Application of the Transfer Matrix Method to the Analysis of Hydro-Mechanical Vibration of NPP Piping

Abstract

The transfer matrix method (TMM) was used for description of harmonic vibrations of piping with transported medium. Apart from 12 well-known mechanical parameters which characterize the state of piping system in each cross section two additional parameters that characterize the vibration of the medium, namely its translation and pressure pulsations were considered. The solution of these equations, which take into account the Poisson contraction of the pipe wall, in the form suitable for the transfer matrix method application was derived. The biggest uncertainty in the analytical modeling is to adopt the boundary conditions for above mentioned 2 parameters for the considered piping section. To solve this problem of identification of the most probable induced frequency we developed the technique of choosing such boundary conditions at which the maximum of energy is confined within the considered piping section. The validity of the approach was tested on some analytical examples. This method was used to analyze the forced vibration of the second circuit loop of unit 1 Zaporizhia Nuclear Power Plant (ZNPP) with VVER-1000 (from Russian: Vodo-Vodyanoi Energetichesky Reactor; Water-Water Power Reactor) arising from turbulent eddies in the flow of steam. Natural frequencies and forms of mechanical, hydrodynamic, and related hydro-mechanical vibration were found, a number of recommendations were given to reduce the vibration levels.

Numerical procedure based on basis and correction solutions for axial stress calculation in pipelines passing through zones of mine subsidence

“…The general elementary solution for each small piece of pipeline is given in form convenient for transfer matrix method, TMM, application, which significantly reduce the number of unknowns (ideally, for any long pipeline we have only matrix with 4 independent unknowns). Other our examples of TMM applications for various 1D tasks are given in [21,22].…”