Application of gamma-densitometry tomography to determine phase spatial variation in two-phase and three-phase bubbly flows Page: 1 of 7
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APPLICATION OF GAMMA-DENSITOMETRY TOMOGRAPHY
TO DETERMINE PHASE SPATIAL VARIATION IN
TWO-PHASE AND THREE-PHASE BUBBLY FLOWS*
J. R. Torczynski, D. R. Adkins, K. A. Shollenberger, and T. J. O'Hern
Engineering Sciences Center
Sandia National Laboratories
Albuquerque, New Mexico 87185-5800 DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor any of their
employees, makes any warranty, express or implied, or assumes any legal liability or responsi-
bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or
process disclosed, or represents that its use would not infringe privately owned rights. Refer-
ence herein to any specific commercial product, process, or service by trade name, trademark,
manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-
mendation, or favoring by the United States Government or any agency thereof. The views
and opinions of authors expressed herein do not necessarily state or reflect those of the
United States Government or any agency thereof.ABSTRACT
Gamma-densitometry tomography is applied to two-phase and
three-phase bubbly flows. Spatially resolved measurements of the
phase volume fractions are presented for air-water and air-water-
sand experiments at various airflow rates. For the conditions
examined, the presence of the solid particulate phase had only a
minimal effect on the gas volume fraction spatial variation.
NOMENCLATURE
cmn = inverse Abel transform coefficient (nondimensional)
dmn = forward Abel transform coefficients (nondimensional)
g = gravitational acceleration (cm/s2)
H = height of air-water interface during airflow (cm)
Hp = height of air-water interface without airflow (cm)
I = intensity (photon/s)
Io = incident intensity (photon/s)
i = data point index (positive integer)
L = path length through attenuating material (cm)
m, n = matrix indices (nonnegative integers)
p = pressure (dyne/cm2)
r = radial position (cm)
x = horizontal position (cm)
z = vertical position (cm)
= attenuation coefficient (cm )
p/p = mass attenuation coefficient (cm2/g)
p = mass density (g/cm3)
y = normalized attenuation coefficient (nondimensional)
= average value along path L
This work was performed at Sandia National Laboratories,
supported by the U. S. Department of Energy, under contract
number DE-AC04-94AL85000.INTRODUCTION
Knowledge of the spatial variations of phase volume fractions
in two-phase and three-phase flows is important in many industrial
processes such as indirect coal liquefaction, in which a reactive
gas is bubbled through a catalyst-laden liquid (a slurry). More
specifically, process efficiency can be affected adversely by
significant spatial nonuniformity in gas volume fraction, which
can induce large-scale buoyancy-driven recirculating flows. Thus,
it is important to be able to characterize the phase volume fraction
spatial variation in multiphase flows.
One method of characterizing the phase volume spatial
variation is gamma-densitometry tomography (GDT). The basic
physics of the interaction of gamma photons with matter is well
known (cf. Meyerhof (1967) or Lamarsh (1983)). In brief, there
are three interaction mechanisms: the photoelectric effect, pair
production, and Compton scattering. The first two are absorptive
(the gamma photon disappears), whereas the last one is not (the
energy and direction of the gamma photon change). These
processes cumulatively yield a mass attenuation coefficient p/p
(units of cm2/g), a constant depending only on the composition of
the material and the gamma photon energy. When multiplied by
the mass density p, here assumed to be constant, the attenuation
coefficient describes the attenuation of a gamma beam of
intensity I passing along a path of length L through the material:
I = Ioexp (-L) . If a mixture of two materials with different g
values is present along the path, a measurement of I/Io yields the
average attenuation coefficient along the path L, where the
value of p at each point along the path is linearly related to the
material volume fractions comprising the mixture at that point.
Measuring in this manner along many different paths provides
the information needed to perform a tomographic reconstruction
of the spatial variation of p and hence the volume fraction spatial
distribution of the materials comprising the mixture. The varieties
of tomographic reconstruction algorithms which accomplish this
DISTRIBUTION OF D C , fMITED
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Torczynski, J.R.; Adkins, D.R.; Shollenberger, K.A. & O`Hern, T.J. Application of gamma-densitometry tomography to determine phase spatial variation in two-phase and three-phase bubbly flows, article, December 31, 1995; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc672666/m1/1/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.