THE UNIVERSITY OF QUEENSLAND

REPORT CH105/17

AUTHORS: Gangfu ZHANG and Hubert CHANSON

APPLICATION OF LOCAL OPTICAL FLOW METHODS TO HIGH-VELOCITY AIR-WATER FLOWS: VALIDATION AND APPLICATION TO SKIMMING FLOWS ON STEPPED CHUTES

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:/http://www.civil.uq.edu.au// First published in 2017 by School of Civil Engineering The University of Queensland, Brisbane QLD 4072, Australia © Zhang and Chanson This book is copyright ISBN No. 978-1-74272-182-8 The University of Queensland, St Lucia QLD, Australia

Application of Local Optical Flow Methods to High-Velocity Air-Water Flows: Validation and Application to Skimming Flows on

Stepped Chutes

by

Gangfu ZHANG

Ph.D. research student, The University of Queensland, School of Civil Engineering, Brisbane, QLD

4072, Australia, Email: g.zhang3@uq.edu.au

and

Hubert CHANSON

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

Australia, Email: h.chanson@uq.edu.au

HYDRAULIC MODEL REPORT No. CH105/17

ISBN 978-1-74272-182-8

The University of Queensland, School of Civil Engineering,

January 2017

ii

ABSTRACT

Stepped spillway flows are characterised by strong turbulence and air entrainment. The overflows

are typically investigated in laboratory, albeit large-size physical models must be used to minimise

potential scale effects. The present study examines the feasibility of two local optical flow

techniques – the Lucas-Kanade method and the Farneback method – applied to high-velocity air-

water skimming flows above several types of stepped roughness. Despite their long prevalence in

the computer vision industry, these methods are not yet widely known to the air-water flow

community. Experimental studies were undertaken in a large-size physical model with three

different types of stepped roughness. The physical meaning of the optical signal was elucidated and

the optical flow results were validated with a synchronised setup consisting of an ultra-high-speed

video camera and a phase-detection probe with a time delay shorter than 1 ms. Sensitivity analysis

results found that the optical flow accuracy was sensitive to the sampling rate selection and to high

velocity gradients. The optical velocity, vorticity, rate-of-strain, turbulence intensity and turbulent

kinetic energy maps were deduced. The results highlighted some effect of cavity shape on the

mainstream spillway flow and the findings were comparable to those obtained in an earlier PIV

study of clear water skimming flow. The present study demonstrated that the local optical flow

algorithms are efficient and robust tools for providing qualitative and quantitative information to

complement existing studies on aerated skimming flows. Importantly, however, the optical flow

method characterises the air-water flow properties next to the sidewall, where the bubble count rate

and interfacial velocity were found to be underestimated, compared to the channel centreline

interfacial properties.

Keywords: Optical flow, Stepped spillway, Lucas-Kanade, Farneback, Air-water flows, Computer

vision, Physical modelling, High-velocity free-surface flows.

iii

TABLE OF CONTENTS

Page

Abstract ii

Keywords ii

Table of contents iii

List of symbols iv

1. Introduction 1

2. Methodology 4

3. Experimental facilities and instrumentation 9

4. Validation techniques 14

5. Application 27

6. Conclusion 37

7. Acknowledgements 39

REFERENCES R-1

Bibliography R-5

Open Access Repositories R-5

Bibliographic reference of the Report CH105/17 R-6

iv

LIST OF SYMBOLS

The following symbols are used in this report:

A a symmetric matrix in the Farneback method;

A1 a symmetric matrix in the Farneback method;

A2 a symmetric matrix in the Farneback method;

b1 a vector in the Farneback method;

b2 a vector in the Farneback method;

c1 a scalar in the Farneback method;

c2 a scalar in the Farneback method;

C time averaged void fraction;

C void fraction vector;

d displacement;

dc critical flow depth (m): dc = (q2/g)1/3;

Ehs objective function in the Horn-Shunck method;

F time averaged bubble count rate (Hz);

F bubble count rate vector;

fsamp sampling rate (Hz);

g gravity constant (m/s2); in Brisbane, Australia, g = 9.80 m/s2;

h step height (m); herein h = 0.1 m;

H1 total head above weir crest (m);

I 8-bit luminance;

I 8-bit luminance vector;

I’ standard deviation of luminance;

I’ luminance standard deviation vector;

ko optical in-plane turbulent kinetic energy (m2/s2);

Lcav step cavity length (m) (herein Lcav = 0.141 m);

Lcrest broad-crested weir crest length (m) (herein Lcrest = 0.60 m);

M1 matrix containing gradient information;

M2 matrix containing coefficients of polynomial expansion;

Q water discharge (m3/s);

q unit discharge (m2/s): i.e. water discharge per unit width;

RcI correlation coefficient between void fraction and average luminance;

RcI’ correlation coefficient between void fraction and luminance standard deviation;

RfI correlation coefficient between bubble count rate and average luminance;

RfI’ correlation coefficient between bubble count rate and luminance standard deviation;

Rmax maximum correlation coefficient;

Re Reynolds number;

t time (s);

Tuaw interfacial turbulence intensity;

v

Tuo optical turbulence intensity;

Uaw streamwise mean interfacial velocity (m/s);

Uc critical flow velocity (m/s): Uc = (g q)1/3;

Uo streamwise mean optical flow (m/s);

Uo streamwise mean optical flow (matrix);

uo optical flow;

uo’ streamwise optical flow fluctuation (m/s);

Vo normal mean optical flow (m/s);

Vo normal mean optical flow (matrix);

W channel width (m) (herein W = 0.985 m for the physical model).

W(x) window function;

w weighting function in the Farneback method;

x longitudinal Cartesian coordinate (m);

x position;

xc camera coordinate;

xim Cartesian coordinate (in image plane);

y normal Cartesian coordinate (m), measured perpendicular to the pseudo-bottom formed

by the step edges;

yc camera coordinate;

yim Cartesian coordinate (in image plane);

z transverse Cartesian coordinate (m);

zc camera coordinate.

αhs regularisation parameter in the Horn-Shunck method;

Δb a vector in the Farneback method;

Δx longitudinal separation (m) between phase-detection probe tips (herein Δx = 6.3 mm);

Δz transverse separation (m) between phase-detection probe tips (herein Δz = 2 mm);

εo,xy optical in-plane rate-of-shear (1/s)

dynamic viscosity (Pa.s) of water;

kinematic viscosity (m2/s) of water;

θ chute slope (herein θ = 45°);

density (kg/m3) of water;

τRmax lag between camera and phase-detection probe (s);

Ø diameter (m);

ωo,z optical spanwise vorticity (1/s).

Abbreviations

AEB advanced engineering building;

BIV bubble image velocimetry;

DOF depth of field;

vi

fps frames per second;

PIV particle image velocimetry;

px pixel;

SSD: sum of squared differences;

SSE sum of squared errors;

TKE turbulent kinetic energy;

UQ The University of Queensland.

1

1. INTRODUCTION

Stepped spillways are structures designed to achieve safe passage of floods (Fig. 1.1). The step

roughness enhances the rate of boundary layer growth and induces 'white waters', that is, free-

surface aeration (Chanson 1997,2001,2015). The entrainment of air leads to a rapid bulking in flow

depth and developments of complex flow patterns downstream of the inception point of aeration

(Matos 2000, Chanson and Toombes 2002). The interactions between air and water modify not only

the flow patterns but also velocity distributions, with profound design implications (Chanson et al.

2015). Velocity determination is therefore of fundamental importance in studies of stepped spillway

flows.

Investigations of stepped spillway flows were historically reliant on physical studies conducted in

large-size models (Horner 1969, Sorensen 1985, Toombes 2002, Gonzalez 2005, Meireles 2011,

Felder 2013). In most laboratory studies, velocity profiles were sampled with intrusive instruments

such as the dual-tip phase-detection conductivity and optical probes (Felder and Chanson 2015). A

correlation analysis is usually applied to determine an average interfacial velocity between the

leading and trailing tips (Jones and Delhaye 1976, Chanson 2002). Despite a reasonably high level

of accuracy, a fundamental limitation of intrusive multiphase flow techniques is their limited

resolution. The quality of the data is sensitive to the spatial configuration of the tips: i.e.,

measurements are unreliable if two sensors are spaced far apart. The data may also be adversely

impacted by the intrusive nature of the instrument: e.g. the leading tip of a dual-tip probe may affect

the trailing tip data. The use of cross-correlation implies that the underlying flow processes must be

assumed stationary (i.e. statistics remain invariant with a shift in time) and therefore unsuitable for

applications to transient flow conditions (Chanson 2005).

Recently, image-based velocimetry has become more attractive and accessible because of the

advancement in computational power. Integral techniques such as the well-established particle

image velocimetry (PIV) were successfully applied to non-aerated spillway flows (e.g. Amador et

al. 2006). Later studies used bubbles as tracer particles under ordinary lighting conditions (e.g.

Bung 2011, Leandro et al. 2014). This modified technique is known as bubble image velocimetry

(BIV) — first described in Ryu et al. (2005) and Ryu (2006). The BIV approach relies upon

interrogation of an image frame pair by computing the spatial cross-correlation. A limit of this

method is its discrete data nature which, for certain tracer size ranges, may cause displacement

vectors to be biased towards integer pixel values, commonly referred to as 'pixel locking' (Chen and

Katz 2005, Corpetti 2006). Direct computation of the correlation surface is expensive, and fast

implementations in the Fourier domain are constrained to displacements smaller than half of the

window size to prevent aliasing artefacts: i.e., obeying the Nyquist criteria (Corpetti 2006). Further,

2

any velocity or seeding gradient in the interrogation region (especially a large region) introduces a

bias towards smaller displacement. Another major limitation is the bias of the sidewall flow

conditions, where boundary friction cannot be neglected. BIV velocity data typically underestimates

the velocity field on the channel centreline, which is significantly larger than the near wall

velocities when measured by an intrusive probe.

Figure 1.1 – Hinze dam stepped spillway, Gold Coast (Australia) - = 51.3º, h = 1.2 m, Stepped

spillway width: W = 75 m (total), including the 12.25 m wide low-flow compound section - From

Top Right: view from downstream on 14 October 2016; general view from the right bank on 14

October 2016; details of the chamfered steps

In contrast to the PIV/BIV approach, the optical flow method is not well-known to the air-water

flow community (Bung and Valero 2016a,b). Liu et al. (2015) applied a modified global method

(i.e. Horn and Schunck 1981) to PIV images and extracted velocity fields with better accuracy and

much higher resolution than the traditional PIV. Bung and Valero (2016a,b,c) compared BIV and

optical flow estimates in seeded and aerated flows: they found comparable accuracies for both

methods, with the optical flow technique providing higher resolution data albeit requiring a much

3

longer computation time.

It is the aim of the present study to investigate the applicability and accuracy of two optical flow

methods applied to high-velocity air-water skimming flows on stepped spillways. The optical flow

inaccuracies caused by brightness variations were limited by the use of ultra-high-speed video

cinematography sampled at up to 22,067 fps at resolutions of up to 1280×800 pixels. The ultra-

high-speed video camera was carefully synchronised with a dual-tip phase-detection probe mounted

next to the wall to allow for direct comparison of the data. The optical flow methods are then

applied to obtain flow patterns and velocity fields in several aerated stepped spillway flows in large-

size physical models.

4

2. METHODOLOGY

2.1 PRESENTATION

The optical flow is defined as the apparent motion field between two consecutive images, and its

true physical meaning depends on the projective nature of the moving objects in 3D camera space.

Therefore, it is difficult to quantitatively connect the physical fluid velocity with the projection of

3D objects onto the image plane (i.e. R3→ R2 mapping) (Liu et al. 2015). Liu et al. (2015) proposed

a physics-based optical flow equation in the image plane:

( , )o

II f I

t

u x (2.1)

where I is the image intensity, T( , )o o ou vu is the optical flow in the image plane (i.e. screen

space), x is the image coordinate vector, and / ix is the spatial gradient in Equation (2.1).

The right-hand-side term summarises luminance variations due to diffusion, fluorescence,

scattering, absorption, and boundary effects of a scalar field quantity ψ, which could represent the

bubble density in BIV images. If the object velocities are essentially two-dimensional, then uo

( 'PP

, Fig. 2.1) is directly proportional to the particle velocity in the camera space ( 'OO

, Fig. 2.1).

This is illustrated in Figure 2.1, where xc, yc, and zc are the camera space coordinates originating

from a pinhole lens.

zc

xc yc

O

PO’

P’ DOF

Image plane

Figure 2.1 – Projection of object velocity onto the image plane (pinhole lens model)

The physical connection between optical flow and object velocities is evident in Eq. (2.1). In the

special case where ( , ) 0f I x and 0 0u , Equation (2.1) reduces to the classic brightness

constancy equation (Horn and Schunck 1981):

5

0o

II

t

u (2.2)

despite that the optical flow is not generally divergence-free (Liu et al. 2015). Note that the

differential nature of optical flow methods implies that they are best applied to continuous patterns,

though Liu et al. (2015) were able to extract velocity fields with better accuracy and much higher

resolution than the traditional PIV method when applying an optical flow method to PIV images.

Existing optical flow algorithms rely on computations of spatial and temporal derivatives to recover

the optical flow from an image pair. These techniques may be generally classified into local

methods (e.g. Lucas-Kanade 1981, Farneback 2003) and global approaches (e.g. Horn and Schunck

1981), which respectively attempt to maximise local and global energy-like expressions. For the

fluid mechanics community, the term 'optical flow' tended to be synonymous to the Horn and

Schunck (1981) approach in the recent literature (Corpetti et al. 2006, Liu and Shen 2008, Liu et al.

2015, Bung and Valero 2016a,b,c). This approach was favoured because it yields a dense estimate

of the flow field: every pixel is processed and an optical flow vector assigned. This is clearly

advantageous over traditional correlation based techniques, despite the relatively more expensive

computation time.

The classic Horn and Schunck method relies on minimising the following global energy functional:

2

( )

T

hs hs

IE I d

to o o ou u u u x (2.3)

where hs is a regularisation parameter governing penalties for large optical flow gradients: i.e., a

large hs results in a smoother flow field. The aperture problem (i.e. motion of a one-dimensional

structure can only be resolved in the direction of non-vanishing gradient) is thus addressed by the

above formulation, since, in regions where the data term is lacking (i.e. first term in the integral),

the regularisation term (i.e. second term in the integral) performs an implicit interpolation. Such a

global approach however provides no confidence measure in different image regions (Barron et al.

1994). The method may be more sensitive to noise than some local methods (i.e. Lucas-Kanade

1981) because the presence of noise increases the magnitude of the data term relative to the

regularisation term, effectively reducing the benefit of smoothing (Barron et al. 1994, Galvin et al.

1998, Bruhn et al. 2005).

Local methods, on the other hand, are generally robust to noise and often benefit from efficient

matrix computations. Efficient dense optical flow estimation is also achievable using local methods

as a result of more recent developments (Farneback 2003). The present investigation focuses on

applications of two local optical flow methods on aerated stepped chute flows: a Lagrangian method

and an Eulerian method. Section 2.2 presents the Lagrangian Lucas-Kanade method, which is

6

applied in Section 5.2 to provide a view of the flow pathlines. Section 2.3 details the Eulerian

Farneback method suitable for quantitative studies of flow patterns. Both algorithms are available in

the open source computer vision toolbox OpenCV 3.1.0.

2.2. LUCAS-KANADE METHOD

For an 8-bit grey level image, the brightness constancy constraint (Eq. (2.2)) implies:

( , , ) ( , , )im im im im im imI x y t I x dx y dy t dt (2.4)

where | 0 256I Z II is the 8-bit pixel intensity, xim and yim are the image plane coordinates

(origin at top left corner), and t is the time. Rewriting the right-hand-side using Taylor expansion

and eliminating higher order terms, it yields:

o

II

t

u (2.5)

where ( / , / )im imI I x I y is the spatial illuminance gradient vector. Equation (2.5) is

underdetermined, and additional constraints may be introduced by assuming that all pixels have

consistent motion in a window W(x) (Lucas and Kanade 1981):

T

0 1 1 0 1 1[ , ,..., ] [ , ,..., ]Tn nI I I I I I

t

ou (2.6)

where x = (xim, yim)T is the position in the image plane. The above inverse problem is usually solved

via an iterative method by minimising the sum of squared errors (SSE).

A suitable window W(x) for tracking must be stable over time and robust to noise, which typically

includes brightness variation, movements normal to the focal plane, and occlusion by other objects.

A feature suitable for tracking does not necessarily correspond to physical flow features. In fact,

most bubbles and droplets are not very-good tracking features, because they often enclose large

regions of approximately uniform light intensity (i.e. aperture problem). Conversely, a window may

be tracked with less effort if it contains large intensity gradients in all directions (i.e. a corner

region). Harris and Stephens (1988) discussed the edge tracking problem and proposed a sum of

squared differences (SSD) operator (i.e. Harris operator):

1( ) Tf d d M d (2.7)

2

1 2

( ) ( ) ( )

( ) ( ) ( )

x x yW W

x y yW W

I I I

I I I

x x

x x

x x x

Mx x x

(2.8)

where d = (Δxim, Δyim)T is a motion vector associated with the image patch. The eigenvalues of M1

are rotationally invariant and proportional to the principal curvatures of the local autocorrelation

function; thus M1 describes the intensity variations of a patch associated with a small shift. Since

7

the gradient information is integrated over W, the size of W inevitably affects the reliability of the

data. Indeed, Bruhn et al. (2005) found that the Lucas-Kanade method with large sizes of W is

particularly resistant to noise.

The existence of solution to Equation (2.6) depends on the invertibility of the matrix M1, since one

or more zero eigenvalues of M1 must indicate either an edge or a uniform region. The present study

used an improved method by Shi and Tomasi (1994) based on the smaller eigenvalue of M1 selected

according to the noise level of the image, which may be also used as a confidence measure of the

estimated optical flow uo (Bruhn et al. 2005). This typically picked up 'salt-and-pepper' textures,

visually corresponding to a mix of interfacial structures. Once a suitable patch is selected, Equation

(2.8) is solved iteratively to calculate the optical flow. The motion of the patch is updated at every

new frame, which provides a pseudo-Lagrangian view of the flow patterns (i.e. pathlines). This

method may be used for flow visualisation, something which cannot be achieved by traditional

PIV/BIV methods (though a PTV method may be applied to obtain bubble pathlines). Note that this

is also known as a sparse method because not all pixels in the image are processed.

2.3 FARNEBACK METHOD

Farneback (2003) introduced a novel technique based on polynomial expansions to estimate the

optical flow at every pixel location (i.e. dense estimate). This is conceptually equivalent to having a

virtual velocity probe in-situ at every pixel location sampled at the same frame rate as the camera,

and thus providing quantitative Eulerian information of the entire viewable flow field. According to

Farneback (2003), the intensity information in the neighbourhood of a pixel may be approximated

with a quadratic polynomial:

1 1 1 1( ) T Tf c x x A x b x (2.9)

where x is the pixel coordinate vector in a local coordinate system, A1 is a symmetric matrix, b1 is a

vector and c1 is a scalar. After a shift by d, the displaced neighbourhood may be obtained by

transforming the initial approximation:

2 2 2 2

1

1 1

( )

( )

T T

TT

f c

f

c

T T1 1 1 1

x x A x b x

x - d

x A x b - 2A d x d A d - b d

(2.10)

and the displacement is then solved by equating the coefficients of x:

2 ,

1

2

2 1 1

-11 1 2

b b A d

d A b b (2.11)

In principle, Equation (2.11) may be solved pointwise (i.e. at every pixel) and the solution may be

8

obtained iteratively starting from an a priori estimate of d. Large displacements may be treated by

first subsampling the image at a coarser resolution (i.e. image pyramid).

Farneback (2003) noted that the pointwise solution of Equation (2.11) is too noisy. Instead the

displacement may be assumed to be slow-varying and satisfy a neighbourhood W of x. This reduces

to a minimisation problem similar to that of Equation (2.6) and the solution is obtained for

(Farneback 2003):

1w w

T Td A A A Δb (2.12)

where w is a weighting function (indexes dropped for clarity), and:

21 2A (x)+ A (x)

A(x) = (2.13)

1

2 2 1Δb(x) = b (x) - b (x) (2.14)

It is interesting to note that that the solution of d depends on the invertibility of the square matrix

w T2M A A . An examination of the individual entries in M1 and M2 reveals some similarity and

difference between the Lucas-Kanade and Farneback methods respectively: M1 summarises the

gradient information in the vicinity of the pixel of interest, while M2 approximates the same

information with the coefficients for a local quadratic polynomial expansion. Consequently, a

smoother velocity field may be expected from the Farneback method because the gradient

information contained in M1 are more sensitive to noise and occlusion. In Farneback's (2003)

benchmark, the Farneback method was capable of processing 100% of the pixels, while lower

average and standard deviation of errors were observed in comparison to the classic Lucas-Kanade

method. Thus the Farneback approach combines benefits from both local (robust to noise) and

global (dense estimate) methods. Govindu (2006) evaluated the affine (i.e. straight lines remain

straight) flow estimation performance of several algorithms, in which the Farneback method

performed much superior in its original application (i.e. two frame motion estimation) than the

classical Horn-Schunck (1981) algorithm adopted by several previous studies

9

3. EXPERIMENTAL FACILITIES AND INSTRUMENTATION

3.1 EXPERIMENTAL FACILITIES

The present study was conducted in three large-size stepped spillway model configurations at the

University of Queensland with very calm inflow conditions. A smooth and stable discharge was

delivered by three pumps driven by adjustable frequency AC motors. The chute inflow was

controlled by an upstream broad crested weir, with its crest made of smooth, painted marine ply.

The model discharge was obtained by integrating measured velocity distributions above the

upstream broad-crested weir (Zhang and Chanson 2015,2016a) (Fig. 3.1):

3

11

20.8966 0.243

3crest

HQg H

W L

(3.1)

where W is the crest width (W = 0.985 m), H1 is the total upstream head above crest, and Lcrest is the

crest length (Lcrest = 0.60 m). The inflow conditions are further detailed in Zhang and Chanson

(2015,2016a).

Figure 3.1 – Photograph of flow above the upstream broad-crested weir – H1/Lcrest = 0.257, flow

direction from left to right

Figure 3.2 presents the stepped model configurations. The base model is a 45° stepped chute,

previously used by Zhang and Chanson (2015,2016a,b) (stepped spillway model I) (Fig. 3.2A). The

chute consists of 12 uniform steps made of smooth painted marine ply, each measuring 0.1 m × 0.1

m × 1.0 m (height × length × width). The second model (II) was built by blocking the step cavities

with up to 33% of the step height (Fig. 3.2B). Finally, stepped spillway model (III) was constructed

by including chamfers of 2 cm size to the uniform steps on model I, and removing the blockages in

model II (Fig. 3.2C). High-speed video investigations were conducted in models I and II, and the

validation studies were performed only in model III.

10

(A) Stepped spillway model I - configuration previously used by Zhang and Chanson (2015)

(B) Stepped spillway model II with partially blocked cavities

(C) Stepped spillway model III with chamfers at step edges - inset: details of chamfers

Figure 3.2 – Definition sketch of stepped spillway model configurations (units: mm)

11

3.2 INSTRUMENTATION

3.2.1 Dual-tip phase-detection probe

A dual-tip phase-detection probe was used to measure the air-water properties during the validation

tests (Section 4). The probe was designed and built at the University of Queensland (UQ) and its

basic design is sketched in Figure 3.3A. Each probe tip is needle-shaped with a silver tip (Ø = 0.25

mm) protruding from a stainless steel tubing (Ø = 0.8 mm). The system responds to resistivity

changes when the probe sensor is in contact with an air or water particle. The longitudinal distance

Δx between the tips was 6.3 mm. Each tip was sampled synchronously with the high-speed video

camera at 10 kHz per sensor for 10 s to 15 s. The probe was positioned 2 mm from the sidewall

during simultaneous recording with the ultra-high-speed camera (Fig. 3.3B)

(A) Sketch of probe design – Inset: view in elevation

(B) Probe position during validation tests on stepped spillway model III with chamfers at step edges

Figure 3.3 – Dual-tip phase detection probe system

12

3.2.2 Ultra-high-speed video camera

Detailed air-water flow features were documented using a Phantom® v2011 ultra-high-speed video

camera, equipped with a Nikkor 50mm f/1.4 lens, producing images with a negligible degree

(~1.3%) of barrel distortion. The typical camera setup is shown in Figure 3.4. A subset of video

movies was recorded with the camera tilted 45° in the streamwise direction, to achieve equal pixel

densities (px/mm) in the streamwise and normal directions (Fig. 3.4 inset). The camera is capable of

recording single-channel 12-bit images at up to 22,607 fps at a resolution of 1280×800 pixels. The

scene was illuminated with a 4×6 high intensity LED matrix and the light intensity was kept as

visually as uniform as possible1. The exposure time was 1 μs to ensure sharp images. The distance

between the near and far planes was expected to be of the order of 1 mm.

The high-speed video movies were converted to 8-bit bitmap images for ease of storage and

analysis. Image processing was performed with Python 2.7 and OpenCV 3.1.0 to yield two-

dimensional mean velocity, turbulence intensity, vorticity and turbulent kinetic energy fields.

Validation studies were performed with a synchronised setup consisting of the camera and phase-

detection probe mounted next to the wall. The camera was activated by a transistor-transistor logic

(TTL) pulse sent through a BNC trigger cable in synchrony with the analogue input sample clock

on the acquisition device. The latency between two devices was typically less than 1 ms.

3.3 EXPERIMENTAL FLOW CONDITIONS

Extensive physical measurements were performed on a total of three stepped spillway model setups,

with three main configurations including uniform triangular steps (I), modified step cavities (II),

and chamfered steps (III). All geometries investigated are summarised in Figure 3.2.

A list of experimental flow conditions is provided in Table 3.1.

1 The LED matrix was not synchronised with the camera. In practice, void waves were observed in the

skimming flow and these contributed to some non-uniformity of the light intensity.

13

Figure 3.4 – Typical ultra-high-speed video camera setup (with alternative configuration)

Table 3.1 – Summary of ultra-high-speed video experiments

Model θ (°) h (m) W (m) λ/k Q (m3/s) dc/h Re(1) Locations

I 45 0.1 1.0 2 0.083 – 0.113 0.90 – 1.10 3.3×105 – 4.5×105 steps 5 – 8

II 45 0.1 1.0 3 0.083 – 0.147 0.90 – 1.10 3.3×105 – 5.9×105 steps 5 – 7

III 45 0.1 1.0 2.33 0.083 – 0.113 0.90(2) – 1.10 3.3×105 – 4.5×105 steps 6 – 8

Notes: (1) – Re = 4q/ν; (2) – Validation tests performed with synchronised phase-detection probe.

14

4. VALIDATION TECHNIQUES

4.1 PRESENTATION

Two series of validation tests were designed to evaluate the performance of the synchronised

camera and phase-detection probe setup, as well as to examine the differences between optical and

phase-detection probe signal outputs. Physical meanings of the optical signal and the lag between

instruments are examined in the water drop test (Section 4.2). Direct comparisons between optical

flow and phase-detection probe data for an aerated flow above chamfered steps (model III) are

provided in Section 4.3.

4.2 WATER DROP TEST

The quality of the synchronisation between the dual-tip phase detection probe and ultra-high-speed

video camera was ascertained by conducting a simple water drop test. During the test, the phase-

detection probe sensors were mounted vertically facing upwards (Fig. 4.1) and small water globules

were dropped onto the leading sensor using a hand-held syringe. The video camera lens was

focused on the probe tip area using a large aperture setting (f/1.4), and brightness variations were

recorded as droplets were penetrated by the probe tips. Both the camera and phase-detection probe

were sampled simultaneously and synchronously at 10 kHz for 10 s. The test was repeated for a

total of 5 times.

Figure 4.1 illustrates a high-speed image sequence of a typical droplet impacting the phase-

detection probe's leading tip. The pixel intensity observed at the leading-tip position was influenced

by the entry (piercing) and exit (drying) of the droplet (Figs. 4.1A and C respectively), but remained

approximately uniform during the penetration (Fig. 4.1B). The brightness information may be

further affected by droplet deformation causing changes in reflection, scatter, diffusion, and

absorption.

(A) Entry

(B) Penetration

(C) Exit

Figure 4.1 – High-speed image sequence of a droplet penetrated by the conductivity probe leading

15

tip (Δx = 6.3 mm, Δz = 2.0 mm)

t (s)

Vol

tage

(V

)

Lum

inan

ce

0 1 2 3 4 5 6 7 8 9 10-1 -60

-0.5 -30

0 0

0.5 30

1 60

1.5 90

2 120

2.5 150

3 180

3.5 210

4 240

4.5 270

0 1 2 3 4 5 6 7 8 9 10-1 -60

-0.5 -30

0 0

0.5 30

1 60

1.5 90

2 120

2.5 150

3 180

3.5 210

4 240

4.5 270conductivity probecamera

(A) Raw conductivity probe and camera signals at leading tip

t (s)

Vol

tage

(V

)

Lum

inan

ce4.4 4.44 4.48 4.52 4.56 4.6

-2 -100

0 0

2 100

4 200

6 300

8 400

4.4 4.44 4.48 4.52 4.56 4.6-2 -100

0 0

2 100

4 200

6 300

8 400conductivity probecamera

(B) Raw conductivity probe and camera signals at leading tip (zoomed in)

Figure 4.2 – Raw conductivity and camera signals at the leading tip position during water drop test

Figure 4.2A compares the raw phase-detection probe leading tip signal, within 0 – 5 V, to the raw

camera luminance values, within 0 – 255, recorded at the same location. A preliminary review

indicated a good correspondence between the two signals, while the passages of droplets were

adequately captured by the camera. Upon further scrutiny, however, the phase information (i.e. air

or water) was lost in the camera data (Fig. 4.2B). Therefore, the luminance information alone

should not be regarded as a reliable indicator of any phase-related quantity, such as the local void

fraction C.

The brightness variation, observed by the camera, appeared to be mostly associated with the light

16

refraction caused by the piercing of a thin film separating air and water: i.e., the air-water interface.

For the signal shown in Figure 4.2, the absolute derivative responses of the raw probe and camera

signals, calculated using a central difference filter, are plotted in Figure 4.3. The good

correspondence between signals observed in Figure 4.2A is reproduced in Figure 4.3A. Close-up

views show that each phase shift (air-to-water or water-to-air) is typically associated with two

pronounced changes in luminance, which are respectively related to the probe sensor tip's piercing

into and exit from an air-water film (Fig. 4.3B). Importantly, the ultra-high-speed camera signal is

able to capture the same subset of interfacial information in the phase-detection conductivity probe

signal, albeit its sensitivity to noise because the central difference scheme is a high-pass filter.

t (s)

|d/d

t(V

olta

ge)|

(V/s

)

|d/d

t(L

umin

ance

)| (1

/s)

0 2 4 6 8 100 0

6000 200000

12000 400000

18000 600000

24000 800000

30000 1000000conductivity probecamera

(A) Derivatives of raw conductivity probe and camera signals at leading tip

t (s)

|d/d

t(V

olta

ge)|

(V/s

)

|d/d

t(L

umin

ance

)| (1

/s)

4.4 4.44 4.48 4.52 4.56 4.60 0

5000 200000

10000 400000

15000 600000

20000 800000

25000 1000000conductivity probecamera

(B) Derivatives of raw conductivity probe and camera signals at leading tip (zoomed in)

Figure 4.3 – Derivatives of raw conductivity and camera signals at the leading tip position.

The quality of synchronisation between the phase-detection probe and ultra-high-speed camera was

17

checked using the normalised cross-correlation between their respective absolute derivative signals

containing the interfacial information. The results are summarised in Table 4.1, where Rmax is the

maximum normalised cross-correlation coefficient and τRmax is the corresponding time lag

indicating the synchronisation delay between the sensors. Herein a positive lag means that the

camera started sampling earlier than the conductivity probe. The correlation between the two

systems was typically weak, ranging between 0.2 – 0.3, because of some effect of noise. The

synchronisation lag between the sensors was found to be of the same order of the sampling interval

(i.e. 0.0001 s), with the camera triggered slightly before the conductivity probe. For a sampling

duration of 15 s (used in subsequent validation experiment), this represented a mismatch of

approximately 0.003%, using a typical time lag τRmax = 4×10-4 s, deemed satisfactory for present

purposes.

Table 4.1 – Time delay between phase-detection conductivity probe and ultra-high-speed video

camera signals (Present study)

Run Rmax τRmax (s)

1 0.243 4×10-4 2 0.266 5×10-4 3 0.308 3×10-4 4 0.264 6×10-4 5 0.206 6×10-4

4.3 SKIMMING FLOW ABOVE CHAMFERED STEPS

4.3.1 Presentation

To understand and assess the suitability of the ultra-high-speed video camera applied to high-

velocity air-water flows, validation studies were performed in a skimming flow above chamfered

steps (stepped spillway model III) using the synchronised high-speed video camera and phase-

detection probe system. Photographs are shown in Figure 4.4, where dc is the critical depth (dc =

(q2/g)1/3) and h is the vertical step height (i.e. drop height) (h = 0.1 m). The leading tip of the phase-

detection probe was located at approximately 2 mm from the channel sidewall and it was

observable directly from the camera. Brightness variations at the probe tip locations indicated

passages of air-water interfaces. The camera and phase-detection probe were sampled at 10 kHz for

15 s during all experiments. The sampling rate and duration were selected as a reasonable balance

between high sampling rate and data storage requirement.

18

(A) t = 0.0 s

(B) t = 4.5 s

(C) t = 9.0 s

Figure 4.4 – Synchronous high-speed video camera and conductivity probe sampling in a skimming

flow over chamfered steps - Flow conditions: dc/h = 0.9, data recorded between step edges 6 – 7,

flow from right to left - The brightness variations at the probe tip locations give indication of

passages of air-water interfaces

The synchronous setup was sampled at 12 different normal elevations y at the same streamwise

position x. The resulting void fraction and bubble count rate distributions are presented in

dimensionless form in Figure 4.5. In Figure 4.5, the centreline data are shown for comparison. The

void fraction profile showed an S-shape typically observed in skimming flows above triangular,

pooled and porous steps (e.g. Chanson and Toombes 2002, Felder and Chanson 2011, Wuthrich and

Chanson 2014, Zhang and Chanson 2017). The wall data showed smaller void fraction values

compared to the centreline data set. The theoretical profile derived by Chanson and Toombes

(2002) is plotted for comparison and shows a good agreement with the experimental data, despite

differences for y/dc < 0.3 because cavity effects were not accounted for (Fig. 4.5A). The bubble

count rate distribution showed smaller values next to the wall than those at the channel centreline

(Fig. 4.5B). The data followed a characteristic shape, with a marked maximum at about y/dc = 0.2 –

0.3 (C = 0.1 – 0.2). This is in contrast to typical channel centreline observations and experimental

data on triangular steps for which the maximum bubble count rate occurs for C = 0.4 – 0.5 (e.g.

Chanson and Toombes 2002, Toombes and Chanson 2008). The interfacial velocity was

substantially smaller near the wall than at the channel centreline by up to 20%.

While this has been rarely acknowledged in the literature, the present void fraction and bubble

count rate data suggests that the air-water flow properties next to the sidewall might not be

representative of the channel centreline properties.

19

C

y/d c

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1C (Wall)C (Centreline)Chanson and Toombes (2002)

(A) void fraction

Fd c/Uc

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

0.8

0.9

1Fd c/Uc (Wall)Fd c/Uc (Centreline)

(B) bubble count rate

Uaw/Uc

y/d c

2 2.5 3 3.50

0.2

0.4

0.6

0.8

1Uaw/Uc (Wall)Uaw/Uc (Centreline)

(C) interfacial velocity

Figure 4.5 – Dimensionless void fraction and bubble count rate distributions in a skimming flow

above chamfered steps obtained with a phase-detection probe. Flow conditions: dc/h = 0.9, phase-

detection probe data recorded between step edges 6 – 7 - Wall leading tip data recorded at 2 mm

from the sidewall

4.3.2 Optical velocity and turbulence intensity fields

The luminance information interpreted by the camera at each pixel location is a complex function

that depends upon the lighting conditions and the local flow composition. The relationships

between local air-water flow parameters (i.e. void fraction C and bubble count rate F) and

luminance information (i.e. average luminance I, and standard deviation I’) are examined in Figure

4.6. In Figure 4.6, all data were normalised by first subtracting the mean (<>) and then dividing by

the l2-norm ( 2 2 21 2 ... nX X X X ). The correlation coefficients are given by the dot products

between pairs of normalised variables, specifically:

0.456cIR

C- < C > I- < I >

|| C |||| I || (4.1)

' 0.812cIR

' '

'

C- < C > I - < I >

|| C |||| I || (4.2)

0.081fIR

F- < F > I- < I >

|| F |||| I || (4.3)

' 0.596fIR

' '

'

F- < F > I - < I >

|| F |||| I || (4.4)

The results suggested that the luminance standard deviation I’ was strongly correlated to the local

20

void fraction C (RcI = 0.812) and negatively correlated to the bubble count rate F (RfI = -0.596).

Since I’ is measured at one point (i.e. leading tip position), a smaller I’ must correspond to less

streamwise texture variation. The variation in I’ with C reflects structural changes in the flow: a

bubbly flow with a small C is visually more homogeneous than a spray region with a large C. On

the other hand, F is directly proportional to the number of interfaces per unit time and hence the

“tracer density” detected by the camera sensor. The average luminance I was a weak indicator for

the void fraction (RcI = 0.456) and independent of the bubble count rate (RfI = -0.081). This was

because: (1) the camera does not actually detect phase information: i.e., it makes no distinction

between air and water; (2) I is sensitive to lighting configuration; (3) the arithmetic average I is

sensitive to flow inhomogeneity (e.g. bubble size distribution at one location) and outliers (e.g.

proneness to extremely bright or dark spots because of flow or lighting conditions).

The above discussion has implications on the accuracy of velocity fields extracted using optical

flow methods. Large changes in luminance between successive frames violate the fundamental

assumption of brightness constancy (Eq. (2.2)). If the standard deviation of luminance I’ may be

used as a rough indicator, the most reliable velocity data are only obtained in low void fraction and

high bubble count rate regions, as implied by Figure 4.6.

(C<C>)/||C||

(I<

I>)/

||I||,

(I'<

I'>

)/||I

'||

-0.5 -0.3 -0.1 0.1 0.3 0.5

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

1

-0.5 -0.3 -0.1 0.1 0.3 0.5

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

1I I'

(A) Relationships between C, I and I’

(F<F>)/||F||

(I<

I>)/

||I||,

(I'<

I'>

)/||I

'||

-0.5 -0.3 -0.1 0.1 0.3 0.5

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

1

-0.5 -0.3 -0.1 0.1 0.3 0.5

-1

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

1I I'

(B) Relationships between F, I and I’

Figure 4.6 – Relationships between local air-water flow properties and luminance signals.

Figure 4.7A shows the contour plot of time-averaged streamwise optical flow field Uo derived from

149,999 consecutive image pairs, with a resolution of 384×384 pixels, recorded during 15 s. The

physical resolution of each image was 0.28 mm/px in both x- and y-directions. Polynomial

21

expansions (Eq. 2.9) were calculated for a neighbourhood size of 7 px (0.96 mm) smoothed with a

Gaussian window with a standard deviation of 1 px (0.28 mm). The averaging window size for

displacement was 15 px (4.2 mm). In Figure 4.7A, xim is the image longitudinal coordinate, y is the

normal distance to the pseudo-bottom, Lcav is the spacing between adjacent chamfer crest centrelines

(Lcav = 0.141 m), and Uc is the critical flow velocity (Uc = (g q)1/3). The velocity field shows an

accelerating flow from right to left, with the largest streamwise velocity occurring next to the

chamfer edge. A few artefacts (1) are clearly visible due to violation of the brightness constancy

assumption. Overall the data appeared unreliable for y/dc > 0.5 (C > 70%) because of intermittent

flow patterns (image features) in the upper region.

In Figure 4.7B, the optical flow velocity data (Uo) was extracted at the average streamwise position

of the leading and trailing tips, and compared to that of the dual-tip phase-detection probe (Uaw).

The centreline interfacial velocity profile is provided further for comparison. For completeness, the

void fraction profile and vertical positions corresponding to C = 0.3, 0.5 and 0.9 are shown in

Figure 4.7B. First the phase-detection probe velocity data were typically 10% to 25% smaller next

to the sidewall than on the channel centreline. The same phenomenon was shown in previous BIV

(Bung 2011) and optical flow studies using the Horn and Schunck method (e.g. Bung and Valero

2016c) and was likely caused by sidewall friction effects. Second the optical flow data showed a

good agreement with the phase-detection probe data for y/dc < 0.3 (C < 0.3), with the optical flow

being slightly smaller than the interfacial velocities. For y/dc > 0.3, increasing discrepancies

between optical flow and phase-detection probe velocity data were observed with increasing

elevations. These differences generally remained below 10% up to y/dc = 0.4 – 0.5 (C ≈ 0.5),

compared to as low as 2% for y/dc = 0.3 – 0.4 (Fig. 4.7C). For y/dc > 0.5, the optical flow should be

regarded as generally unreliable as seen in Figure 4.7C. For comparison, the standard deviation of

luminance I’ is plotted in Figure 4.7C. The I’ data display a close correspondence with the

uncertainties in optical flow velocity.

Overall, the present analysis suggests that the Farneback technique is rather reliable in determining

velocity field next to the sidewall up to C = 0.5 (i.e. y < Y50), but the data quality decreases rapidly

otherwise. However it must be stressed that the velocity field next to the sidewall may not be

representative of the centreline velocity distributions, and the sidewall velocity data (2) were

typically 10 – 25% smaller.

1 indicated by black arrows in Figure 4.7A. 2 Herein the phase-detection probe recorded interfacial velocities about 2 mm from the sidewall.

22

chamfer

glass stain

conductivityprobe

Step (chamfer) 7

Trapezoidal cavity between steps 6 – 7

(A) Streamwise optical flow field derived using the Farneback method (flow from right to left)

Uaw/Uc, Uo/Uc (m/s)

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

Y90

Y50

Y30

CUo

Uaw (Wall)Uaw (Centreline)

y/dc

|(Uo-

Uaw

)/U

aw| (

%)

I'0 0.2 0.4 0.6 0.8 1

0 15

8 18

16 21

24 24

32 27

40 30

48 33

56 36

64 39

72 42

80 45|error|I'

(B, Left) Optical flow and interfacial velocity profiles

(C, Right) Difference between optical flow and phase-detection probe data

Figure 4.7 – Comparison between optical flow and phase-detection probe data - Symbols: Uo:

streamwise optical flow, Uaw: streamwise interfacial velocity, Uc: critical flow velocity - Flow

conditions: dc/h = 0.9, step edges 6 – 7

Figure 4.8A presents the streamwise optical flow turbulence intensity field between step edges 6 – 7

for dc/h = 0.9, defined as:

23

'2o

oo

uTu

U (4.5a)

where '2ou is the characteristic magnitude of the streamwise optical flow fluctuations. This

definition of Tuo is comparable to that of the interfacial turbulence intensity:

'2aw

awaw

uTu

U (4.5b)

In Figure 4.8A, the data for y/dc > 0.5 were culled out because of unreliable estimates of Uo. The

present data were qualitatively consistent with those by Bung and Valero (2016c) despite being

smaller in magnitude. The Tuo values were generally of the order of 0.1, with the largest values

found next to the chamfer. Violations of the brightness constancy constraint could lead to erroneous

Tuo values, as seen around (xim/Lcav = 0.1, y/dc = 0.1) due to stained glass. Figure 4.8B compares

Tuo to the interfacial turbulence intensity Tuaw deduced from the synchronously sampled phase-

detection probe signals. The void fraction distribution is shown for completeness. The turbulence

intensity quantities did not seem directly comparable, as Tuaw was generally an order of magnitude

larger than Tuo, despite both instruments encoding similar information (i.e. interfaces). Importantly,

the Tuo distribution conforms to the general perception that flow fluctuations are the largest at

regions of significant vorticity/rate-of-strain, and might be used as another indicator for the

fluctuations in the flow field.

Step (chamfer) 7

Trapezoidal cavity between steps 6 – 7

Tuo, Tuaw

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

0.7Y90

Y50

Y30

TuawTuoC

(A) Tuo field between steps 6 – 7 (B) Comparison between Tuo and Tuaw

Figure 4.8 – Comparison between streamwise optical flow turbulence intensity and interfacial

24

turbulence intensity - Flow conditions: dc/h = 0.9, step edges 6 – 7

4.3.3 Effects of sampling rate

The differential nature of optical flow methods reflects a natural trade-off between accuracy and

storage requirements. A higher sampling rate may result in smoother gradient approximations and

satisfy better the brightness constancy constraint. Herein the effects of various sampling rates were

investigated between 500 Hz and 10,000 Hz, by sub-sampling the original video signal (3).

The percentage error (%) relative to the baseline (i.e. original video signal) in each case was

estimated as:

2

,

2

1(%) 100

sampo f o

n o

U Uerror

n U (4.6)

where n is the number of subsample sets, Uo,fsamp is the streamwise optical flow for a sampling rate

of fsamp, and Uo is the optical flow obtained from the original video (10,000 Hz). Figure 4.9 shows

the effects of sampling rate on the streamwise optical flow, for sampling rates from 5,000 Hz down

to 500 Hz (the total number of images is the same for all sampling rates). The results show a general

trend of increasing error with decreasing sampling rates. The largest errors were associated with

regions of large velocity gradients (e.g. next to the chamfer) or of low temporal homogeneity (yim >

200 px). Quantitatively, halving the original sampling rate (i.e. 5,000 Hz) typically results in less

than a 5% difference from the baseline case. Further reductions in sampling rate yielded errors

increasing to more than 10% especially in regions with large velocity gradients.

The effects of sampling rate on the streamwise turbulent optical flow is examined in Figure 4.10, in

which the percentage error relative to the base case was estimated as:

2'2 '2,

'2

1(%) 100

sampo f o

n o

u uerror

n u

(4.7)

where '2, sampo fu is the characteristic turbulent streamwise optical flow fluctuation for a sampling rate

of fsamp and '2ou is that of the baseline case (10,000 Hz). Increasing errors in '2

ou were observed

with decreasing sampling rate.

Contrary to the velocity data, the largest and smallest errors were respectively associated with 3 The original video signal was sampled at 10,000 Hz. An effective sampling rate of 5,000 Hz may be

simulated by sampling every 2nd frame of the original video i.e. the frame sets {0, 2, 4, …, 149,998} and {1,

3, 5, …, 149,999}. Subsampling every nth frame will result in n sets of subsamples.

25

regions of high visual homogeneity and those of large velocity gradients. This was caused naturally

by large turbulent fluctuations in regions with high levels of shear. Quantitatively, sampling rates

lower than 5,000 Hz largely result in more than 10% errors except in high shear regions. The

present results suggest that a minimum sampling rate of greater than 5,000 Hz is desirable

especially if turbulence properties are of interest.

(A) 5,000 Hz

(B) 2,000 Hz

(C) 1,000 Hz

(D) 500 Hz

Figure 4.9 – Uncertainties in streamwise optical flow estimation using different sampling rates

compared to the base case: (A) 5,000 Hz, (B) 2,000 Hz, (C) 1,000 Hz, (D) 500 Hz

26

(A) 5,000 Hz

(B) 2,000 Hz

(C) 1,000 Hz

(D) 500 Hz

Figure 4.10 – Effects of sampling rate on streamwise optical flow fluctuation

27

5. APPLICATION

5.1 PRESENTATION

Ultra-high-speed video observations were undertaken in aerated skimming flows over triangular

and trapezoidal stepped cavities: i.e., stepped spillway models I and II. The relevant geometries and

flow conditions are summarised in Section 2. The following subsections demonstrate the use of two

local optical flow methods applied to the ultra-high-speed camera data to visualise and analyse the

flow patterns. Specifically, the classic Lucas-Kanade method and the Farneback method were each

used to provide a pseudo-Lagrangian view of the fluid pathlines and to determine the apparent

velocity field. In the latter case, corresponding turbulence intensity, vorticity, rate-of-strain, and

turbulent kinetic energy (TKE) fields were also derived. The non-intrusive optical techniques may

complement traditional phase-detection probe data, especially in areas hard to reach by intrusive

instruments and provide further insights into complex aerated spillway flows. All video movies

were recorded at 22,607 Hz at a resolution of 1280×800 pixels for a duration of 1.472 s (33,286

frames).

5.2 FLOW PATTERNS

High speed videos were sampled at 22,607 Hz at a resolution of 1280×800 pixels, for several

skimming flow discharges above triangular (model I) and trapezoidal (model II) stepped cavities.

The Lucas-Kanade algorithm was applied to help visualise the flow pattern. Figure 5.1 shows

typical optical flow pathlines in both stepped spillway configurations, in which the flow direction is

from left to right. The videos were recorded at the same location (step edges 5 – 7) for the same

dimensionless discharge (dc/h = 0.9). For each video, 22,000 frames were analysed in sets of 1,000

frames as flow features (i.e. textured regions) grew unstable over time and might be lost if they

were occluded or exited the image boundaries. Each sub-clip provides a short-lived view of the flow

patterns for a duration of 0.044 s, and they are processed and aggregated to produce Figure 5.1,

which displays tracked pathlines for a duration of 0.973 s. Pathline termini were marked with green

circles. Note that the optical pathlines might be different from flow streamlines as a result of

unsteadiness over a small time scale.

Visually, the optical pathlines in both configurations divided the flow into a fast, skimming region

above the pseudo-bottom formed by the stepped edges (y > 0) and a slow, recirculating flow in the

cavities (y < 0). (Note that the average velocity of a tracked feature may be inferred from the length

of its pathline.) In the free-stream above the pseudo-bottom formed by the step edges, the pathlines

were mostly parallel albeit displaying some mild curvature next to the pseudo-bottom. The

observation was consistent with flow detachment above and re-attachment upstream of each step

28

edge to generate alternating low and high pressure zones (Zhang and Chanson 2016a). Beneath the

pseudo-bottom, the recirculating fluid appeared to be more stable in the triangular cavities (Fig.

5.1A) than in the trapezoidal cavities (Fig. 5.1B), implying some effect of stepped cavity geometry.

In the upper spray region, Figure 5.1A displays a strong upward ejection of droplets compared to

the smoother flow in Figure 5.1B. This was a result of intense turbulence and strong instabilities

next to the inception point (step edge 5 / 4 for model I / II). Overall, the present observations

demonstrated the applicability of the Lucas-Kanade method to visualise high-velocity air-water

flows on stepped chute.

5.3 QUANTITATIVE OBSERVATIONS

For the same videos described in the previous section, the Farneback method was applied to derive

quantitative optical flow information. Herein all results shown were obtained by analysing 33,286

frames sampled at 22,607 Hz corresponding to a duration of 1.472 s. For efficiency reasons the

original videos were sub-sampled at every 5th frame, equivalent to a sampling rate of 4,521 Hz. This

was expected to yield reasonable estimates especially of first-order quantities (i.e. average velocity,

see Section 4.2.3).

5.3.1 Mean flow field

Figures 5.2 and 5.3 show the normalised streamwise and normal optical flow fields (Uo and Vo) for

both spillway configurations, where xi is the streamwise position of the inception point and Lcav is

the step cavity length (Lcav = 141.4 mm). The stepped roughness was masked and void fraction

maps on the middle plane (obtained using a phase-detection probe) were provided for ease of

reference. Visually, the flow was supercritical and accelerated from left to right in both

configurations (Fig. 5.2A & Fig. 5.3A). The streamwise optical flow was slower above the

trapezoidal cavities, which was associated with an increase in the normal flow (Fig. 5.2B & Fig.

5.3B). This demonstrates that the cavity geometry can have an impact on the mean flow, as

previously shown (Takahashi et al. 2006, Gonzalez and Chanson 2008). Downstream of each step

edge, a strong shear layer develops and expands downward into the step cavity. The observation

was consistent with PIV results in a clear water skimming flow by Amador et al. (2006), BIV and

optical flow results in the aerated flow region by Bung (2011) and Bung and Valero (2016a), and

physical measurements in an aerated skimming flow by Felder and Chanson (2011).

29

(A) Pathlines above triangular cavities (frames 1 – 22,000)

(B) Pathlines above trapezoidal cavities (frames 1 – 22,000)

Figure 5.1 – Optical pathlines above triangular and trapezoidal cavities - Green points indicate

termini of pathlines - Flow conditions: dc/h = 0.9, steps 5 – 8, flow direction from left to right

30

(A) Streamwise optical flow field (Uo)

(B) Normal optical flow field (Vo)

(C) Void fraction map (on middle plane) – black dots indicate measurement locations

Figure 5.2 – Optical flow and void fraction distribution above triangular cavities - Flow conditions:

dc/h = 0.9, steps 5 – 8, flow from left to right; void fraction data obtained using a phase-detection

probe

31

(A) Streamwise optical flow field

(B) Normal optical flow field

(C) Void fraction map (on middle plane) – black dots indicate measurement locations

Figure 5.3 – Optical flow and void fraction distribution above trapezoidal cavities - Flow

conditions: dc/h = 0.9, steps 5 – 8, flow from left to right; void fraction data obtained using a phase-

detection probe

32

5.3.2 Mean flow deformation

The streamwise and normal optical flow components provide further information on the visual

deformation of the flow in different regions. Specifically, the optical spanwise vorticity and in-

plane rate-of-strain are defined as:

,o o

o z

V U

x y

(5.1)

,

o o

o xy

U V

y x (5.2)

where the derivative terms were estimated by convolving an optical flow field with the appropriate

Sobel operator of dimensions 3×3:

1 0 11

2 0 28

1 0 1x

oo

VV (5.3)

1 2 11

0 0 08

1 2 1y

oo

UU (5.4)

where * denotes convolution, and Uo and Vo are the streamwise and normal optical flow field (of

dimensions 800×1200 pixels) respectively. Note that the normalised Sobel operators place more

weight on adjacent pixels and therefore exhibit an averaging effect. The optical vorticity and rate-

of-shear fields for stepped spillway configurations I and II are shown in Figures 5.4 and 5.5. Both

the vorticity and rate-of-strain maps showed similar patterns and identified the step edge as a source

of significant turbulent production (i.e. under the turbulent viscosity hypothesis). High levels of

vorticity and shear strain rate were observed in the developing shear layer past each step edge,

which extend up to the flow impingement upon the next step edge. The present results were

qualitatively and quantitatively similar to those of Djenidi et al. (1999) on d-type roughness

boundary layer flows and of Amador et al. (2006) in clear water skimming flow. No significant

difference was found between different stepped configurations herein.

33

(A) Spanwise optical vorticity field

(B) In-plane optical rate-of-strain field

Figure 5.4 – Optical spanwise vorticity and in-plane rate-of-strain above triangular cavities - Flow

conditions: dc/h = 0.9, steps 5 – 8, flow from left to right

(A) Spanwise optical vorticity field

34

(B) In-plane optical rate-of-strain field

Figure 5.5 – Optical spanwise vorticity and in-plane rate-of-strain above trapezoidal cavities - Flow

conditions: dc/h = 0.9, steps 5 – 8, flow from left to right

5.3.3 Turbulence characteristics

The strength of visual flow fluctuations may be characterised by the streamwise optical flow

turbulence intensity '2 /o o oTu u U . Figure 5.6A and 5.7A show contour maps of Tuo for the two

stepped configurations. In the overflow (y > 0), Tuo is predominantly of O(0.1) with maximum

values next to the pseudo-bottom. Very large Tuo values exceeding 100% were observed in the

cavities, partly on account of the much smaller mean velocities. The general trend for Tuo was in

agreement with that found by Bung and Valero (2016c), despite their use of a global method (Horn-

Schunck) on only 100 frames at 1,220 Hz. Herein the dominant Tuo values were much larger than

those reported for smooth open channel flows (Nezu and Nakagawa 1993, Nezu 2005).

Figures 5.6B and 5.7B show contour maps of the optical turbulent kinetic energy estimated from the

streamwise and normal optical flow components, using the same definition as Amador et al. (2006):

'2 '23

4o o ok u v (5.5)

For both stepped spillway configurations, the largest ko were observed next to the pseudo-bottom.

This was corroborated by the high rate-of-shear identified in this region (Fig. 5.4 & Fig. 5.5) which

removes energy from the mean flow above. The optical turbulent kinetic energy estimates ko were

much larger for the trapezoidal cavities (model II) than for the triangular cavities (model I), which

implied a larger rate of energy dissipation. This might explain the lower mean velocity field

observed in Figure 5.3A. It could be caused by instabilities associated with the more irregular cavity

shape. The dominant ko values ranged between 0.2 – 0.4 m2/s2, consistent with findings by Amador

et al. (2006) in a clear water skimming flow using a PIV technique.

35

(A) Optical streamwise turbulence intensity field

(B) Optical turbulent kinetic energy field

Figure 5.6 – Optical turbulence properties above triangular cavities. Flow conditions: dc/h = 0.9,

steps 5 – 8, flow from left to right

(A) Optical streamwise turbulence intensity field

36

(B) Optical turbulent kinetic energy field

Figure 5.7 – Optical turbulence properties above trapezoidal cavities. Flow conditions: dc/h = 0.9,

steps 5 – 8, flow from left to right

37

6. CONCLUSION

The present work explores the applicability of local optical flow methods to high-velocity air-water

flows on stepped spillways. Validation studies were performed in a large-size stepped spillway

model using a synchronised ultra-high-speed camera and phase-detection probe setup. Tests in two

large-size stepped spillway configurations demonstrated that the optical flow methods can provide

useful qualitative and quantitative information on complex air-water flow patterns.

The main conclusions may be summarised as follows:

(1) The high-speed video camera detects changes in brightness due to reflectance difference

associated with passages of air-water interfaces. The standard deviation of luminance correlates

with void fraction and bubble count rate, and may be used as a predictor for uncertainties in optical

flow estimation.

(2) The streamwise optical flow was in close agreement with those determined by the phase-

detection probe next to the sidewall, with increasing differences for C > 0.5. The reliability of

optical flow estimates was sensitive to velocity gradients and the sampling rate. For small regions

with large differences in motion vectors a minimum sampling rate of 5,000 Hz is desirable. This

sensitivity was amplified when estimating quantities beyond the first order such as the turbulence

intensity. Occlusions such as glass stain and large three dimensional movements also lead to locally

unreliable optical flow. These conclusions are expected to apply equally to both the Lucas-Kanade

method and the Farneback method due to similarity in their formulations.

(3) The optical flow technique characterises the air-water flow properties next to the channel

sidewall. In the sidewall region, the bubble count rate and interfacial velocity distributions were

found to be underestimated compared to the channel centreline interfacial properties.

(4) The Lucas-Kanade method may be used to help visualise the flow field by following small

textured regions along their pathlines. Application of the method revealed broadly similar flow

patterns in skimming flows above triangular and trapezoidal stepped cavities.

(5) The Farneback method can be used to efficiently estimate the instantaneous apparent velocity

field (less than 1 s per frame (1)). The results showed a slower flow motion above the trapezoidal

cavities than the triangular cavities. The flow deformation tensor may be derived from the mean

optical flow and suggested the step edge as a source of significant turbulence production. Second

order quantities such as the turbulence intensity and turbulent kinetic energy were also derived and

1 The Farneback calculation was performed on 1280×800 pixels per frame on a personal computer (PC) with

a processor i7-4790 at 3.60 GHz CPU (4 cores with hyperthreading), 16 GB RAM and Win64 OS. The

OpenCV implementation in C++ is CPU bound and single-threaded. The computation time on a single core

with the given parameters in the report is < 1 s per frame.

38

indicated stronger turbulence for the trapezoidal cavities than the triangular ones. The results were

comparable to those obtained with PIV in a clear water skimming flow.

Local optical flow techniques are efficient and robust methods applicable to complex air-water

flows. Being capable to assign a motion vector to each pixel is a major advantage in comparison to

conventional PIV techniques. Global methods may be used to overcome some limitations of local

methods such as sensitivity to velocity gradients or non-smoothness in weakly textured regions.

Further research is needed on the behaviours of different techniques in disparate flows.

39

7. ACKNOWLEDGMENTS

The authors thank Professor Daniel BUNG (FH Aachen, Germany) for his detailed review of the

report and very valuable comments. The writers acknowledge the technical assistance of Jason

VAN DER GEVEL and Stewart MATTHEWS (The University of Queensland, Australia). The

financial support of the Australian Research Council (ARC DP120100481) and of the University of

Queensland is acknowledged. Gangfu Zhang was the recipient of an Australian Postgraduate Award

(APA).

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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 & 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, 82 pages (ISBN 9781742720531).

AUD$60.00

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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

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 Flood Plain 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, 82 pages (ISBN 9781864999969).

AUD$60.00

DOCHERTY, N.J., and CHANSON, H. (2010). "Characterisation of Unsteady Turbulence in Breaking Tidal Bores including the Effects of Bed Roughness." Hydraulic Model Report No. CH76/10, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 112 pages (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 & 3 videos (ISBN 9781864999730).

AUD$60.00

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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

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 & 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

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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

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

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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 & HANDLING (per report) AUD$10.00 GRAND TOTAL

OTHER HYDRAULIC RESEARCH REPORTS

Reports/Theses Unit price Quantity Total price FELDER, S. (2013). "Air-Water Flow Properties on Stepped Spillways for Embankment Dams: Aeration, Energy Dissipation and Turbulence on Uniform, Non-Uniform and Pooled Stepped Chutes." Ph.D. thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia.

AUD$100.00

REICHSTETTER, M. (2011). "Hydraulic Modelling of Unsteady Open Channel Flow: Physical and Analytical Validation of Numerical Models of Positive and Negative Surges." MPhil thesis, School of Civil Engineering, The University of Queensland, Brisbane, Australia, 112 pages.

AUD$80.00

TREVETHAN, 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 & 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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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://http://www.civil.uq.edu.au// Email: enquiries@civil.uq.edu.au

Recent Research Report CE Unit price Quantity Total price CALLAGHAN, 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

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

HANDLING (per order) AUD$10.00 GRAND TOTAL

Note: Prices include postages and processing.

PAYMENT INFORMATION

1- VISA Card

Name on the card :

Visa card number :

Expiry date :

Amount :

AUD$ ...........................................

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2- Cheque/remittance payable to: THE UNIVERSITY OF QUEENSLAND and crossed "Not

Negotiable".

N.B. For overseas buyers, cheque payable in Australian Dollars drawn on an office in

Australia of a bank operating in Australia, payable to: THE UNIVERSITY OF

QUEENSLAND and crossed "Not Negotiable".

Orders of any Research Report 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://http://www.civil.uq.edu.au// Email: enquiries@civil.uq.edu.au