# The use of acoustic inversion to estimate the bubble size distribution in pipelines

Timothy G. Leighton, Kyungmin Baik, Jian Jiang

## Abstract

The most popular technique for estimating the gas bubble size distribution (BSD) in liquids is through the inversion of measured attenuation and/or sound speed of a travelling wave. The model inherent in such inversions never exactly matches the conditions of the measurement, and the size of the resulting error (which could well be small in quasi-free field conditions) cannot be quantified if only a free field code exists. Users may be unaware of errors because, with sufficient regularization, such inversions can always be made to produce an answer, the accuracy of which is unknown unless independent (e.g. optical) measurements are made. This study was commissioned to assess the size of this error for the mercury-filled steel pipelines of the target test facility (TTF) of the spallation neutron source at Oak Ridge National Laboratory, TN, USA. Large errors in estimating the BSD (greater than 1000% overcounts/undercounts) are predicted. A new inversion technique appropriate for pipelines such as TTF gives good BSD estimations if the frequency range is sufficiently broad. However, it also shows that implementation of the planned reduction in frequency bandwidth for the TTF bubble sensor would make even this inversion insufficient to obtain an accurate BSD in TTF.

## Acknowledgements

This work is supported by the ORNL, TN, USA. ORNL is managed by UT-Battelle, LLC, under contract DE-AC05-00OR22725 for the US Department of Energy; and by the UK Science and Technology Facilities Council (STFC). The authors thank B. Riemer and M. Wendel (ORNL) and C. Densham, O. Caretta and T. Davenne (STFC) and Ron Roy of Boston University for advice, discussions and access to facilities.