1) The document analyzes the dynamic behavior of a direct spring-operated pressure relief valve and the influence of the poppet's radial clearance on that behavior. 2) A mathematical model is developed and represented in MATLAB/Simulink. Simulation results show that smaller radial clearances lead to longer opening times and greater pressure overshoots, while larger clearances result in shorter opening times and smaller overshoots. 3) An optimal poppet radial clearance is estimated that provides a settling time of 0.02 seconds and minimizes pressure overshoot. The model can predict valve behavior and help select optimal settings.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
129
DYNAMIC BEHAVIOUR OF HYDRAULIC PRESSURE
RELIEF VALVE
B. J. Patil1
, Dr. V. B. Sondur2
1
Asst. Prof, Mechanical Engineering Department, Maratha Mandal Engineering College, Belgaum,
Karnataka, India
2
Founder Director, Sondur’s Academy, Belgaum, Karnataka, India
ABSTRACT
This paper discusses the influence of the radial clearance of the poppet of the direct spring
operated pressure relief valve type DPRS06K315 on the dynamic behaviour of the valve. The
mathematical model of the valve has been developed; these mathematical terms have been
represented in Matlab/SIMULINK. The results obtained by a simulation describe dynamic behaviour
of the valve and its influence on the system dynamic with respect to the poppet clearance.
Keywords: Radial Clearance, Simulation, Dynamic, Mathematical Model, SIMULINK, Valve Type
DPRS06K315.
I. INTRODUCTION
The pressure relief valves are used to safeguard the hydraulic components from greater
pressure[1]. This is one of the most important elements of a hydraulic system and is essentially
required for safe operation of the system. Its main function is to limit the system pressure within a
specified limit. It is normally a closed type and it opens when the pressure exceeds a specified
maximum value by diverting pump flow back to the reservoir. The simplest type valve consists of a
poppet held in a seat against the spring force as shown in fig 1 [2]. The oil enters from the opposite
side of the poppet. As system pressure exceeds the set value of pressure, the poppet lifts and the oil is
escaped through the orifice to the storage tank directly. It decreases the system pressure and as the
pressure reduces to the set limit again the valve closes.
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
130
Fig.1: DPRS06K315 Pressure Relief Valve
Relief and safety valves are fundamental equipments for oil and gas pipelines and
load/unload terminals[3]. The installation integrity and workers safety depend on the appropriate
design and performance of these equipments. In spite of the importance of relief valves, there is lack
of information about the dynamic behaviour of these equipments.[1] Thus, users are forced to work
using valve characteristics supplied only by manufactures. Further, the information supplied by
manufactures is generally restricted to situations of maximum pressure relief flow. The full dynamic
behaviour of the relief valves during their opening stage, which is fundamental for analysis of
transients during their actuation, is usually not available.[3]
In spite of the importance of relief valves, only a few works about its dynamic behaviour has
been published. Catalani (1984) performed a dynamic stability analysis of a relief valve and
identified the effects of its components on its stability[5]. The undesired phenomenon named chatter
(abrupt oscillations of the disc) was studied by MacLeod (1985) who modeled, using differential
equations, the dynamic of a relief valve and identified the conditions to avoid it[7]. In 1991 Shing
made a study about the dynamic and static characteristics of a two stage pilot relief valve and
determined the governing parameters of the valve response which could be improved.
The dynamic of a direct operated relief valve with directional damping was studied by
Dasgupta et al (2001) using the bondgraph technique. Maiti et al (2002) studied the dynamic
characteristics of a two-stage pressure relief valve with proportional solenoid control of its pilot
stage[6,13]. According to their results, the overall dynamic behaviour is dominated by the solenoid
characteristic relating force to applied voltage. Boccardi et al (2004) analyzed experimentally the
water/vapour two phase flows through a relief valve [3]. A new correlation for the discharge
coefficient was developed, by comparing the experimental data with the solution of the flow based
on a homogeneous model. The objective of this work is to simulate the dynamic behaviour of a
direct acting spring loaded pressure relief valve (PRV) during its actuation. The identification of its
governing parameters will allow the extension of the analysis to more general and real cases.[3]
II. MATHEMATICAL MODEL
Considering the fig.2 the total mass of the moving parts m is equal to the mass of the plunger
plus one third mass of the spring, the differential equation of the dynamic behavior is derived as
follows

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
131
Fig..2: Physical System of Pressure Relief Valve Model
The dynamic behaviour of the valve is described by the following set of mathematical
relations. The effect of the transmission lines is neglected.
The Poppet Valve Throttling Area.
The following mathematical expression for the poppet valve area Ap
Ap = ߨ(Rଶ
− (R − X ∗ tan(alphaሻሻଶ
ሻ (1)
Where R- radius of the poppet, X – poppet displacement
Equation of Motion of the Poppet
M.
ௗమଡ଼
ௗ௧మ + Fv + Fs − Fୗୖ − Ad ∗ Pd − Qsଶ
ρ/A = 0 (2)
where: x – poppet displacement, t – time, Fv – viscosity friction force, Fs – spring force,
FSR – Seat reaction force , A– poppet area normal to pressure, Pd – system pressure,
FV- Viscosity friction force is given as Fv = C.
ୢ୶
ୢ୲
(3)
where: C – viscous force coefficient.
FS-The spring force which acts on the poppet as Fs = K*. (X0 + X) (4)
Where K – spring stiffness, X0- pre –compressed spring length, X- poppet displacement.
Seat Reaction Force
The poppet displacement in the closure direction is limited mechanically. When reaching its
seat, a seat reaction force takes place due to the action of the spring stiffness.

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
132
Fୗୖ = ൜
0 X > 0
K(X0 + Xሻ X < 0
(5)
Flow Rate Through the Clearance of the Damping spool
Qd =
୮୧∗ୈୢ∗௖య∗(୔ି୔ୢሻ
(ଵଶ∗୫୳∗୐ሻ
(6)
Flow Rate Through the Poppet Valve
Qs = Cd. Ax. ට
ଶ∗(୔ି୔଴ሻ
ρ
(7)
Where AX – poppet valve area
Continuity Equation Applied to the Damping spool Chamber
Qௗ − Ad ∗
ୢଡ଼
ୢ୲
=
୚బା୅ୢ∗ଡ଼
୆
∗
ୢ୔೏
ୢ୲
(8)
ୢ୔
ୢ୲
=
୆
୚୮
(Qp − Qs − Qௗ − ݈ܳ݁ܽ݇ሻ (9)
III. DAMPING COEFFICIENT
To find the damping coefficient of the system, we should consider the poppet as piston and
the surrounding area of the poppet as a cylinder which is called as dash pot as shown in fig 3. The
poppet is moving to and fro in a cylinder full of viscous fluid as shown in fig 3. We should consider
the damping resistance due to the pressure difference on the two sides of the piston. The pressure
difference is caused by the restriction to the fluid flow due to the piston motion.
Fig. 3: Dash pot

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
133
It can be shown that if clearance between the piston and cylinder is small, the first two
components of the damping are negligible and the total damping is wholly due to the third
component, and is given by
C =
ଵଶ.ఓ
గ
.
୅୮మ∗୐
ୈ୫∗ୡయ (10)
Where C= Viscous damping coefficient N.s/m.
µ = Coefficient of viscosity of the fluid Pa.s
Ap = Area of the piston m2
L= Length of the Piston m.
Dm = Mean diameter of the piston and the cylinder
c = clearance between the piston and the cylinder.
IV. SIMULINK MODEL
Based on the derived differential equation of the pressure relief valve poppet movement, fluid
flow rate, pressure at inlet of the valve and the damping chamber the simulation model in
MATLAB/SIMULINK has been obtained as shown in fig.4. A scope block is connected to monitor
the time response of the pressure relief valve. The connections to the various blocks in the model
have been made by considering the Equations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 which are obtained in
chapter 4 mathematical modelling.
Fig. 4: Simulink Model
V. SIMULATION RESULTS
The transient response of the valve is calculated for different values of the poppet radial
clearance. The transient response of valve input is calculated and plotted as shown in fig 5-9. The
simulation results show that the radial clearance has a significant effect on the valve response. For
smaller radial clearance, flow rate into the damping spool chamber is throttled and the pressure
building in this chamber is delayed. The poppet takes a longer time to open which results in greater
pressure overshoot. For larger radial clearance, the damping effect weakens and the poppet takes a
short time to open which results in lesser pressure overshoot.

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
134
Fig.5: Simulation results of response of the pressure relief valve pressure for damping poppet radial
clearance of 10e-6 m
Fig.6: Simulation results of response of the pressure relief valve pressure for damping poppet radial
clearance of 15e-6 m

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
135
Fig.7: Simulation results of response of the pressure relief valve pressure for damping poppet radial
clearance of 20e-6 m
Fig.8: Simulation results of response of the pressure relief valve pressure for damping poppet radial
clearance of 25e-6 m

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
136
Fig.9: Simulation results of response of the pressure relief valve pressure for damping poppet radial
clearance of 30e-6 m
VI. CONCLUSION
The effect of the poppet clearance geometry on the system dynamic characteristics has been
examined by means of the shown mathematical model. Under the same operating conditions, the
behaviour of the pressure relief valve is varied, by chasing the poppet clearance. The simulation
results are presented through system Pressure, Fig. 5-9. An optimum value of the radial clearance is
estimated from the graph as shown in Fig. 9. This figure shows that the settling time is within 0.02
seconds and the maximum percentage of overshoot is considerably reduced.
By using the simulation model, it is possible to predict the pressure relief valve behaviour
during its working. In addition, by using the mathematical model it is possible to select the optimal
setting points of the pressure relief valve (poppet radial clearance with respect to the system
requirements
VII ACKNOWLEDGEMENT
I would like to take this opportunity to thanks Mr. Anand Samant, Managing Director, PSPL,
Belgaum and Late shri Suresh Hundre, Polyhydron Pvt. Ltd., Belgaum and Siddhartha Hundre,
Corporate Manager, Polyhydron Pvt. Ltd, Belgaum., who allowed me to analyse the valve for
research from their organisations.

9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 10, October (2014), pp. 129-137 © IAEME
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VIII. REFERENCE
[1] API RP 520, 2000, “Sizing, Selection and Installation of Pressure Relieving Devices in
Refineries” Seventh edition, American Petroleum Institute.
[2] The catalogue of DPR 06 and DPR 10- Polyhydron Pvt. Ltd, Belgaum.
[3] Boccardi, G., Bubbico, R., Celata, G.P and Mazzarotta. B., 2005, “Two –phase Flow
Through Pressure Safety Valves- Experimental Investigation an Model Prediction”, Chemical
Engineering Science Vol.6.0, pp. 5284-5293.
[4] A.J. Ortega, B.N. Azevedo, L.F.G. Pires, A.O. Nieckele, “A numerical model about the
dynamic behaviour of a pressure relief valve”, Proc. 12th Brazilian Congress of Thermal
Engineering and Sciences, Belo Horizonte, MG, 2008, pp. -8.
[5] Catalini, L. 1984, “Dynamic stability analysis of spring loaded safety valve- Elements for
improved valves performance through assistance.
[6] Devices “. Conference on structural Mechanical in Reactors, August 22-26.
[7] Dasgupta, K and Karmakar, R., 2002” Modelling and dynamic of single stage pressure relief
valve with directional damping”, Simulation Modelling Practice, vol.10, pp.51-57.
[8] Fox.R. w. And Mcdonald, a.T., 1998, “Introduction to Fluid Mechanics”, John Wiley & Sons
Inc.
[9] Macleod, G. 1985, “Safety valve dynamic instability: an analysis of chatter”, ASME journal
of Pressure Vessel Technology, Vol. 107, pp. 172-177.
[10] Maiti, R. Saha, R. And Watton, J., 2002, “The static and dynamic characteristics of a pressure
relief valve with a proportional solenoid- controlled pilot stage”, Proc Instn Mech Engrs,
Vol. 216, Part I, pp. 143-156.
[11] Zappe, R. W., 1998, “Valve selection handbook”, Fourth edition, Goulf Professional
Publishing.
[12] A.J. Ortega, B.N. Azevedo, L.F.G. Pires, A.O. Nieckele, Analysis of the discharge coefficient
of a spring-loaded pressure relief valve during its dynamic behavior, Proc. 20th International
Congress of Mechanical Engineering, Gramado, Brazil, 2009, 1-9.
[13] S. Sethi, Y.S. Lai, A simulation model to predict performance characteristics of safety relief
valve, Proc. 1st Summer Computer Simulation Conference, Vancouver, Canada, 1993,
pp. 800-806.
[14] K. Dasgupta, R. Karmakar, Dynamic Analysis of Pilot Operated Pressure Relief Valve,
Simulation Modeling Practice and Theory, Vol.10, pp. 35-49, 2002.
[15] Chitthaarth.M.R, Charles Dhonynaveen.I.A, Sunil Kumar.G and Dr.K.Manivannan, “A Study
and Analysis on HCCI Engine's Inlet Valve”, International Journal of Mechanical
Engineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp. 545 - 554, ISSN Print:
0976 – 6340, ISSN Online: 0976 – 6359.
[16] Yuvraj K Lavhale and Prof. Jeevan Salunke, “Overview of Failure Trend of Inlet & Exhaust
Valve”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 5,
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