A novel acoustic forced vibration study for application in high temperature gas reactors
Excessive vibration of pipes, structures or components has been determined as one of the main causes of Nuclear Power Plant degradation. These vibrations can lead to potential damage of plant systems, structures and components, which can negatively impact the plant performance and safety integrity of an operational unit. Should resonance conditions be experienced due to the vibrations, the vibration can be further amplified and when this exceeds a permissible limit, potential failure of the structure can occur. In the nuclear environment being able to predict such phenomena is highly important. Specialised analysis provides a proactive risk management process to predict such phenomena before they occur. This approach is becoming more necessary and important during the design of new generation Nuclear Power Plants. This Research Report taps into this requirement and aims to provide a method in determining the acoustic pressure distribution for predicting high fluid vibrational areas or possible resonance conditions. Various methods have been employed by specialists to produce adequate acoustic solutions. In various papers by Cepkauskas, he introduces a transformation technique used to change the form of the problem to a nonhomogenous differential equation with homogenous boundary conditions by utilising an auxiliary function. Cepkauskas also demonstrated that, unlike other solutions produced, an auxiliary function defined on the interior of the media is unnecessary. In this Research Report, we investigate the Cepkauskas methodology and adapt it further by using a one dimensional wave equation and non-homogenous boundary conditions and through the transformation technique to produce four forcedvibration acoustic solutions with different boundary conditions existing in a pipeloop configuration. Specific Jolley series have been selected that ensure a proper representation of each of the four forced-vibration acoustic solutions. The Jolley series have been applied to determine the acoustic pressure distribution within a pipe over a series of incremental lengths and time. It is demonstrated that these acoustic forced-vibration solutions can be used to properly couple various individual pipes, while still maintaining the physical acoustic behaviour within the pipe-loop or a pipe system. A general acoustic subroutine is developed using the selected Jolley series and applied to specific conditions in two pipe-loop systems (general pipe-loop and a simplistic HTGR pipe-loop). For the HTGR pipe-loop, pipe geometries and fluid temperatures from a Computation Fluid Dynamic (CFD) software computer code, Flownex is used to calculated these conditions and provides the input for the acoustic loop subroutine model for steady state conditions. The series of unknown constants required at the pipe to pipe interface that are necessary to maintain pressure distribution and pressure gradient continuity, are solved via matrix operations and applying Kramers rule. In order to verify accuracy and gain confidence in the mathematics of this methodology, the subroutine is applied to two case studies, a general pipe-loop model and a model representing a simplified HTGR environment. This methodology can also be used to determine the natural and forced frequencies in a system to predict potential flow-induced vibrations or resonant conditions. It can also be used for other various applications that will be further elaborated on in this Research Report. The results of this study has led to the publication of this work at the 20th International Conference on Structural Mechanics in Reactor Technology, (SMiRT-20) in Finland on August 2009, Division V, Paper 1577, where it was open for judgement and no significant findings on this methodology were found, but received well by the conference.