6.4. Check valve / Non-return valve

Fig. 6.4.1 Schematized check valve

Fall type

Type label	Description	Active
Heat Check valve	Ideal check valve; closes if Q < 0, opens if p1 > p2 + ∆preopen	No

6.4.1. Mathematical model

Ideal check valve

An open check valve is modelled as a resistance by the following equations.

Pressure difference:

(6.4.1)$$\mathrm{\Delta }p=p_1-p_2=\frac{\xi }{2\rho }\frac{\dot{m}\left|\dot{m}\right|}{A^2}+g\rho (y_2-y_1)$$

Continuity:

(6.4.2)$${\dot{m}}_1={\dot{m}}_2$$

Temperature difference:

(6.4.3)$$\dot{m}{c}_{p2}{T}_2=\dot{m}{c}_{p1}{T}_1+fr\cdot Q_{\text{gen}}$$

with:

Variable	Description	Units
$p_1/p_2$	pressure at connection point	Pa
$\rho$	density at upstream connection point	kg/m³
$y_1/Y_2$	Heat node (elevation) heights	m
$\xi$	valve loss coefficient	-
$\dot{m}$	mass flow	kg/s
A	Valve inlet area	m2
$c_1/c_2$	specific heat of the fluid	J/kg/K
fr	fraction of generated heat that is transferred to the fluid	-
fr	fraction of generated heat that is transferred to the fluid	-

The discharge area of the check valve may differ from the cross sectional area of the adjacent pipes. The heat generated in the check valve (due to friction) is partially absorbed by the fluid. The extend to which this generated heat is absorbed by the fluid can be set with the ‘fraction of generated heat that is transferred to the fluid’. The rest of the heat is lost. The generated heat is given by:

(6.4.4)$$Q_{\text{gen}}=\xi \frac{{\dot{m}}^3}{2A^2{\rho }^2}$$

The criteria for opening and closing are defined separately.

Closure criteria

An ideal check valve closes when:

(6.4.5)$$Q_1<0$$

Opening criteria

A closed valve (re)opens when the pressure difference across the valve exceeds a specified value (the default is 0):

(6.4.6)$$p_1-p_2>\mathrm{\Delta }{p}_{\text{reopen}}$$

6.4.2. Heat Check valve properties

The check valve is modelled as an ideal check valve, which closes without reverse flow. However, in practice a check valve does not behave ideally, but closes after flow reversal. The closure is accompanied with a certain amount of reverse flow and pressure surges, depending on the valve type.

Note: The $\mathrm{\Delta }{p}_{\text{reopen}}$ may not correspond with the results of $\mathrm{\Delta }p$, because of discretization errors. The $\mathrm{\Delta }{p}_{\text{reopen}}$ approaches $\mathrm{\Delta }p$ for small $\mathrm{\Delta }t$.

Alternatively, the closure behaviour of check valves may be modelled with the component valve. The valve position is then prescribed as function of (closure) time. In the case of damped check valves the valve may be closed in two stages: A stage of passive and a stage of active damping.

Note: The initial state of the check valve (i.e., open or closed) is set automatically if the option Automatic is chosen. If the option Open or Closed is chosen, the initial state is automatic corrected during the steady-state calculation and a warning message is shown to the user if the initial state of the check valve is altered.

6.4.2.1. Hydraulic specifications

Description	Input	SI-units	remarks
Inner diameter	real	[m]
Loss coefficient	real	[-]
Delta_p for reopen	real	[N/m2]
Initial state	Open Closed Automatic		Default = Automatic
Fraction gen. heat to fluid	real	[-]	Default = 0

6.4.2.2. Component messages

Table 6.4.1 Component messages

Message	Type	Explanation
Starts in closed phase	Info
Starts in open phase	Info
Closes	Info
Starts in closed phase	Opens