Sage Journals: Discover world-class research

Abstract

This article presents detailed experimental results of the influencing factors of flow rate, set pressure, and inlet pipe length of a pressure relief valve. In order to analyze the influence of different flow rates on the instability characteristics of pressure relief valve, the multi-stage output of pump flow is realized. In terms of modeling, we investigated the theory concerning instability in the system: the 3% rule boundary. Data analyses on typical stable, cycling, and chatter instability conditions are conducted. The stable boundaries of the 3% rule and the quarter-wave model are drawn, which are consistent with the experimental results.

Keywords

Pressure relief valve dynamic instability flutter chatter stable boundary

Introduction

Pressure relief valve (PRV) is used to keep the pressure of the controlled system or loop constant through the overflow action of the valve port and to achieve the purpose of regulating, stabilizing, and limiting the pressure.^1–6 The unstable operation of the PRV causes great harm, which is mainly expressed as follows: decrease of discharge capacity, insufficient function of constant pressure regulation or overpressure protection and the resonance of the whole pipeline system, or the serious damage to the sealing surface of the PRV. Scholars have paid increasing attention on how to reduce the vibration and noise of hydraulic circuits.

The operation of PRV includes three stages: opening, continuous discharge, and re-seating. The disk leaves the valve seat to reach sufficient valve lift, and its discharge capacity reaches the rated capacity, thus completing the opening process. The process in which the disk returns to the seat from the fully open position and the sealing is formed again is the process of re-seating. Re-seating pressure, also known as closing pressure, is the inlet pressure when the disk re-contacts the valve seat after discharge, namely, the valve lift turns to zero. The PRV with qualified operation performance should meet the following requirements: during the whole process of opening, discharging, and re-seating, the PRV is in a stable flow state, without flutter or chatter.

The working medium of PRV is a typical turbulent flow fluid. The motions of flow vary irregularly so that quantities such as velocity and pressure show a random variation with the time and space coordinates. Unsteady turbulent flow can be defined as a flow in which the time-average physical quantities change in time. How to study PRV with unsteady turbulent flow by an effective experimental method has become an essential problem.

Some scholars focused on local stability of PRV to seek the stability domain. The stability criterion in the classical control theory was used near the equilibrium point of the system.

Izuchi⁷ investigated the stability of a PRV through experiments and analysis. It was found that the dynamic instability was caused by the interaction effect between the pressure wave propagation through the inlet pipe and the valve disk motion. Li et al.⁸ focused on the numerical analysis of the dynamic behavior of a PRV. The authors found that the axial force exerted by the fluid on the valve clack first decreases with the increase of the valve opening and then increases. Wu et al.⁹ established a mathematical model of PRV and conducted stability analysis. Applying the deformation data to the PRV model, the stability and relative stability could be analyzed quantitatively through both the frequency-domain analysis method and the time-domain analysis method to detect the influence of fitting clearance after deformation. Yang et al.¹⁰ analyzed the mathematical model of pilot-operated PRV, and the dynamics simulation model with strong vibration environment was built. The simulation results showed that, when the system is stable, the pilot valve is affected by little interference and the system will attenuate vibration to be stable, but when the interference exceeds the critical value, the system generates periodic oscillation. Chen et al.¹¹ proposed a cartridge one-way PRV, which has the characteristics of direct detection. Theoretical analysis and simulation results indicated that the direct detection characteristic forms the interstage negative feedback, which can effectively reduce the steady-state override pressure.

The above studies greatly promote the engineering application of PRV. However, the stability of the PRV is essentially a fluid–structure interaction problem. Its stability is affected not only by the structure of the valve itself, but also by the hydraulic pipeline and other hydraulic components in the pipeline. Therefore, the impact of pipeline on the stability of the PRV cannot be ignored.

The local stability analysis is based on the linear equation linearized near the equilibrium point of the system, but the system itself is a non-linear system. The local stability analysis of PRV cannot meet the requirement of large range stability. When the disk deviates from the set equilibrium point, the experimental results differ from the theoretical results of linearization calculation near the equilibrium point. In addition, the conclusion of the local stability criterion is only applicable to static stability judgment of the system, and the global dynamic behavior cannot be understood. Therefore, the global stability of the PRV can be reflected more truthfully using the non-linear model of the system.

In recent years, increasing attention has been paid to the numerical simulation as an effective auxiliary research method due to the rapid development of computational fluid dynamics.^12–15 However, experimental study is still the basic method to promote the research on PRV.

To sum up, the local and global stability of elevating force caused by the working medium on the disk are the decisive factors affecting the working stability of the PRV. However, there is still much room for improvement in the existing experimental and numerical computation methods.

The rest of the article is organized as follows. In section “Basic principles of PRV,” the fundamental concept of PRV is presented. In section “Instability characteristic experiment of PRV,” the details of experimental objectives, principles, devices, and procedures are introduced. In section “Experimental results and analysis,” the data analyses for typical stable, cycling, and chatter instability conditions are presented. Then in section “Stable boundary analysis,” the work is concluded by showing the stable boundaries of the 3% rule and the quarter-wave model, and finally concluding comments are provided in section “Conclusion.”

Basic principles of PRV

Figure 1 shows the typical PRV components, the precise definitions of which are given in Appendix 2 .

Figure 1.

Typical PRV components.

The reaction force acting on the inlet side of the disk is acting against the spring force plus the force applied by the back pressure on the top of the disk, as shown in Figure 2. When the valve is closed, as shown in Figure 2(a), the inlet pressure acting on the disk surface is counteracted by spring force and back pressure force. At initial opening, as shown in Figure 2(b), the escaped fluid forms a thin film on the seat surface and forms a reaction force that prompts the disk to lift when the disk holder flows downward. In the initial stage, these forces are formed very slowly. As shown in Figure 2(c), as the flow rate increases gradually, the velocity difference between the fluid and the valve seat becomes increasingly larger, and the momentum and reaction forces are sufficient to further lift the disk. Overpressure continues to increase to achieve the full opening of the disk. At the closing stage, spring forces and back pressure force bring the disk back to the seat position due to reduced momentum and reaction force.

Figure 2.

The operating principle of PRV: (a) closing state, (b) initial opening state, and (c) full opening state.

Figure 3 illustrates the full stroke of the disk from the set pressure (A) to the relieving pressure (B) through overpressure stage and returning to the closing position (C) through the blowdown stage. Moreover, details of the operational characteristics are explained in Appendix 3.

Figure 3.

Typical PRV lift characteristic.

Instability characteristic experiment of PRV

The experimental objectives are to measure the mechanical properties of PRV at different set pressures and inlet pipe lengths to study the relevant parameter changes in the fluid field during PRV instability.

Figure 4 illustrates the system configuration of the instability characteristic experiment of PRV, and Figure 5 illustrates the field picture of the instability characteristic experiment of PRV. The programmable multi-stage speed function of the frequency converter is used to realize the multi-stage output of pump flow, adjust the different precompressed spring lengths, and study the influence of set pressure on the instability characteristic of PRV. The length of the inlet pipe of PRV is changed to study the effect of inlet pressure loss on the instability characteristics of PRV. The experimental platform for instability characteristics of PRV contains a frequency converter, an electric motor pump unit, an electromagnetic flow meter, a reservoir, a pressure sensor, an accelerometer, a laser displacement sensor, a data acquisition system, and a computer. In order to reduce the effect of piston pulse on the electric motor pump unit, the reservoir should have enough volume capacity and weight.

Step 1. To adjust the visible light spot project center on the valve spindle, the laser displacement sensor is installed on the fixed bracket. Install accelerometer on the top of the valve spindle. Adjust the set pressure by the adjustment screw of PRV to be 0.1 MPa. The inlet pipe length is 0, 1, 2, 3, 4, and 5 m. The programmable multi-stage speed function of the frequency converter is used to realize the multi-stage output of pump flow, which is 20, 30, 40, 50, and 60 L/min.

Step 2. Observe the action of the PRV to estimate whether it can be reached and maintained in full open condition. Record the valve primary pressure, valve back pressure, valve lift, acceleration, and flow rate of PRV. Observe whether there is a phenomenon of instability and record mechanical properties through auditory, tactile, or visual observations. If chatter, flutter, or cycling occurs for the PRV, it should be recorded. Then gradually reduce the flow rate of the pump, observe the rise and fall of the valve stem, and turn off the electric motor pump unit.

Step 3. Adjust the set pressure by the adjustment screw of PRV to be 0.2, 0.3, 0.4, and 0.5 MPa and repeat steps 1 and 2.

Figure 4.

The system configuration of the instability characteristic experiment.

Figure 5.

The field of the instability characteristic experiment.

Experimental results and analysis

A certain pressure value between the set and closing pressure of PRV may not necessarily correspond to the stable equilibrium point between the spring force and the elevating force. A small change in disk position may lead to a change in the resultant force, resulting in the disk tending to the full opening or closing position. Such effect can be classified as “static instability.”¹⁶ As shown in Figure 6, static instabilities can be observed at t = 5, 9.7, 48.6, and 61.3 s, while “dynamic instability” refers to the abnormal self-excited oscillation of the disk. As shown in Figure 7, the PRV has three different forms of dynamic instability: cycling, flutter, and chatter.^17–19 The main types of dynamic instability are summarized in Table 1.

Figure 6.

The forms of static instability.

Figure 7.

The forms of dynamic instability.

Table 1.

Summary of the main types of dynamic instability and their description.

Type	Description	Feature	Possible trigger
Cycling	Open and close multiple times during a pressure relief event	Low frequency (<1 Hz)	Valve oversizing or inlet pressure loss
Flutter	Self-excited periodic oscillation that does not result in the valve completely closing off	High frequency (>10 Hz)	Interaction between valve dynamics and the inlet piping
Chatter	Rapid oscillatory motion that involves the valve repeatedly impacting with its seat	Noisy, high frequency (scores of Hz)	Overly long inlet pipe or large inlet flow rate

In order to analyze the influence of different flow rates on the instability characteristics of PRV, multi-stage output of pump flow is realized using the programmable multi-stage speed function of the frequency converter, which is 20, 30, 40, 50, and 60 L/min. Figure 8 illustrates the curve of pump outlet flow rate and pressure, indicating that the flow rate and pressure gradually increase.

Figure 8.

The pump outlet flow rate and pressure.

Table 2 shows the instability characteristics of PRV at different set pressures and inlet pipe lengths summarized in the experiment.

Table 2.

The instability characteristics of PRV at different set pressures and inlet pipe lengths.

Set pressure, p_s (MPa)	Inlet pipe length, L_i (m)
Set pressure, p_s (MPa)	0	1	2	3	4	5
0.1	Cycling	Stable	Stable	Cycling	Cycling	Cycling
0.2	Stable	Stable	Stable	Chatter	Chatter	Chatter
0.3	Stable	Stable	Stable	Chatter	Stable	Stable
0.4	Stable	Stable	Chatter	Stable	Chatter	Stable
0.5	Stable	Stable	Stable	Stable	Chatter	Stable

PRV: pressure relief valve.

No flutter instability was found in the experiment according to Table 2. Indeed, the flutter instabilities are virtually existent in the actual system. Although we have artificially separated three instability mechanisms, in an actual system they probably co-exist. For example, pressure and velocity oscillations during flutter might reach such large amplitudes that the valve pressure reaches blowdown pressure and cycling will also occur. Flutter may also rapidly translate into chatter. Such transitions can exhibit hysteresis.

Data analysis for typical stable conditions

The experimental data at the set pressure of 0.5 MPa and the inlet pipe length of 0 m are selected. Figure 9 illustrates the valve lift, velocity, and acceleration curves of PRV core in the stable condition. As one of the most important parameters to characterize the movement of the moving parts in the PRV opening process, the change of the valve lift can directly reflect whether the PRV is stable or not. It is shown that when the flow rate (see Figure 8) is low, the lift of disk is very small, and with the increase of the flow rate, the valve lift rises steadily and finally stabilizes at 5 mm. The velocity and acceleration of the disk are in the ranges of ±0.18 m/s and ±1.2 m/s², respectively. It is shown that the PRV is basically in the stable discharge stage.

Figure 9.

The valve lift, velocity, and acceleration of PRV in the stable condition.

Figure 10 illustrates the valve primary pressure curve of PRV in the stable condition. At low flow rates (see Figure 8), the PRV valve primary pressure of 0.5 MPa is quickly established, and the set pressure increases slightly with the increase of flow rate. In the steady flow stage, the valve primary pressure is basically stable and the pressure fluctuation only occurs in the flow transition stage.

Figure 10.

The valve primary pressure of PRV in the stable condition.

Data analysis for typical cycling instability

The experimental data at the set pressure of 0.1 MPa and the inlet pipe length of 0 m are selected. Figure 11 illustrates the valve lift, velocity, and acceleration curves of PRV under cycling instability. It is shown that when the flow rate is 40 L/min (see Figure 8), the lift of the disk oscillates during the overflow process, but the disk is not in contact with the valve seat, the oscillation frequency is 0.3 Hz, and the rest stage is the stable discharge stage. The velocity and acceleration of the disk are in the ranges of ±0.15 m/s and ±1.2 m/s², respectively.

Figure 11.

The valve lift, velocity, and acceleration of PRV with cycling instability characteristic.

Figure 12 illustrates the valve primary pressure curve of PRV in cycling instability condition. At low flow rates (see Figure 8), the valve primary pressure of 0.1 MPa is quickly established. When the flow rate is 40 L/min (see Figure 8), the oscillation of the disk at lift causes the fluctuation of valve primary pressure, and the oscillation frequency is 0.3 Hz.

Figure 12.

The valve primary pressure of PRV with cycling instability characteristic.

Data analysis for typical chatter instability

The experimental data at the set pressure of 0.5 MPa and the inlet pipe length of 4 m are selected. Figure 13(a) illustrates the valve lift, velocity, and acceleration of PRV in the time domain during chatter instability. It is shown that the fluctuation of the displacement curve increases significantly, showing a wave-like oscillation. The disk hits the valve seat with a high frequency, which is extremely unfavorable to the sealing surface of PRV, easily causes damage to the sealing surface, and produces great noise. The valve lift, velocity, and acceleration of the disk increase with the increase of flow rate (see Figure 8) and finally reach 2.5 mm, 0.54 m/s, and 890 m/s², respectively. The curve has obvious periodic features. Figure 13(b) shows the spectrogram of the measured signal. It is shown that the spectrum is characterized by a peak spectral curve with a uniform distribution, in which the fundamental frequency is 58.2 Hz.

Figure 13.

The valve lift, velocity, and acceleration of PRV with chatter instability characteristic: (a) time domain and (b) frequency domain.

Figure 14(a) illustrates the valve primary pressure of PRV with chatter instability characteristic in the time domain. Figure 14(b) shows the spectrogram of the measured signal. It is shown that the spectrum is characterized by a peak spectral curve with a uniform distribution, in which the fundamental frequency is 58.2 Hz. There are resonance components at 118 and 176 Hz, and it has two and three times multiple relationships between the corresponding frequency and the fundamental frequency. With the increase of flow rate, pressure amplitude increases. The chatter instability of PRV causes fluid pressure fluctuation in the system and becomes the vibration source of the system. The frequent opening and closing of the disk and seat cause a change in fluid flow momentum, slight compression of the fluid, and deformation of the pipe material. The fluid will undergo significant pressure changes, causing damage to the piping and connecting parts. The additional pressure will be attached to the normal flow pressure in the pipeline, and the high-frequency pressure wave will be generated with the disturbance of pressure and velocity.

Figure 14.

The valve primary pressure of PRV with chatter instability characteristic: (a) time domain and (b) frequency domain.

Stable boundary analysis

The 3% rule boundary

The authors conducted a qualitative analysis on the dynamic instability of PRV and concluded that excessive inlet pipe pressure drop, excessive inlet pipe length, or too small inlet pipe diameter will lead to unstable flow, thus causing chatter or flutter of the PRV.^20–23 The PRV is vulnerable to unstable opening in this case. According to the qualitative analysis of the vibration mechanism above, it is assumed that the friction pressure loss of the inlet pipe does not exceed 3% of the set pressure in the stability condition, that is, the “3% rule stable boundary”

Δ p_{fric} \leq 0.03 p_{s}

(1)

where Δp_fric is the inlet pipe friction pressure loss and p_s is the set pressure.

The pressure loss formula for fluid flow in a circular pipe^24,25 is

Δ p_{fric} = λ \frac{L_{i}}{D_{i}} \frac{ρ}{2} {(\frac{q_{v}}{A_{i}})}^{2}

(2)

where λ is the Fanning friction factor, L_i is the inlet pipe length, D_i is the inlet pipe internal diameter, A_i is the inlet pipe area, ρ is the fluid density, and q_v is the volume flow rate.

Then, the 3% rule stable boundary is

L_{i} < \frac{0.06 p_{s} D_{i} A_{i}^{2}}{λ ρ q_{v}^{2}}

(3)

Figure 15 illustrates the stable boundary of the 3% rule at different set pressures.

Figure 15.

The stable boundary of the 3% rule at different set pressures.

It is shown that the stable boundary of inlet pipe pressure drop is the function of inlet pipe length and volume flow rate. The larger the set pressure of PRV is, the larger the stable range is, that is, the critical inlet pipe length and critical volume flow rate increase with the increase of set pressure.

Quarter-wave model boundary

The presence of inlet pipe gives rise to the formation of acoustic standing waves, which can couple with the valve dynamics and result in dynamic instability. Typically, one encounters the first, quarter-wave, harmonic of the pipe, that is, a standing wave of wavelength that is four times the pipe length. The valve acts as a damper on the pipeline acoustic dynamics and the phase shift between the valve and the pipeline motion determines whether this damping is positive or negative. It is then possible to derive an approximate analytical expression for the flow rate at which this negative damping first arises.

The stable boundary was obtained as²⁶

q > \frac{2 {(1 + δ)}^{3 / 2}}{ω_{1}^{2} - 1} μ σ

(4)

where q is the driving mass flow rate, q = q_m/q_m,cap, δ is the spring pre-compression parameter, $δ = k x_{0} / (A_{i} p_{b})$ , μ is the mass flow rate parameter, $μ = A_{i} ρ ω_{v} x_{ref} / q_{m, cap}$ , σ is the velocity–mass flow rate parameter, $σ = C_{d} d_{0} π \sqrt{ρ p_{ref}} / (A_{i} ρ ω_{v})$ , and ω₁ is the first pipe eigenfrequency, ω₁ = π/(2γ).

The stable boundary can also be expressed as

q > \frac{8 {(1 + δ)}^{3 / 2} γ^{2}}{π^{2} - 4 γ^{2}} μ σ

(5)

q_{m} > \frac{8 {(1 + δ)}^{3 / 2} γ^{2} μ σ q_{m, cap}}{π^{2} - 4 γ^{2}}

(6)

The capacity mass flow rate q_m,cap is defined as the mass flow rate q_m passing through the valve at the pressure exceeding 10% of set pressure and the maximum disk lift

q_{m, cap} = C_{d} π d_{0} (x_{m} - x_{0}) \sqrt{ρ p_{0}}

(7)

where p₀ is the design pressure, p₀ = 1.1p_s, γ is the inlet pipe length parameter, $γ = L_{i} ω_{v} / a$ , ω_v is the valve natural frequency, $ω_{v} = \sqrt{k / m}$ , and x_ref is the reference displacement of the disk, $x_{ref} = A_{0} p_{ref} / k$ .

Table 3 shows the variable parameter values (see Appendix 1 for details) in the stable boundary condition of the quarter-wave model.

Table 3.

Dimensionless parameters for several set pressures.

p _s (MPa)	x ₀ (mm)	q _m,cap (kg/s)	δ	σ	μ	γ
0.1	0	16.4	0	5.8	0.0068	0–0.34
0.2	1.7	23.3	1	5.8	0.0048	0–0.34
0.3	3.3	28.5	2	5.8	0.0039	0–0.34
0.4	5	32.9	3	5.8	0.0034	0–0.34
0.5	6.6	36.8	4	5.8	0.003	0–0.34

Figure 16 illustrates the stable boundary of the quarter-wave model at different set pressures.

Figure 16.

The stable boundary of the quarter-wave model at different set pressures.

It is shown that the stable boundary of the quarter-wave model is a function between the inlet pipe length and the volume flow rate. The greater the set pressure of the PRV is, the smaller the stable range is. When the volume flow rate is the same, for the PRV with fixed set pressure, the shorter the inlet pipe is, the more stable the PRV is. When the inlet pipe length is the same, the greater the volume flow rate is, the more stable the PRV is.

According to different set pressures, the dynamic instability characteristic and stable boundary of PRV are shown in Figures 17 –21. Different symbols represent the measurement points: circles show test runs that are fully stable, plus signs are unstable (cycling), and x-type signs are unstable (chatter). Two theoretical predictions are presented for completeness, the dashed line shows the critical inlet pipe length corresponding to the 3% rule, and the solid line is the analytical boundary for the quarter-wave model. In both cases, the stability criterion is that the measurements should lie beneath these curves.

Figure 17.

The dynamic instability characteristic and stable boundary at the set pressure of 0.1 MPa.

Figure 18.

The dynamic instability characteristic and stable boundary at the set pressure of 0.2 MPa.

Figure 19.

The dynamic instability characteristic and stable boundary at the set pressure of 0.3 MPa.

Figure 20.

The dynamic instability characteristic and stable boundary at the set pressure of 0.4 MPa.

Figure 21.

The dynamic instability characteristic and stable boundary at the set pressure of 0.5 MPa.

Figure 15 shows the trend of the critical pipe lengths computed according to the 3% rule stable boundary. It is important to note that the 3% rule stable boundary predicts that the critical pipe length should increase with set pressure, whereas the real tendency is just the opposite. The 3% rule stable boundary is designed to avoid instability due to inlet pressure drop, but it is unsuitable to predict any other instability type. As an example, change in inlet pipe diameter plays only a marginal role in the quarter-wave instability as it does not affect the wavelength of the quarter wave. Yet, the allowable pipe length according to the 3% rule changes heavily with the pipe diameter (for constant flow rate). Nevertheless, the 3% rule limits the inlet piping length, so its application might result in pipe lengths that are short enough to avoid quarter-wave coupling, but such cases are merely coincident. Indeed, the 3% rule is sufficient to avoid severe valve oscillations in the case of an inlet pipe diameter equal to that of the PRV inlet, but it is not sufficient.

We also depict the trend of the quarter-wave model stable boundary upon varying set pressure as shown in Figure 16. We found that, the higher the set pressure, the lower the critical pipe length for stability. This trend was also found in experimental tests. The quarter-wave model boundary provides a good explanation of the trends in the experimental data.

In our previous work,²⁷ we reported that, for high flow rates, the valve is stable, which, upon decreasing the flow rate, loses its stability via a Hopf bifurcation. A non-impacting oscillation occurs, the amplitude of which increases with decreasing the flow rate, and once the valve disk reaches the seat impacting periodic orbit occurs, the amplitude of which decreases with decreasing flow rate. Finally, for very low flow rates, chaos-like impacting motions were observed. Our future plan is to analyze hybrid motion consisting of flow rate, impacting, set pressure, inlet pipe, and outlet pipe. Obviously, laboratory measurements are also needed to verify the theoretical and numerical results.

Conclusion

This article places emphasis on the dynamic instability of PRV. The experimental platform for instability characteristics is designed. The experimental scheme of instability characteristics is formulated to obtain the characteristic curve of the measured elevating force and differential pressures between the valve inlet and outlet. The programmable multi-stage speed function of a frequency converter is used to realize the multi-stage output of pump flow and study the influence of flow rate, set pressure, and inlet pipe length on the instability characteristic of PRV. Through the analysis and comparison of the lift characteristic experimental results of PRV, the following conclusions are drawn:

In the stable condition, the lift of the disk increases steadily with the increase of flow rate. In cycling instability, low-frequency oscillation occurs in the overflow process of the disk, but the disk does not come into contact with the valve seat. The oscillation frequency f < 1 Hz, the velocity of the disk is in the range of ±0.15 m/s, and the acceleration is in the range of ±1.2 m/s². In chatter instability, the disk hits the seat with high frequency and produces great noise. The lift, velocity, and acceleration of the disk increase with the increase of flow rate, which finally reach 2.5 mm, 0.54 m/s, and 890 m/s², respectively.

The stable boundary of the 3% rule is the function between inlet pipe length and volume flow rate. The critical inlet pipe length and critical volume flow rate increase with the increase of set pressure. The stable boundary of the quarter-wave model is a function of inlet pipe length and volume flow rate, and the greater the set pressure of the PRV is, the smaller the stability range is. For the PRV with fixed set pressure, the shorter the inlet pipe is, the more stable the PRV is when the volume flow rate is the same, and the greater the volume flow rate is, the more stable the PRV is when the inlet pipe length is the same.

Footnotes

Appendix

Appendix 3

Operational characteristics.

Name	Description
Set pressure (or called opening pressure)	The inlet pressure at which the valve begins to open. For liquid service, set pressure is defined as the pressure at which the first vertical steady stream of liquid appears
Back pressure	The static pressure existing at the outlet of a PRV due to pressure in the discharge system
Closing pressure	The value of decreasing inlet static pressure at which the valve disk re-establishes contact with the seat or at which lift becomes zero
Primary pressure	The pressure at the inlet in a PRV
Relieving pressure	Set pressure plus overpressure
Blowdown	The difference between the actual set pressure of a PRV and the actual closing pressure
Overpressure	A pressure increase over the set pressure of a PRV

Handling Editor: Xiaoxiao Han

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities of China (No. FRF-TP-17-026A1), the General Financial Grant from the China Postdoctoral Science Foundation (No. 2017M620621), and the National Natural Science Foundation of China (No. 51774019).

ORCID iD

Wei Ma

References

Yonezawa

Ogawa

Ogi

et al . Flow-induced vibration of a steam control valve. J Fluid Struct 2012; 35: 76–88.

Galbally

García

Hernando

et al . Analysis of pressure oscillations and safety relief valve vibrations in the main steam system of a boiling water reactor. Nucl Eng Design 2015; 293: 258–271.

Bolin

Engeda

Analysis of flow-induced instability in a redesigned steam control valve. Appl Therm Eng 2015; 83: 40–47.

CFD simulation of flow-pressure characteristics of a pressure control valve for automotive fuel supply system. Energ Convers Manag 2015; 101: 658–665.

Mehrzad

Javanshir

Ranji

et al . Modeling of fluid-induced vibrations and identification of hydrodynamic forces on flow control valves. J Central South Univ 2015; 22: 2596–2603.

Yan

Wei

et al . Effect of measurement volume shift and fringe distortion due to beam refractions through the plane window for LDA applications. J Mech Eng 2015; 51: 198–203.

Izuchi

Stability analysis of safety valve. In: Proceedings of the 10th topical conference on gas utilization, San Antonio, TX, 21–25 March 2010. Sydney, NSW, Australia: AICE.

Xia

Dai

et al . Numerical simulation on fluid dynamic behavior of high-pressure safety valves. In: Proceedings of the 2010 Asia-pacific power and energy engineering conference, Chengdu, China, 28–31 March 2010, pp.1–4. New York: IEEE.

Deng

Stability analysis of a direct-operated seawater hydraulic relief valve under deep sea. Math Probl Eng 2017; 2017: 5676317.

10.

Yang

Zhou

et al . Simulation of self-excited vibration behavior of pilot valve core on pilot-operated pressure relief valve with strong vibration. J Huazhong Univ Sci Technol 2015; 43: 58–63.

11.

Chen

Wang

Gong

et al . Characteristics of cartridge one-way relief valve. J Jilin Univ 2016; 46: 465–470.

12.

Song

Cui

Cao

et al . A CFD analysis of the dynamics of a direct-operated safety relief valve mounted on a pressure vessel. Energ Convers Manag 2014; 81: 407–419.

13.

Song

Wang

Park

et al . A fluid-structure interaction analysis of the spring-loaded pressure safety valve during popping off. Proced Eng 2015; 130: 87–94.

14.

Vallet

Ferrari

Rit

et al . Single phase CFD inside a water safety valve. In: Proceedings of the ASME pressure vessels and piping conference, Bellevue, Washington, DC, 18–22 July 2010, pp.335–342. New York: ASME.

15.

Beune

Kuerten

JGM

Van Heumen

MPC

. CFD analysis with fluid-structure interaction of opening high-pressure safety valves. Comput Fluid 2012; 64: 108–116.

16.

Hős

Bazsó

On the static instability of liquid poppet valves. Period Polytech Mech Eng 2015; 59: 1–7.

17.

Darby

The dynamic response of pressure relief valves in vapor or gas service, part I: mathematical model. J Loss Prev Process Ind 2013; 26: 1262–1268.

18.

Aldeeb

Darby

Arndt

The dynamic response of pressure relief valves in vapor or gas service. Part II: experimental investigation. J Loss Prev Process Ind 2014; 31: 127–132.

19.

Darby

Aldeeb

AA.

The dynamic response of pressure relief valves in vapor or gas service. Part III: model validation. J Loss Prev Process Ind 2014; 31: 133–141.

20.

Hős

Champneys

AR.

Grazing bifurcations and chatter in a pressure relief valve model. Physica D: Nonlin Phenom 2012; 241: 2068–2076.

21.

Hős

Bazsó

Champneys

Model reduction of a direct spring-loaded pressure relief valve with upstream pipe. IMA J Appl Math 2015; 80: 1009–1024.

22.

Hős

Champneys

Paul

et al . Dynamic behaviour of direct spring loaded pressure relief valves: III valves in liquid service. J Loss Prev Process Ind 2016; 43: 1–9.

23.

Hős

Champneys

Paul

et al . Dynamic behaviour of direct spring loaded pressure relief valves connected to inlet piping: IV review and recommendations. J Loss Prev Process Ind 2017; 48: 270–288.

24.

Zhang

Liu

et al . Influence of changed fuel injection pulse width and pressure on discharge coefficient in diesel engine. Trans Chin Soc Agri Eng 2015; 31: 71–76.

25.

Yan

et al . Effects of fuel injection pressure on combustion process and emission of diesel engine. J Chin Agri Mech 2016; 37: 129–134.

26.

Hős

Champneys

Paul

et al . Dynamic behavior of direct spring loaded pressure relief valves in gas service: model development, measurements and instability mechanisms. J Loss Prev Process Ind 2014; 31: 70–81.

27.

Zhou

et al . Bifurcation analysis and experimental study of direct-acting relief valve. J Vib Meas Diagn 2016; 36: 529–535.

Experimental research on the dynamic instability characteristic of a pressure relief valve

Abstract

Keywords

Introduction

Basic principles of PRV

Instability characteristic experiment of PRV

Experimental results and analysis

Data analysis for typical stable conditions

Data analysis for typical cycling instability

Data analysis for typical chatter instability

Stable boundary analysis

The 3% rule boundary

Quarter-wave model boundary

Conclusion

Footnotes

Appendix

Declaration of conflicting interests

Funding

ORCID iD

References