DynamicReliefValve

Copyright © EDF 2002 - 2026

ThermoSysPro Version 4.2

This component model is documented in Sect. 13.13 of the ThermoSysPro book.

Dynamic relief valve

Relief valves are used to limit the pressure in a system.
When the set pressure level is exceeded, the relief valve opens.
It closes again once the system pressure reaches the valve reseting pressure.s

Following assumptions are made:

• the fluid is subsonic and incompressible.

• the volume inside the valve is negligible, so that inertia is neglected.

Modelica component model

The equations mentioned below are implemented in the component DynamicReliefValve, located in the WaterSteam.PressureLosses sub-library.
This component has 2 connectors:

• C1: fluid inlet,

• C2: fluid outlet.

Nomenclature

Symbol	Description	Unit	Definition	Modelica name
\(A_{\mathrm{i}}\)	Clapper section at the inlet	\(\mathrm{m}^{2}\)		A
\(A_{\mathrm{o}}\)	Clapper section at the outlet	\(\mathrm{m}^{2}\)		A2
\(C_{\mathrm{v}}\)	Flow coefficient of the valve	U.S. [USG/min]		Cvmax
\(D\)	Valve damping	\(-\)		D
\(f_{\mathrm{d}}\)	Force acting on the clapper due to damping	\(\mathrm{N}\)		Fd
\(f_{\mathrm{h}}\)	Hydraulic force acting on the clapper	\(\mathrm{N}\)		Fh
\(f_{\mathrm{s}}\)	Force acting on the clapper due to the spring	\(\mathrm{N}\)		Fr
\(f_{\mathrm{t}}\)	Total force acting on the clapper	\(\mathrm{N}\)		Ft
\(f_{\mathrm{w}}\)	Force acting on the clapper due to the weight of the clapper	\(\mathrm{N}\)		Fp
\(h\)	Fluid specific enthalpy	\(\mathrm{J} / \mathrm{kg}\)		h
\(h_{\mathrm{c}}\)	Valve height	\(\mathrm{m}\)	\(h_{\mathrm{c}}=z_{\max }-z_{\min }\)	-
\(K_{\mathrm{e}}\)	Valve spring stiffness	\(\mathrm{N} / \mathrm{m}\)		Ke
\(\dot{m}\)	Fluid mass flow rate	\(\mathrm{kg} / \mathrm{s}\)		Q
\(M\)	Valve mass	\(\mathrm{kg}\)		m
\(P_{\mathrm{i}}\)	Fluid pressure at the inlet	\(\mathrm{Pa}\)		C1.P
\(P_{\mathrm{o}}\)	Fluid pressure at the outlet	\(\mathrm{Pa}\)		C2.P
\(v\)	Clapper velocity	\(\mathrm{m} / \mathrm{s}\)		v
\(z\)	Clapper position	\(\mathrm{m}\)		z
\(z_{\min }\)	Clapper minimum position (valve fully closed)	\(\mathrm{m}\)		z_min
\(z_{\max }\)	Clapper maximum position (valve fully open)	\(\mathrm{m}\)		z_max
\(\delta\)	Difference between the free spring length and the spring length when the valve is closed	\(\mathrm{m}\)		-
\(\Delta P\)	Pressure loss of the fluid between the valve inlet and outlet	\(\mathrm{Pa}\)	\(P_{\mathrm{i}}-P_{\mathrm{o}}\)	deltaP
\(\rho\)	Fluid density	\(\mathrm{kg} / \mathrm{m}^{3}\)		rho
\(\rho_{\text {water, } 60^{\circ} \mathrm{F}}\)	Density of water at \(60^{\circ} \mathrm{F}\left(15.5556^{\circ} \mathrm{C}\right) .\)	\(\mathrm{kg} / \mathrm{m}^{3}\)		rho60F
\(\Omega\)	Valve position	\(-\)		Ouv

Governing equations

Static momentum balance equation

• Validity domain:

\(\forall \dot{m}\) and \(C_{\mathrm{v}} \geq 0\). For \(C_{\mathrm{v}}=0, \Delta P\) must be defined.

• Mathematical formulation:

\[\Delta P \cdot C_{\mathrm{v}} \cdot\lvert C_{\mathrm{v}}\rvert =1.732189 \times 10^{12} \cdot \frac{\dot{m} \cdot \lvert \dot{m} \rvert }{\rho \cdot \rho_{\text {water, } 60^{\circ} F}}\]

• Comments:

This equation is the same as the control valve \(C_{\mathrm{v}}=f_{v}(\Omega)\) where \(f_{v}\) is the valve characteristic. It is assumed that \(\Omega=\frac{z-z_{\min }}{z_{\max }-z_{\min }}\).

Clapper equation

• Validity domain:

\( z_{\min} \leq z \leq z_{\max} \)

• Mathematical formulation:

\[ M \cdot \frac{\mathrm{d} u}{\mathrm{d}t}=\left\{\begin{array}{l} f_{\mathrm{t}} \text{ if } z_{\min }<z<z_{\max } \ f_{\mathrm{t}} \text{ if } z \leq z_{\min } \text{ and } f_{\mathrm{t}}>0 \ f_{\mathrm{t}} \text{ if } z \geq z_{\max } \text{ and } f_{\mathrm{t}}<0 \ 0 \text{ else }\end{array}\right.\]

\[ u =\left\{\begin{array}{l}\frac{\mathrm{d} z}{\mathrm{d} t} \text{ when } z_{\min }<z<z_{\max } \ 0 \text{ when } z \leq z_{\min } \text{ or } z \geq z_{\max }\end{array}\right.\]

\[ f_{\mathrm{t}} = f_{\mathrm{w}}+f_{\mathrm{s}} +f_{\mathrm{d}}+ f_{\mathrm{h}} \ f_{\mathrm{w}} = -M \cdot g \ f_{\mathrm{d}} = -D \cdot \frac{\mathrm{d} z}{\mathrm{d} t} \ f_{\mathrm{s}} = -K_{\mathrm{e}} \cdot (z - z_{\min} + \delta) \ f_{\mathrm{h}} = P_{\mathrm{i}} \cdot A_{\mathrm{i}} - P_{\mathrm{o}} \cdot A_{\mathrm{o}}\]

• Comments:

The velocity and acceleration are set to zero when the clapper hits the mechanical stops. The equal sign is replaced by \(\leq\) or \(\geq\) in the transition conditions \(z=z_{\min }\) and \(z=z_{\max }\) because equal signs are not recognized by solvers to compare real values.

References

El Hefni, Baligh and Bouskela, Daniel (2019). Modeling and Simulation of Thermal Power Plants with ThermoSysPro, sect. 13.1. Springer Nature Switzerland AG.