A synthesis of previous literature is used to derive a model of an in-service direct-spring pressure relief valve. The model couples low-order rigid body mechanics for the valve to one-dimensional gas dynamics within the pipe. Detailed laboratory experiments are also presented for three different commercially available values, for varying mass flow rates and length of inlet pipe. In each case, violent oscillation is found to occur beyond a critical pipe length, which may be triggered either on valve opening or closing. The test results compare favorably to the simulations using the model. In particular, the model reveals that the mechanism of instability is a Hopf bifurcation (flutter instability) involving the fundamental, quarter-wave pipe mode. Furthermore, the concept of the effective area of the valve as a function of valve lift is shown to be useful in explaining sudden jumps observed in the test data. It is argued that these instabilities are not alleviated by the 3% inlet line loss criterion that has recently been proposed as an industry standard.

A previous study of gas-service direct-spring pressure relief valves connected to a tank via a straight pipe is continued by deriving a reduced-order model for predicting oscillatory instabilities such as valve flutter and chatter. The reduction process uses collocation to take into account a finite number N of acoustic pressure waves within the pipe, resulting in a set of 2N + 3 ordinary differential equations. Following a novel non-dimensionalization, it is shown analytically that the model can exhibit, at experimentally realistic parameter values, instabilities associated with coupling between the valve and acoustic waves in the pipe. The thresholds for each instability are such that for a given flow rate, the first mode to go unstable as the inlet pipe length increases is the quarter-wave mode, then a three-quarter wave, a 5/4-wave etc. Thus the primary mode of instability should always be due to the quarter wave. In the limit of low flow rates, a simple approximate expression is found for the quarter-wave instability threshold in the form of inlet pipe length against mass flow rate. This threshold curve is found to agree well with simulation of the full model. For higher flow rates there is a need to include fluid convection, inlet pressure loss and pipe friction in order to get good agreement. The reduced model enables the dependence of the stability curve on key dimensionless physical parameters to be readily computed.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractPrevious studies into direct-spring pressure relief valves connected to a tank via a straight pipe are adapted to take account of liquid sonic velocity. Good agreement is found between new experimental data and simulations of a coupled fluid-structure mathematical model. Upon increasing feed mass flow rate, there is a critical pipe length above which a quarter-wave instability occurs. The dependency is shown to be well approximated by a simple analytical formula derived from a reduced-order model. Liquid service valves are found to be stable for longer inlet pipes than for the gas case. However, the instabilities when they do occur are more violent and the valve is found to jump straight into chatter, in which it impacts repeatedly with its seat. Flutter-type oscillations are never observed. These observations are explained by finding that the quarter-wave Hopf bifurcation is subcritical. Water hammer effects can also be observed, which result in excessive overpressure values during chatter. In addition a new, Helmholtz-like instability -not encountered in gas service -is identified for short pipes with small reservoir volumes. This can also be predicted analytically and is shown to explain a valve-only instability found in previous work that incorporated significant mechanical damping.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractRecent progress by a number of different groups and authors is reviewed on the stability properties of direct-spring pressure relief valves connected to pressure vessels with or without piping systems. Various different notions of stability and mechanisms for instability are revealed both in the case of gas and liquid service. It is stressed that it is not the valve itself that is stable or unstable, rather the harmful vibrations arise through interactions between the valve and its surroundings -the inlet piping, the reservoir, and any outlet piping. A distinction is drawn between underlying instability mechanisms and how these may be triggered during transient operations. The purpose of the work is to provide a coherent simplified account that will be of practical use for proposing new operational guidelines and mitigation strategies. Among these various mechanisms, oscillatory instability due to the interaction with a quarter-wave acoustic mode in the inlet piping is argued to be the most important to mitigate.

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