# Pressure Relief Valve (IL)

Pressure-relief valve in an isothermal liquid network

Since R2020a

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, $\stackrel{^}{p}$, 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

`$\stackrel{^}{p}=\frac{{p}_{control}-{p}_{set}}{{p}_{max}-{p}_{set}},$`

where:

• pcontrol is the control pressure. When you set Opening pressure specification to `Pressure differential`, the control pressure is pA ̶ pB. 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.

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

• pmax is the maximum of pressure regulation range, pmax = pset + prange, where prange is the value of the Pressure regulation range parameter.

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

`$\stackrel{^}{p}=\frac{{p}_{control}-{p}_{s}}{{p}_{max}-{p}_{s}},$`

where:

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

• pmax = ps + prange, where prange is the value of the Pressure regulation range parameter.

• pcontrol is the pressure differential between ports A and B, pA ̶ pB.

### 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

`$\stackrel{˙}{m}=\frac{{C}_{d}{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{valve}}{{A}_{port}}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$`

where:

• Cd is the value of the Discharge coefficient.

• Avalve is the instantaneous valve open area.

• Aport 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 pApB.

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

`$\Delta {p}_{crit}=\frac{\pi \overline{\rho }}{8{A}_{valve}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$`

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. PRloss 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 wish to capture this increase in pressure, clear the Pressure recovery check box. In this case, PRloss 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

`${A}_{valve}=\stackrel{^}{p}\left({A}_{max}-{A}_{leak}\right)+{A}_{leak},$`

where:

• Aleak is the value of the Leakage area parameter.

• Amax 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 parameter. If the parameter is nonzero, the block smoothly saturates the control pressure between pset and pmax. 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 Avalve 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

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

where:

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

• $\Delta p={p}_{A}-{p}_{B}.$

• $\Delta {p}_{crit}=\frac{\pi \sqrt{2\overline{\rho }}}{8{C}_{d}K}{\left({\mathrm{Re}}_{crit}v\right)}^{2},$ where Cd is the discharge coefficient, Recrit is the critical Reynolds number, and ν is the kinematic viscosity. In this parameterization, Cd and Recrit 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:

• ΔpTLU is the Pressure drop vector parameter.

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

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

`${K}_{Leak}=\frac{{\stackrel{˙}{V}}_{TLU}\left(1\right)}{\sqrt{|\Delta {p}_{TLU}\left(1\right)|}},$`

where $\stackrel{˙}{V}$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`=`KMax,

`${K}_{Max}=\frac{{\stackrel{˙}{V}}_{TLU}\left(end\right)}{\sqrt{|\Delta {p}_{TLU}\left(end\right)|}},$`

where $\stackrel{˙}{V}$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

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0.$`

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

### Opening Dynamics

When you select Opening dynamics, the block introduces lag in the flow response to the valve opening. Avalve becomes the dynamic opening area, Adyn; otherwise, Avalve is the steady-state opening area. The instantaneous change in dynamic opening area is calculated based on the Opening time constant parameter, τ:

`${\stackrel{˙}{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau }.$`

By default, the block clears the Opening dynamics check box.

Steady-state dynamics are set by the same parameterization as valve opening, and are based on the control pressure, pcontrol. A nonzero Smoothing factor can provide additional numerical stability when the orifice is in near-closed or near-open position.

### Faults

To model a fault, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, 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 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:

`$\stackrel{˙}{m}={K}_{Leak}\overline{\rho }\sqrt{\Delta p}.$`

• `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:

`$\stackrel{˙}{m}={K}_{Max}\overline{\rho }\sqrt{\Delta p}$`

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

`$\stackrel{˙}{m}={K}_{Last}\overline{\rho }\sqrt{\Delta p},$`

where

`${K}_{Last}=\frac{|\stackrel{˙}{m}|}{\overline{\rho }\sqrt{|\Delta p|}}.$`

### Predefined Parameterization

You can populate the block with pre-parameterized manufacturing data, which allows you to model a specific supplier component.

1. In the block dialog box, next to Selected part, click the "<click to select>" hyperlink next to Selected part in the block dialogue box settings.

2. The Block Parameterization Manager window opens. Select a part from the menu and click Apply all. You can narrow the choices using the Manufacturer drop down menu.

3. You can close the Block Parameterization Manager menu. The block now has the parameterization that you specified.

4. You can compare current parameter settings with a specific supplier component in the Block Parameterization Manager window by selecting a part and viewing the data in the Compare selected part with block section.

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.

## Ports

### Conserving

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Entry or exit point to the valve.

Entry or exit point to the valve.

### Input

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Varying-signal set pressure for controlled valve operation.

#### Dependencies

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

## Parameters

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### Parameters

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.

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.

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.

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`.

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`.

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

#### Dependencies

To enable this parameter, set

• Set pressure control to `Controlled`

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

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```

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```

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```.

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```.

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```.

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 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.

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

Upper Reynolds number limit for laminar flow through the valve.

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`.

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.

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```.

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

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

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.

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, enable faults for the block by clicking the hyperlink.

## Version History

Introduced in R2020a

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