PRV Stability Inlet Line Critical Length

Research by Chiyoda, Pentair and ioMosaic showed that pressure relief valve (PRV) instability leading to flutter and/or chatter is due to the coupling of the PRV disk motion with the quarter wave pipe/fluid mode frequency without resonance. Izuchi simplified his detailed modeling analysis to restrict the inlet line length for stable PRV operation and derived an analytical expression for simple inlet line geometries. 

In a recent presentation (March 10, 2021) on PRV stability by the Center of Safety Excellence (CSE), Keszthelyi et al. validated, using actual measurements, the inlet line critical length criteria proposed by several authors. The measurements were obtained at CSE’s PRV test facility in Germany. The evaluation showed that the inlet line critical length criterion originally derived by Izuchi and later simplified by Melhem showed the best performance vs. actual measurements of critical line length. 

In his presentation, Keszthelyi suggested that Izuchi’s original derivation of inlet line critical length is missing 1 from a square root of the critical line length, Lcrit, equation.

PRV-Stability-Inlet-Line-Critical-Length-calculation Where c is the speed of sound, !n is the undamped circular natural frequency, xo is the initial compression of the PRV spring at zero lift, fn is the PRV frequency, x is the PRV disk lift, and Lcrit is the critical inlet line length. 

This short communication confirms that the original equation is correct (1 is not needed) and was developed for initial opening of the PRV. The original equation is recommended for use in PRV stability screening because it was derived without the impact of damping. However, 1 should be added to the square root term at full opening of the pressure relief valve.

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