Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.3.4 - Turbulence Measurements in Air-Water Self-Aerated Flows: Basic Analysis and Results
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 Material Information
Title: 10.3.4 - Turbulence Measurements in Air-Water Self-Aerated Flows: Basic Analysis and Results Experimental Methods for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Chanson, H.
Felder, S.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: turbulence measurements
air-water flows
signal analysis
phase-detection probes
 Notes
Abstract: The two-phase gas-liquid flow properties of high-velocity open channel flows were studied experimentally in a large-size channel. The physical facility was equipped with a succession of triangular cavities associated with some strong interactions between air entrainment and flow turbulence. Detailed air-water flow measurements were collected with intrusive phase-detection probes for several flow conditions. The entire measurement technique was tested and a detailed sensitivity analysis was performed to assess the optimum sampling rate and duration. The new two-phase flow measurements demonstrated the high levels of turbulence in the high-speed, highly turbulent free-surface flows. These were highlighted by a strong rate of kinetic energy dissipation and dimensionless shear stress.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: 1034-Chanson-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Turbulence Measurements in Air-Water Self-Aerated Flows: Basic Analysis and Results


Hubert Chanson and Stefan Felder

The University of Queensland, School of Civil Engineering
Brisbane QLD 4072, Australia
E-mail: h.chanson@uq.edu.au


Keywords: turbulence measurements, air-water flows, signal analysis, phase-detection probes




Abstract

The two-phase gas-liquid flow properties of high-velocity open channel flows were studied experimentally in a large-size
channel. The physical facility was equipped with a succession of triangular cavities associated with some strong interactions
between air entrainment and flow turbulence. Detailed air-water flow measurements were collected with intrusive
phase-detection probes for several flow conditions. The entire measurement technique was tested and a detailed sensitivity
analysis was performed to assess the optimum sampling rate and duration. The new two-phase flow measurements
demonstrated the high levels of turbulence in the high-speed, highly turbulent free-surface flows. These were highlighted by a
strong rate of kinetic energy dissipation and dimensionless shear stress.


Introduction

In high-speed open channel flows, the interaction between
the highly turbulent waters and the atmosphere is associated
with some major deformation, twist and warp of the
free-surface. Across the air-water interface, some air is
continuously entrapped while water droplets are ejected.
The resulting air-water flow mixture extends through the
entire air-water column as illustrated by photographs and
laboratory observations (Kobus 1984, Wood 1991, Chanson
1997) (Fig. 1). The white waters are a complex two-phase
gas-liquid flow motion with the void fractions ranging from
small, often non-zero values close to the invert to 100%
above the free-surface. The latter is usually defined as the
location where the void fraction equals 90% because the
air-water flow behaves as a homogenous mixture below
while ejected droplets and splashing tend to have a free-fall
trajectory for void fractions larger than 95% (Cain and
Wood 1981, Chanson 1997, Chanson and Carosi 2007). A
basic feature of the white waters is the level of interactions
between the air-water structures and the turbulence
(Brocchini and Peregrine 2002, Chanson and Toombes 2002,
Chanson and Carosi 2007). Recent experimental findings
hinted that the intermediate region where the void fraction
ranges from 30% to 70% may play a major role in terms of
turbulent energy dissipation (Chanson and Carosi 2007,
Felder and Chanson 2009).
To date, relatively limited data are available on the
two-phase gas-liquid properties of these high-speed
free-surface flows despite five decades of experimental
measurements. A knowledge gap encompasses the
turbulence characteristics in the two-phase gas-liquid flow
region. The experimental methods rely primarily on the use
of intrusive phase-detection probes based upon the needle
probe design introduced in the 1960s (Neal and Bankoff


1963). The needle probe design is considered as the most
reliable intrusive phase detection probe design (Jones and
Delhaye 1973, Bachalo 1994, Chanson 1997). This type of
sensor is designed to pierce bubbles and droplets. The
sensor itself may be an optical fibre or
conductivity/resistivity probe. The principle behind the
optical probe is the change in optical index between the two
phases (Cartellier 1992, Cartellier and Barrau 1998). The
conductivity probe is based upon the difference in electrical
resistivity between air and water. (Herringe 1973, Serizawa
et al. 1975). While the most recent measurement techniques
are based upon the same sensor design, some recent
advances in signal processing led to some advancement and
new turbulence characteristic measurements (Chanson 2002,
Chanson and Carosi 2007b).
In the present study, the two-phase gas-liquid flow
properties of high-speed open channel flows were studied
experimentally in a large-size channel with triangular
cavities (Fig. 2). The physical facility was selected for the
level of strong interactions between air entrainment and
flow turbulence. Detailed turbulence data were collected
with intrusive phase-detection probes for several discharges.
First the entire measurement technique was tested and a
detailed sensitivity analysis was performed to assess the
effects of sampling rate and duration on the multiphase flow
properties. Using the validated metrology, data acquisition
and signal processing, some new two-phase flow
measurements were performed in the high-speed, highly
turbulent free-surface flows.






Paper No


the) l fctcriM vIcw ui m uanll spllway uptc1auu1 bcc11n 11ui
the left bank (shutter seed: 1/800 s)


(B) Details of the free-surface and white waters (shutter
speed: 1/1,000 s)
Figure 1: Free-surface aeration down the North Pine
spillway on 22 May 2009. Dam height: 40m, dam
completion: 1976.


Nomenclature

C void fraction defined as the volume of air per
unit volume of air and water
Cmean depth-averaged void fraction:
Yo
Cma = 1/Y90 fC dy
0
c instantaneous void fraction: c = 0 in water and c
= 1 in air
DH hydraulic diameter (m) or equivalent pipe
diameter
d equivalent clear water flow depth (m): d =
(1-Cmean)Y90
d, critical flow depth (m): d = Qw2 /(g W2)
E specific energy (m)
F bubble count rate (Hz) defined as half the
number of air-water interfaces impacting the


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

probe sensor per unit time
Fmax maximum bubble count rate (Hz) in a
cross-section
f Darcy-Weisbach friction factor
g gravitational constant (ms-1)
H total head (m)
Hmax upstream total head (m) above the sampling
location
h vertical step height (m)
K inverse of the dimensionless expansion rate of
the shear layer
L, distance (m) from the channel upstream end to
the onset of free-surface aeration
1 horizontal step length (m)
Qw water discharge (m3s1)
qw water discharge per unit width (m2s-')
Re Reynolds number defined as:
Re=pUDH /w
Tu turbulence intensity
Uw depth-averaged flow velocity (ms-1)
V air-water interfacial velocity (ms-1)
V90 characteristic velocity (ms-1) at y = Y90
W channel width (m)
x longitudinal distance (m)
Y90 characteristic distance (m) where C = 90%
y distance (m) normal to the pseudo-bottom
formed by the step edges

Greek letters
0 angle between the pseudo-bottom formed by the
step edges and the horizontal
p, water density (kgm-3)
gv water dynamic viscosity (Pas)

Subscripts
air air
max maximum value in a cross-section
w water
90 flow conditions were y = Y90


Broad-cres


d,- ,


Dcvloping '
bolundy a;.


mixini layer '

av) it vw o riuliunthe exper
(A) General view of the experiment






Paper No


A-- 'I Impact of large
Cavily Large vortical vertical structures
recirculatory motion structures on cavity wall
(B) Details of the cavity flow
Figure 2: Free-surface aeration in a skimming flow above
a stepped spillway


Experimental Facility and Instrumentation

New experiments were conducted at the University of
Queensland in a 3.2 m long, 1 m wide chute with flow rates
ranging from 0.014 to 0.250 m3s -. The chute consists of a
broad-crest followed by 10 identical steps (h= 0.10, 1 = 0.20
m, 26.6 slope). The open channel facility is a permanent
facility and the inflow quality has been verified in this and
previous studies (Jempson 2001, Gonzalez and Chanson
2007). Waters are supplied by a pump controlled with
adjustable frequency AC motor drive enabling an accurate
discharge adjustment. The water discharge was measured
from the upstream head above the crest, and the
head-discharge relationship was checked with detailed
velocity distribution measurements on the crest itself
(Gonzalez and Chanson 2007). The air-water flow
properties were measured using an array of two single-tip
resistivity probes (0 = 0.35 mm, Pt) and a double-tip
resistivity probe (0 = 0.25 mm, Pt). In the latter, the
longitudinal separation between tips was 7.5 mm. Both
phase detection probes were excited by an electronic system
(Ref. UQ82.518) designed with a response time less than 10
gs and calibrated with a square wave generator. The probe
signals were sampled at 20 kHz per sensor for 45 s (see
below).
The translation of the probes in the direction normal to the
pseudo-bottom formed by the step edges was controlled by a
fine adjustment traverse mechanism connected to a
MitutoyoTM digimatic scale unit with an accuracy of less
than 0.2 mm.

Experimental flow conditions
On a stepped chute, the waters flow as a succession of
free-falling nappes at low flow rates. At each step edge, the
flow takes off and hits the step below as a free-falling jet,
sometimes followed by a hydraulic jump. The energy
dissipation occurs by jet breakup in air, by jet impact the
following step, and with the formation of a fully developed
or partial hydraulic jump. At large flow rates with an


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

identical chute geometry (step height, mean slope), the
water skims over the pseudo-invert formed by the step
edges (i.e. skimming flow) as a coherent stream cushioned
by the recirculating fluid trapped between them (Fig. 2 & 3).
The external edges of the steps form a pseudo-bottom over
which the waters flow. In the triangular cavities, some
recirculating vortices develop and are maintained through
the transmission of shear stress from the water flowing past
the edge of the steps. At the upstream end, the flow is
non-aerated. After a few steps the flow is characterized by a
strong air entrainment and by vortices at the step toes (Fig. 2
& 3). For some intermediate discharges, a transition flow
regime is observed, characterized by a chaotic behaviour
and strong splashing and droplet projections downstream of
the inception point of free-surface aeration. The transition
flow exhibits some significant longitudinal variations in
flow properties between adjacent steps. The flow seems
very chaotic and does not present the coherent appearance
of skimming flows.
The present observations indicated a nappe flow regime for
dimensionless discharges do/h < 0.5 and a skimming flow
regime for d,/h > 0.9, where d, is the critical flow depth:
d, =Qw2 /(g W2) and h is the vertical step height. The
results were in agreement with the literature (Chanson
2001).
The air-water flow measurements were conducted with
dimensionless discharges d,/h between 1.01 and 1.85. The
probe sensors were located on the channel centreline at the
step edges for all flow rates. The flow conditions
corresponded to Reynolds numbers ranging from 4x105 to
1.0x 106 where Re = pwUwDH/tw with p, and Lw the water
density and viscosity respectively, Uw the flow velocity and
DH the hydraulic diameter (or equivalent pipe diameter).
The details are summarised in Table 1 and compared with
earlier studies conducted on slopes of 1:2.5 and 1:3.5 with
large Reynolds numbers to minimise the potential scale
effects. These were specifically discussed by Chanson
(2009) and Felder and Chanson (2009).


(A) dj/h = 1.15, Re = 4.85x10 inception of free-surface
aeration at step edge 4






Paper No


(B) d,/h = 1.85, Re = 9.9x10 inception of free-surface
aeration at step edge 8
Figure 3: Photographs of skimming flows (present study).

Ref. 0 h do/h Re Sampling
o m
Chanson & 15.9 0.10 0.63to 2x105to 20 kHz for 20s
Toombes 1.9 xl106 per sensor
(2002) 21.8 0.54 to 1.6x105 (0=0.025 mm)
1.49 to 7x105
Gonzalez& 15.9 0.05 0.7to 8x104to 20 kHzfor20s
Chanson 3.2 8x105 per sensor
(2004) 0.10 0.83 to 3x105 to (0=0.025 mm)
1.70 8.7x105
Chanson& 21.8 0.10 1.0to 3.8x105 20 kHz for 45s
Carosi 1.57 to per sensor
(2007) 7.1x105 (0=0.25 mm)
Felder& 21.8 0.05 1.17to 1.7x105 20 kHzfor45s
Chanson 3.05 to 6.9 per sensor
(2009) 105 (0=0.25 mm)
Present 26.6 0.10 1.0to 4x105to 20 kHzfor45s
study 1.85 lxl06 per sensor
(0=0.25 mm)

Table 1: Experimental investigations of air-water flow
properties down stepped chutes.



Signal Processing and Data Analysis

The measurement principle of phase-detection intrusive
probes is based upon the difference in optical index or
electrical resistivity between air and water. The intrusive
probe sensor is designed to pierce the incoming bubbles,
droplets and gas-liquid interfaces. A typical signal output is
shown in Figure 4. The signal processing may be conducted
on the raw signal output and on a thresholded "square wave"
signal (Fig. 4). The thresholded signal analysis relies upon
some arbitrary discrimination between the two phases. The
technique may be based upon single or multiple thresholds,
or some signal pattern recognition. The resulting
square-wave signal yields the instantaneous void fraction c:
c = 0 in water and c = 1 in air (Fig. 4B). It is used to
calculate the time-averaged void fraction, bubble count rate,
the air/water chord times, the bubble/droplet chord lengths
and their statistical moments (mean, median, std, skewness,
kurtosis), and the streamwise particle grouping analysis.
In high-velocity free-surface flows, the most robust
discrimination technique is the single threshold technique
with a threshold set at about 45-55% of the air-water


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

voltage range (Toombes 2002, Chanson and Carosi 2007b).
Figure 4B illustrates the single-threshold output using a
50% threshold.
A series of sensitivity analysis experiments were conducted
in the stepped chute to assess the effect of a number of
parameters on the two-phase flow properties. The flow
conditions are summarised in Table 2. A typical example is
presented in Figure 5, showing the effect of the single
threshold level on the time-averaged void fraction C and
bubble count rate F. The results suggest that a threshold
level between 25% and 85% has little effect on the void
fractions data as found by Herringe and Davies (1974), but
the bubble count rate data were more sensitive to the
threshold level (Fig. 5). Herein the experimental data were
processed with a single threshold set at 50% of the air-water
range that was deemed to be an optimum to investigate the
air-water column in the high-velocity free-surface flows.

Ref Q d,/h Re Flow Sampling
m3s-1 regime
TRA 0.058 0.70 2.3x105 Transition Step edge
10
SK 0.173 1.45 6.9xl05 Skimming Step edge
10


Table 2: Sensitivity analysis tests.


(A) Raw probe output


1 5
12
09
06
03
> 0
S-03
-0 6
-09
12


1 101 1 02 1 03 1 04 1 05 1 06 1 07 1 08 1 09 1 1
Time (s)
(B) Thresholded signal (single-treshold (50%))
Figure 4: Probe signal output: d,/h = 1.29, Re = 5.6x
step edge 9, C = 0.59, F = 161 Hz, V= 3.75 m/s.


(105,


I I I I34

26
22
18
14

S06
02
SLeading sensor 0:
Traling sensor






Paper No


0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1


15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Air-water threshold (%)
Figure 5: Effect of the air-water threshold on the
time-averaged void fraction C (x symbols) and bubble count
rate F (square symbols) in a high-velocity open channel flow.
Sampling rate: 20 kHz per sensor, sampling duration: 45 s,
sensor size: 0.25 mm.

Basic air-water flow properties
The time-averaged void fraction C is the proportion of time
that the probe sensor spends in the air. Past experiences
suggested that the sensor orientation has little effect on the
void fraction data, but it must be stressed that the
phase-detection probe sensors are designed to pierce the
bubbles/droplets with minimum interference. Simply the
probe sensor should face the bubbles/droplets as illustrated
in Figure 6. The bubble count rate F is defined as the
number of bubbles impacting the probe tip per second in a
bubbly flow. More generally, it is calculated as half the
number of gas-liquid interfaces detected by the probes. It is
noteworthy that the bubble count rate and void fraction are
related. In a free-surface flow, the experimental data showed
some form of parabolic relationship:
F
[1] = 4C (1 -C)
Fmax
where Fma is the maximum bubble frequency in the
cross-section. Toombes and Chanson (2008) demonstrated
the theoretical validity and advanced a more general
expression.
When two or more phase detection sensors are
simultaneously sampled, a correlation analysis provides
some additional information on the bubbly flow properties.
A well-known application is the use of dual tip probe in
which the two sensors are aligned with the flow direction
(Fig. 6). For a range of void fractions (0.02 < C < 0.98), a
cross-correlation analysis between the two probe sensor
outputs gives the time averaged interfacial velocity V. The
turbulence intensity Tu may be derived from the relative
width of the cross-correlation function (Chanson and
Toombes 2002). More generally, when two probe sensors
are separated by a transverse or longitudinal distance, their
signals may be analysed in terms of the auto- and
cross-correlation functions (Chanson and Carosi 2007).
Herein a detailed sensitivity analysis was conducted to
assess the impact of the air-water threshold, sampling rate
and duration on the basic air-water flow properties over the
entire air-water column (Table 2). Some basic results are
regrouped in Figures 5, 7 and 8. The results demonstrated


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

that the sampling frequency had to be greater than 10 kHz,
with little differences between the sampling rates of 20 and
40 kHz per sensor. The sampling duration had to be greater
than 20 s to have negligible effects on the void fraction,
bubble count rate and air-water velocity, while the advanced
correlation analyses including the estimate of the turbulence
intensity required a sampling duration of 45 s or larger.
Overall the findings justified the selection of the sampling
rate and duration (20 kHz, 45 s) used during the present
study.


Figure 6: Photograph of the dual-tip conductivity probe
(0 = 0.25 mm). Top: Three-quarter view, flow from bottom
left to top right, Re = 3.5x105. Bottom: Looking
downstream at the probe tip, d/h = 1.59, Re = 7.9x05.





0.8


0.6


0.4 y = 37 mm, SK v y = 4mm, TRA
S y = 60 mm, SK L y = 14mm, TRA
o y = 72 mm, SK o y = 56mm, TRA
0.2

V V V V V
0
1 2 3 4 5 6 78 10 20 30 40 50
Sampling frequency (kHz)
(A) Effect on the void fraction C


El - El - E -
_L< -X-





7--






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


1 2 3 4 5 6 7810
Sampling frequency (kHz)
(B) Effect on the bubble count rate F

4 i


20 30 40 50


Sy 7mm,SK V y 4mm, TRA
Sy 50mm,SK y 14mm, TRA
0 y 72 mm, SK 0 y 56 mm, TRA
1.5
1 2 3 4 5 6 78 10 20 30 40 50
Sampling frequency (kHz)
(C) Effect on the air-water interfacial velocity V
Figure 7: Effect of the sampling frequency on the void
fraction, bubble count rate and interfacial velocity
measurements in a high-velocity open channel flow.
Air-water threshold: 50%, sampling duration: 45 s, sensor
size: 0.25 mm.


1 2 3 4 567810 20 30 50 70100 200
Sampling duration (s)
(A) Effect on the void fraction C and bubble count rate F


1 2 3 4 567810 20 30 50 70100 200
Sampling duration (s)
(B) Effect on the air-water interfacial velocity V and
turbulence intensity Tu
Figure 8: Effect of the sampling duration on the void
fraction, bubble count rate, interfacial velocity and
turbulence intensity measurements in a high-velocity open
channel flow. Air-water threshold: 50%, sampling
frequency: 20 kHz, sensor size: 0.25 mm.


Basic Results

On the steep stepped chute, the open channel flow
non-aerated at the upstream end of the chute (Fig. 2A & 3).
The air entrainment occurred when the turbulent shear next
to the free-surface exceeded the resistance offered by
surface tension and buoyancy. Downstream, some intense
air-water mixing took place and large amounts of air were
entrained. The observations indicated some very-strong
interactions between main stream turbulence, step cavity
recirculation zones and free-surface which were associated
with some turbulent dissipative processes.
The location LI of the inception point of free-surface
aeration was observed. LI represents the longitudinal
distance measured from the downstream end of the
broad-crest (Fig. 2A). The results are presented in a
dimensionless form in Figure 9 in which the observations
are compared with the empirical correlation:
(2)
0.713
LI = 9.719 (sin )0.0796 qw 1
hcose g sin 0 (hcos )3

where 0 is the angle between the slope formed by the step
edges and the horizontal, qw is the water discharge per unit
width (q, = Qw/W) and g is the gravity acceleration.
Equation (2) was developed for and validated with
prototype and laboratory steep stepped chute data (Chanson
1994,2001). It is shown in Figure 4 for 0 = 26.60 and
compared with present and earlier experimental data sets.
All data highlighted that the location of the air entrainment
inception LI moved downstream with increasing flow rate.


Paper No


J '... A- - -
- -" - e
A ------



0 - -







y 37 mm, SK y 4 mm, TRA
y 60 mm, SK y 14mm, TRA
y 72 mm, SK o y 32 mm, TRA






Paper No


0-26.60, h=0.1 m
S0-21.80, h=0.05 m
0=21.80, h=0.1 m
S6-15.90, h=0.05 m
A 0-15.90, h=0.1 m
Correlation Chanson 0=26.6

-


-A
o A t






I I I I
0 2 4 6 8
.I'.i -I sin6 (h cos0)3)


I 0< A
0 0,
'^
'-,
o


10 12


Figure 9: Dimensionless location L1/(hcosO) of the
inception point of free-surface aeration on stepped spillways
- Comparison with Equation (2) calculated for 0 = 26.60

Air-water flow properties
Downstream of the inception point of free-surface aeration,
both visual observations and intrusive measurements
showed some substantial free-surface aeration, and the flow
aeration remained sustained downstream all along the chute
(Fig. 2 & 3). Figure 10 illustrates some typical
dimensionless distributions of void fraction, bubble count
rate and velocity downstream of the inception point.
In the skimming flow, the void fraction distributions
followed a smooth S-shape that was modelled by an
analytical solution of the advective diffusion for air bubbles:
/ 3 3

(3) C =1- tanh2 K'- D + (3D
2xDo 3Do


where y' = y/Y90, y is the distance measured normal to the
pseudo-invert formed by the step edges, Y90 is the
characteristic distance where C = 90%. K' is an integration
constant and Do is a function of the depth-averaged void
fraction Cmean only. Equation (3) was first developed by
Chanson and Toombes (2002) and it is compared with
experimental data in Figure 10.
The dimensionless distributions of bubble count rate showed
consistently a characteristic shape with a maximum value
Fmax observed for void fractions between 0.40 and 0.55. This
is seen in Figure 10 with the dimensionless count rate data
F/Fmax. A characteristic feature of all the experiments (not
shown in Fig. 10) was a distinct seesaw pattern in terms of
the dimensionless maximum bubble count rate Fmaxdc/Vc
and depth-averaged void fraction Cmean. The longitudinal
oscillations had a wave length of about two step cavities.
This pattern was observed for a range of slopes and step
heights (Boes 2000, Chanson and Toombes 2002, Yasuda
and Chanson 2003, Felder and Chanson 2009) and it is
thought to be caused by the strong interference between the
vortex shedding in the shear layers behind each step edge
and the free-surface (Fig. 2B & 3).
The dimensionless distributions of interfacial velocity
showed a self-similar shape. At each step edge, the velocity


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

distributions compared favourably with a power-law
function for y' = y/Y90 < 1 and with an uniform profile for
y/Y9o> 1:
(4) V _y'/N
V90
(5) V =
V90
where V90 is the characteristic air-water velocity at y = Y90.
Equations (6) and (7) are compared with the data in Figure
10. Herein, the velocity power law exponent 1/N was about
1/10 in average (i.e. N = 10), but it varied between adjacent
step edges. For example, in Figure 10, the velocity data
were close to a 1/7th power law. The fluctuations in velocity
power law exponent were believed to result from the
complicated interference between adjacent shear layers and
cavity flows.


1.4 Cdata
SX F data
0 V data
1.2 C theory
S- V 1/7th power law

1 U

8 0.8 --


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
C, F/Fmax, V/V90
Figure 10: Dimensionless distributions of void fraction C,
bubble count rate F/Fmax and velocity VV90 in air-water
skimming flows on a stepped spillway: do/h = 1.85, Re =
Ixl06, step edge 10, Y90 = 0.101 m, V90 = 4.54 m/s, Fmx =
76.4 Hz, Cmean = 0.21.

Typical distributions of turbulent intensity are presented in
Figure 11. The turbulent intensity profiles exhibited some
maximum turbulence level for 0.3 < y/Y90 < 0.7 (Fig. 11A).
The experimental data showed further a strong correlation
between the turbulence intensity Tu and the dimensionless
bubble count rate FdN/V. This is illustrated in Figure 11B
which presents the turbulence intensity Tu as a function of
the bubble count rate. The data collapsed reasonably well
into a linear trend:

(6) Tu= 0.35 +0.032 V

While the quantitative result differs from earlier studies
(Chanson and Carosi 2007), Equation (6) demonstrated a
monotonic increase in turbulence levels with an increase in
bubble count rate. The limit for zero bubble count rate (i.e.
Tu = 0.35) was close to monophase flow measurements on a
stepped chute and above d-type roughness (Amador et al.
2006, Tachie and Adane 2007). It is proposed that the
continuous twist and warp of the air-water interfacial
structure induced some large turbulence levels that were
measured by the double-tip conductivity probe.






Paper No


0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
C, Tu
(A) Normal distributions of turbulence intensity and void
fraction: d/h = 1.17, 1.29 & 1.77


F 0.8


0.6|


U -I
0 3 6 9 12 15 18 21 24 27 30
FdN/V
(B) Turbulence intensity versus bubble count rate: do/h =
1.02, 1.17 & 1.29 Comparison with Equation (6)
Figure 11: Dimensionless distributions of turbulence
intensity and void fraction in air-water skimming flows on a
stepped spillway: All measurements at step edge 10.

However the data scatter must be noted (Fig. 2). This was
typical to all data sets and it appeared to be related to some
variations in the auto-correlation function properties within
a cross-section.

Turbulent kinetic energy dissipation and boundary
friction
The rate of energy dissipation AH/Hmax was estimated at
several steps along the chute based upon the detailed
air-water flow measurements. Hmax is the upstream total
head above the step location, AH = Hmax E, and E is the
specific energy of the flow at the sampling location:

(7) E=dcosO+ U2
2g
where d is the equivalent clear water depth (d =
(1-Cmea)Y90) and Uw is the flow velocity (Uw = qw/d). The
total head H is proportional to the total energy per unit


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

volume and the specific energy E equals the total head using
the local bed elevation as potential energy reference
(Henderson 1966). The present results showed
systematically a decreasing rate of energy dissipation on the
stepped chute with increasing discharge from about
AH/Hma = 60% for dh/h < 1.2 down to 50% for d,/h = 1.85.
The trend was consistent with earlier studies (Matos 2000,
Chanson 1994,2001). The present results were obtained
with a fully-developed, aerated flow at the stepped chute
downstream end. For larger discharges, the flow might not
be fully-developed before the downstream end, and the rate
of turbulent energy dissipation could be considerably
smaller.
The high-velocity skimming flow was characterized by
some significant form losses (Fig. 2). Some dissipation
mechanisms are sketched in Figure 2B. Downstream of the
inception point of air entrainment, the average turbulent
shear stress between the high-speed flows and the
recirculation motion was deduced from the measured slope
of the total energy line. The dimensionless boundary shear
stress may be expressed in terms of a dimensionless friction
coefficient:

8 g -H Y(1 C)dy
(8) f o
U,2
where f is the equivalent Darcy-Weisbach friction factor of
the air-water skimming flow, and the term (-9H/9x) is the
slope of the total head line (Henderson 1966). The data are
presented in Figure 12 where the friction factor is shown as
a function of the dimensionless cavity height hcosO/DH,
where DH is the hydraulic diameter. hcosO represents the
cavity depth measured normal to the flow direction.
In average, the equivalent Darcy friction factor was f Z 0.22
downstream of the inception point of air entrainment for the
present study. The findings indicated larger turbulent shear
stresses than on a smooth chute and these were consistent
with experimental study of open channel flows past d-type
roughness (Coleman et al. 1997, Tachie and Adane 2007).
The present results are compared with earlier data sets
(Table 1) in Figure 12. All the laboratory data were close
and compared favourably with a simplified analytical model
of the maximum shear stress in the developing shear layer
downstream of each step edge. The latter may be expressed
in dimensionless form as: f=2 /(KJ) where 1/K is the
dimensionless expansion rate of the shear layer (Chanson et
al. 2002). The theoretical expression predicts f = 0.2 for K =
6 that is close to the observations (Fig. 12).


I I I1 I I I I I I I I I I I I I I I

A
A -

E h 1
[] -
5 A a -
S/--
E O0 E E
-- a
o a a



0 dc/h=l 02
A D dc/h=l 17
A dc/h=l 29
0 35 + 0 0325 x
1 1 1 1 1 1 1 1 1 1 1 I


1.4

1.2






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


5
3
2

1
0.7
0.5
^ 0.3
0.2


0.1
0.07
0.05
0.03
0.02
0.1


Figure 12: Friction f,
flows on a stepped cha


0.2 0.3 0.4 0.5 0.6 0.70.8 1
h cosO/DH
actor f for high-velocity air-water
nnel.


Discussion

In a high-speed skimming flow above the stepped, triangular
cavities, the basic mechanisms of turbulent dissipation
included cavity recirculation, momentum exchange with the
free stream, and interactions between free-surface and
mainstream turbulence. The interactions between mixing
layer and horizontal step face, and skin friction at the step
downstream end contributed to further energy dissipation on
moderate slopes (Lin and Rockwell 2001). At each step
edge, highly coherent small-scale vortices were formed
abruptly at the step corer because of the large gradient of
vorticity at the corer. The initial region of the mixing layer
was dominated by a train of sequential small-scale vortices
which paired to form large scale vortical structures that were
advected downstream. The three dimensional nature of
recirculating vortices is believed to play a role to further the
rate of energy dissipation. Gonzalez and Chanson (2008)
demonstrated quantitatively some means to enhance the
flow resistance with passive turbulence manipulation of the
cavity recirculation motion. More recently Carosi and
Chanson (2008) showed some turbulent energy dissipation
in the bulk of the aerated flow in the form of large-scale
vortices. The turbulent structures were produced in the
developing shear layers and cavity region, ejected into the
main flow and interacted with the "free-surface". The
dissipation process was linked with both the entrapment and
advection of air bubbles within the main flow and the
formation and ejection of water droplets above the
"free-surface".
Further features of the cavity recirculation motion included
the simultaneous occurrence of outflows of fluid from the
cavities as well as inflows into the cavities, together with a
sequential cavity ejection process. Visual observations
showed a pattern similar to the sequential ejection
phenomenon observed in boundary layer flow past d-type
roughness (Djenidi et al. 1999). Figure 13 presents a sketch
of two successive cavity ejection. It is believed that the
initiating mechanism for the cavity outflows is likely to be
triggered by the skimming flow rather than by the cavity
recirculatory motion (Djenidi et al. 1998, Gonzalez and


Chanson 2008).


of
-h

inflow
h f3 outflow


0=26 6, h=0 1 m
o 0=21 8, h=0 05 m
0=21 8, h=0 I m
A 015 9, h=0 05 m
A 0=15 9, h=0 I m
Mixing Layer model



0 mm

A A AA A


I I I I I I


Paper No


Mixing
Ivecr


recirculation region ',t il- .




shear layer ,

S .

luid ejection
SdJ ..,... (burst)




Figure 13: Sequential cavity ejection process in a
high-velocity skimming flow above a stepped chute. Sketch
representing the cavity ejections of two adjacent cavities.


Conclusions

The present study focused on high-velocity open channel
flows and the deformation, twist and warp of the
free-surface that are associated with major free-surface
aeration. The two-phase gas-liquid flow properties were
studied experimentally in a large-size channel with
triangular cavities. Some detailed measurements were
collected in the air-water flow with intrusive
phase-detection probes. The entire measurement technique
was tested and a detailed sensitivity analysis was performed
to assess an optimum sampling rate and duration. The
optimum sampling rate and duration were found to be 20
kHz and 45 s using a single-threshold technique set at 50%
of the air-water range. The experiments demonstrated that,
for the investigated flow conditions, the sampling rate had
to be greater than 10 kHz, with a sampling duration equal to
or larger than 45 s.
In the air-water skimming flows, the new two-phase flow
measurements demonstrated the high levels of turbulence in
the high-speed, highly turbulent free-surface flows. These
were highlighted by a strong rate of kinetic energy
dissipation and large dimensionless shear stresses. The
equivalent Darcy friction factor was f z 0.22 in average
downstream of the inception point of air entrainment. The
data compared favourably with a simplified analytical
model of the maximum shear stress in the developing shear
layer downstream of each step edge.
Lastly it must be stressed that most detailed gas-liquid flow
measurements were performed in laboratory under
controlled flow conditions. A challenge remains to conduct
field measurements in a prototype facility (e.g. Fig. 1)






Paper No


operating with Reynolds numbers typically between 10 and
109.


Acknowledgements

The authors acknowledge the technical assistance of Ahmed
Ibrahim, Graham Illidge and Clive Booth. Some
experimental measurements were undertaken by Rhys
Collins and Henry Cheung.


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