Check Valve (IL)

Check valve in an isothermal system

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Description

The Check Valve (IL) block models the flow through a valve from port A to port B, and restricts flow from traveling from port B to port A. When the pressure at port B meets or exceeds the set pressure threshold, the valve begins to open.

You can enable faulty behavior by setting Enable faults to On.

Pressure Control

There are two options for valve control:

• When Opening pressure differential is set to Pressure differential, the control pressure is the pressure differential between ports A and B. The valve begins to open when P_control meets or exceeds the Cracking pressure differential.

• When Opening pressure differential is set to Pressure at port A, the control pressure is the pressure difference between port A and atmospheric pressure. When P_control meets or exceeds the Cracking pressure (gauge), the valve begins to open.

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.

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.

Numerically-Smoothed Pressure

At the extremes of the control pressure range, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. A smoothing function is applied to every calculated control pressure, but primarily influences the simulation at the extremes of this range.

The Smoothing factor, s, is applied to the normalized pressure, $$\widehat{p}$$:

$${\widehat{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{p}}_{}^2+{\left(\frac{s}{4}\right)}^2}-\frac{1}{2}\sqrt{{\left(\widehat{p}-1\right)}^2+{\left(\frac{s}{4}\right)}^2},$$

and the smoothed pressure is:

Faulty Behavior

When faults are enabled, the valve open area becomes stuck at a specified value in response to one or both of these triggers:

• Simulation time — Faulting occurs at a specified time.

• Simulation behavior — Faulting occurs in response to an external trigger. This exposes port T.

Three fault options are available in the Opening area when faulted parameter:

• Closed — The valve area freezes at the Leakage area.

• Open — The valve area freezes at the Maximum opening area.

• Maintain at last value — The valve freezes at the open area when the trigger occurs.

Once triggered, the valve remains at the faulted area for the rest of the simulation.

You can set the block to issue a fault report as a warning or error message in the Simulink Diagnostic Viewer with the Reporting when fault occurs parameter.

Ports

Conserving

A — Liquid port

isothermal liquid

Entry point to the valve.

B — Liquid port

isothermal liquid

Exit point to the valve.

Input

T — External fault trigger

physical signal

Physical signal port for an external fault trigger. Triggering occurs when the value is greater than 0.5. There is no unit associated with the trigger value.

Dependencies

This port is visible when Enable faults is set to On and Enable external fault trigger is set to Fault when T >= 0.5.

Parameters

Parameters

Opening pressure specification — Pressure differential used for valve control

Pressure differential (default) | Pressure at port A

Specifies the control pressure differential. The Pressure differential option refers to the pressure difference between ports A and B. The Pressure at port A option refers to the pressure difference between port A and atmospheric pressure.

Cracking pressure differential — Threshold pressure

0.01 MPa (default) | positive scalar

Pressure beyond which the valve operation is triggered. This is the set pressure when the control pressure is the pressure differential between ports A and B.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential.

Cracking pressure (gauge) — Threshold pressure

0.1 MPa (default) | positive scalar

Gauge pressure beyond which valve operation is triggered when the control pressure is the pressure differential between port A and atmospheric pressure.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure at port A.

Maximum opening pressure differential — Valve differential pressure maximum

0.1 MPa (default) | positive scalar

Maximum valve differential pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure differential.

Maximum opening pressure (gauge) — Valve pressure maximum

0.2 MPa (default) | positive scalar

Maximum valve gauge pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

Dependencies

To enable this parameter, set Opening pressure specification to Pressure at port A.

Maximum opening area — Area of fully opened valve

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

Cross-sectional area of the valve in its fully open position.

Leakage area — Valve gap area when in fully closed position

1e-12 m^2 (default) | positive scalar

Sum of all gaps when the valve is in its 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 valve entry or exit

inf m^2 (default) | positive scalar

Cross-sectional area at the entry and exit ports A and B. These areas 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 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 valve.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar

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.

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 account for flow response 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 flow 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 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.

Faults

Enable faults — Fault option

Off (default) | On

Enable externally or temporally triggered faults. When faulting occurs, the valve area normally set by the opening parameterization will be set to the value specified in the Opening area when faulted parameter.

Opening area when faulted — Set faulted area

Closed (default) | Open | Maintain at last value

Sets the faulted valve area. You can choose for the valve to seize at the fully closed or fully open position, or at the valve area when faulting is triggered.

Dependencies

To enable this parameter, set Enable faults to On.

Enable external fault trigger — External trigger option

Off (default) | Fault when T >= 0.5

Enables port T. A physical signal at port T that is greater than 0.5 triggers faulting.

Dependencies

To enable this parameter, set Enable faults to On.

Enable temporal fault trigger — Temporal trigger option

Off (default) | On

Enables fault triggering at a specified time. When the Simulation time for fault event is reached, the valve area will be set to the value specified in the Opening area when faulted parameter.

Dependencies

To enable this parameter, set Enable faults to On.

Simulation time for fault event — Time at which faulting is triggered

5 s (default) | positive scalar

When the Simulation time for fault event is reached, the valve area is set to the value specified in the Opening area when faulted parameter.

Dependencies

To enable this parameter, set Enable faults to On and Enable temporal fault trigger to On.

Reporting when fault occurs — Fault condition report

None (default) | Warning | Error

Reporting preference for the fault condition. When reporting is set to Warning or Error, a message is displayed in the Simulink Diagnostic Viewer. When Error is selected, the simulation will stop if faulting occurs.

Dependencies

To enable this parameter, set Enable faults to On.

Model Examples

Hydrostatic Transmission

A hydraulic transmission system built of a variable-displacement pump and a fixed-displacement motor. The pipes between the pump and the motor are connected by two replenishing valves (check valves) and a charge pump on the pump side and two pressure relief valves on the motor side. The motor dirves a mechanical load consisting of an inertia, viscous friction, and time-varying torque. The system is tested with both positive and negative pump flow rate by varying the pump displacement.

Hydraulic Actuator with Dual Counterbalance Valves

An actuator controlled by a 4-way directional valve and loaded with an overriding load, requiring the use of counterbalance valves to prevent the load from creeping when the directional valve is in the neutral position. In the neutral position, the directional valve connects ports A and B to the reservoir while blocking the pressure port P. The counterbalance valves block flow from returning to the reservoir, thus holding the actuator in place.