Abstract
A mathematical model for predicting an unstable working condition called cycling of a pressure relief valve controlled by weight and spring is proposed. The valve is connected to a reservoir used to store liquid cargo by a long pipe. A transient, compressible and one-dimensional fluid dynamic equation in the pipe is numerically solved, with boundary conditions given by the valve and reservoir dynamics. The effect of valve moving part damping coefficient is analysed, which can be changed by adding dampers. Installing a damper may solve the cycling problem for weight-loaded and spring-loaded pressure relief valves. The damping coefficient of the installed damper should be carefully selected, especially for spring-loaded valves. Too large damping coefficient may cause overpressure in the reservoir when the valve opens and too low pressure when the valve closes. After all, installing damper is a theoretically possible way to prevent cycling occurrence when the pipe length is too long in some practical situations.
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