Pilot-Operated Check Valve (IL)

Check valve with pilot pressure control in an isothermal liquid system

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Description

The Pilot-Operated Check Valve (IL) block models a flow-control valve with variable flow directionality based on the pilot-line pressure. Flow is normally restricted to travel from port A to port B in either a connected or disconnected spool-poppet configuration, according to the Pilot configuration parameter.

Pilot-Operated Check Valve Schematic

The control pressure, p_control is:

$$p_{control}=p_{pilot}{k}_p+\left(p_A-p_B\right),$$

where:

• p_pilot is the control pilot pressure differential.

• k_p is the Pilot ratio, the ratio of the area at port X to the area at port A: $$k_p=\frac{A_X}{A_A}.$$

• p_A – p_B is the pressure differential over the valve.

When the control pressure exceeds the Cracking pressure differential, the poppet moves to allow flow from port B to port A.

There is no mass flow between port X and ports A and B.

Valve Pressure Control with a Pilot Port

The pilot pressure differential for valve control can be configured in two ways:

• When the Opening pilot pressure specification parameter is set to Pressure at port X relative to port A, the pilot pressure is the pressure differential between port X and port A.

• When Opening pilot pressure specification is set to Pressure at port X relative to atmospheric pressure, the pilot pressure is the pressure difference between port X and atmospheric pressure.

When Pilot configuration is set to Disconnected pilot spool and poppet, the relative pressure at port X must be positive. If the measured pilot pressure is negative, the control pressure is only based on the pressure differential between ports A and B. In the Rigidly connected pilot spool and poppet setting, the pilot pressure is the measured pressure differential according to the opening specification.

Mass Flow Rate Equation

Mass is conserved through the valve:

$${\dot{m}}_A+{\dot{m}}_B=0.$$

The mass flow rate through the valve is calculated as:

$$\dot{m}=\frac{C_d{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where:

• C_d is the Discharge coefficient.

• A_valve is the instantaneous valve open area.

• A_port is the Cross-sectional area at ports A and B.

• $$\overline{\rho }$$ is the average fluid density.

• Δp is the valve pressure difference, p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, the flow regime transition point between laminar and turbulent flow:

$$\Delta p_{crit}=\frac{\pi \overline{\rho }}{8A_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{C_d}\right)}^2.$$

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PR_loss is calculated as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\left(1-C_d^2\right)}-C_d\frac{A_{valve}}{A_{port}}}{\sqrt{1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\left(1-C_d^2\right)}+C_d\frac{A_{valve}}{A_{port}}}.$$

Pressure recovery describes the positive pressure change in the valve due to an increase in area. If you do not wish to capture this increase in pressure, set the Pressure recovery to Off. In this case, PR_loss is 1.

The opening area, A_valve, is also impacted by the valve opening dynamics.

Opening Parameterization

The linear parameterization of the valve area is

$$A_{valve}=\widehat{p}\left(A_{\max }-A_{leak}\right)+A_{leak},$$

where the normalized pressure,$$\widehat{p}$$, is

$$\widehat{p}=\frac{p_{control}-p_{cracking}}{p_{\max }-p_{cracking}}.$$

Opening Dynamics

If opening dynamics are modeled, a lag is introduced to the flow response to the modeled control pressure. p_control becomes the dynamic control pressure, p_dyn; otherwise, p_control is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:

$${\dot{p}}_{dyn}=\frac{p_{control}-p_{dyn}}{\tau }.$$

By default, Opening dynamics is set to Off.

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry point to the valve. When the control pressure exceeds the cracking pressure, liquid is able to exit from this port.

B — Liquid port

isothermal liquid

Liquid exit point from the valve. When the control pressure exceeds the cracking pressure, liquid is able to enter the valve from this port.

X — Pressure port

isothermal liquid

Pressure port that contributes to the flow control through the valve.

Parameters

Pilot configuration — Valve geometry

Rigidly connected pilot spool and poppet (default) | Disconnected pilot spool and poppet

Valve geometry. The valve can either have an opening mechanism that is connected to the valve poppet, in the case of the Rigidly connected pilot spool and poppet setting, or an opening mechanism that is aligned with, but moves freely away from, the valve poppet, in the case of the Disconnected pilot spool and poppet setting. The configuration choice determines the pilot pressure calculation.

Opening pilot pressure specification — Reference pressure differential for valve control

Pressure at port X relative to port A (default) | Pressure at port X relative to atmospheric pressure

Reference pressure differential used for valve control. This differential defines the pilot pressure differential, which is added to the pressure differential between ports A and B and compared against the valve threshold Cracking pressure differential.

Cracking pressure differential — Pressure threshold

0.01 MPa (default) | positive scalar

Set pressure for the valve operation.

Maximum opening pressure differential — Maximum pressure differential in opened valve

0.02 MPa (default) | positive scalar

Maximum pressure differential in an opened valve. This value provides an upper limit to simulation pressures so that results remain physical.

Pilot ratio — Pilot port area ratio

1 (default) | positive scalar in the range of (0,1]

Ratio of port area X to port area A.

Maximum opening area — Maximum valve area

1e-4 m^2 (default) | positive scalar

Maximum valve area. This value is used to determine the normalized valve pressure and the valve opening area during operation.

Leakage area — Gap area when in fully closed position

1e-10 m^2 (default) | positive scalar

Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.

Cross-sectional area at ports A and B — Area at conserving ports

inf m^2 (default) | positive scalar

Areas at the entry and exit ports A and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the valve.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor accounting for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

12 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the orifice.

Pressure recovery — Whether to account for pressure increase in area expansions

Off (default) | On

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.

Opening dynamics — Whether to introduce flow lag due to valve opening

Off (default) | On

Whether to account for transient effects to the fluid system due to opening the valve. Setting Opening dynamics to On approximates the opening conditions by introducing a first-order lag in the pressure response. The Opening time constant also impacts the modeled opening dynamics.

Opening time constant — Valve opening time constant

0.1 s (default) | positive scalar

Constant that captures the time required for the fluid to reach steady-state conditions when opening or closing the valve from one position to another. This parameter impacts the modeled opening dynamics.

Dependencies

To enable this parameter, set Opening dynamics to On.