Stability and Self-sustained Oscillations in Nozzle-Flapper Valve with Pipe Line

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This paper discusses the stability of a system consisting of nozzle-flapper valve and a pipe line and several features of the self-sustained oscillations occurring in the system. Conclusions are as follows: (1) It is shown that the multiple modes of oscillations may simultaneously become unstable in a system with a long pipe line. (2) It is made clear that the most effective nonlinear characteristic for limiting the amplitude of the unstable oscillation is the collision of the flapper with the nozzle tip. (3) A basic equation of the system including the equivalent nonlinear terms for the collision is proposed and approximately analysed to derive the frequency and the amplitude of the self-sustained oscillations. (4) The selective occurrence of a self-sustained oscillation is also investigated for a system having two unstable modes, and it is concluded that either of the two unstable modes selectively develops to a sustained oscillation.
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