# Pressure Compensator Valve (IL)

Pressure-maintaining valve for external component in an isothermal system

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

## Description

The Pressure Compensator Valve (IL) block represents an isothermal liquid pressure compensator, such as a pressure relief valve or pressure-reducing valve. Use this valve when you would like to maintain the pressure at the valve based on signals from another part of the system.

When the pressure differential between ports X and Y (the control pressure) meets or exceeds the set pressure, the valve area opens (for normally closed valves) or closes (for normally open valves) in order to maintain the pressure in the valve. The pressure regulation range begins at the set pressure. Pset is constant in the case of a `Constant` valve, or varying in the case of a `Controlled` valve. A physical sign at port Ps provides a varying set pressure.

### Pressure Control

Pressure regulation occurs when the sensed pressure, PxPY, or Pcontrol, exceeds a specified pressure, Pset. The Pressure Compensator Valve (IL) block supports two modes of regulation:

• When Set pressure control is set to `Controlled`, connect a pressure signal to port Ps and set the constant Pressure regulation range. pressure regulation is triggered when Pcontrol is greater than Pset, the Set pressure differential, and below Pmax, the sum of the set pressure and the user-defined Pressure regulation range.

• When Set pressure control is set to `Constant`, the valve opening is continuously regulated between Pset and Pmax by either a linear or tabular parametrization. When Opening parametrization is set to ```Tabular data```, 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 Pressure recovery is set to `Off`, PRloss is 1.

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

### Valve Opening Parametrization

The linear parametrization of the valve area for `Normally open` valves is:

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

and for `Normally closed` valves is:

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

For tabular parametrization of the valve area in its operating range, Aleak and Amax are the first and last parameters of the Opening area vector, respectively.

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, 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 the modeled control pressure. pcontrol becomes the dynamic control pressure, pdyn; otherwise, pcontrol is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:

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

By default, Opening dynamics is set to `Off`. A nonzero Smoothing factor can provide additional numerical stability when the orifice is in near-closed or near-open position.

Steady-state dynamics are set by the same parametrization as the valve opening, and are based on the control pressure, pcontrol.

### 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`, the valve area freezes at the Leakage area.

• When Opening parameterization is set to `Tabulated data`, 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`, the valve area freezes at the Maximum opening area.

• When Orifice parameterization is set to `Tabulated data`, 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.

## Ports

### Conserving

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Entry or exit port of the liquid to or from the valve.

Entry or exit port of the liquid to or from the valve.

Absolute pressure in units of MPa, denoted Px.

Absolute pressure in units of MPa, denoted Py.

### Input

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Pressure differential for controlled valve operation, specified as a physical signal.

#### Dependencies

To enable this parameter, 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

Normal operating condition of the pressure compensator valve. A reducing valve is a `Normally open` valve and a relief valve is a `Normally closed` valve.

Valve operation method. The valve can operate according to a specified pressure regulation range or Opening parametrization.

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

#### Dependencies

To enable this parameter, set Set pressure control to `Constant`.

Magnitude of pressure differential that triggers operation of a constant valve when pressure exceeds (```Normally closed```) or falls below (```Normally open```).

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parametrization to `Linear`.

Operational pressure range of the valve. The pressure regulation range lies between the Set pressure differential and the maximum valve operating pressure.

#### Dependencies

To enable this parameter, set either:

• Set pressure control to `Controlled`

• Set pressure control to `Constant` and Opening parametrization to `Linear`

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 parametrization to `Linear`

Sum of all gaps when the valve is in 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 either:

• Set pressure control to `Controlled`

• Set pressure control to `Constant` and Opening parametrization to `Linear`

Vector of pressure differential values for the tabular parameterization of opening area. The vector elements must correspond one-to-one to the values in the Opening area vector parameter. The pressures must be greater than 0 and are listed in ascending order.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parametrization to `Tabulated data`.

Vector of opening area values for the tabular parameterization of opening area. The vector elements must correspond one-to-one to the values in the Pressure differential vector parameter. Area vectors for normally open valves list elements in descending order. Area vectors for normally closed valves list elements in ascending order.

The opening area vector must have the same number of elements as the Pressure differential vector. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Set pressure control to `Constant` and Opening parametrization 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 that determines 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.

Select to account for pressure increase when fluid flows from a region of a smaller cross-sectional area to a region of larger cross-sectional area.

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.

Select to account for transient effects to the fluid system due to the valve opening. When Opening dynamics is set to `On`, the block approximates the opening conditions by introducing a first-order lag in the flow response.

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`.