Modelling leaks in primary piping of nuclear power plants

Abstract

Leaks in pressurized tubes generate acoustic waves that propagate through the walls of these tubes, which can be captured by accelerometers or by acoustic emission sensors. The knowledge of how these walls can vibrate, or in another way, how these acoustic waves propagate in this material is fundamental in the detection and localization process of the leak source. The objective of this paper is to present an analytic model, through the derivation and solution of the motion equations of a cylindrical shell, which allows visualizing the behavior of the tube surface excited by a point source. Since the cylindrical surface has a closed pattern in the circumferential direction, waves that are beginning their trajectory will meet with another that has already completed the turn over the cylindrical shell, in the clockwise direction as well as in the counter clockwise direction, generating constructive and destructive interferences. After enough time of propagation, peaks and valleys in the shell surface are formed, which can be visualized through a graphic representation of the analytic solution. To check the theoretical results, measures were performed in an experimental setup, with the objective of mapping the tube surface accelerations and displacements when a point source is excited at several frequencies. The comparisons showed an excellent agreement between the theoretical results and the experimental mapping, validating thus the analytic model.