Symmetric velocity profiles reconstruction in channels with a circular cross-section by ultrasonic flow measurements

This article presents an effective approach to the problem of full characterization and reconstruction of flow velocity profiles at each point of a circular cross-section of a transport channel in a radial symmetry case. The approach is based on the application of special multi-sensor flow meters designed for high-precision measurements of differences between the propagation times in ultrasonic signals recorded in parallel measurement planes and on solving an Abel-type integral equation – a well-known ill-posed problem. In our case, the problem can be formulated as a well-posed one according to Tikhonov by a reasonable use of a priori information about the velocity distribution. A practical algorithm is provided for determining an error in the reconstructed profile. All algorithms considered in the study can be utilized in the case of limited experimental data.