# 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 Pressure control 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

Linear parameterization of valve area is:

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

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:

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

In the Tabulated data parameterization, 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.

### 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.

## Ports

### Conserving

expand all

Entry or exit point to the valve.

Entry or exit point to the valve.

### Input

expand all

Varying-signal set pressure for controlled valve operation.

#### Dependencies

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

## Parameters

expand all

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.

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

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.

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

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

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 Opening parameterization to Tabulated data.

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.

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.

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.

Initial cross-sectional area of the opening at the time of dynamic opening. This value is used to calculate the instantaneous opening area at the following time step.

#### Dependencies

To enable this parameter, set Opening dynamics to On.

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.

Introduced in R2020a

Get trial now