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Shadow imaging in bubbly gas–liquid two-phase flow in porous structures

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Abstract

Shadow imaging is used for the investigation of bubbly gas–liquid two-phase flow in a porous structure. The porous structure is made of Somos\({^{\textregistered }}\) WaterShed XC 11122, a clear epoxy resin used in rapid prototyping. Optical access is provided by using an aqueous solution of sodium iodide and zinc iodide having the same refractive index as the structure material (\(n = 1.515\)). Nitrogen is injected into the continuous phase at volumetric transport fractions in the range of \(\dot{\varepsilon } = 2.4-4.1\,\%\) resulting in a hold-up of \(\varepsilon = 0.94-2.17\,\%\). The obtained images of overlapping bubble shadows are processed to measure the bubble dimensions. Therefore, a new processing sequence is developed to determine bubble dimensions from overlapping bubble shadows by ellipse fitting. The accuracy of the bubble detection and sizing routine is assessed processing synthetic images. It is shown that the developed technique is suitable for volumetric two-phase flow measurements. Important global quantities such as gas hold-up and total interfacial area can be measured with only one camera. Operation parameters for gas–liquid two-phase flows are determined to improve mass and heat transfer between the phases.

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Abbreviations

A :

Area (mm2)

C :

Constant \(((\sqrt{\hbox {pix}}\,s){^{-1}})\)

D :

Sum of algebraic distances (−)

F :

Frequency threshold (Hz)

F :

Function (−)

L :

Length (mm)

Re :

Reynolds number (−)

V :

Volume (mm3)

\(a-f\) :

Coefficients (−)

\({\mathbf{{a}}}\) :

Coefficients vector (−)

a :

Major semi-axis (mm)

b :

Minor semi-axis (mm)

c :

Minor semi-axis (mm)

d :

Diameter (mm)

e :

Numerical eccentricity (−)

h :

Height (mm)

k :

Curvature (1/pix)

k :

Number of drawings (−)

n :

Refractive index (−)

p :

Sample size (−)

s :

Slip (−)

s :

Perimeter length (pix)

v :

Velocity (m/s)

\({\mathbf{{x}}}\) :

Variables vector (−)

x, y :

Positions (pix)

\(x^{\prime},y^{\prime}\) :

First-order derivatives (−)

\(x^{\prime\prime},y^{\prime\prime}\) :

Second-order derivatives (1/pix)

\(\epsilon\) :

Relative error (%)

\(\varepsilon\) :

Porosity (−)

\(\varepsilon\) :

Hold-up (%)

\(\dot{\varepsilon }\) :

Volumetric transport fraction (%)

\(\eta\) :

Dynamic viscosity (kg/(m s))

\(\rho\) :

Density (kg/m3)

\(\sigma\) :

Coefficient of variation (−)

\(\sigma\) :

Surface tension (mN/m)

\(\sigma\) :

Standard deviation (−)

32:

Sauter mean

a:

Major semi-axis

b:

Bubble

c:

Cell

e:

Edging

h:

Hydraulic

int:

Interstitial

l:

Liquid

mean:

Arithmetic mean

min:

Minimum

o:

Oblate

p:

Pore

pipe:

Pipe

pr:

Prolate

PU:

Periodic unit

sp:

Spherical

b/w:

Black and white

CAD:

Computer-aided design

FFT:

Fast Fourier transform

LED:

Light-emitting diode

PIV:

Particle image velocimetry

PMMA:

Polymethyl methacrylate

PTV:

Particle tracking velocimetry

PU:

Periodic unit

\(\hbox {P} \& \hbox {ID}\) :

Process and instrumentation diagram

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Acknowledgments

We gratefully acknowledge financial support from the Swiss Confederation’s innovation promotion agency (CTI) in cooperation with DSM Nutritional Products.

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Authors and Affiliations

  1. Institute of Process Engineering, ETH Zürich, Sonneggstrasse 3, 8092, Zürich, Switzerland

    Marco Altheimer, Richard Häfeli, Carmen Wälchli & Philipp Rudolf von Rohr

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  1. Marco Altheimer
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  2. Richard Häfeli
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  3. Carmen Wälchli
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  4. Philipp Rudolf von Rohr
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Correspondence to Marco Altheimer.

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Altheimer, M., Häfeli, R., Wälchli, C. et al. Shadow imaging in bubbly gas–liquid two-phase flow in porous structures. Exp Fluids 56, 177 (2015). https://doi.org/10.1007/s00348-015-2042-3

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  • DOI: https://doi.org/10.1007/s00348-015-2042-3

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