TY - JOUR

T1 - Particle sizing using passive ultrasonic measurement of particle-wall impact vibrations

AU - Carson, G.

AU - Mulholland, A.J.

AU - Nordon, A.

AU - Tramontana, M.

AU - Gachagan, A.

AU - Hayward, G.

PY - 2008/10/21

Y1 - 2008/10/21

N2 - In continuously stirred reactor vessels the non-invasive recovery of the particle size could be used to monitor the reaction process. Experimental and numerical investigations have shown empirically that the frequency of the peak vibration response arising from the particle-wall impact is inversely proportional to the particle size. The passive monitoring of these impact vibrations using an ultrasonic transducer has the potential therefore of non-invasively recovering the particle size. However, the vessel geometry,
uid loading, variable impact position and velocity, stirrer
and transducer eects, and noise levels make this problem very complex. There are a large number of system parameters and this makes empirical derivations of cause and eects extremely dicult. The rst objective of this paper is to derive an analytical expression for the vibrations arising from a spherical particle impacting a circular plate. Using a series expansion in terms of the plate loss parameter, an
expression for the frequency of the peak pressure in terms of the system parameters is derived. In particular, its explicit dependency on the impacting particle size and
the impact velocity is found. The inverse problem of recovering the particle size from the experimental data is then investigated. A set of experiments are described
where the impact vibrations are recorded using an ultrasonic transducer attached to the rear of a thin plate. The results show that it is possible to recover the particle
size using this approach. Data from a second set of experiments, involving multi particle impact with a vessel wall in a continuously stirred reactor, are then used.
The inverse problem of recovering the particle size from the vibration spectrum was then investigated with encouraging results.

AB - In continuously stirred reactor vessels the non-invasive recovery of the particle size could be used to monitor the reaction process. Experimental and numerical investigations have shown empirically that the frequency of the peak vibration response arising from the particle-wall impact is inversely proportional to the particle size. The passive monitoring of these impact vibrations using an ultrasonic transducer has the potential therefore of non-invasively recovering the particle size. However, the vessel geometry,
uid loading, variable impact position and velocity, stirrer
and transducer eects, and noise levels make this problem very complex. There are a large number of system parameters and this makes empirical derivations of cause and eects extremely dicult. The rst objective of this paper is to derive an analytical expression for the vibrations arising from a spherical particle impacting a circular plate. Using a series expansion in terms of the plate loss parameter, an
expression for the frequency of the peak pressure in terms of the system parameters is derived. In particular, its explicit dependency on the impacting particle size and
the impact velocity is found. The inverse problem of recovering the particle size from the experimental data is then investigated. A set of experiments are described
where the impact vibrations are recorded using an ultrasonic transducer attached to the rear of a thin plate. The results show that it is possible to recover the particle
size using this approach. Data from a second set of experiments, involving multi particle impact with a vessel wall in a continuously stirred reactor, are then used.
The inverse problem of recovering the particle size from the vibration spectrum was then investigated with encouraging results.

KW - particle sizing

KW - passive ultrasonic measurement

KW - vessel wall vibrations

UR - http://dx.doi.org/10.1016/j.jsv.2008.03.005

U2 - 10.1016/j.jsv.2008.03.005

DO - 10.1016/j.jsv.2008.03.005

M3 - Article

VL - 317

SP - 142

EP - 157

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 1-2

ER -