Several
technologically important processes/process equipment involve dispersed
gas-liquid flows, for example bubble columns, gas-liquid stirred vessels and
other process equipment used in chemical process industry. For efficient design
of these reactors/process equipment, along with the other flow/process
variables, measurements of gas volume fraction, bubble size and velocity
distribution are crucial. These measurements are not only important to improve
the understanding of underlying flow processes, but also to provide reliable
experimental data for the development and verification of 
reactor-scale/detailed CFD models used for design and performance optimization.

Over
the last few decades, several non-intrusive (i.e. photographic, laser Doppler anemometry (LDA) etc.) and intrusive techniques (i.e. voidage probes,
wire-mesh sensor, fiber optics etc.) have been developed and used for
measurements of bubble size and velocity distributions. While non-intrusive
techniques, especially photographic techniques, are most straight forward, but
are not suitable for measurement of bubble size distribution in dense/opaque
gas-liquid flow conditions. Therefore, intrusive techniques i.e. voidage probe,
wire mesh sensor etc. are used to measure the bubble size distribution in dense
gas-liquid flows. These measurement techniques provide measurements of chord
length distributions and conversion of chord length distribution to bubble size
distribution still continues to be a challenging problem.

In the present
study, ?in-house? developed dual tip voidage probe was used to measure the
bubble chord length distribution. Various methods have been suggested in the
literature to convert the chord length data to bubble size distribution. Clark
and Turton (1988) proposed a non-parametric method by using numerical backward
transformation that required more sample size to obtain a consistent bubble
size distribution. In case of less sample size, the method showed numerical
instability. Later, Liu et. al. (1996) proposed a
non-parametric analytical backward transformation method using Parzen window
that needs to be optimized by iterative process. The main advantage of these
method is that model does not require a prior assumption of the bubble shape
distribution. The disadvantage of aforementioned method is the requirement of
large data size and instability of backward transformation method. Keeping the
above mentioned disadvantages in the mind, Santana et.
al. (2006) proposed a method based on maximum entropy density. The method is
fast, stable and required less number of sample size. Most of the comparisons
of methods of converting bubble chord length to bubble size distribution
available in open literature are based on synthetically generated data with
known distribution (Rayleigh and bimodal). The experimental validation of these
method is not available in the literature. The objective of the present work is
to implement and validate above mentioned methods (numerical backward
transform, Parzen window and maximum entropy) in an ?in-house? developed
voidage fluctuation analysis tool (v-FAT) and verify the bubble size
distribution predicted by these methods using synthetic as well as experimental
data on bubble size distribution measured directly from high-speed imaging, for
bubbles of different shape.

Experiments
were performed in a rectangular bubble column of 5 cm width ´ 50 cm height ´ 2 cm depth, made of plexiglass, as
shown in Figure 1 (a). All the experiments were carried out using compressed
air as the gas phase and demineralized water as the liquid phase. Air was
injected through a needle sparger. The needle size was varied to generate
bubbles of different sizes. ?In-house? developed dual-tip voidage probes were used
for measurements of bubble rise velocity and bubble chord lengths inside the
column. A typical signal
acquired through the dual tip voidage probe with a sampling frequency of 5 kHz
is shown in Figure 2(a). An ?in-house? developed voidage
fluctuation analysis tool (v-FAT) was used for processing of voltage signals to
get bubble rise velocity and chord lengths. The raw signal contains noise which needs to be selectively
removed using appropriate noise removal threshold (NRT). After removing the
noise and baseline correction (as shown in Figure 2(b)), the signal was
normalized (Figure 2(c)) and converted into square peaks using appropriate
phase discrimination threshold (PDT) (Figure 2(d)). As shown in
Figure 2(d), the velocity of the j^th
bubble was calculated as where,
is
distance between the probe tips and.
The chord length of this j^th bubble was
calculated as.
Further details of the voidage probes and data processing will be provided in
the full length manuscript.

Photographic
experiments were also carried out in the same column in the interrogation
window of 5 cm x 5 cm, using a high speed camera (Fastec Imaging, USA). The
images were acquired with a frame grabbing speed of 500 frames/s (see Figure
1(b) (i)) and were processed (see Figure 1(b) (ii)) using image processing
software to measure bubble size and bubble rise velocity distribution. These
measurements were further used to verify the different methods (numerical
backward transform, Parzen window and maximum entropy)
used for conversion of chord length to bubble size distribution. Further
results of the photographic measurements of bubble size and rise velocity
distribution will be provided in the full length manuscript.

The
synthetic data of chord lengths was generated from a known bubble size
distribution (Rayleigh and bimodal) for validation and analysis of the three
above-mentioned methods. The methods were implemented in the vFAT code to convert
chord length to size distribution and the resultant bubble size distribution
was compared with the original known (Rayleigh) size distribution as shown in
Figure 3(a). The maximum entropy method showed a good agreement with the
original bubble size distribution. It was also found that maximum entropy
method is numerically most stable. The numerical backward transform method was
found to become unstable as bin size was decreased or number of bins was
increased. It was also noticed that the accuracy of Parzen window method
depends on the Parzen?s window width.

Further
experiments were performed using the dual tip conductivity probes to measure
the chord length distribution for a needle sparger comprised of three needles
(ID= 0.8 mm) and gas flow rate of 2.77 cm³/s. The experimentally
obtained chord length distributions were converted to bubble size distribution
using the aforementioned methods. A comparison of the bubble size distribution
is shown in Figure 3(b). The actual bubble size distribution measured using
photography is also shown in Figure 3(b). It can be seen that the maximum
entropy method shows a good agreement with the photographic results. Further,
it can also be seen that the numerical backward transformation method leads to
unrealistic (negative) results for the bubble diameter in the range of 0-2 mm.
Experiments were also performed to calculate the bubble rise velocity
distribution and it was found that results obtained from the photographic and
dual tip probe techniques are in a good agreement (see Figure 4). Further
experiments will be performed for different needles size and gas flow rates to
generate bubbles of different shapes (i.e. spherical, ellipsoid etc.). With
appropriate selection of needles, bi-dispersed and poly-dispersed bubbly flows
will be generated. The experimental verification of bubble size and rise
velocity distribution calculated by different methods (implemented in v-FAT)
and photographic results for different bubble shape regimes and
bi-/poly-dispersed flows will be reported in full length manuscript.

The present
work will help to compare the predictive abilities of different methods to
convert chord length data to bubble size distribution and verify the
predictions using the experimental data. Such an experimental verification is very
much required for reliable measurements of bubble size distribution in
dispersed gas-liquid flows.

References

Clark,
N.N., Turton, R., 1988. Chord length distribution related to bubble size
distributions in multiphase flows. International Journal of Multiphase Flow 14,
413-424.

Liu,
W., Clark, N.N., Karamavruc, A.I., 1996. General
method for the transformation of chord length data to local bubble size
distribution. AIChE Journal 42,
2713-2720

Santana,
D., Rodriguez, J., Almendros-Ibanez, J.A., Martinez,
B.C., 2006. Characteristic lengths and maximum entropy from probe signals in
ellipsoidal bubble regime. International Journal of Multiphase Flow 32,
1123-1139