Pilot-Operated Check Valve (IL)

Check valve with pilot pressure control in an isothermal liquid system

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Libraries:
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Directional Control Valves

Description

The Pilot-Operated Check Valve (IL) block models a flow-control valve that allows variable-direction flow based on the pilot-line pressure. The free flow direction is from port A to port B and the valve opens when the control pressure rises above the cracking pressure. When the control pressure exceeds the value of the Cracking pressure differential parameter or the value of the first element of the Control pressure vector or Reference pressure differential vector parameters, the poppet moves to allow flow in either direction. There is no mass flow at port X or between port X and ports A and B.

When the Pilot pressure direction parameter is Pilot-to-open, 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.

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

  • When Opening pilot pressure specification is Gauge pressure at port X, p_pilot is the pressure difference between port X and atmospheric pressure.

• k_p is the value of the Pilot ratio parameter, which is 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 Pilot pressure direction parameter is Pilot-to-close, the control pressure is

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

where p_pilot = p_X - p_B.

Spool Configuration

When the Pilot pressure direction parameter is Pilot-to-open, you can configure the spool and poppet as either rigidly connected or disconnected. When the Spool configuration parameter is 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 based only on the pressure differential between ports A and B. When the Spool configuration parameter is Rigidly connected pilot spool and poppet, the pilot pressure is the measured pressure differential according to the opening specification.

When the Pilot pressure direction parameter is Pilot-to-close, the pilot spool and poppet are disconnected. The relative pressure at port X must be positive. If the measured pilot pressure is negative, the control pressure is based only on the pressure differential between ports A and B.

Area vs. Pressure Opening Parameterizations

When Opening parameterization is Linear - Area vs. pressure or Tabulated data - Area vs. pressure, the mass flow rate through the valve is

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

where:

• C_d is the value of the Discharge coefficient parameter.

• A_valve is the instantaneous valve open area.

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

• $$\overline{\rho }$$ 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,

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

The pressure loss is the pressure reduction in the valve due to a decrease in area. PR_loss is

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

The pressure recovery is the positive pressure change in the valve due to an increase in area. If you do not want to capture this increase in pressure, clear the Pressure recovery check box. In this case, PR_loss is 1.

Linear Area vs. Pressure

When Opening parameterization is Linear - Area vs. pressure, the valve area is

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

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

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

When the valve is in a near-open or near-closed position, you can maintain numerical robustness in your simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smoothly saturates the control pressure between p_max and p_cracking. For more information, see Numerical Smoothing.

Tabulated Area vs. Pressure

When Opening parameterization is Tabulated data - Area vs. pressure, the block interpolates the area of the valve as

$$A_{valve}=tablelookup\left(p_{control,TLU},A_{valve,TLU},p_{control},interpolation=linear,extrapolation=nearest\right),$$

where:

• p_control,TLU is the Control pressure vector parameter

• A_valve,TLU is the Opening area vector parameter.

The area of the valve saturates between the first and last element of the Opening area vector parameter. The first element of the Control pressure vector parameter corresponds to the cracking pressure differential.

Volumetric Flow Rate vs. Pressure Parameterization

When Opening parameterization is Tabulated data - Volumetric flow rate vs. pressure, the mass flow rate is

$$\dot{m}=\overline{\rho }K\frac{\Delta p}{{\left(\Delta p^2+\Delta p_{crit}^2\right)}^{1/4}},$$

and

$$K\text{=tablelookup}\left(\Delta p_{ref,TLU},\frac{{\dot{V}}_{ref,TLU}}{\sqrt{\Delta p_{ref,TLU}}},p_{control},interpolation=linear,extrapolation=nearest\right),$$

where:

• Δp_ref,TLU is the Reference pressure differential vector parameter.

• $$\dot{V}$$_ref,TLU is the Reference volumetric flow rate vector parameter.

The value of K saturates between the values $$\frac{{\dot{V}}_{ref,TLU}\left(1\right)}{\sqrt{\Delta p_{ref,TLU}\left(1\right)}}$$ and $$\frac{{\dot{V}}_{ref,TLU}\left(\text{end}\right)}{\sqrt{\Delta p_{ref,TLU}\left(\text{end}\right)}}$$, which means that the first elements of the Reference pressure differential vector and Reference volumetric flow rate vector parameters correspond to the leakage mass flow rate and the last elements correspond to the maximum mass flow rate.

Opening Dynamics

If you select Opening dynamics, the block introduces a lag to the flow response to the modeled control pressure. p_control becomes the dynamic control pressure, p_dyn. The instantaneous change in dynamic control pressure depends on the Opening time constant parameter, τ,

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

By default, the Opening dynamics check box is cleared.

Mass Conservation

Mass is conserved through the valve,

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

Examples

Pilot-Operated Check Valve Test Rig

This example shows a test rig for the Pilot-Operated Check Valve (IL) block. The valve connects to three ideal pressure sources, two of which create the pressure differential across the main flow line, while the third applies pressure to the pilot port X. This pressure allows flow through the valve even if the main pressure differential is negative.

Model

Simulation Results from Scopes

Simulation Results from Simscape Logging

The plots below show the behavior of the pilot-operated check valve under various pressure conditions. The valve opens when the control pressure is larger than the cracking pressure differential. The control pressure is , where is the pilot pressure determined using the pressure at port X and is the pilot ratio. If the pilot pressure is sufficiently large, the valve opens even if the pressure differential is negative. With and the valve opened, fluid flows from port B to port A.

Ports

Conserving

A — Liquid port

isothermal liquid

Isothermal liquid conserving port associated with the valve entry. When the control pressure exceeds the cracking pressure, liquid can exit from this port.

B — Liquid port

isothermal liquid

Isothermal liquid conserving port associated with the valve exit. When the control pressure exceeds the cracking pressure, liquid can enter the valve from this port.

X — Pressure port

isothermal liquid

Isothermal liquid conserving port associated with the pressure port that contributes to the flow control through the valve. There is no mass flow through this port.

Parameters

Pilot pressure direction — Whether pilot pressure assists with valve opening or valve closing

Pilot-to-open (default) | Pilot-to-close

Whether the pilot pressure assists with valve opening or closing. If you set the parameter to Pilot-to-open, the pilot pressure assists the valve opening. If you set the parameter to Pilot-to-close, the pilot pressure assists the valve closing.

Spool configuration — Valve geometry

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

Valve geometry. Use Rigidly connected pilot spool and poppet to model a valve with an opening mechanism connected to the valve poppet, or Disconnected pilot spool and poppet to model an opening mechanism that is aligned with, but moves freely away from, the valve poppet. This parameter determines the pilot pressure calculation.

Dependencies

To enable this parameter, set Pilot pressure direction to Pilot-to-open.

Opening pilot pressure specification — Reference pressure differential for valve control

Pressure difference of port X relative to port A (default) | Gauge pressure at port X

Reference pilot pressure differential to use for the valve control. The block adds the pilot pressure differential to the pressure differential between ports A and B and compared against the valve threshold Cracking pressure differential.

Dependencies

To enable this parameter, set Pilot pressure direction to Pilot-to-open.

Opening parameterization — Method of calculating valve opening

Linear - Area vs. pressure (default) | Tabulated data - Area vs. pressure | Tabulated data - Volumetric flow rate vs. pressure

Method of calculating valve opening:

• Linear - Area vs. pressure — The valve opening area corresponds linearly to the valve pressure.

• Tabulated data - Area vs. pressure — The block determines the valve mass flow rate from a table of area values with respect to the pressure differential.

• Tabulated data - Volumetric flow rate vs. pressure — The block determines the valve mass flow rate from a table of volumetric flow rate values with respect to the pressure differential.

Cracking pressure differential — Pressure threshold

0.01 MPa (default) | positive scalar

Set pressure for the valve operation.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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. The block uses this value to determine the normalized valve pressure and the valve opening area during operation.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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 saturates to the specified leakage area. This parameter contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

Control pressure vector — Control pressure values for tabular parameterization

[0.01 : 0.01 : 0.1] MPa (default) | 1-by-n vector

Vector of pressure differential values for the tabular parameterization of the valve opening area. The first element of this vector is the cracking pressure differential.

The vector elements must correspond one-to-one with the elements in the Opening area vector parameter. The elements are in ascending order and must be greater than 0. The block employs linear interpolation between the table data points.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Opening area vector — Valve opening areas for tabular parameterization

[1e-10, 1e-05, 2e-05, 3e-05, 4e-05, 5e-05, 6e-05, 7.5e-05, 8.5e-05, .0001] m^2 (default) | 1-by-n vector

Vector of valve opening areas for the tabular area parameterization of the valve opening area. The first element of this vector is the leakage area when the valve is fully closed and the last element is the maximum valve area.

The vector elements must correspond one-to-one with the elements in the Control pressure vector parameter. The elements are in ascending order and must be greater than 0. The block employs linear interpolation between the table data points.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Area vs. pressure.

Reference pressure differential vector — Pressure differential vector for tabular volumetric flow rate parameterization

[0.01 : 0.01 : 0.1] MPa (default) | 1-by-n vector

Vector of pressure differential values for the tabular volumetric flow rate parameterization. These values are the free flow data when the pilot pressure is 0. The vector elements must correspond one-to-one with the elements in the Reference volumetric flow rate vector parameter. The elements are in ascending order and must be greater than 0. The block employs linear interpolation between the table data points.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

Reference volumetric flow rate vector — Vector of volumetric flow rate for tabulated data parameterization

[.000358, .045, .11, .191, .284, .39, .505, .63, .764, .905] .* 1e-3 m^3/s (default) | 1-by-n vector

Vector of volumetric flow rate values for the tabular parameterization. These values are the free flow data when the pilot pressure is 0. This vector must have the same number of elements as the Reference pressure differential vector parameter. The vector elements must be in ascending order.

Dependencies

To enable this parameter, set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure.

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 the block uses in the pressure-flow rate equation that determines the mass flow rate through the valve.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the orifice.

Smoothing factor — Numerical smoothing factor

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

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure.

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.

Dependencies

To enable this parameter, set Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

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. Selecting Opening dynamics approximates the opening conditions by introducing a first-order lag in the pressure response.

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, select Opening dynamics.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

R2025a: Parameterize block by using tabulated data

Parameterize the block with tabulated data for area and pressure or for volumetric flow rate and pressure. Set Opening parameterization to Linear - Area vs. pressure to preserve the previous block functionality

R2025a: Model pilot-to-close check valve

Set the Pilot pressure direction parameter to Pilot-to-close to model a valve where the pilot pressure assists the valve closing. Set Pilot pressure direction to Pilot-to-open to preserve the previous block functionality.