Non-linear response of a fluid valve

Nayfeh, Ali H.; Bouguerra, H.

doi:10.1016/0020-7462(90)90031-4

Cited by 23 publications

(18 citation statements)

References 12 publications

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“…Similar forms of oscillatory instability have been observed and analyzed in other valve systems for example, in simple plug valves [4], compressor valves [7], ball valves subject to harmonic excitation [17], pilot-operated two-stage valves [2,19], and fluid dampers with embedded blow-off valves [6].…”

Section: Introductionsupporting

confidence: 60%

Bifurcation Analysis of a Simplified Model of a Pressure Relief Valve Attached to a Pipe

Bazsó¹,

Champneys²,

Hős³

2014

SIAM J. Appl. Dyn. Syst.

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Abstract.A two-parameter bifurcation analysis is performed on a mathematical model that represents the motion of a pressure relief valve connected to a reservoir via a pipe. The system comprises a dimensionless system of five differential equations representing the valve position and velocity, the reservoir pressure, and the velocity and pressure components of a quarter-wave within the pipe. Two key dimensionless parameters represent the mass flow rate into the reservoir and the length of the pipe. It is found that there are two independent forms of Hopf bifurcation: a so-called valve-only instability, which involves the valve alone and occurs when the flow rate is too low, and a coupled acoustic resonance, which involves quarter-waves within the pipe, that occurs when the pipe is too long. Secondary bifurcations are also traced including curves of grazing bifurcations where the valve body first impacts with its seat. Using a mixture of simulation and numerical continuation, it is found that these instabilities interact in a complex bifurcation diagram that involves HopfHopf interaction, bistability through catastrophic grazing bifurcations, and, for long enough pipes, subcritical torus bifurcations. A particularly important discovery is a range of parameters for which the valve-only instability is subcritical, so that large amplitude impacting chaotic motion coexists with the stable equilibrium operation.

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Section: Introductionsupporting

confidence: 60%

Bifurcation Analysis of a Simplified Model of a Pressure Relief Valve Attached to a Pipe

Bazsó¹,

Champneys²,

Hős³

2014

SIAM J. Appl. Dyn. Syst.

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“…Oscillations in other valve systems have also been studied, e.g. in plug valves (D'Netto and Weaver, 1987), compressor valves (Habing and Peters, 2006), ball valves (Nayfeh and Bouguerra, 1990), pilot-operated two-stage valves (Botros et al, 1997;Zung and Perng, 2002;Ye and Chen, 2009) and control valves (Misra et al, 2002). Again, such studies go beyond the scope of the present work.…”

Section: Introductionmentioning

confidence: 97%

“…This paper shall focus on the first of these, specifically instability due to interaction between the valve and the inlet pipe (although, as we shall see, this can also be interpreted as an effective negative restoring force on the valve provided by an acoustic wave). Instabilities due to the other four effects identified by Green and Woods have been analyzed by a number of other authors (Kasai, 1968;McCloy and McGuigan, 1964;Madea, 1970a,b;Nayfeh and Bouguerra, 1990;Vaughan et al, 1992;Moussou et al, 2010;Beune, 2009;Song et al, 2011). Conventional PRVs subject to built-up back pressure have also been widely investigated (Francis and Betts, 1998;Chabane et al, 2009;Moussou et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

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

Hős

Champneys

Paul

et al. 2014

Journal of Loss Prevention in the Process Industries

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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.

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“…Instabilities due to the other four effects identified by Green and Woods have been analysed by a number of other authors, see, for example, Kasai (1968), McCloy & McGuigan (1964), Madea (1970a,b), Nayfeh & Bouguerra (1990), Vaughan et al (1992), Moussou et al (2010), Beune (2009) and Song et al (2013). Conventional PRVs subject to built-up back pressure have also been widely investigated, see, e.g.…”

Section: Of 16 C Hős Et Almentioning

confidence: 99%

Model reduction of a direct spring-loaded pressure relief valve with upstream pipe

2014

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A mathematical model is developed of a spring-loaded pressure relief valve connected to a reservoir of compressible fluid via a single, straight pipe. The valve is modelled using Newtonian mechanics, under assumptions that the reservoir pressure is sufficient to ensure choked flow conditions. The usual assumptions of ideal gas theory lead to a system of first-order partial differential equations for the motion, energy and momentum of the fluid in the pipe. A reduced-order model is derived using a collocation method under the assumption that the dominant pipe dynamics corresponds to a standing quarter wave. The model comprises just five non-linear ordinary differential equations, representing the position and velocity of the valve body, the pressure in the tank and the velocity and pressure amplitudes of the pipe quarter wave. Through comparison with simulations of the full model using a Lax-Wendroff method, it is shown that the reduced model is quantitatively accurate and is able to predict the onset of an oscillatory valve-chatter instability. The basic trends of this instability are shown to be robust to the inclusion of pipe friction and convective effects.

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Non-linear response of a fluid valve

Cited by 23 publications

References 12 publications

Bifurcation Analysis of a Simplified Model of a Pressure Relief Valve Attached to a Pipe

Bifurcation Analysis of a Simplified Model of a Pressure Relief Valve Attached to a Pipe

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

Model reduction of a direct spring-loaded pressure relief valve with upstream pipe

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