Pressure-Reducing Valve (IL)

Pressure-reducing valve in an isothermal system

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Description

The Pressure-Reducing Valve (IL) block models a pressure-reducing valve in an isothermal liquid network. The valve remains open when the pressure at port B is less than a specified pressure. When the pressure at port B meets or surpasses this set pressure, the valve closes. The block functions based on the differential between the set pressure and the pressure at port B. 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 P_B is greater than P_set, the Set pressure (gauge), and below P_max, the sum of the set pressure and the user-defined Pressure regulation range. The pressure at port B acts as the control pressure, P_control, for this valve.

• When Set pressure control is set to Constant, the valve opening is continuously regulated between P_set and P_max by either a linear or tabular parameterization. When the Tabulated data option is selected, P_set and P_max are the first and last parameters of the Pressure differential vector, respectively.

Mass Flow Rate Equation

Momentum is conserved through the valve:

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

The mass flow rate through the valve is calculated as:

$$\dot{m}=\frac{C_d{A}_{valve}\sqrt{2\overline{\rho }}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{A_{valve}}{A_{port}}\right)}^2\right)}}\frac{\Delta p}{{\left[\Delta p^2+\Delta p_{crit}^2\right]}^{1/4}},$$

where:

• C_d is the Discharge coefficient.

• A_valve is the instantaneous valve open area.

• A_port is 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 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, PR_loss is 1.

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

Closing Parameterization

Linear parameterization of the valve area is

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

where the normalized pressure,$$\widehat{p}$$, is

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

At the extremes of the valve pressure range, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. 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:

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

In the Tabulated data parameterization, A_max and A_leak 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. A_valve becomes the dynamic opening area, A_dyn; otherwise, A_valve is the steady-state opening area. The instantaneous change in dynamic opening area is calculated based on the Opening time constant, τ:

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

By default, Opening dynamics are turned Off.

Steady-state dynamics are set by the same parameterization as the valve opening, and are based on the control pressure, p_control. A nonzero Smoothing factor can provide additional numerical stability when the valve 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, 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 Leakage area, 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

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 pressure threshold for controlled valve operation.

Dependencies

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

Tr — External fault trigger

physical signal

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

Parameters

Set pressure control — Valve operation method

Constant (default) | Controlled

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

Opening parameterization — Method of modeling valve opening or closing

Linear (default) | Tabular data

Method of modeling the valve opening or closing. The valve opening is either parametrized linearly, which correlates the opening area to the provided pressure range, or by a table of values you provide that correlate the valve opening area to pressure differential data.

Dependencies

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

Set pressure (gauge) — Gauge pressure beyond which valve operation is triggered

0.1 MPa (default) | positive scalar

Gauge pressure beyond which valve operation is triggered.

Dependencies

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

Pressure regulation range — Valve operational pressure range

0.1 MPa (default) | positive scalar

Operational pressure range of the valve. The pressure regulation range begins at the Set pressure (gauge) and the end of the range is the maximum valve operating pressure.

Dependencies

To enable this parameter, set either:

• Set pressure control to Controlled

• Set pressure control to Constant and Opening parameterization to Linear

Maximum opening area — Area of a 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

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 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 parameterization to Linear

Pressure differential vector — Vector of 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.

Dependencies

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

Opening area vector — Valve opening areas for tabular parameterization

[1e-05, 8e-06, 6e-06, 4e-06, 2e-06, 1e-10] 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 descending 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 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 that determines the 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 in the range [0,1]

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.

Pressure recovery — Accounts 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 Pressure recovery is set to Off.

Opening dynamics — Whether to account for flow response to valve opening

Off (default) | On

Accounts for transient effects to the fluid system due to valve opening. Opening dynamics set to On approximates opening conditions by introducing a first-order lag in the flow response. The Opening time constant also impacts the modeled opening dynamics.

Initial opening area — Open area at the start of the simulation

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

Initial cross-sectional area of 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.

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 dynamics to On.

Faults

Enable faults — Fault option

Off (default) | On

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.

Opening area when faulted — Set faulted characteristics

Closed (default) | Open | Maintain last value

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.

Fault trigger — External or temporal trigger option

Temporal (default) | External

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.

Simulation time for fault event — Time at which faulting is triggered

5 s (default) | positive scalar

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