Dynamic behaviour of direct spring loaded pressure relief valves in gas service: II reduced order modelling

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.     

Dynamic behavior of direct spring loaded pressure relief valves in gas service: Model development,measurements and instability mechanisms

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.