A theory on the vibrations of a fuel pin model in parallel two-phase flow

The equation of motion of the fuel pin model in the parallel two-phase flow is formulated by taking account of elastic restoring force; inertia force acting on the fuel pin model and on the virtual mass of the two-phase fluid; centrifugal force; Coriolis' force; the momentum change of the two-phase flow and damping effects. The resultant pressure difference between both the surfaces of the fuel pin model is employed into this equation as an external force. The author represents the distributions of the two-phase flow virtual mass, the damping effect and the resultant pressure difference in terms of delta function series. By substituting these distributions into the original equation and applying modal analysis techniques, the coupled ordinary differential equations with the time variant coefficients quasi-periodically changing are obtained. This paper can show the significant conclusion that there exist two main causes to the occurrence of an extraordinarily strong vibration of a fuel pin model in parallel two-phase flow; that is, the so-called parametric excitation due to the nearly periodic change of the virtual mass and the resonance of the fundamental vibration to the quasi-periodic external force resulting from the pressure fluctuations