Dynamic behaviour of direct spring loaded pressure relief valves: III valves in liquid service

Abstract

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.

Dynamic behaviour of direct spring loaded pressure relief valves connected to inlet piping: IV review and recommendations

“…In Tamura et al (2012a) a standing quarter-wave was found numerically in the stub pipe of several relief valves during the oscillations. We also point to our previous work Hős et al (2014); Hős et al (2015); Hős et al (2016)) where, besides mathematical modelling, a large amount of experimental evidence was provided for the presence of quarter-wave instabilities in both liquid and gas service.…”

“…We found the above formula to be particularly accurate in the case of liquid service valves Hős et al (2016). If the valve is in gas service, the above formula can be still used provided that the gas properties (notably density and sonic velocity) are evaluated at set pressure.…”

“…For gases, we have a 2 = γRp r , where R stands for the specific gas constant. In the case of liquids though, any quantitative prediction of valve instability requires precise estimation of the sonic velocity, which should be carried out with care, see Wiley and Streeter (1978); Hős et al (2016). In theory the sonic velocity a 2 = E/ρ, with E being the bulk modulus of the liquid and ρ being density.…”

“…Mathematical models implementing these approaches are typically capable of predicting full opening-closing cycles within engineering accuracy, however, special care must be devoted to properly implement the coupling to the reservoir and valve equations at the boundaries, taking care of possible shocks and inlet losses (see e.g. Hős et al (2014b); Hős et al (2016)). …”

“…It seems natural to assume that the valve and the Helmholtz resonator (pipe and reservoir) might come into resonance. Indeed, in Hős et al (2016) it was shown that there is a form of instability, when the pressure fluctuation in the vessel is compensated by the quarter-wave in such a way that although the pressure in the pipe oscillates, the fluid moves in a plug-like way such that the pressure is approximately constant at the valve-end of the pipe. After performing the necessary computations, we found in Hős et al (2016) that the critical dimensionless pipe length γ for instability and frequency of motion are given by…”