# Pressure Relief Valve (IL)

Pressure-relief valve in an isothermal system

• Library:
• Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Pressure Control Valves

• ## Description

The Pressure Relief Valve (IL) models 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

Two valve control options are available:

• When Set pressure control is set to `Controlled`, connect a pressure signal to port Ps and define the constant Pressure regulation range. The valve response will be triggered when Pcontrol, the pressure differential between ports A and B, is greater than Pset and below Pmax. Pmax is the sum of Pset and the pressure regulation range.

• When Set pressure control is set to `Constant`, the valve opening is continuously regulated between Pset and Pmax. There are two options for pressure regulation available in the Opening pressure specification parameter: Pcontrol can be the pressure differential between ports A and B or the pressure differential between port A and atmospheric pressure. The opening area is then modeled by either linear or tabular parameterization. When the `Tabulated data` option is selected, Pset and Pmax are the first and last parameters of the Pressure differential vector, respectively.

### Mass Flow Rate Equation

Momentum is conserved through the valve:

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

The mass flow rate through the valve is calculated as:

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

where:

• Cd is the Discharge coefficient.

• Avalve is the instantaneous valve open area.

• Aport is 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 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, PRloss is 1.

The opening area Avalve is determined by the opening parameterization (for `Constant` valves only) and the valve opening dynamics.

### Opening Parameterization

When you set Opening parameterization to ```Linear - Area vs. pressure```, the block calculates the opening area as

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

where the normalized pressure, $\stackrel{^}{p}$, is

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

At the extremes of the valve pressure range, you can maintain numerical robustness in your simulation by adjusting the block . With a nonzero smoothing factor, a smoothing function is applied to all calculated valve pressures, but primarily influences the simulation at the extremes of these ranges.

When the Smoothing factor, f, is nonzero, a smoothed, normalized pressure is instead applied to the valve area:

`${\stackrel{^}{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\stackrel{^}{p}}_{}^{2}+{\left(\frac{f}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\stackrel{^}{p}-1\right)}^{2}+{\left(\frac{f}{4}\right)}^{2}}.$`

When you set Opening parameterization to `Tabulated data - Volumetric flow rate vs. pressure`, Aleak and Amax are the first and last parameters of the Opening area vector, respectively. The smoothed, normalized pressure is also used when the smoothing factor is nonzero with linear interpolation and nearest extrapolation.

When you set Opening parameterization to ```Tabulated data - Area 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:

`$\stackrel{˙}{m}=\overline{\rho }\stackrel{˙}{V},$`

where:

• $\stackrel{˙}{V}$ 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, ΔpTLU(1), the mass flow rate is calculated as:

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

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

where VTLU(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, ΔpTLU(end), the mass flow rate is calculated as:

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

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

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

### Opening Dynamics

If Opening dynamics are modeled, a lag is introduced to the flow response to 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, τ:

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

By default, Opening dynamics are turned `Off`.

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.

### Faulty Behavior

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

• Simulation time — Faulting occurs at a specified time.

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

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

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

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

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

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

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

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

• `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 applied is larger than the , and the maximum is smaller than the Maximum orifice area, in proportion to the Smoothing factor value.

Once triggered, 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 freezes at the mass flow rate associated with the first elements of the Volumetric flow rate vector and the Pressure drop vector:

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

• `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:

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

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

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

where

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

### Predefined Parameterization

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

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.

## 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`.

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 Fault trigger is set to `External`.

## 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`.

Operational pressure range of the valve. The pressure regulation range begins at the valve set pressure and the end of the range is the maximum valve operating pressure.

#### 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.

#### 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.

#### 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`.

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 Pressure recovery is set to `Off`.

Whether to account for transient effects to the fluid system due to valve opening. 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.

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 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.

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

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Whether a fault trigger occurs due to an external event or at a specified time.

When set to `External`, port Tr is enabled. A physical signal at port Tr that is greater than `0.5` triggers faulting.

When set to `Temporal`, 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`.

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 Fault trigger to `Temporal`.

## Version History

Introduced in R2020a