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 model valve opening either linearly or by tabulated data, and you can enable faulty behavior by setting Enable faults to On.

Area Parameterization

When Opening parameterization is set to Linear - Area vs. pressure, the valve open area is linearly related to the opening pressure differential.

Opening Pressure

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.

Opening Area and Pressure

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

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

When you set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, A_valve is the linearly interpolated value of the Opening area vector parameter versus Pressure differential vector parameter curve for a simulated pressure differential.

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.

Tabulated Volumetric Flow Rate Parameterization

When Opening parameterization is set to Tabulated data - Volumetric flow rate vs. pressure, the valve opens according to the user-provided tabulated data of volumetric flow rate and pressure differential between ports A and B.

Within the limits of the tabulated data, the mass flow rate is calculated as:

$$\dot{m}=\overline{\rho }\dot{V},$$

where:

• $$\dot{V}$$ is the volumetric flow rate.

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

When the simulation pressure falls below the first element of the Pressure drop vector, Δp_TLU(1), the mass flow rate is calculated as:

$$\dot{m}=K_{Leak}\overline{\rho }\sqrt{\Delta p}.$$

$$K_{Leak}=\frac{V_{TLU}(1)}{\sqrt{\left|\Delta p_{TLU}(1)\right|}},$$

where V_TLU(1) is the first element of the Volumetric flow rate vector.

When the simulation pressure rises above the last element of the Pressure drop vector, Δp_TLU(end), the mass flow rate is calculated as:

$$\dot{m}=K_{Max}\overline{\rho }\sqrt{\Delta p}.$$

$$K_{Max}=\frac{V_{TLU}(end)}{\sqrt{\left|\Delta p_{TLU}(end)\right|}},$$

where V_TLU(end) is the last element of the Volumetric flow rate vector.

Opening Dynamics

The linear parameterization supports valve opening and closing 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:

$$p_{smoothed}={\widehat{p}}_{smoothed}\left(p_{\max }-p_{set}\right)+p_{set}.$$

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

• Open

• Maintain at last value

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.

Faulting in the Linear Parameterization

In the linear parameterization, the fault options are defined by the valve area:

• 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.

Faulting in the Tabulated Data Parameterization

In the tabulated parameterization, the fault options are defined by the mass flow rate through the valve:

• Closed — The valve freezes at the mass flow rate associated with the first elements of the Volumetric flow rate vector and the Pressure drop vector:

  $$\dot{m}=K_{Leak}\overline{\rho }\sqrt{\Delta p}.$$

• Open — The valve freezes at the mass flow rate associated with the last elements of the Volumetric flow rate vector and the Pressure drop vector:

  $$\dot{m}=K_{Max}\overline{\rho }\sqrt{\Delta p}.$$

• Maintain at last value — The valve freezes at the mass flow rate and pressure differential when the trigger occurs:

  $$\dot{m}=K_{Last}\overline{\rho }\sqrt{\Delta p},$$

where

$$K_{Last}=\frac{\left|\dot{m}\right|}{\overline{\rho }\sqrt{\left|\Delta p\right|}}.$$

Predefined Parameterization

Pre-parameterized manufacturer data is available for this block. This data allows you to model a specific supplier component.

To load a predefined parameterization,

1. Click the "Select a predefined parameterization" hyperlink in the property inspector description.

2. Select a part from the drop-down menu and click Update block with selected part.

3. If you change any parameter settings after loading a parameterization, you can check your changes by clicking Compare block settings with selected part. Any difference in settings between the block and pre-defined parameterization will display in the MATLAB command window.

Note

Predefined block parameterizations use available data sources to supply parameter values. The block substitutes engineering judgement and simplifying assumptions for missing data. As a result, expect some deviation between simulated and actual physical behavior. To ensure accuracy, validate the simulated behavior against experimental data and refine your component models as necessary.

To learn more, see List of Pre-Parameterized Components.

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 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 valve mass flow rate is determined from a table of area values with respect to pressure differential.

• Tabulated data - Volumetric flow rate vs. pressure: The valve mass flow rate is determined from a table of volumetric flow rate values with respect to pressure differential.

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.

Dependencies

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

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 parameterization to Linear - Area vs. pressure and 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 parameterization to Linear - Area vs. pressure and 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 parameterization to Linear - Area vs. pressure and 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.

Dependencies

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

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.

Dependencies

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

Pressure differential vector — Differential 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 vector elements must correspond one-to-one with the elements in the Opening area vector parameter. The elements are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set:

• Set pressure control to Constant.

• Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure.

• Opening pressure specification to Pressure differential.

, 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 parameterization of the valve opening area. The vector elements must correspond one-to-one with the elements in the Pressure differential vector parameter. The elements are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

Dependencies

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

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.

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.

Dependencies

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

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Dependencies

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

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.

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.

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.

Dependencies

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

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 parameterization to Linear - Area vs. pressure and Opening dynamics to On.

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 of valve opening. This vector must have the same number of elements as the Pressure drop vector parameter. The vector elements must be listed in ascending order.

Dependencies

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

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 characteristics

Closed (default) | Open | Maintain at last value

Sets the faulted valve area or mass flow rate. You can choose for the valve to seize at the fully closed or fully open position, or at the conditions when faulting is triggered. This parameter sets the area when Opening parameterization is set to Linear - Area vs. pressure and the mass flow rate when Opening parameterization is set to Tabulated data.

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.

Open Model

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.

Open Model

Version History

Introduced in R2020a