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The paper investigates longitudinal strain waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid situated both between the shells and within the inner shell. The study takes into account the effects that the following factors have upon the magnitude and velocity of the wave: viscosity, fluid motion inertia, the medium surrounding the outer shell, and structural damping in the shell material. As it is impossible to evaluate the strain wave models proposed via qualitative analysis methods, using numerical methods is necessary. We numerically investigated the model presented using a specific difference scheme to represent its equations, one similar to the Crank --- Nicolson scheme for the thermal conductivity equation. We show that the velocities and amplitudes of strain waves in the shells do not change when disregarding the following factors: the fluid inside the shell, structural damping in the shell material, and the influence of the surrounding elastic medium. The waves evolve in the positive direction of the abscissa axis. At the same time, taking nonlinearity into account leads to increased wave velocity as compared to the linear case, when the wave propagation velocity equals the speed of sound, which means the waves become supersonic. We performed a numerical study of this case and obtained results matching the exact solution. If we take into account the effect that the fluid motion inertia within the inner shell has upon the wave velocity, then a decrease in the strain wave velocity is observed. Taking into account the presence of an elastic medium surrounding the outer shell leads to an increase in velocity. Considering the viscous properties of the fluid within the inner shell and the damping properties of the shell material results in decreased strain wave magnitudes. The models proposed can form the basis for designing modern non-destructive testing devices
The paper investigates longitudinal strain waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid situated both between the shells and within the inner shell. The study takes into account the effects that the following factors have upon the magnitude and velocity of the wave: viscosity, fluid motion inertia, the medium surrounding the outer shell, and structural damping in the shell material. As it is impossible to evaluate the strain wave models proposed via qualitative analysis methods, using numerical methods is necessary. We numerically investigated the model presented using a specific difference scheme to represent its equations, one similar to the Crank --- Nicolson scheme for the thermal conductivity equation. We show that the velocities and amplitudes of strain waves in the shells do not change when disregarding the following factors: the fluid inside the shell, structural damping in the shell material, and the influence of the surrounding elastic medium. The waves evolve in the positive direction of the abscissa axis. At the same time, taking nonlinearity into account leads to increased wave velocity as compared to the linear case, when the wave propagation velocity equals the speed of sound, which means the waves become supersonic. We performed a numerical study of this case and obtained results matching the exact solution. If we take into account the effect that the fluid motion inertia within the inner shell has upon the wave velocity, then a decrease in the strain wave velocity is observed. Taking into account the presence of an elastic medium surrounding the outer shell leads to an increase in velocity. Considering the viscous properties of the fluid within the inner shell and the damping properties of the shell material results in decreased strain wave magnitudes. The models proposed can form the basis for designing modern non-destructive testing devices
As operational experience shows, it can hardly be excluded that some detached or loosened parts and even foreign objects (hereinafter referred to as the ‘loose parts’) may appear in the main circulation loop of VVER reactor plants. Naturally, the sooner such incidents are detected and evaluated, the more time will be available to eliminate or at least minimize damage to the reactor plant main equipment. The paper describes a method for localizing the impact of loose parts located in the coolant circulation circuit of a VVER reactor plant. To diagnose malfunctions of the reactor plant main equipment, it is necessary to accurately determine the place where the acoustic anomaly occurred. Therefore, if some loose parts make themselves felt, it is important to track the path of their movement along the main circulation circuit as well as their location using physical barriers. The method is based on the representation of the surface, along which an acoustic wave travels, as a 3D model of the reactor plant (RP) main circulation circuit. The model has the form of a graph in which the vertices characterize the control points on the RP surface and the edges are the distances between them. The method uses information about the acoustic wave velocity and the time difference of arrivals (TDOAs) of the signal received by various sensors. It is shown that, when the effect is received by more than three sensors, along with an estimate of the impact coordinate, it becomes possible to estimate the average acoustic wave velocity. To determine time of arrival, the signal dispersion change point detection method is used. Provided that the average size between the control points on the RP surface was 300 mm, the average localization error was about 600 mm. The developed algorithm can be easily adapted to any VVER reactor plant. The obtained deviation values are acceptable for practical use.
In VVER reactor plants, it is impossible to completely exclude the appearance of loose, loosely fixed and foreign objects in the main circulation circuit. Operational experience shows that early detection and estimation of the parameters of such incidents can provide the time required to eliminate or minimize damage to the main equipment of the reactor plant. For this reason, most modern power units with pressurized water reactors (PWR, VVER) are equipped with a loose parts monitoring system (LPMS). At the units under construction, these systems are laid down as standard ones; the power units put into commercial operation in the Soviet period were also equipped with them. The requirements for them are established by international standards. Ongoing research work in this area is aimed at determining the root cause of the acoustic anomaly and the localization of its epicenter. Also, no less significant are the works aimed at determining the mass of a loose object (LO). The most precise definition of this parameter will make it possible to have an idea of the nature of the LO before its withdrawal from the primary circuit and to conclude about whether this object is accidentally found or it is a detached part of the steam generators, main circulation pumps, internal devices or shut-off and control valves.
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