Pressure Relief Valve (IL)

Pressure-relief valve in an isothermal liquid network

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

Description

The Pressure Relief Valve (IL) block represents a pressure relief valve in an isothermal liquid network. The valve remains closed when the pressure is less than a specified value. When this pressure is met or surpassed, the valve opens. This set pressure is either a threshold pressure differential over the valve, between ports A and B, or between port A and atmospheric pressure. For pressure control based on another element in the fluid system, see the Pressure Compensator Valve (IL) block.

Pressure Control

For linear preparameterizations, the normalized pressure, $$\widehat{p}$$, which controls the valve opening area, depends on the value of the Set pressure control parameter.

When you set Set pressure control to Constant and Opening parameterization to Linear - Area vs. pressure, the normalized pressure is

$$\widehat{p}=\frac{p_{control}-p_{set}}{p_{max}-p_{set}},$$

where:

• p_control is the control pressure. When you set Opening pressure specification to Pressure differential, the control pressure is p_A ̶ p_B. When you set Opening pressure specification to Pressure at port A, the control pressure is the difference between the pressure at port A and atmospheric pressure.

• p_set is the set pressure. When Opening pressure specification is Pressure differential, p_set is the value of the Set pressure differential parameter. When Opening pressure specification is Pressure at port A, p_set is the value of the Set pressure (gauge) parameter.

• p_max is the maximum of pressure regulation range, p_max = p_set + p_range, where p_range is the value of the Pressure regulation range parameter.

When you set Set pressure control to Controlled, the normalized pressure is

$$\widehat{p}=\frac{p_{control}-p_s}{p_{max}-p_s},$$

where:

• p_s is the value of the signal at port Ps.

• p_max = p_s + p_range, where p_range is the value of the Pressure regulation range parameter.

• p_control is the pressure differential between ports A and B, p_A ̶ p_B.

Opening Parameterization

The mass flow rate depends on the values of the Set pressure control and Opening parameterization parameters.

Area vs. Pressure Parameterizations

When you set Set pressure control to Controlled, or to Constant and Opening parameterization to Linear - Area vs. pressure or Tabulated data - Area vs. pressure, the mass flow rate 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.

• A_valve is the instantaneous valve open area.

• A_port is the value of 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 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.

When you set Set pressure control to Controlled, or to Constant and Opening parameterization to Linear - Area vs. pressure, the opening area is

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

where:

• A_leak is the value of the Leakage area parameter.

• A_max is the value of the Maximum opening area parameter.

When the valve is in a near-open or near-closed position in the linear parameterization, 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_set and p_max. For more information, see Numerical Smoothing.

When you set Set pressure control to Constant and Opening parameterization to Tabulated data - Area vs. pressure, the block interpolates A_valve from the Opening area vector parameter with respect to the Pressure differential vector or Opening pressure (gauge) vector parameter, depending on the value of the Pressure control specification parameter. The block also uses the smoothed, normalized pressure when the smoothing factor is nonzero with linear interpolation and nearest extrapolation.

Volumetric Flow Rate vs. Pressure Parameterization

When you set Set pressure control to Constant and Opening parameterization 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.

The mass flow rate is

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

where:

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

• $$\Delta p=p_A-p_B.$$

• $$\Delta p_{crit}=\frac{\pi \sqrt{2\overline{\rho }}}{8C_{d}K}{\left({\mathrm{Re}}_{crit}v\right)}^2,$$ where C_d is the discharge coefficient, Re_crit is the critical Reynolds number, and ν is the kinematic viscosity. In this parameterization, C_d and Re_crit are fixed at 0.64 and 150, respectively.

When the block operates in the limits of the tabulated data,

$$K=tablelookup\left(\Delta p_{TLU},K_{TLU},\Delta p,interpolation=linear,extrapolation=nearest\right),$$

where:

• Δp_TLU is the Pressure drop vector parameter.

• $${\text{K}}_{TLU}=\frac{{\dot{V}}_{TLU}}{\sqrt{\Delta p_{TLU}}},$$ where $$\dot{V}$$_TLU is the Volumetric flow rate vector parameter.

When the simulation pressure falls below the first element of the Pressure drop vector parameter, K=K_Leak,

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

where $$\dot{V}$$_TLU(1) is the first element of the Volumetric flow rate vector parameter.

When the simulation pressure rises above the last element of the Pressure drop vector parameter, K=K_Max,

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

where $$\dot{V}$$_TLU(end) is the last element of the Volumetric flow rate vector parameter.

Conservation of Mass

The block conserves mass through the valve such that

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

where $$\dot{m}$$ is the mass flow rate into the valve through the port indicated by the A or B subscript.

Opening Dynamics

When you set Opening dynamics to On, the block introduces a control pressure lag and replaces p_control with the dynamic control pressure, p_dyn. The block calculates the dynamic control pressure based on the Opening time constant parameter, τ

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

When you select Opening dynamics, the valve response slows and the valve does not respond to changes instantly. This figure shows the valve area in response to a step in the valve input pressure for three parameter settings:

• When you clear Opening dynamics and set Smoothing factor to 0, the valve area mirrors the step change in the pressure at the input.

• When you select Opening dynamics, set Opening time constant to 0.1 s, and Smoothing factor to 0, the valve area response is delayed and less sharp.

• When you select Opening dynamics, set Opening time constant to 0.1 s, and the Smoothing factor parameter to a nonzero value, here 0.2, the valve area response is delayed and less sharp and the valve response near the opening is smoothed.

A nonzero value for the Smoothing factor parameter provides additional numerical stability when the valve area is changing and in the near-closed or near-open position. For more information, see Numerical Smoothing.

Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. Use the fault parameters to specify the fault properties. For more information about fault modeling, see Introduction to Simscape Faults.

The Opening area when faulted parameter has three fault options:

• Closed — The valve freezes at its smallest value, depending on the Opening parameterization parameter:

  • When you set Opening parameterization to Linear - Area vs. pressure, the valve area freezes at the Leakage area parameter.

  • When you set Opening parameterization to Tabulated data - Area vs. pressure, the valve area freezes at the first element of the Opening area vector parameter.

• Open — The valve freezes at its largest value, depending on the Opening parameterization parameter:

  • When you set Opening parameterization to Linear - Area vs. pressure, the valve area freezes at the Maximum opening area parameter.

  • When you set Orifice parameterization to Tabulated data - Area vs. pressure, the valve area freezes at the last element of the Opening area vector parameter.

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

Due to numerical smoothing at the extremes of the valve area, the minimum area the block uses is larger than the Leakage area parameter, and the maximum is smaller than the Maximum orifice area parameter, in proportion to the Smoothing factor parameter value.

After the fault triggers, the valve remains at the faulted area for the rest of the simulation.

When you set Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, the fault options are defined by the volumetric flow rate through the valve:

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

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

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

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

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

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

where

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

Generate Derived Data Sheet

Since R2026a

You can generate a derived data sheet for the Pressure Relief Valve (IL) block. Derived data sheets use built-in MATLAB live scripts to provide information about the block parameterization. The script imports the parameters from the selected Pressure Relief Valve (IL) block and uses the parameters to generate characteristic plots. You can use the derived data sheet to investigate block behavior, check block parameterizations, or share component-level design. To generate the derived data sheet:

1. Double-click the Pressure Relief Valve (IL) block.

2. In the block dialog box, click the Open live script button next to Derived data sheet.

3. In the live script, click the Generate data sheet button.

The derived data sheet includes performance curves for pressure verses volumetric flow rate for the selected block.

Examples

Priority Valve Controlling Two Hydraulic Motors

A pressure-compensated 3-way flow control valve. This valve maintains constant flow rate through the main hydraulic motor, which is connected to the pressure-compensated outlet of the flow control valve. It acts as a priority valve, diverting the excess flow to the auxiliary hydraulic motor if the main hydraulic motor receives enough fluid to maintain a preset angular velocity. The auxiliary motor is shut off completely if there is insufficient flow to power the main hydraulic motor.

• Open Model

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 drives 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

Ports

Conserving

A — Liquid port

isothermal liquid

Entry or exit point to the valve.

B — Liquid port

isothermal liquid

Entry or exit point to the valve.

Input

Ps — Set pressure signal

physical signal

Varying-signal set pressure for controlled valve operation.

Dependencies

To enable this port, set Set pressure control to Controlled.

Parameters

Part Repository

Part selection — Open Block Parameterization Manager

button

Use the Select part button to open the Block Parameterization Manager tool and view the available parts.

Active part — Active part

part ID

Active part associated with the block.

Dependencies

To enable this parameter, apply a part to the block by using the Block Parameterization Manager.

Status — Restore default part parameters

button

Click the Restore parameters button to restore the parameterization to the active part. The name of the parameter is Status: unmodified if the part uses the default properties for the parameter, and Status: modified if the parameters have been modified from the associated active part.

Dependencies

To enable this parameter, apply a part to the block by using the Block Parameterization Manager.

Manage — Clear part association

button

Use the Clear part association button to clear the active part associated with the block.

Dependencies

To enable this parameter, apply a part to the block by using the Block Parameterization Manager.

Parameters

Set pressure control — Valve operation method

Constant (default) | Controlled

Valve operation method. A Constant valve opens linearly over a fixed pressure regulation range or in accordance with tabulated pressure and opening area data that you provide. A Controlled valve opens according to a variable set pressure signal at port Ps over a fixed pressure regulation range.

Opening parameterization — Method of modeling constant valve opening or closing

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

Method of modeling valve opening or closing. The valve opening is either parametrized linearly or by a table of values that correlate area to pressure differential.

Opening pressure specification — Pressure differential used for valve control

Pressure differential (default) | Pressure at port A

Pressure differential used for the valve control. Selecting Pressure differential sets the pressure difference between port A and port B as the trigger for pressure control. Selecting Pressure at port A sets the gauge pressure at port A, or the difference between the pressure at port A and atmospheric pressure, as the trigger for pressure control.

Set pressure (gauge) — Threshold pressure

0.1 MPa (default) | positive scalar

Gauge pressure beyond which valve operation is triggered when the Pressure control specification is with respect to port A.

Dependencies

To enable this parameter, set Set pressure control to Constant and Pressure control specification to Pressure at port A.

Set pressure differential — Threshold pressure

0 MPa (default) | positive scalar

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

Dependencies

To enable this parameter, set Set pressure control to Constant and Pressure control specification to Pressure differential.

Pressure regulation range — Valve operational pressure range

0.1 MPa (default) | positive scalar

Valve operational range. The valve begins to open at the set pressure value, and is fully open at p_max, the end of the pressure regulation range, where p_max = p_set + p_range.

Dependencies

To enable this parameter, set

• Set pressure control to Controlled

• Set pressure control to Constant and Opening parameterization to Linear - Area vs. pressure

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 either:

• Set pressure control to Controlled

• Set pressure control to Constant and Opening parameterization to Linear - Area vs. pressure

Leakage area — Valve gap area when in fully closed position

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

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

Dependencies

To enable this parameter, set either:

• Set pressure control to Controlled.

• Set pressure control to Constant and Opening parameterization to Linear - Area vs. pressure

Opening pressure (gauge) vector — Differential pressure values for tabular parameterization

[0.2 : 0.2 : 1.2] 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.

The first element of this parameter is the pressure setting of the valve, at which the valve begins to open. The last element is the maximum pressure, at which the valve is fully open. The difference between the two is the pressure regulation range of the valve.

Dependencies

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

Pressure differential vector — Differential pressure values for tabular parameterization

[0.2 : 0.2 : 1.2] 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.

The first element of this parameter is the pressure setting of the valve, at which the valve begins to open. The last element is the maximum pressure, at which the valve is fully open. The difference between the two is the pressure regulation range of the valve.

Dependencies

To enable this parameter, set Set pressure control to Constant, and set

• Opening parameterization to Tabulated data - Volumetric flow rate vs. pressure, or

• Opening parameterization to Tabulated data - Area vs. pressure and Opening pressure specification to Pressure differential.

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

[1e-09, 3.6e-05, 8.9e-05, .00015, .00023, .00031] (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.

Opening area vector — Valve opening areas for tabular parameterization

[1e-10, 2e-06, 4e-06, 6e-06, 8e-06, 1e-05] 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. The first element of this vector is the leakage area.

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 determining mass flow rate through the valve.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor accounting for discharge losses in theoretical flows. The default discharge coefficient for a valve in Simscape™ Fluids™ is 0.64.

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.

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

Accounts for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area. This increase in pressure is not captured when you clear the Pressure recovery check box.

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 valve opening. Selecting Opening dynamics 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 or Tabulated data - 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 or Tabulated data - Area vs. pressure and select Opening dynamics.

Faults

Pressure Relief Valve Area fault — Option to model opening area fault

Add fault

Option to model a valve area fault in the block. To add a fault, click the Add fault hyperlink. When a fault occurs, the valve area normally set by the opening parameterization is set based on the value specified in the Opening area when faulted parameter.

Opening area when faulted — Faulted valve characteristics

Closed (default) | Open | Maintain last value

Faulted valve type. You can choose for the valve to seize when the valve is opened, closed, or at the area when the fault triggers.

Dependencies

To enable this parameter, click the Add fault hyperlink.

Utilities

Derived data sheet — Generate block data sheet

button

Use the Open live script button to open a MATLAB live script that generates the block data sheet which provides information about the block parameterization.

Extended Capabilities

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

Version History

Introduced in R2020a

R2026a: Generate a derived data sheet

Use the Derived data sheet parameter in the Utilities section to generate a derived data sheet that includes performance curves for pressure verses volumetric flow rate.

R2024a: Model faults with the Simscape faults interface

The Pressure Relief Valve (IL) block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.

R2022b: Access pre-parameterized block options

The block supports pre-parameterization options. Suppliers include Daikin, Kawasaki Heavy Industries, Parker, and Yuken.