2. EXPERIMENTAL APPARATUS AND INSTRUMENTATION 2.1 Experimental apparatus

2. EXPERIMENTAL APPARATUS AND INSTRUMENTATION

2.1 Experimental apparatus

New experiments were performed in the Gordon McKay Hydraulics Laboratory at the University of Queensland. The experimental channel was previously used by CHANSON and TOOMBES (2001, 2002, 2003), CHANSON and GONZALEZ (2004), GONZALEZ (2005) and GONZALEZ et al. (2005).

A 1.5 m deep basin, whose surface area was 6.8 m * 4.8 m, provided water into a 1m wide stepped chute. The feeding basin was connected to the chute by a convergent sidewall with a 4.8:1 contraction ratio to minimize inflow turbulence.

The test section was a 1 m wide with an upstream 0.6 m long broad-crested weir with upstream rounded. The broad-crested weir was followed by ten identical marine ply steps (0.10 m high and 0.25 m long). The stepped chute ended with a horizontal concrete canal which led water into a pump sump (Figure 2.1 and Figure 2.2).

The pump was controlled by an adjustable frequency AC motor drive which permitted to regulate the flow rate and to have a steady discharge during the experiments.

Figure 2.2- General view of the experimental channel courtesy of Carlos A. Gonzalez

Experimental investigations were conducted for dimensionless flow rates dc/h between 1.0 and 1.57,

where dc is the critical depth and h is the step height (Table 2-1).

H1 [m] Flow rate [dc/h] Discharge qw [m2/s] Instrumentation 0.15 1.0 0.095 single-tip probe [Ø=0.35 mm] 0.173 1.15 0.116 _{double-tip probe[Ø=0.25 mm]} single-tip probe[Ø=0.35 mm] 0.20 1.33 0.143 single-tip probe [Ø=0.35 mm] 0.2175 1.45 0.161 single-tip probe[Ø=0.35 mm] double-tip probe[Ø=0.25 mm] 0.235 1.57 0.180 single-tip probe [Ø=0.35 mm]

Table 2-1 Summary of experimental flow conditions

2.2 Instrumentation

The instrumentation utilised to collect the data included: -Point gauges

-Single tip conductivity probe -Double tip conductivity probe

2.2.1 Point gauges

Clear water depth along the centreline of the channel was measured by two vertical point gauges. One was placed at the broad crested weir to measure the critical water depth dcrest; the other one was placed

at 0.66 m upstream the edge of the weir to measure the total head upstream the crest. Both point gauges are shown in Figure 2.3.

Figure 2.3- Point gauges courtesy of Carlos A. Gonzalez

Flow rates were estimated with the point gauge at 0.66 m upstream the edge of the weir. The discharges were calculated based upon detailed velocity distribution measurements above the weir crest by GONZALEZ (2005): 2 3 w 1 w 1

Q

H

2

q

1.013 0.37

g

(H )

W

W

3

⎛

⎞

⎛

⎞

=

=

_⎜

−

_⎟

⋅

_⎜

_⎟

⎝

⎠

⎝

⎠

H1 is the upstream total head above the broad crested weir crest;

∆z is the weir crest elevation W is the channel width.

This relationship was derived for 0.05≤H1/W≤0.22.

2.2.2 Conductivity probes

Air-water flow properties were measured with phase-detection intrusive probes: namely single-tip conductivity probes and double-tip conductivity probes (Figure 2.4).

The probes were developed at the Hydraulics Laboratory of the University of Queensland. They were excited by an electronic system (Ref. UQ82.518). The electronic system is called Air Bubble detector

and it was constructed by the New Zealand Institute for Industrial Research and Development. It was designed with a response time less than 10µs (Figure 2.5). When an air bubble or a droplet impacts on the probe the Air-Bubble detector translates the change in resistance into a voltage. The voltage signal could be read by a computer. In the present study, the signal output was scanned at 20 kHz for 45 s.

Figure 2.4- Single-tip conductivity probe courtesy of Carlos A. Gonzalez

2.2.2.1 Single tip conductivity probe

A single-tip probe was used to investigate air-water flow properties by measuring void fraction, bubble count rate and bubble chord size. The probe consisted of a sharpened rod (platinum wire Ø=0.35 mm) coated with non-conductive epoxy and set into a stainless steel surgical needle (Ø=1.42 mm) acting as the second electrode sketched in Figure 2.6.

The single-tip probe could detect bubbles larger than 0.35 mm.

When two single tip probes were used, the second probe was fixed at a known transverse distance ∆z from the reference probe by using a PVC spacer (Figure 2.7, Figure 2.8). In Figure 2.9 all different PVC spacer are shown.

Figure 2.6- Single-tip conductivity probe

Figure 2.7- Sketch of two single-tip conductivity probes separated by a known transverse distance ∆z

Figure 2.8- Two single-tip conductivity probes [Ø=0.35 mm, ∆z=6.3 mm] (A) view from downstream (B) view from a side

Figure 2.9- All PVC spacer used. They are marked in red with their thickness in mm.

2.2.2.2 Double tip conductivity probe

A double-tip probe was used to be able to measure the velocity, turbulence intensity and

chord-length. A double-tip probe is characterized by a second tip (trailing) behind the first,

which is the leading tip. The leading and the trailing tip are aligned along a streamline. Each

sensor consisted of a sharpened rod (platinum wire Ø=0.25 mm) which was insulated except

for its tip and set into a metal supporting tube (stainless steel surgical needle Ø=0.5 mm

(internal) and 0.8 mm (external)). The stainless steel tube acted as the second electrode and it

was separated from the inner wire by some insulating epoxy. The longitudinal and the

transverse spacing between probe sensors was measured with a microscope. This yielded

∆x=7.0, 9.6 mm and ∆z=1.4 mm as shown in Figure 2.10 and 2.11.

Figure 2.11- Double-tip conductivity probe [Ø=0.25 mm, ∆x=7.0 and ∆z=1.4 mm] Step edge 10. Flow rate: dc/h=1.5.

2.3 Data processing

The principle of conductivity probe measurement is based upon the difference in electrical resistivity between air and water. The resistance of water is one thousand times lower than the resistance of air bubbles. Thus, if the probe tip is in contact with water, current will flow between the tip and the supporting metal; if it is in contact with air no current will flow. When an air bubble impacts on the probe, the increase in resistance is converted into a sudden drop of the output voltage as it is sketched in Figure 2.12.In Figure 2.13 a typical signal output is shown.

Although the signal is theoretically rectangular, the probe response is not a square-wave signal because the transitions (from water to air and from air to water) are not instantaneous. This is due to the finite size of the tip, the wetting and drying time of the interface covering the tip and to the response time of the probe and electronics. A threshold voltage was selected to investigate the air-water flow properties: when the value of the voltage was higher than the selected threshold the probe tip was assumed to be in water, when it was lower than the selected threshold, the probe tip was assumed to be in air.

The threshold was set about 45-55% of the air-water voltage range. This choice was supported by previous analyses. The single threshold technique is defined by TOOMBES (2002) and CHANSON (2002) as the most suitable and reliable method to investigate the flows with a very wide range of void fraction, bubble frequency and bubbles/droplets size.

The air concentration or void fraction C is the proportion of time that the probe tip is in the air. Past experience showed that the probe orientation with the flow direction had little effect on the void fraction accuracy (e.g. SENE 1984, CHANSON 1998). This was checked with the present probes. In the present study, the probe tip was aligned with the main flow direction as shown in Figure 2.14 and in Figure 2.15.

The bubble count rate F is the number of bubbles impacting the probe tip per second. The measurement is sensitive to the probe tip size, bubble sizes and velocity. The air/water chord time is defined as the time spent by the air/water phase on the sensor. Bubble chord times were calculated from the raw signal.

Correlation and statistical analyses were done at each step edges for all discharges to investigate the air water flow properties.

Time [s] Vol tage [ V ] 1 1,1 1,2 1,3 1,4 1,5 0,4 0,8 1,2 1,6 2 2,4 2,8 3,2 3,6 4 4,4

Figure 2.13 A- Signal output of single-tip conductivity probe Flow rate: dc/h=1.5 Step edge 10, y=22 mm, C=0.105, F=111.6

Time [s] Vo lt age [ V ] 1 1,02 1,04 1,06 1,08 1,1 1,12 1,14 1,16 1,18 1,2 0 0,4 0,8 1,2 1,6 2 2,4 2,8 3,2 3,6 4 Trailing tip Leading tip

Figure 2.13 B- Signal output of single-tip conductivity probe Flow rate: dc/h=1.5 Step edge 10, y=22 mm, C=0.104, F=139.4

Figure 2.14- Single-tip probe [Ø=0.35 mm]. Flow rate: dc/h=1.57

2.3.1 Correlation analyses

When two probe sensors are separated by a transverse or streamwise distance and simultaneously sampled, their signal may be analysed in terms of auto-correlation and cross-correlation functions Rxx

and Rxy respectively. In the present study the correlation analyses were conducted on the raw probe

output signals. The original data of 900,000 samples were segmented and sub-divided into fifteen segments of 60,000 samples.

Basic correlation analysis results included the maximum cross-correlation coefficient (Rxy)max, the

characteristic time lag τ for which Rxx=0.5 (τ0.5)xx, the characteristic time lag τ for which

Rxy=0.5*(Rxy)max (τ0.5)xy, the time lag for which Rxy=0 (T0)xx, the time lag for which Rxy=0 (T0)xy. and

the integral time scales Txx Txy where:

xx (R 0) xx xx 0 T R ( )d τ=τ = τ= =

∫

_∫

Rxx is the normalised auto-correlation function

τ is the time lag

Rxy is the normalised cross-correlation function between the two probe output signals.

Txx represents the integral time scale of the longitudinal bubbly flow structures. It is a characteristic

time of the eddies advecting the air-water interfaces in the streamwise direction. Txy(z, x) is a

characteristic time scale of the vortices with a transverse length scale z or x advecting the air-water flow structure. The experiments were repeated with different transverse and longitudinal spacing z and with different double tip probes at the same step edge for same flow conditions with different transverse spacing z or with different longitudinal distance.

A correlation analysis may also provide additional air-water flow properties such as velocity and turbulence levels. The velocity measurement is based upon the estimation of the time taken to a bubble to go from the leading to the trailing tip. For flows characterized by a high level of turbulence it is not possible to detect all bubbles and it is not likely to happen that the bubble impacting on the leading tip is the same one impacting the trailing tip. For these reasons the cross-correlation technique is commonly used with large values of void fraction (C > 0.10) (CHANSON 1997, CROWE et al. 1998, CHANSON 2002).

In the present study, the air-water interfacial velocities were deduced from a correlation analysis between the two sensors of the double-tip probe. The time averaged velocity equals:

T

x

V

=

∆

T is the air- water interfacial travel time for which the cross-correlation function is maximum ∆x is the longitudinal distance between probe sensors.

Turbulence levels may be derived from the relative width of the cross-correlation function: 2 2 u ' T t Tu 0.851 V T ∆ − ∆ = ≈ ⋅ (2-5) where:

∆T is the value of the time scale satisfying Rxy(T+∆T)=Rxymax/2

Rxy is the normalised cross-correlation function (Rxymax is the maximum value).

∆t is the characteristic time for which the normalised autocorrelation function equals 0.5 T is the characteristic time for which the cross-correlation function is maximum.

Equation 2-8 characterises the turbulent velocity fluctuations in the streamwise distance (CHANSON and TOOMBES 2002). Physically, a thin narrow cross-correlation function ((∆T2_{- ∆t}2₎1/2 _{/T) << 1)}

must correspond to little fluctuations in the interfacial velocity, hence a small turbulence level Tu. Although Equation 2-8 might not be equal to the turbulence intensity u’/V, it can provide some average velocity fluctuations or some turbulence level.

2.3.2 Bubble chord calculations

A single-tip probe can provide the void fraction, the number of bubbles or droplets per second, which is the bubble count rate, and the bubbles/droplets chord time. The air/water chord time is defined as the time spent by the air/water phase on the probe sensor. Bubble chord times could be calculated from the raw signal and they were presented as probability distribution functions. For both air and water chord time distributions, mean, standard deviation, skewness and kurtosis were calculated.

The bubble chord time is related to the bubble chord size by the following expression:

ch

ch V t

= ⋅

ch is the bubble chord size which is not the diameter but a characteristic streamwise air/water size; tch is the air/water chord time,

V is the local interfacial velocity.

It is not possible to measure the interfacial velocity with a single tip probe. Thus the single-tip probe chord time results are presented in terms of pseudo-bubble/droplet chord size ch~ defined as:

w ch

ch U = ⋅t (2-7) where Uw is the mean flow velocity: Uw=qw/d , qw is the flow rate per unit width and d is the

equivalent clear-water depth. The pseudo chord size differs from the air/water chord length because the local interfacial velocity V is not equal to the mean flow velocity Uw. A re-analysis of some chord

size data of GONZALEZ et al. (2005) obtained in the same chute with smooth steps was done to assess the validity of pseudo chord size.

For the data set of GONZALEZ et al. (2005), a systematic comparison was conducted between true chord size and pseudo chord size data. Both data sets were measured with the same probe system (Ø=0.025 mm). The comparison showed that by using equation 2-9 the pseudo chord size overestimated the true chord size by 1.98% in average for C < 0.97. Two additional comparisons were

conducted to assess any difference induced by using different probe systems: a comparison between true chord sizes for two sensor sizes (Ø=0.025 mm and Ø=0.25 mm) and another one between two pseudo chord size data sets for Ø= 0.025 mm and Ø=0.35 mm. The true chord sizes measured with a 0.25 mm probe sensor were in average 18% larger than those measured with a 0.025 mm probe sensor; the pseudo chord sizes overestimated by 28% in average with the 0.35 mm probe sensor compared to those measured with the 0.025 mm probe sensor. All three comparisons and the results are detailed in Appendix C.

In the present study, air/water chord time data collected with a single tip probe (Ø=0.35 mm) will be presented in terms of pseudo-chord size because the results are easier to comprehend and to compare with visual observations. The data sets obtained with a double tip probe (Ø=0.25 mm) will be presented in terms of true chord size because the interfacial velocity V can be provided.

2.4 Experimental procedure

The stepped chute geometry consisted of ten identical steps which were 0.10 m high and 0.25 m long. This corresponded to a 22° slope. Two rails were attached to the sidewall and a trolley carrying the instruments could move parallel to the pseudo bottom formed by the step edges. The probes were fixed on the trolley and their translation was controlled by a fine adjustment travelling mechanism connected to a MitutoyoTM _{digimatic scale unit, whose accuracy is 0.025 mm. All measurements were}

conducted downstream of the inception point, on the channel centreline (z=0) and at step edges, with y=0 at the pseudo bottom. When two single tip probes were used, the reference probe was placed on the channel centreline (z=0) and the second probe was fixed at a known transverse distance z.

For each discharge, the probe was moved from y=0 up to y=150 mm. Data were recorded at 20 kHz for 45 s with a minimum of 30 measurement points per cross section. This represented 900,000 samples per measurement point.