc/h = 0.8, Q = 0.037 m3/s, Re = 2.83×105; step edges 4-10. Legend applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

F x dc / Vc

y / d

c

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Tu

y/dc

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Step edge 4Step edge 5Step edge 6Step edge 7Step edge 8Step edge 9Step edge 10

D-5


SK: dc/h = 1.1, Q = 0.0594 m3/s, Re = 4.57×105; step edges 5-10. Legend applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

F x dc /Vc

y / d

c

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Tu

y / d

c

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Step edge 5Step edge 6Step edge 7Step edge 8Step edge 9Step edge 10

D-6


SK: dc/h = 1.3, Q = 0.0763 m3/s, Re = 5.87×105; step edges 5-10. Legend applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

F x dc /Vc

y / d

c

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tu

y / d

c

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25


D-7


SK: dc/h = 1.5, Q = 0.0946 m3/s, Re = 7.28×105; Step edges 5-10. Legend applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc /Vc

y / d

c

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y / d

c

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

4

8

12

16

20


D-8


SK: dc/h = 1.7, Q = 0.114 m3/s, Re = 8.78×105; Step edges 6-10. Legend applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc /Vc

y / d

c

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 102468

1012141618

Step edge 6Step edge 7Step edge 8Step edge 9Step edge 10

D-9

Table D.1 - Characteristic air-water properties for the flat stepped configuration (θ = 26.6°, h = 0.10

m) with a double-tip conductivity probe (Ø = 0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Q [m3/s]

Re [-]

Flow Regime

Step edge

Y90 [mm]

Cmean [-]

F max

[Hz] V90

[m/s] Tumax

[-] qw

[m2/s] 3 30.82 0.3916 50.60 2.21 1.76 0.0402 4 43.22 0.5317 108.51 1.21 2.95 0.0263 5 92.73 0.8531 78.18 2.58 0.95 0.0345 6 51.61 0.6588 131.64 2.98 1.70 0.0431 7 42.24 0.5254 184.67 2.48 1.86 0.0477 8 60.99 0.7125 158.44 2.58 2.09 0.0403 9 41.78 0.6185 194.38 2.95 1.96 0.0407

0.5 0.018 1.40×105 NA

10 48.50 0.6505 187.20 2.55 1.73 0.0407 4 41.35 0.2381 66.49 2.95 1.49 0.0801 5 53.05 0.4168 132.84 2.90 1.34 0.0811 6 59.91 0.5595 177.42 2.95 1.43 0.0714 7 44.34 0.3706 217.67 3.10 1.82 0.0780 8 55.45 0.4940 231.27 3.09 1.62 0.0786 9 54.72 0.4725 250.62 3.19 1.51 0.0767

0.8 0.037 2.83×105 TRA

10 46.24 0.3989 272.47 3.35 2.47 0.0825 5 55.40 0.2239 53.80 3.37 3.58 0.1199 6 58.55 0.3103 132.56 3.15 1.72 0.1218 7 71.39 0.3770 138.18 3.22 1.78 0.1203 8 64.19 0.3106 188.96 3.29 1.85 0.1308 9 68.68 0.3482 185.40 3.40 1.97 0.1336

1.1 0.059 4.57×105 SK

10 62.94 0.3075 232.58 3.46 2.17 0.1414 5 60.14 0.1411 27.36 3.10 8.37 0.1308 6 65.25 0.2335 77.84 3.17 1.80 0.1450 7 72.50 0.3056 104.60 3.24 2.11 0.1431 8 75.39 0.3180 154.02 3.26 1.86 0.1577 9 78.19 0.3464 154.80 3.40 1.44 0.1548

1.3 0.076 5.87×105 SK

10 73.93 0.3014 196.71 3.56 1.78 0.1631 5 69.04 0.1022 21.76 3.40 - - 6 72.79 0.1821 46.96 3.35 2.35 0.1625 7 76.19 0.2361 78.69 3.54 2.53 0.1777 8 79.02 0.2924 117.27 3.76 2.14 0.1903 9 85.05 0.3028 127.76 3.76 2.03 0.1864

1.5 0.095 7.28×105 SK

10 84.72 0.3006 164.20 3.44 2.43 0.1864 6 80.53 0.1307 31.02 3.76 2.01 0.2163 7 82.82 0.1936 53.80 3.88 2.38 0.2162 8 82.85 0.2114 85.84 3.88 2.08 0.2157 9 90.84 0.2729 106.62 4.00 2.34 0.2366

1.7 0.114 8.7×105 SK

10 92.59 0.2771 131.16 3.44 2.43 0.1864

E-1

APPENDIX E - AIR-WATER FLOW PROPERTIES ON GABION STEPPED CONFIGURATION

In this section the air-water properties on the gabion stepped configuration are presented. The data

were recorded for a wide range of dimensionless discharges, varying from dc/h = 0.5 to dc/h = 1.7

(Table E-1).

Fig. E-1 - Definition sketch of the stepped chute

E-2

Notation










90Y

0

w dyVC1q











θ chute slope;

Abbreviations




E-3

Fig. E-2 - Air-water flow properties on the gabion stepped spillway (θ = 26.6°) as functions of y/dc-

NA: dc/h = 0.5, Q = 0.018m3/s, Re = 1.40×105; step edges 2-10 and bottom channel. Legend applies

to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

F x dc /Vc

y / d

c

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

1.2


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.2

Tu

y / d

c

0 0.45 0.9 1.35 1.8 2.250

0.2

0.4

0.6

0.8

1

1.2


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10123456789

Gabion Steps - Step edge 3Gabion Steps - Step edge 4Gabion Steps - Step edge 5Gabion Steps - Step edge 6Gabion Steps - Step edge 7Gabion Steps - Step edge 8Gabion Steps - Step edge 9Gabion Steps - Step edge 10Gabion Steps - Bottom Step

E-4

Fig. E-3 - Air-water flow properties on the gabion stepped spillway (θ = 26.6°) as functions of y/dc-

TRA: dc/h = 0.8, Q = 0.036m3/s, Re = 2.83×105; step edges 4-10and bottom channel. Legend

applies to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

F x dc /Vc

y / d

c

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

1.2


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.2

0.4

0.6

0.8

1

1.2

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Gabion steps - Step edge 4Gabion steps - Step edge 5Gabion steps - Step edge 6Gabion steps - Step edge 7Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Gabion steps - Bottom Step

E-5

Fig. E-4 - Air-water flow properties on the gabionstepped spillway (θ = 26.6°) as functions of y/dc-

SK: dc/h = 1.1, Q = 0.059m3/s, Re = 4.57×105;Step edges 5-10and bottom channel. Legend applies

to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc /Vc

y / d

c

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

4

8

12

16

20Gabion steps - Step edge 5Gabion steps - Step edge 6Gabion steps - Step edge 7Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Gabion steps - Bottom Step

E-6

Fig. E-5 - Air-water flow properties on the gabionstepped spillway (θ = 26.6°) as functions of y/dc -

SK: dc/h = 1.3, Q = 0.076m3/s, Re = 5.87×105; Step edges 6-10and bottom channel. Legend applies

to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc /Vc

y / d

c

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

3

6

9

12

15

18

Gabion steps - Step edge 6Gabion steps - Step edge 7Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Gabion steps - Bottom Step

E-7


SK: dc/h = 1.5, Q = 0.094m3/s, Re = 7.28×105; Step edges 8-10 and bottom step. Legend applies to

all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

F x dc / Vc

y / d

c

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 102468

1012141618

Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Gabion steps - Bottom Step

E-8


SK: dc/h = 1.7, Q = 0.114m3/s, Re = 8.78×105; step edges 8-10 and bottom step. Legend applies to

all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

F x dc /Vc

y / d

c

0 2 4 6 8 10 12 140

0.1

0.2

0.3

0.4

0.5

0.6

0.7


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

Gabion steps - Step edge 8Gabion steps - Step edge 9Gabion steps - Step edge 10Gabion steps - Bottom Step

E-9

Table E-1 - Characteristic air-water properties for the gabion stepped spillway (θ=26.6°, h = 0.10


dc/h [-]

Q [m3/s]

Re [-]

Flow Regime

Step edge

Y90 [mm]

Cmean [-]

F max

[Hz] V90

[m/s] Tumax

[-] qw

[m2/s] 2 22.72 0.2203 30.51 1.54 0.98 0.0253 3 22.41 0.5701 61.91 2.07 1.63 0.0169 4 24.43 0.5459 77.71 1.92 1.50 0.0188 5 25.42 0.5789 79.18 1.52 1.54 0.0169 6 28.53 0.5608 89.22 1.67 1.86 0.0204 7 26.18 0.5932 100.11 1.77 1.59 0.0185 8 28.39 0.6015 101.29 1.74 1.59 0.0191 9 27.54 0.5810 125.84 2.00 1.76 0.0212 10 26.82 0.5890 104.00 1.82 1.57 0.0186

0.5 0.018 1.40×105 NA

Bottom 40.95 0.3816 88.44 1.51 2.21 0.0340 4 34.61 0.3516 64.62 3.01 1.66 0.0613 5 39.33 0.5727 130.76 2.90 1.33 0.0459 6 36.83 0.4223 168.09 2.92 1.67 0.0545 7 41.96 0.4665 189.87 2.87 1.45 0.0598 8 35.35 0.4245 232.47 2.89 1.55 0.0583 9 36.51 0.4907 240.69 3.15 1.91 0.0557 10 35.76 0.4119 264.04 3.29 1.86 0.0639

0.8 0.037 2.83×105 TRA

Bottom 44.82 0.3177 266.33 3.03 2.48 0.0757 5 37.69 0.2274 44.33 3.35 1.77 0.0892 6 40.16 0.2722 88.24 3.54 1.56 0.0933 7 47.27 0.3537 131.47 3.54 1.27 0.0963 8 47.71 0.3227 162.40 3.54 1.40 0.1053 9 47.48 0.3584 178.49 3.65 1.37 0.1039 10 47.15 0.2836 188.76 3.76 1.81 0.1111

1.1 0.059 4.57×105 SK

Bottom 60.62 0.2151 205.33 3.63 2.60 0.1372 6 47.57 0.1897 48.02 3.55 1.72 0.1249 7 51.72 0.2760 86.29 3.84 1.51 0.1226 8 54.39 0.2957 132.18 3.76 1.36 0.1298 9 57.70 0.3506 150.51 3.88 1.30 0.1308 10 57.38 0.2601 168.27 4.00 1.72 0.1449

1.3 0.076 5.87×105 SK

Bottom 73.37 0.1850 172.56 3.88 2.68 0.1820 8 62.18 0.2167 88.04 4.00 1.74 0.1714 9 68.47 0.2859 116.78 4.00 1.35 0.1703 10 65.85 0.2411 135.42 4.13 1.81 0.1741

1.5 0.095 7.28×105 SK

Bottom 85.99 0.1611 136.91 3.88 2.64 0.2254 8 69.53 0.1666 66.73 4.13 1.75 0.1915 9 74.96 0.2212 89.22 4.13 1.42 0.2071 10 74.64 0.1952 104.31 4.28 1.90 0.2178

1.7 0.114 8.78×105 SK

Bottom 98.73 0.1376 99.36 4.13 2.40 0.2749

F-1

APPENDIX F - AIR-WATER FLOW PROPERTIES ON CAPPED STEPPED CONFIGURATION

In this section the air-water properties measured on the capped stepped configuration are presented.

The basic air-water properties include the void fraction (C), the Bubble count rate (F), the

interfacial velocity (V), the turbulent intensity (Tu) and the relationship between the Bubble count

rate and the void fraction. The distributions were recorded for a wide range of dimensionless

discharges, varying from dc/h = 0.5 to dc/h = 1.7 (Table F.1). The characteristic air-water properties

are summarised in dimensioned form in Table F.1.

Fig. F-1 - Definition sketch of the stepped chute

F-2

Notation










90Y

0

w dyVC1q











θ chute slope;

Abbreviations




F-3

Fig. F-2 - Air-water flow properties on the capped stepped spillway (θ = 26.6°) as functions of y/dc -

NA: dc/h = 0.5, Q = 0.018 m3/s, Re = 1.40×105; step edges 2-10 and bottom channel. Legend



C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

F x dc /Vc

y / d

c

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Tu

y / d

c

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12 Capped steps - Step edge 2Capped steps - Step edge 3Capped steps - Step edge 4Capped steps - Step edge 5Capped steps - Step edge 6Capped steps - Step edge 7Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-4

Fig. F-3 - Air-water flow properties on the capped stepped spillway (θ = 26.6°) as functions of y/dc

- TRA: dc/h = 0.8, Q = 0.037 m3/s, Re = 2.83×105; step edges 4-10 and bottom channel. Legend



C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

F x dc / Vc

y / d

c

0 3 6 9 12 15 18 21 24 270

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


V / Vc

y / d

c

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.80

0.25

0.5

0.75

1

1.25

1.5

1.75

Tu

y / d

c

0 0.5 1 1.5 2 2.50

0.25

0.5

0.75

1

1.25

1.5

1.75


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25Capped steps - Step edge 4Capped steps - Step edge 5Capped steps - Step edge 6Capped steps - Step edge 7Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-5


SK: dc/h = 1.1, Q = 0.059 m3/s, Re = 4.57×105; step edges 5-10 and bottom channel. Legend applies

to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

F x dc / Vc

y / d

c

0 3 6 9 12 15 18 21 24 270

0.2

0.4

0.6

0.8

1

1.2


V / Vc

y / d

c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.2

0.4

0.6

0.8

1

1.2

Tu

y / d

c

0 0.3 0.6 0.9 1.2 1.5 1.8 2.10

0.2

0.4

0.6

0.8

1

1.2


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25Capped steps - Step edge 5Capped steps - Step edge 6Capped steps - Step edge 7Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-6


SK: dc/h = 1.3, Q = 0.076 m3/s, Re = 5.87×105; step edges 6-10 and bottom channel. Legend applies

to all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

F x dc / Vc

y / d

c

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


V / Vc

y / d

c

0 0.6 1.2 1.8 2.4 3 3.6 4.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tu

y / d

c

0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2.55

7.510

12.515

17.520

22.5

Capped steps - Step edge 6Capped steps - Step edge 7Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-7


SK: dc/h = 1.5, Q = 0.094 m3/s, Re = 7.28×105; step edges 7-10 and bottom step. Legend applies to

all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

F x dc / Vc

y / d

c

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


V / Vc

y / d

c

0 0.6 1.2 1.8 2.4 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tu

y / d

c

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

4

8

12

16

20

Capped steps - Step edge 7Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-8


SK: dc/h = 1.7, Q = 0.114 m3/s, Re = 8.78×105; step edges 8-10 and bottom step. Legend applies to

all figures.


C

y / d

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc /Vc

y / d

c

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V / Vc

y / d

c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y / d

c

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

F x

dc

/ Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 102468

1012141618

Capped steps - Step edge 8Capped steps - Step edge 9Capped steps - Step edge 10Capped steps - Bottom step

F-9

Table F.1 - Characteristic air-water properties for the capped stepped spillway (θ = 26.6°, h = 0.10


dc/h [-]

Q [m3/s]

Re [-]

Flow Regime

Step edge

Y90 [mm]

Cmean [-]

F max

[Hz] V90

[m/s] Tumax

[-] qw

[m2/s] 2 30.20 0.2237 31.49 1.38 0.86 0.02803 29.98 0.4194 63.27 2.25 2.01 0.03314 43.05 0.5280 100.11 1.97 1.22 0.03635 39.37 0.4866 131.20 2.16 1.23 0.03786 41.87 0.4992 132.18 2.21 1.46 0.04057 38.99 0.4981 145.24 2.23 1.49 0.03998 39.50 0.5527 131.53 2.33 1.54 0.03579 34.05 0.5578 152.38 2.37 1.72 0.031910 38.04 0.5223 161.18 2.50 2.05 0.0400

0.5 0.018 1.40×105 NA

Bottom 47.17 0.5287 136.29 2.24 1.87 0.03934 38.47 0.2671 53.53 3.79 2.01 0.06925 77.39 0.6363 106.09 2.82 1.90 0.07386 51.31 0.4593 165.58 3.06 1.29 0.07457 69.56 0.5642 205.18 2.81 1.16 0.08068 53.97 0.4145 234.22 3.02 1.35 0.09099 55.54 0.5089 235.71 3.18 1.35 0.080010 40.75 0.3803 289.24 3.33 2.05 0.0768

0.8 0.037 2.83×105 TRA

Bottom 53.59 0.4057 229.04 3.26 2.57 0.08145 62.43 0.2336 37.87 3.18 1.49 0.12126 57.80 0.2451 99.82 3.35 1.87 0.13957 89.46 0.4897 132.42 3.42 1.28 0.13118 67.23 0.3700 196.29 3.65 1.25 0.13589 73.66 0.4347 203.49 3.54 1.10 0.135110 60.07 0.2742 242.11 3.75 1.91 0.1438

1.1 0.059 4.57×105 SK

Bottom 79.01 0.2855 213.62 3.73 2.12 0.15586 67.92 0.1992 69.02 3.35 2.20 0.17627 88.57 0.3651 96.80 3.50 1.96 0.17108 74.71 0.3307 157.47 3.65 1.46 0.17009 88.36 0.3857 156.87 3.54 1.21 0.182410 73.68 0.2670 194.98 3.71 2.18 0.1894

1.3 0.076 5.87×105 SK

Bottom 92.01 0.2440 169.71 3.54 2.21 0.18377 92.02 0.2650 77.49 3.65 1.37 0.20388 84.64 0.2769 125.31 3.76 1.74 0.20729 94.87 0.3291 128.04 3.65 1.96 0.202610 85.06 0.2648 156.47 3.88 2.06 0.2116

1.5 0.095

7.28×105 SK

Bottom 100.55 0.2239 152.96 3.76 2.55 0.23288 89.22 0.2231 89.82 3.84 1.85 0.22969 98.06 0.2729 107.69 3.88 1.89 0.229210 90.69 0.2309 123.69 4.10 2.27 0.2440

1.7 0.114 8.78×105 SK

Bottom 108.23 0.2002 130.47 4.00 2.66 0.2842

G-1

APPENDIX G - AIR-WATER FLOW PROPERTIES ON FULLY-CAPPED STEPPED CONFIGURATION

The air-water properties measured on the fully-capped stepped configuration are presented. The

data were recorded for a wide range of dimensionless discharges, varying from dc/h = 0.5 to dc/h =

1.7 (Table G-1).

Fig. G-1 - Definition sketch of the stepped chute

G-2

Notation










90Y

0

w dyVC1q











θ chute slope;

Abbreviations




G-3

Fig. G-2 - Air-water flow properties on the fully-capped stepped spillway (θ = 26.6°) as functions

of y/dc - NA: dc/h = 0.5, Q = 0.018m3/s, Re = 1.40×105; step edges 5-10 and bottom channel.

Legend applies to all figures.


C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

F x dc/Vc

y/d c

0 2 4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2


V/Vc

y/d c

0 0.75 1.5 2.25 3 3.75 4.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Tu

y/d c

0 0.45 0.9 1.35 1.8 2.25 2.70

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

Fully-capped steps - Step edge 5Fully-capped steps - Step edge 6Fully-capped steps - Step edge 7Fully-capped steps - Step edge 8Fully-capped steps - Step edge 9Fully-capped steps - Step edge 10Fully-capped steps - Bottom Step

G-4

Fig. G-3 - Air-water flow properties on the fully-capped stepped spillway (θ = 26.6°) as functions of

y/dc- TRA: dc/h = 0.8, Q = 0.037m3/s, Re = 2.83×105; step edges 4-10and bottom channel. Legend



C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.25

0.5

0.75

1

1.25

1.5

F x dc/Vc

y/d c

0 3 6 9 12 15 18 21 24 270

0.25

0.5

0.75

1

1.25

1.5


V/Vc

y/d c

0 0.75 1.5 2.25 3 3.75 4.50

0.25

0.5

0.75

1

1.25

1.5

Tu

y/d c

0 0.5 1 1.5 2 2.50

0.25

0.5

0.75

1

1.25

1.5


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25Fully-capped steps - Step edge 4Fully-capped steps - Step edge 5Fully-capped steps - Step edge 6Fully-capped steps - Step edge 7Fully-capped steps - Step edge 8Fully-capped steps - Step edge 9Fully-capped steps - Step edge 10Fully-capped steps - Bottom step

G-5


y/dc - SK: dc/h = 1.1, Q = 0.059 m3/s, Re = 4.57×105; step edges 5-10 and bottom channel. Legend



C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

F x dc/Vc

y/d c

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


V/Vc

y/d c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tu

y/d c

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Fully-capped steps - Step edge 5Fully-capped steps - Step edge 6Fully-capped steps - Step edge 7Fully-capped steps - Step edge 8Fully-capped steps - Step edge 9Fully-capped steps - Step edge 10Fully-capped steps - Bottom step

G-6


of y/dc - SK: dc/h = 1.3, Q = 0.076m3/s, Re = 5.87×105; step edges 6-10and bottom channel. Legend



C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

F x dc/Vc

y/d c

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


V/Vc

y/d c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Tu

y/d c

0 0.45 0.9 1.35 1.8 2.25 2.70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

4

8

12

16

20

Fully-capped steps- Step edge 6Fully-capped steps- Step edge 7Fully-capped steps- Step edge 8Fully-capped steps- Step edge 9Fully-capped steps- Step edge 10Fully-capped steps- Bottom step

G-7


of y/dc- SK: dc/h = 1.5, Q = 0.094 m3/s, Re = 7.28×105; Step edges 7-10 and bottom step. Legend



C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

F x dc/Vc

y/d c

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


V/Vc

y/d c

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tu

y/d c

0 0.4 0.8 1.2 1.6 2 2.4 2.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 102468

1012141618

Fully-capped steps- Step edge 7Fully-capped steps- Step edge 8Fully-capped steps- Step edge 9Fully-capped steps- Step edge 10Fully-capped steps- Bottom step

G-8


y/dc - SK: dc/h = 1.7, Q = 0.114 m3/s, Re = 8.78×105; step edges 8-10 and bottom step. Legend



C

y/d c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

F x dc/Vc

y/d c

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


V/Vc

y/d c

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tu

y/d c

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


C

F x

dc/

Vc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

Fully-capped steps - Step edge 8Fully-capped steps - Step edge 9Fully-capped steps - Step edge 10Fully-capped steps - Bottom step

G-9

Table G.1 - Characteristic air-water properties for the fully-capped stepped spillway (θ = 26.6°, h =

0.1 m) with a double-tip conductivity probe (Ø = 0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Q [m3/s]

Re [-]

Flow Regime

Step edge

Y90 [mm]

Cmean [-]

F max

[Hz] V90

[m/s] Tumax

[-] qw

[m2/s]

5 45.84 0.5614 122.02 2.42 2.86 0.04326 55.37 0.5328 147.98 2.26 1.49 0.05487 47.60 0.5133 188.24 2.48 1.37 0.05288 36.76 0.4462 211.64 2.76 1.40 0.05019 49.95 0.6601 171.80 2.64 1.67 0.041210 37.34 0.4910 186.07 2.58 1.76 0.0432

0.5 0.018 1.40×105 NA

Bottom 58.26 0.5295 164.87 2.48 2.04 0.05654 36.33 0.1963 38.29 3.50 1.94 0.07325 59.44 0.5091 102.69 3.01 1.29 0.07716 47.17 0.3970 172.13 3.10 1.52 0.08237 80.67 0.6219 197.67 2.93 1.27 0.08478 53.17 0.3661 247.53 3.18 1.57 0.09949 69.53 0.5418 225.80 3.26 1.39 0.097410 46.42 0.3669 297.71 3.44 1.75 0.0950

0.8 0.037 2.83×105 TRA

Bottom 62.96 0.3948 244.11 3.47 2.20 0.10225 66.55 0.2547 58.31 3.13 2.30 0.12826 63.44 0.2716 118.18 3.13 2.00 0.13427 78.39 0.3598 120.38 3.15 1.51 0.14108 65.89 0.2820 178.49 3.35 1.67 0.14039 74.18 0.3603 165.58 3.44 1.51 0.147510 64.20 0.2758 226.13 3.54 2.16 0.1551

1.1 0.059 4.57×105 SK

Bottom 86.80 0.2763 185.13 3.65 2.51 0.16406 71.07 0.2303 89.91 3.22 2.04 0.15987 81.96 0.2763 96.29 3.35 1.80 0.16828 76.29 0.2735 136.82 3.54 1.73 0.17689 84.69 0.3315 136.53 3.63 1.41 0.187210 74.91 0.2540 179.87 3.75 2.24 0.1921

1.3 0.076 5.87×105 SK

Bottom 98.67 0.2427 169.00 3.76 2.56 0.21607 83.38 0.2007 67.78 3.54 1.84 0.2064

8 78.46 0.2200 93.11 3.88 1.90 0.2149

9 86.72 0.2806 109.11 3.88 1.68 0.2172

10 82.57 0.2406 129.96 4.00 2.50 0.2139

1.5 0.095

7.28×105 SK

Bottom 104.20 0.2249 144.33 3.96 2.56 0.2498

8 83.63 0.1746 66.67 4.00 1.74 0.25119 86.33 0.2098 85.27 4.07 1.73 0.246010 84.70 0.1767 98.82 4.28 2.23 0.2605

1.7 0.114 8.78×105 SK

Bottom 106.00 0.1705 110.96 4.13 2.40 0.3047

H-1

APPENDIX H - LONGITUDINAL DISTRIBUTION OF CHARACTERISTIC AIR-WATER PROPERTIES

H.1 INTRODUCTION

In this section the longitudinal distributions of characteristic air-water properties of the flow are

presented. The main characteristic air-water properties were the flow height (Y90), the mean air

concentration (Cmean), the maximum bubble frequency (Fmax), the characteristic flow velocity (V90),

the maximum turbulent intensity (Tumax), the discharge ratio (qw/q), the mean specific interface area

(amean) and the maximum specific interface area (amax). All parameters were derived from the air-

water property data presented in Appendices D to G. All values are presented in dimensionless

form. For each configuration the values obtained are firstly presented in tabular format and then

plotted as functions of the step edge. Note that step edge 1 corresponded to the downstream end of

the broad-crested weir.

Notation

a specific interface area, defined as the air-water surface area per unit volume of air and

water (m-1);

amax maximum value of specific interface area in a cross section (m-1);

amean mean specific interface area in a cross section of fluid normal to the flow direction (m-1)

90Y

090mean dya

Y

1a

B stepped spillway width (m);

C void fraction defined as the volume of air per unit volume, also called air concentration;

Cmean depth averaged void fraction defined in terms of Y90 : Cmean = 1 - d/Y90;






q water discharge per unit width (m2/s) defined as q = Q/B;



90Y

0

w dyVC1q





H-2

V90 interfacial velocity (m/s) at y = Y90; Vc critical flow velocity (m/s) defined as cc dgV ;






θ chute slope.

H-3

H.2 FLAT STEPPED CONFIGURATION

Table H-1 - Longitudinal distribution of characteristic air-water properties for the measurements on

the flat stepped spillway (θ = 26.6°, h = 0.10 m) with a double-tip conductivity probe (Ø = 0.25

mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Re [-]

Step edge

Y90/dc [-]

Cmean

[-] Fmax×dc/Vc

[-] qw/q

[-] V90/Vc

[-] Tumax

[-] amax×dc

[-] amean×dc

[-] 3 0.616 0.392 3.612 1.147 3.16 1.76 5.30 2.74 4 0.864 0.532 7.747 0.750 1.72 2.95 12.87 8.04 5 1.855 0.853 5.581 0.984 3.69 0.95 6.18 3.84 6 1.032 0.659 9.398 1.232 4.25 1.70 13.79 7.13 7 0.845 0.525 13.184 1.363 3.54 1.86 22.13 10.93 8 1.220 0.712 11.312 1.151 3.69 2.09 13.46 8.45 9 0.836 0.619 13.877 1.162 4.22 1.96 26.72 11.25

0.5 1.40×105

10 0.970 0.650 13.365 1.163 3.64 1.73 22.34 10.06 4 0.517 0.238 6.004 1.130 3.33 1.49 6.99 2.93 5 0.663 0.417 11.996 1.144 3.27 1.34 14.74 11.69 6 0.749 0.560 16.022 1.007 3.34 1.43 19.49 11.96 7 0.554 0.371 19.656 1.101 3.50 1.82 22.47 15.28 8 0.693 0.494 20.885 1.109 3.48 1.62 23.28 15.79 9 0.684 0.473 22.632 1.082 3.60 1.51 25.22 16.34

0.8 2.83×105

10 0.578 0.399 24.605 1.164 3.78 2.47 26.72 18.58 5 0.504 0.224 5.697 1.049 3.24 3.58 7.06 3.13 6 0.532 0.310 14.037 1.066 3.03 1.72 18.34 9.03 7 0.649 0.377 14.632 1.053 3.10 1.78 19.12 14.69 8 0.584 0.311 20.009 1.144 3.17 1.85 25.35 16.14 9 0.624 0.348 19.632 1.169 3.27 1.97 24.50 18.61

1.1 4.57×105

10 0.572 0.307 24.628 1.238 3.33 2.17 28.88 18.14 5 0.463 0.141 3.149 0.891 2.75 5.77 4.68 1.21 6 0.502 0.233 8.961 0.988 2.80 1.80 13.03 5.24 7 0.558 0.306 12.041 0.975 2.87 2.11 16.67 12.26 8 0.580 0.318 17.730 1.074 2.88 1.86 24.69 15.00 9 0.601 0.346 17.820 1.054 3.01 1.44 24.26 19.32

1.3 5.87×105

10 0.569 0.301 22.645 1.111 3.15 1.78 28.73 19.87 5 0.460 0.102 2.690 - 2.80 3.92 4.01 0.82 6 0.485 0.182 5.806 0.893 2.76 2.35 8.18 2.76 7 0.508 0.236 9.730 0.976 2.92 2.53 13.33 6.75 8 0.527 0.292 14.501 1.046 3.10 2.14 19.86 9.81 9 0.567 0.303 15.798 1.025 3.10 2.03 21.02 15.16

1.5 7.28×105

10 0.565 0.301 20.304 1.025 3.00 1.73 28.12 18.97 6 0.474 0.131 4.084 0.849 2.67 2.43 6.12 1.43 7 0.487 0.194 7.082 0.985 2.91 2.01 9.74 3.64 8 0.487 0.211 11.301 0.985 3.00 2.38 15.37 6.27 9 0.534 0.273 14.036 0.983 3.00 2.08 18.71 10.91

1.7 8.7×105

10 0.545 0.277 17.265 1.078 3.10 2.34 23.02 12.90

H-4

Fig. H-1 - Longitudinal distribution of characteristic air-water properties for flat stepped spillway (θ

= 26.6°, h = 0.10 m); double-tip conductivity probe (Ø = 0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)

(A) Dimensionless flow height

Step edge

Y90

/dc

0 1 2 3 4 5 6 7 8 9 100

0.3

0.6

0.9

1.2

1.5

1.8

Flat steps - dc/h = 0.5Flat steps - dc/h = 0.8Flat steps - dc/h = 1.1Flat steps - dc/h = 1.3Flat steps - dc/h = 1.5Flat steps - dc/h = 1.7

(B) Mean void fraction

Step edge

Cm

ean

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1


(C) Dimensionless maximum bubble frequency

Step edge

Fm

ax*d

c / V

c

0 1 2 3 4 5 6 7 8 9 100

4

8

12

16

20

24


(D) Dimensionless interfacial velocity

Step edge

V90

/Vc

0 1 2 3 4 5 6 7 8 9 100

0.51

1.52

2.53

3.54

4.5


H-5

(E) Maximum turbulent intensity

Step edge

Tu m

ax

0 1 2 3 4 5 6 7 8 9 100

0.9

1.8

2.7

3.6

4.5

5.4Flat steps - dc/h = 0.5Flat steps - dc/h = 0.8Flat steps - dc/h = 1.1Flat steps - dc/h = 1.3Flat steps - dc/h = 1.5Flat steps - dc/h = 1.7

(F) Discharge ratio

Step edge

q w/q

0 1 2 3 4 5 6 7 8 9 100

0.4

0.8

1.2

1.6

2

Flat steps - dc/h = 0.5Flat steps - dc/h = 0.8Flat steps - dc/h = 1.1Flat steps - dc/h = 1.3Flat steps - dc/h = 1.5Flat steps - dc/h = 1.7qw/q = 1

(G) Dimensionless mean specific interfacial area

Step edge

a mea

n*d c

0 1 2 3 4 5 6 7 8 9 100

2.55

7.510

12.515

17.520


(H) Dimensionless maximum specific interfacial area

Step edge

a max

*dc

0 1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30


H-6

H.3 GABION STEPPED CONFIGURATION


the gabion stepped spillway (θ = 26.6°, h = 0.10 m) with a double-tip conductivity probe (Ø = 0.25

mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Re [-]

Step edge

Y90/dc [-]

Cmean [-]

Fmax×dc/Vc

[-] qw/q

[-] V90/Vc

[-] Tumax

[-] amax×dc

[-] amean×dc

[-] 2 0.454 0.220 2.178 0.722 2.20 0.98 3.89 1.69 3 0.448 0.570 4.420 0.482 2.95 1.63 8.13 5.00 4 0.489 0.546 5.548 0.538 2.74 1.50 9.85 6.90 5 0.508 0.579 5.653 0.482 2.17 1.54 10.34 8.02 6 0.571 0.561 6.370 0.582 2.39 1.86 11.11 8.25 7 0.524 0.593 7.147 0.528 2.53 1.59 12.05 8.77 8 0.568 0.601 7.231 0.547 2.48 1.59 12.58 9.25 9 0.551 0.581 8.984 0.606 2.85 1.76 14.41 10.12 10 0.536 0.589 7.425 0.532 2.60 1.57 12.96 9.33

0.5 1.40×105

Bottom 0.819 0.382 6.314 0.972 2.16 2.21 12.27 8.99 4 0.433 0.352 5.836 0.865 3.40 1.66 6.98 3.96 5 0.492 0.573 11.808 0.648 3.28 1.33 15.05 10.48 6 0.460 0.422 15.179 0.769 3.29 1.67 19.95 14.36 7 0.524 0.466 17.146 0.843 3.24 1.45 21.84 15.40 8 0.442 0.425 20.993 0.823 3.27 1.55 25.20 17.88 9 0.456 0.491 21.735 0.786 3.55 1.91 24.85 16.86 10 0.447 0.412 23.844 0.901 3.71 1.86 26.42 19.54

0.8 2.83×105

Bottom 0.560 0.318 24.051 1.069 3.42 2.48 29.01 18.15 5 0.343 0.227 4.695 0.780 3.23 1.77 5.82 2.19 6 0.365 0.272 9.344 0.816 3.41 1.56 10.96 5.74 7 0.430 0.354 13.921 0.842 3.41 1.27 16.79 9.92 8 0.434 0.323 17.197 0.922 3.41 1.40 20.33 12.31 9 0.432 0.358 18.901 0.909 3.51 1.37 21.98 13.80 10 0.429 0.284 19.988 0.972 3.62 1.81 22.10 14.71

1.1 4.57×105

Bottom 0.551 0.215 21.743 1.201 3.50 2.60 25.50 13.91 6 0.366 0.190 5.528 0.851 3.14 1.72 6.85 2.27 7 0.398 0.276 9.933 0.835 3.40 1.51 11.94 6.13 8 0.418 0.296 15.216 0.884 3.33 1.36 18.29 10.35 9 0.444 0.351 17.326 0.891 3.43 1.30 20.83 12.75 10 0.441 0.260 19.370 0.987 3.54 1.72 21.87 12.90

1.3 5.87×105

Bottom 0.564 0.185 19.864 1.239 3.43 2.68 23.16 11.70 8 0.415 0.217 10.887 0.942 3.30 1.74 13.21 5.55 9 0.456 0.286 14.440 0.936 3.30 1.35 17.52 9.49 10 0.439 0.241 16.746 0.957 3.41 1.81 19.66 10.55

1.5 7.28×105

Bottom 0.573 0.161 16.930 1.239 3.19 2.64 20.54 8.69 8 0.409 0.167 8.785 0.872 3.20 1.75 10.98 3.22 9 0.441 0.221 11.745 0.943 3.20 1.42 14.68 5.92 10 0.439 0.195 13.732 0.992 3.31 1.90 16.02 6.27

1.7 8.7×105

Bottom 0.581 0.138 13.079 1.252 3.20 2.40 16.35 4.94

H-7

Fig. H-2 - Longitudinal distribution of characteristic air-water properties for gabion stepped

spillway (θ = 26.6°, h = 0.10 m); double-tip probe (Ø = 0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)


Step edge

Y90

/dc

0 1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

1

Gabion steps - dc/h = 0.5Gabion steps - dc/h = 0.8Gabion steps - dc/h = 1.1Gabion steps - dc/h = 1.3Gabion steps - dc/h = 1.5Gabion steps - dc/h = 1.7


Step edge

Cm

ean

0 1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6



Step edge

Fm

ax*d

c/V

c

0 1 2 3 4 5 6 7 8 9 10 110

4

8

12

16

20

24



Step edge

V90

/Vc

0 1 2 3 4 5 6 7 8 9 10 110

0.6

1.2

1.8

2.4

3

3.6


H-8


Step edge

Tu m

ax

0 1 2 3 4 5 6 7 8 9 10 110

0.4

0.8

1.2

1.6

2

2.4

2.8


(F) Discharge ratio distribution

Step edge

q w/q

0 1 2 3 4 5 6 7 8 9 10 110

0.250.5

0.751

1.251.5

1.752

Gabion steps - dc/h = 0.5Gabion steps - dc/h = 0.8Gabion steps - dc/h = 1.1Gabion steps - dc/h = 1.3Gabion steps - dc/h = 1.5Gabion steps - dc/h = 1.7qw/q = 1


Step edge

a mea

n*d c

0 1 2 3 4 5 6 7 8 9 10 110

2.55

7.510

12.515

17.520



Step edge

a max

*dc

0 1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25

30


H-9

H.4 CAPPED STEPPED CONFIGURATION


the capped stepped spillway (θ = 26.6°, h = 0.10 m) with a double-tip conductivity probe (Ø = 0.25

mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Re [-]

Step edge

Y90/dc [-]

Cmean [-]

Fmax×dc/Vc

[-] qw/q

[-] V90/Vc

[-] Tumax

[-] amax×dc

[-] amean×dc

[-] 2 0.604 0.224 2.248 0.800 1.97 0.86 4.42 1.94 3 0.600 0.419 4.517 0.946 3.22 2.01 6.22 4.07 4 0.861 0.528 7.147 1.037 2.81 1.22 10.33 7.43 5 0.787 0.487 9.367 1.081 3.08 1.23 12.66 8.71 6 0.837 0.499 9.436 1.158 3.16 1.46 12.64 8.81 7 0.780 0.498 10.369 1.139 3.18 1.49 13.33 9.27 8 0.790 0.553 9.390 1.021 3.33 1.54 11.88 8.49 9 0.681 0.558 10.879 0.910 3.39 1.72 14.14 10.11 10 0.761 0.522 11.507 1.143 3.57 2.05 13.26 9.58

0.5 1.40×105

Bottom 0.943 0.529 9.730 1.123 3.19 1.87 14.03 9.67 4 0.481 0.267 4.834 0.976 4.27 2.01 5.25 2.24 5 0.967 0.636 9.580 1.041 3.18 1.90 13.24 8.71 6 0.641 0.459 14.952 1.052 3.46 1.29 18.37 12.14 7 0.870 0.564 18.529 1.137 3.17 1.16 22.77 15.06 8 0.675 0.414 21.151 1.282 3.41 1.35 24.50 16.17 9 0.694 0.509 21.286 1.128 3.59 1.35 23.72 15.87 10 0.509 0.380 26.120 1.083 3.75 2.05 28.36 18.32

0.8 2.83×105

Bottom 0.670 0.406 20.684 1.149 3.68 2.57 24.23 16.82 5 0.568 0.234 4.010 1.060 3.06 1.49 5.37 2.51 6 0.525 0.245 10.570 1.221 3.23 1.87 12.40 5.71 7 0.813 0.490 14.022 1.147 3.30 1.28 17.87 13.42 8 0.611 0.370 20.785 1.189 3.51 1.25 25.07 15.30 9 0.670 0.435 21.548 1.182 3.41 1.10 25.25 18.72 10 0.546 0.274 25.638 1.258 3.61 1.91 30.07 19.19

1.1 4.57×105

Bottom 0.718 0.285 22.621 1.363 3.60 2.12 26.53 17.26 6 0.522 0.199 7.946 1.200 2.97 2.20 10.13 3.70 7 0.681 0.365 11.143 1.165 3.10 1.96 15.02 10.27 8 0.575 0.331 18.127 1.158 3.23 1.46 22.45 13.15 9 0.680 0.386 18.058 1.243 3.14 1.21 23.02 17.52 10 0.567 0.267 22.445 1.290 3.28 2.18 27.80 17.41

1.3 5.87×105

Bottom 0.708 0.244 19.537 1.251 3.14 2.21 25.36 17.07 7 0.613 0.265 9.582 1.120 3.01 1.37 13.12 6.17 8 0.564 0.277 15.495 1.139 3.10 1.74 20.02 9.23 9 0.632 0.329 15.833 1.113 3.01 1.96 21.07 15.69 10 0.567 0.265 19.348 1.163 3.19 2.06 24.26 14.66

1.5 7.28×105

Bottom 0.670 0.224 18.914 1.279 3.10 2.55 24.42 15.04 8 0.525 0.223 11.824 1.046 2.97 1.85 15.92 6.43 9 0.577 0.273 14.176 1.044 3.00 1.89 18.90 10.61 10 0.533 0.231 16.282 1.111 3.17 2.27 21.03 10.71

1.7 8.7×105

Bottom 0.637 0.200 17.175 1.295 3.10 2.66 22.18 11.01

H-10

Fig. H-3 - Longitudinal distribution of characteristic air-water properties for capped stepped

spillway (θ=26.6°, h=0.1 m)


Step edge

Y90

/dc

0 1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

1

Capped steps - dc/h = 0.5Capped steps - dc/h = 0.8Capped steps - dc/h = 1.1Capped steps - dc/h = 1.3Capped steps - dc/h = 1.5Capped steps - dc/h = 1.7


Step edge

Cm

ean

0 1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6



Step edge

F max

*dc/

Vc

0 1 2 3 4 5 6 7 8 9 10 110

4

8

12

16

20

24

28



Step edge

V90

/Vc

0 1 2 3 4 5 6 7 8 9 10 110

0.8

1.6

2.4

3.2

4


H-11


Step edge

Tu m

ax

0 1 2 3 4 5 6 7 8 9 10 110

0.4

0.8

1.2

1.6

2

2.4

2.8



Step edge

q w/q

0 1 2 3 4 5 6 7 8 9 10 110

0.4

0.8

1.2

1.6

2

Capped stepsm - dc/h = 0.5Capped stepsm - dc/h = 0.8Capped stepsm - dc/h = 1.1Capped stepsm - dc/h = 1.3Capped stepsm - dc/h = 1.5Capped stepsm - dc/h = 1.7qw/q = 1


Step edge

a mea

n*d c

0 1 2 3 4 5 6 7 8 9 10 110

5

10

15

20



Step edge

a max

*dc

0 1 2 3 4 5 6 7 8 9 10 11048

121620242832


H-12

H.5 FULLY-CAPPED STEPPED CONFIGURATION


the fully capped stepped spillway (θ=26.6°, h = 0.10 m) with a double-tip conductivity probe (Ø =

0.25 mm, Δx = 6.2 mm, Δz = 1.35 mm)

dc/h [-]

Re [-]

Step edge

Y90/dc [-]

Cmean [-]

Fmax×dc/Vc

[-] qw/q

[-] V90/Vc

[-] Tumax

[-] amax×dc

[-] amean×dc

[-] 5 0.917 0.561 8.711 1.234 3.45 2.86 10.69 6.72 6 1.107 0.533 10.564 1.565 3.23 1.49 13.17 9.59 7 0.952 0.513 13.439 1.507 3.54 1.37 15.41 9.97 8 0.735 0.446 15.110 1.430 3.93 1.40 16.08 11.29 9 0.999 0.660 12.265 1.176 3.77 1.67 13.83 9.13 10 0.747 0.491 13.284 1.233 3.69 1.76 14.99 10.88

0.5 1.40×105

Bottom 1.165 0.530 11.770 1.614 3.55 2.04 14.09 9.12 4 0.454 0.196 3.458 1.032 3.95 1.94 3.57 1.49 5 0.743 0.509 9.273 1.088 3.40 1.29 11.13 8.16 6 0.590 0.397 15.544 1.161 3.50 1.52 17.77 11.59 7 1.008 0.622 17.850 1.195 3.31 1.27 20.91 13.43 8 0.665 0.366 22.353 1.403 3.59 1.57 24.97 16.92 9 0.869 0.542 20.391 1.375 3.68 1.39 22.14 14.59 10 0.580 0.367 26.885 1.341 3.89 1.75 27.00 17.56

0.8 2.83×105

Bottom 0.787 0.395 22.044 1.443 3.91 2.20 23.24 14.96 5 0.605 0.255 6.175 1.122 3.01 2.30 8.07 4.42 6 0.577 0.272 12.514 1.174 3.01 2.00 16.35 8.04 7 0.713 0.360 12.747 1.234 3.03 1.51 17.01 13.13 8 0.599 0.282 18.901 1.228 3.23 1.67 24.70 15.39 9 0.674 0.360 17.533 1.291 3.32 1.51 21.15 17.31 10 0.584 0.276 23.946 1.357 3.41 2.16 28.08 18.47

1.1 4.57×105

Bottom 0.789 0.276 19.604 1.435 3.51 2.51 22.99 15.11 6 0.547 0.230 10.350 1.089 2.85 2.04 14.70 5.79 7 0.630 0.276 11.084 1.146 2.97 1.80 15.20 9.85 8 0.587 0.273 15.750 1.205 3.14 1.73 20.66 11.51 9 0.651 0.332 15.717 1.275 3.22 1.41 19.47 15.08 10 0.576 0.254 20.706 1.308 3.32 2.24 24.89 16.10

1.3 5.87×105

Bottom 0.759 0.243 19.455 1.471 3.33 2.56 22.78 13.51 7 0.556 0.201 8.381 1.134 2.92 1.84 11.48 4.38 8 0.523 0.220 11.514 1.181 3.19 1.90 14.87 6.03 9 0.578 0.281 13.492 1.194 3.19 1.68 17.42 9.99 10 0.550 0.241 16.070 1.176 3.30 2.50 19.49 10.37

1.5 7.28×105

Bottom 0.695 0.225 17.847 1.373 3.27 2.56 21.65 11.02 8 0.492 0.175 8.776 1.144 3.10 1.74 11.70 3.90 9 0.508 0.210 11.225 1.121 3.15 1.73 14.50 5.98 10 0.498 0.177 13.009 1.187 3.31 2.23 16.26 5.89

1.7 8.7×105

Bottom 0.624 0.171 14.606 1.388 3.20 2.40 17.65 6.37

H-13

Fig. H-4 - Longitudinal distribution of characteristic air-water properties for fully-capped stepped

spillway (θ=26.6°, h=0.10 m)


Step edge

Y90

/dc

0 1 2 3 4 5 6 7 8 9 10 110

0.2

0.4

0.6

0.8

1

1.2

Fully-capped steps - dc/h = 0.5Fully-capped steps - dc/h = 0.8Fully-capped steps - dc/h = 1.1Fully-capped steps - dc/h = 1.3Fully-capped steps - dc/h = 1.5Fully-capped steps - dc/h = 1.7


Step edge

Cm

ean

0 1 2 3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

0.5

0.6

0.7



Step edge

F max

* d

c/V

c

0 1 2 3 4 5 6 7 8 9 10 110

5

10

15

20

25



Step edge

V90

/Vc

0 1 2 3 4 5 6 7 8 9 10 110

0.51

1.52

2.53

3.54


H-14


Step edge

Tu

max

0 1 2 3 4 5 6 7 8 9 10 110

0.5

1

1.5

2

2.5

3



Step edge

q w/q

0 1 2 3 4 5 6 7 8 9 10 110

0.4

0.8

1.2

1.6

2

Fully-capped steps - dc/h = 0.5Fully-capped steps - dc/h = 0.8Fully-capped steps - dc/h = 1.1Fully-capped steps - dc/h = 1.3Fully-capped steps - dc/h = 1.5Fully-capped steps - dc/h = 1.7qw/q = 1


Step edge

a m

ean

* d c

0 1 2 3 4 5 6 7 8 9 10 110

4

8

12

16

20



Step edge

a m

ax *

dc

0 1 2 3 4 5 6 7 8 9 10 110

6

12

18

24

30


I-1

APPENDIX I - VIDEO MOVIES OF AIR BUBBLE MOTION INSIDE THE GABIONS

I.1 PRESENTATION

The gabion stepped configuration was characterised by the entrainment and motion of air bubbles

inside the gabions. For all porous configurations, air bubbles were seen flowing through the gravel

material. A series of video movies were taken with a digital camera PentaxTM K-7 during some

basic experiments. The movie files are deposited with the digital record of the publication at the

institutional open access repository of the University of Queensland:

{http://espace.library.uq.edu.au/}. They are listed as part of the technical report deposit at

{http://espace.library.uq.edu.au/list/author_id/193/}. The list of the movies is detailed in section I.2,

including the filenames, file format, and a description of each video.

All the movies are Copyrights Hubert CHANSON 2013.

I.2 LIST OF DIGITAL VIDEO MOVIES

Filename Format Description IMGP4537.avi HD movie

(1280×720 pixels, 30

fps)

Gabion stepped spillway ( = 26.6°, h = 0.1 m), Transition flow regime (dc/h = 0.85), step cavity 7-8 Some red wool strings were attached to the wire mesh to visualise the cavity flow patterns.

IMGP4566.avi HD movie (1280×720 pixels, 30

fps)

Gabion stepped spillway ( = 26.6°, h = 0.1 m), Skimming flow regime (dc/h = 1.5), step cavity 7-8 Some red wool strings were attached to the wire mesh to visualise the cavity flow patterns.


fps)

Gabion stepped spillway ( = 26.6°, h = 0.1 m), Nappe flow regime (dc/h = 0.5), step cavity 6-7 Note the aerated cavity and bubbly motion inside the gabion gravels.


fps)

Capped gabion stepped spillway ( = 26.6°, h = 0.1 m), Skimming flow regime (dc/h = 1.3), step cavities 7-8 & 8-9


fps)

Capped gabion stepped spillway ( = 26.6°, h = 0.1 m), Nappe flow regime (dc/h = 0.5), step cavity 5-6 Note the aerated cavity and the free-surface line in the gabions.

I.3 MOVIE FILES

The movies files of Appendix I are available in the institutional open access repository of the

I-2

University of Queensland (Brisbane, Australia) and they are deposited at UQeSpace

{http://espace.library.uq.edu.au/}. The digital video files are a series of HD movies. The deposited

movie files (Section I.2) were converted to Flash video for video streaming. At request, the second

author might provide the original movies as a single compressed file.

The copyrights of the movies remain the property of Hubert CHANSON. Any use of the movies

available in the digital appendix must acknowledge and cite the present report:

WUTHRICH, D., and CHANSON, H. (2014). "Aeration and Energy Dissipation over Stepped

Gabion Spillways: a Physical Study." Hydraulic Model Report No. CH92/13, School of Civil

Engineering, The University of Queensland, Brisbane, Australia, 171 pages & 5 video movies

(ISBN 9781742720944).

Further details on the report including the digital appendix may be obtained from Professor Hubert

CHANSON {[email protected]}.

R-1

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Spillways." Jl of Hyd. Engrg., ASCE, Vol. 125, No. 9, pp. 969-971. Discussion : Vol. 127, No.

6, pp. 519-525.

CHANSON, H. (1994). "Hydraulics of Skimming Flows over Stepped Channels and Spillways." Jl

of Hyd. Res., IAHR, Vol. 32, No. 3, pp. 445-460. Discussion : Vol. 33, No. 3, pp. 414-419 (ISSN

0022-1686).

CHANSON, H. (1994). "Comparison of Energy Dissipation between Nappe and Skimming Flow

Regimes on Stepped Chutes." Jl of Hyd. Res., IAHR, Vol. 32, No. 2, pp. 213-218. Errata : Vol.

33, No. 1, p. 113. Discussion : Vol. 33, No. 1, pp. 114-143 (ISSN 0022-1686).

FELDER, S. and CHANSON, H. (2012). "Air-Water Flow Measurements in Instationary Free-

Surface Flows: a Triple Decomposition Technique." Hydraulic Model Report CH85/12, School

of Civil Engineering, The University of Queensland, Brisbane, Australia, 161 pages.

FELDER, S., and CHANSON, H. (2013). "Aeration, Flow Instabilities, and Residual Energy on

Pooled Stepped Spillways of Embankment Dams." Journal of Irrigation and Drainage

Engineering, ASCE, Vol. 139, No. 10, pp. 880-887 (DOI: 10.1061/(ASCE)IR.1943-

4774.0000627) (ISSN 0733-9437).

FELDER, S., FROMM, C. and CHANSON, H. (2012). "Air Entrainment and Energy Dissipation

on a 8.9° Slope Stepped Spillway with Flat and Pooled Steps." Hydraulic Model Report

CH86/12, University of Queensland, School of Civil Engineering, Brisbane, Australia, 73 pages.

FELDER, S., GUENTHER, P. and CHANSON, H. (2012). "Air-Water Flow Properties and Energy

Dissipation on Stepped Spillways: a Physical Study of Several Pooled Stepped Configurations."

Hydraulic Model Report CH87/12, University of Queensland, School of Civil Engineering,


KNAUSS, J. (1995). "ΤΗΣ ΓΡΙΑΣ ΤΟ ΠΗΔΗΜΑ, der Altweibersprung. Die Rätselhafte Alte Talsperre

in der Glosses-Schlucht bei Alyzeia in Akarnanien." Archäologischer Anzeiger, Vol. 5, pp. 138-162.

MEIRELES, I., and MATOS, J. (2009). "Skimming Flow in the Nonaerated Region of Stepped

Spillways over Embankment Dams." Journal of Hydraulic Engineering, Vol. 135, No. 8, pp.

685-689.

SCHLENKHOFF, A., and BUNG, D.B. (2009). "Prediction of Oxygen Transfer in Self-aerated

Skimming Flow on Embankment Stepped Spillways." Proc. 33rd IAHR Biennial Congress,

IAHR-ASCE-EWRI, Vancouver, Canada, 9-14 Aug., 8 pages (CD-ROM).

STEPHENSON, D. (1980). "The Stability of Gabion Weirs." Intl Water Power and Dam

Construction, Vol. 32, No. 4, pp. 24-28.

THORWARTH, J. (2008). Hydraulisches Verhalten der Treppengerinne mit eingetieften Stufen –

Selbstinduzierte Abflussinstationaritäten und Energiedissipation (Hydraulics of Pooled Stepped

Spillways – Self-induced Unsteady Flow and Energy Dissipation). Ph.D. Thesis, University of

Aachen, Aachen, Germany, 239 pages (in German).

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Internet bibliography

Air entrainment on chute and stepped

spillways

{http://www.uq.edu.au/~e2hchans/self_aer.html}

Embankment overflow stepped spillways:

earth dam spillways with precast concrete

blocks

{http://www.uq.edu.au/~e2hchans/over_st.html}

Timber crib weirs {http://www.uq.edu.au/~e2hchans/tim_weir.html}

Research Papers in Hydraulic Engineering

and Environmental Fluid Mechanics

{http://www.uq.edu.au/~e2hchans/reprints.html}

Open Access Repositories

OAIster {http://www.oaister.org/}

UQeSpace {http://espace.library.uq.edu.au/}

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Bibliographic reference of the Report CH92/13 The Hydraulic Model research report series CH is a refereed publication published by the School of

Civil Engineering at the University of Queensland, Brisbane, Australia.

The bibliographic reference of the present report is:

WUTHRICH, D., and CHANSON, H. (2014). "Aeration and Energy Dissipation over Stepped

Gabion Spillways: a Physical Study." Hydraulic Model Report No. CH92/13, School of Civil

Engineering, The University of Queensland, Brisbane, Australia, 171 pages and 5 video movies

(ISBN 9781742720944).

The Report CH92/13 is available, in the present form, as a PDF file on the Internet at UQeSpace:

http://espace.library.uq.edu.au/

It is listed at:

http://espace.library.uq.edu.au/list/author_id/193/

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HYDRAULIC MODEL RESEARCH REPORT CH

The Hydraulic Model Report CH series is published by the School of Civil Engineering at the

University of Queensland. Orders of any reprint(s) of the Hydraulic Model Reports should be

addressed to the School Secretary.

School Secretary, School of Civil Engineering, The University of Queensland

Brisbane 4072, Australia - Tel.: (61 7) 3365 3619 - Fax : (61 7) 3365 4599

Url: http://www.eng.uq.edu.au/civil/ Email: [email protected]

Report CH Unit price Quantity Total price

WUTHRICH, D., and CHANSON, H. (2014). "Aeration and Energy Dissipation over Stepped Gabion Spillways: a Physical Study." Hydraulic Model Report No. CH92/13, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 171 pages and 5 video movies (ISBN 9781742720944).

AUD$60.00

WANG, H., and CHANSON, H. (2013). "Free-Surface Deformation and Two-Phase Flow Measurements in Hydraulic Jumps". Hydraulic Model Report No. CH91/13, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 108 pages (ISBN 9781742720746).

AUD$60.00

SIMON, B., and CHANSON, H. (2013). "Turbulence Measurements in Tidal Bore-like Positive Surges over a Rough Bed". Hydraulic Model Report No. CH90/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 176 pages (ISBN 9781742720685).

AUD$60.00

REUNGOAT, D., CHANSON, H., and CAPLAIN, B. (2012). "Field Measurements in the Tidal Bore of the Garonne River at Arcins (June 2012)." Hydraulic Model Report No. CH89/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 121 pages (ISBN 9781742720616).

AUD$60.00

CHANSON, H., and WANG, H. (2012). "Unsteady Discharge Calibration of a Large V-Notch Weir." Hydraulic Model Report No. CH88/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 50 pages and 4 movies (ISBN 9781742720579).

AUD$60.00

FELDER, S., FROMM, C., and CHANSON, H. (2012). "Air Entrainment and Energy Dissipation on a 8.9° Slope Stepped Spillway with Flat and Pooled Steps." Hydraulic Model Report No. CH86/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 80 pages (ISBN 9781742720531).

AUD$60.00

FELDER, S., and CHANSON, H. (2012). "Air-Water Flow Measurements in Instationary Free-Surface Flows: a Triple Decomposition Technique." Hydraulic Model Report No. CH85/12, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 161 pages (ISBN 9781742720494).

AUD$60.00

REICHSTETTER, M., and CHANSON, H. (2011). "Physical and Numerical Modelling of Negative Surges in Open Channels." Hydraulic Model Report No. CH84/11, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 82 pages (ISBN 9781742720388).

AUD$60.00

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BROWN, R., CHANSON, H., McINTOSH, D., and MADHANI, J. (2011). "Turbulent Velocity and Suspended Sediment Concentration Measurements in an Urban Environment of the Brisbane River FloodPlain at Gardens Point on 12-13 January 2011." Hydraulic Model Report No. CH83/11, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 120 pages (ISBN 9781742720272).

AUD$60.00

CHANSON, H. "The 2010-2011 Floods in Queensland (Australia): Photographic Observations, Comments and Personal Experience." Hydraulic Model Report No. CH82/11, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 127 pages (ISBN 9781742720234).

AUD$60.00

MOUAZE, D., CHANSON, H., and SIMON, B. (2010). "Field Measurements in the Tidal Bore of the Sélune River in the Bay of Mont Saint Michel (September 2010)." Hydraulic Model Report No. CH81/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 72 pages (ISBN 9781742720210).

AUD$60.00

JANSSEN, R., and CHANSON, H. (2010). "Hydraulic Structures: Useful Water Harvesting Systems or Relics." Proceedings of the Third International Junior Researcher and Engineer Workshop on Hydraulic Structures (IJREWHS'10), 2-3 May 2010, Edinburgh, Scotland, R. JANSSEN and H. CHANSON (Eds), Hydraulic Model Report CH80/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 211 pages (ISBN 9781742720159).

AUD$60.00

CHANSON, H., LUBIN, P., SIMON, B., and REUNGOAT, D. (2010). "Turbulence and Sediment Processes in the Tidal Bore of the Garonne River: First Observations." Hydraulic Model Report No. CH79/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 97 pages (ISBN 9781742720104).

AUD$60.00

CHACHEREAU, Y., and CHANSON, H., (2010). "Free-Surface Turbulent Fluctuations and Air-Water Flow Measurements in Hydraulics Jumps with Small Inflow Froude Numbers." Hydraulic Model Report No. CH78/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 133 pages (ISBN 9781742720036).

AUD$60.00

CHANSON, H., BROWN, R., and TREVETHAN, M. (2010). "Turbulence Measurements in a Small Subtropical Estuary under King Tide Conditions." Hydraulic Model Report No. CH77/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 82pages (ISBN 9781864999969).

AUD$60.00

DOCHERTY, N.J., and CHANSON, H. (2010). "Characterisation of Unsteady Turbulence in Breaking Tidal Bores including the Effects ofBed Roughness." Hydraulic Model Report No. CH76/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 112pages (ISBN 9781864999884).

AUD$60.00

CHANSON, H. (2009). "Advective Diffusion of Air Bubbles in Hydraulic Jumps with Large Froude Numbers: an Experimental Study." Hydraulic Model Report No. CH75/09, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 89 pages and 3 videos(ISBN 9781864999730).

AUD$60.00

CHANSON, H. (2009). "An Experimental Study of Tidal Bore Propagation: the Impact of Bridge Piers and Channel Constriction." Hydraulic Model Report No. CH74/09, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 110 pages and 5 movies (ISBN 9781864999600).

AUD$60.00

CHANSON, H. (2008). "Jean-Baptiste Charles Joseph BÉLANGER (1790-1874), the Backwater Equation and the Bélanger Equation." Hydraulic Model Report No. CH69/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 40 pages (ISBN 9781864999211).

AUD$60.00

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GOURLAY, M.R., and HACKER, J. (2008). "Reef-Top Currents in Vicinity of Heron Island Boat Harbour, Great Barrier Reef, Australia: 2. Specific Influences of Tides Meteorological Events and Waves."Hydraulic Model Report No. CH73/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 331 pages (ISBN 9781864999365).

AUD$60.00

GOURLAY, M.R., and HACKER, J. (2008). "Reef Top Currents in Vicinity of Heron Island Boat Harbour Great Barrier Reef, Australia: 1. Overall influence of Tides, Winds, and Waves." Hydraulic Model Report CH72/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 201 pages (ISBN 9781864999358).

AUD$60.00

LARRARTE, F., and CHANSON, H. (2008). "Experiences and Challenges in Sewers: Measurements and Hydrodynamics." Proceedings of the International Meeting on Measurements and Hydraulics of Sewers,Summer School GEMCEA/LCPC, 19-21 Aug. 2008, Bouguenais, Hydraulic Model Report No. CH70/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia (ISBN 9781864999280).

AUD$60.00

CHANSON, H. (2008). "Photographic Observations of Tidal Bores (Mascarets) in France." Hydraulic Model Report No. CH71/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 104 pages, 1 movie and 2 audio files (ISBN 9781864999303).

AUD$60.00

CHANSON, H. (2008). "Turbulence in Positive Surges and Tidal Bores. Effects of Bed Roughness and Adverse Bed Slopes." Hydraulic Model Report No. CH68/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, 121 pages and 5 movie files (ISBN 9781864999198)

AUD$70.00

FURUYAMA, S., and CHANSON, H. (2008). "A Numerical Study of Open Channel Flow Hydrodynamics and Turbulence of the Tidal Bore and Dam-Break Flows." Report No. CH66/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, May, 88 pages (ISBN 9781864999068).

AUD$60.00

GUARD, P., MACPHERSON, K., and MOHOUPT, J. (2008). "A Field Investigation into the Groundwater Dynamics of Raine Island." Report No. CH67/08, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, February, 21 pages (ISBN 9781864999075).

AUD$40.00

FELDER, S., and CHANSON, H. (2008). "Turbulence and Turbulent Length and Time Scales in Skimming Flows on a Stepped Spillway. Dynamic Similarity, Physical Modelling and Scale Effects." Report No. CH64/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, March, 217 pages (ISBN 9781864998870).

AUD$60.00

TREVETHAN, M., CHANSON, H., and BROWN, R.J. (2007). "Turbulence and Turbulent Flux Events in a Small Subtropical Estuary." Report No. CH65/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, November, 67 pages (ISBN 9781864998993)

AUD$60.00

MURZYN, F., and CHANSON, H. (2007). "Free Surface, Bubbly flow and Turbulence Measurements in Hydraulic Jumps." Report CH63/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, August, 116 pages (ISBN 9781864998917).

AUD$60.00

KUCUKALI, S., and CHANSON, H. (2007). "Turbulence in Hydraulic Jumps: Experimental Measurements." Report No. CH62/07, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 96 pages (ISBN 9781864998825).

AUD$60.00

CHANSON, H., TAKEUCHI, M, and TREVETHAN, M. (2006). "Using Turbidity and Acoustic Backscatter Intensity as Surrogate Measures of Suspended Sediment Concentration. Application to a Sub-Tropical Estuary (Eprapah Creek)." Report No. CH60/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 142 pages (ISBN 1864998628).

AUD$60.00

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CAROSI, G., and CHANSON, H. (2006). "Air-Water Time and Length Scales in Skimming Flows on a Stepped Spillway. Application to the Spray Characterisation." Report No. CH59/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998601).

AUD$60.00

TREVETHAN, M., CHANSON, H., and BROWN, R. (2006). "Two Series of Detailed Turbulence Measurements in a Small Sub-Tropical Estuarine System." Report No. CH58/06, Div. of Civil Engineering, The University of Queensland, Brisbane, Australia, Mar. (ISBN 1864998520).

AUD$60.00

KOCH, C., and CHANSON, H. (2005). "An Experimental Study of Tidal Bores and Positive Surges: Hydrodynamics and Turbulence of the Bore Front." Report No. CH56/05, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998245).

AUD$60.00

CHANSON, H. (2005). "Applications of the Saint-Venant Equations and Method of Characteristics to the Dam Break Wave Problem." Report No. CH55/05, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, May (ISBN 1864997966).

AUD$60.00

CHANSON, H., COUSSOT, P., JARNY, S., and TOQUER, L. (2004). "A Study of Dam Break Wave of Thixotropic Fluid: Bentonite Surges down an Inclined plane." Report No. CH54/04, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, June, 90 pages (ISBN 1864997710).

AUD$60.00

CHANSON, H. (2003). "A Hydraulic, Environmental and Ecological Assessment of a Sub-tropical Stream in Eastern Australia: Eprapah Creek, Victoria Point QLD on 4 April 2003." Report No. CH52/03, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, June, 189 pages (ISBN 1864997044).

AUD$90.00

CHANSON, H. (2003). "Sudden Flood Release down a Stepped Cascade. Unsteady Air-Water Flow Measurements. Applications to Wave Run-up, Flash Flood and Dam Break Wave." Report CH51/03, Dept of Civil Eng., Univ. of Queensland, Brisbane, Australia, 142 pages (ISBN 1864996552).

AUD$60.00

CHANSON, H,. (2002). "An Experimental Study of Roman Dropshaft Operation : Hydraulics, Two-Phase Flow, Acoustics." Report CH50/02, Dept of Civil Eng., Univ. of Queensland, Brisbane, Australia, 99 pages (ISBN 1864996544).

AUD$60.00

CHANSON, H., and BRATTBERG, T. (1997). "Experimental Investigations of Air Bubble Entrainment in Developing Shear Layers." Report CH48/97, Dept. of Civil Engineering, University of Queensland, Australia, Oct., 309 pages (ISBN 0 86776 748 0).

AUD$90.00

CHANSON, H. (1996). "Some Hydraulic Aspects during Overflow above Inflatable Flexible Membrane Dam." Report CH47/96, Dept. of Civil Engineering, University of Queensland, Australia, May, 60 pages (ISBN 0 86776 644 1).

AUD$60.00

CHANSON, H. (1995). "Flow Characteristics of Undular Hydraulic Jumps. Comparison with Near-Critical Flows." Report CH45/95, Dept. of Civil Engineering, University of Queensland, Australia, June, 202 pages (ISBN 0 86776 612 3).

AUD$60.00

CHANSON, H. (1995). "Air Bubble Entrainment in Free-surface Turbulent Flows. Experimental Investigations." Report CH46/95, Dept. of Civil Engineering, University of Queensland, Australia, June, 368 pages (ISBN 0 86776 611 5).

AUD$80.00

CHANSON, H. (1994). "Hydraulic Design of Stepped Channels and Spillways." Report CH43/94, Dept. of Civil Engineering, University of Queensland, Australia, Feb., 169 pages (ISBN 0 86776 560 7).

AUD$60.00

POSTAGE and HANDLING (per report) AUD$10.00 GRAND TOTAL

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OTHER HYDRAULIC RESEARCH REPORTS

Reports/Theses Unit price Quantity Total priceTREVETHAN, M. (2008). "A Fundamental Study of Turbulence and Turbulent Mixing in a Small Subtropical Estuary." Ph.D. thesis, Div. of Civil Engineering, The University of Queensland, 342 pages.

AUD$100.00

GONZALEZ, C.A. (2005). "An Experimental Study of Free-Surface Aeration on Embankment Stepped Chutes." Ph.D. thesis, Dept of Civil Engineering, The University of Queensland, Brisbane, Australia, 240 pages.

AUD$80.00

TOOMBES, L. (2002). "Experimental Study of Air-Water Flow Properties on Low-Gradient Stepped Cascades." Ph.D. thesis, Dept of Civil Engineering, The University of Queensland, Brisbane, Australia.

AUD$100.00

CHANSON, H. (1988). "A Study of Air Entrainment and Aeration Devices on a Spillway Model." Ph.D. thesis, University of Canterbury, New Zealand.

AUD$60.00

POSTAGE and HANDLING (per report) AUD$10.00 GRAND TOTAL

CIVIL ENGINEERING RESEARCH REPORT CE

The Civil Engineering Research Report CE series is published by the School of Civil Engineering

at the University of Queensland. Orders of any of the Civil Engineering Research Report CE should

be addressed to the School Secretary.


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Tel.: (61 7) 3365 3619 Fax : (61 7) 3365 4599


Recent Research Report CE Unit price Quantity Total priceCALLAGHAN, D.P., NIELSEN, P., and CARTWRIGHT, N. (2006). "Data and Analysis Report: Manihiki and Rakahanga, Northern Cook Islands - For February and October/November 2004 Research Trips." Research Report CE161, Division of Civil Engineering, The University of Queensland (ISBN No. 1864998318).

AUD$10.00

GONZALEZ, C.A., TAKAHASHI, M., and CHANSON, H. (2005). "Effects of Step Roughness in Skimming Flows: an Experimental Study." Research Report No. CE160, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July (ISBN 1864998105).

AUD$10.00

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CHANSON, H., and TOOMBES, L. (2001). "Experimental Investigations of Air Entrainment in Transition and Skimming Flows down a Stepped Chute. Application to Embankment Overflow Stepped Spillways." Research Report No. CE158, Dept. of Civil Engineering, The University of Queensland, Brisbane, Australia, July, 74 pages (ISBN 1 864995297).

AUD$10.00

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Aeration and Energy Dissipation over Stepped Gabion Spillways

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