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An effective method for the calculations of stress and residual strength of complex spatial pipelines at static and dynamic loading with taking into account the vibration of internal liquid and Puasson coupling is presented. It based on the well-known transfer matrix approach. The method utilizes the exact mechanical equations for the stress-strained state of straight beam with distributed mass, which connect unknown parameters of forces and displacements at the end of beam calculation element with the parameters at the beginning of the element. At that general solution scheme and calculation models are the same for static and dynamic calculations, the only differenceare the equations. Two different methods are used to find natural vibration frequencies of the distributed mass system: straightforward ("brute force") and quick, based on Williams-Wittrick frequencies counter. Within such counter a special procedure is developed for taking into account fluid vibration with consideration of volumetric balance condition at T-nozzles. The excellent accuracy of the method is demonstrated by the modeling of thinwalled, water filled pipe behavior after the rod impact.Two seismic analysis procedures are implemented on the base of developed method: standard response spectrum procedure and normal-mode summation procedure ("exact" dynamical), which uses accelerograms.These methods and procedures have been already implemented in calculation software complex for pipeline strength assessment with the possibility of building of arbitrary complexity models by the user-friendly, visual way. Their effectiveness is demonstrated by the seismic calculation for primary circuit pipings of Zaporizhia NPP.

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.

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This Paper presents an improved estimation of reactor core baffle temperature distribution, during operation, at the nominal power level to address swelling problems of the reactor internals. Swelling is the main limiting factor in the reactor core internals long term operation of VVER-1000 nuclear units. The material irradiation-induced swelling and creep models are very sensitive to temperature distribution in metal, thus a more detailed analysis of the core baffle metal thermohydraulic cooling characteristics is required. A framework for CFD analysis of VVER-1000 reactor baffle cooling is presented. Firstly, an analytical model was developed to obtain boundary conditions and simplify CFD analysis. Secondly, the CFD analysis was performed using 60 - degree symmetry, which included: core, baffle and core barrel, it is limited by the height of the baffle. Core is simplified as an equivalent coolant domain with considering of spatial volumetric energy release. Core baffle is presented as monolithic body with considering of gamma-ray heat generation. Model includes cooling ribs and simplified geometry of connecting studs, with cooling flow of the coolant through the nuts grooves. Calculated convection coefficient and temperature are in good agreement with analytical model, and give a more accurate result comparing to RELAP5/mod3.2. Obtained temperature field was used to estimate baffle swelling process and justify safe long term operation of the reactor internals.