Enhanced stability of pressure relief valves: mechanistic design and analysis

Abstract

Pressure-relief valves, often the critical last line of defence in process engineering, are known to be susceptible to valve chatter. Such behaviour has been shown to arise from a flutter instability, or Hopf bifurcation, associated with the fundamental, quarter-wave acoustic mode of their inlet piping. Here, a novel design concept is proposed and analyzed for eliminating this instability. The concept involves using an oversized valve with reduced lift and adopting a discharge characteristic that enhances the blow-down effect, so that the valve opens immediately to its upper lift limit upon reaching set pressure. The concept is demonstrated numerically using an updated version of a 1D fluid pipe dynamics mathematical model solved using a Lax-Wendroff method. Stability properties are analysed using dynamical systems theory, applied to an improved reduced-order modal model. It is shown how the valve settles to a stable so-called pseudo equilibrium, in contact with the upper stop, provided the coefficient of restitution of is not too large. Such stable operation is reached despite the equivalent regular valve being unstable to the quarter-wave Hopf bifurcation. Parameter studies using the reduced-order model demonstrate the extent of the enhanced stability effect, which is confirmed using the full model for the case of gas service valves.

Figures (10)

• Figure 1: The mechanistic working mode for an oversized valve with blowdown effect and upper stop: virtual lift region; admissible region but dynamically unstable; stable equilibrium branch; unstable equilibrium branch; location of the upper stop; critical valve lift, such that without the upper stop, the valve would be unstable for all lift values below this line; $\diamondsuit$ the fold point; $\rightarrow$ ideal path segments of a pressure-relief event. More details including parameter values used to produce this simulation are given in \ref{['sec:stability']}.
• Figure 2: (a) Definition sketch of pressure-relief system, with zoom at the valve in (b); see text for details. Insets show physical diagrams, taken from valve-inset.
• Figure 3: (a) The effective areas of different geometries where $\hat{A}_{\rm eff} = A_{\rm eff}/A_{\rm 0}$ and $\tilde{x}=x/(x-x_{\rm max})$ (blue CFD; red analytical estimation). (b) The fitted jet angles (+), or if fitting was not possible, their best approximations (o). The blue lines correspond to the geometrical deflection angle.
• Figure 4: Equilibrium curves with different half open angles $\alpha$ with varying set pressure: solid line is dimensionless lift $\frac{x}{D/4}$ versus the tank pressure $\frac{p_r - p_b}{p_{\rm set}}$; dashed line is dimensionless lift $\frac{x}{D/4}$ versus the valve end pressure $\frac{p_v - p_b}{p_{\rm set}}$. Here the dimensionless parameter $\delta$ is equal to $p_{\rm set}/p_b$.
• Figure 5: Solutions to the PDM h superimposed onto the different equilibrium curves for the cases in Fig. \ref{['fig:geometric-aeff-demos']} with: left, $\alpha = \pi/3$; right, $\alpha = \pi/2$. The simulations were run with $\dot{m}_{\rm in} = 0.5~{\rm kg/s}$ and $L = 0.1 ~{\rm m}$. Here red lines show equilibrium lift versus tank pressure, blue lines show equilibrium lift versus valve pressure, black lines show simulated valve lift versus tank pressure