Pressure Compensator Valve (IL)

Pressure-maintaining valve for external component in an isothermal system

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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. P_set 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, P_x – P_Y, or P_control, exceeds a specified pressure, P_set. 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 P_control is greater than P_set, the Set pressure differential, and below P_max, 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 P_set and P_max by either a linear or tabular parametrization. When Opening parametrization is set to Tabular data, 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 Pressure recovery is set to Off, PR_loss is 1.

The opening area, A_valve, 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:

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

and for Normally closed valves is:

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

The normalized pressure, $$\widehat{p}$$, is:

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

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

Opening Dynamics

If opening dynamics are modeled, a lag is introduced to the flow response to the modeled control pressure. p_control becomes the dynamic control pressure, p_dyn; otherwise, p_control is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:

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

By default, Opening dynamics is set to Off.

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

Ports

Conserving

A — Liquid port

isothermal liquid

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

B — Liquid port

isothermal liquid

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

X — Pressure reference, MPa

isothermal liquid

Absolute pressure in units of MPa, denoted P_x.

Y — Pressure reference, MPa

isothermal liquid

Absolute pressure in units of MPa, denoted P_y.

Input

Ps — Controlled pressure differential

physical signal

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

Dependencies

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

Parameters

Valve specification — Valve bias

Normally open (default) | Normally closed

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.

Set pressure control — Constant or controlled valve operation

Constant (default) | Controlled

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

Opening parameterization — Method of modeling constant valve opening or closing

Linear (default) | Tabulated data

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.

Set pressure differential — Range outside of which constant valve operation is triggered

0 MPa (default) | scalar

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.

Pressure regulation range — Valve operational pressure range

0.1 MPa (default) | scalar

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

Maximum opening area — Area of 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 parametrization to Linear

Leakage area — 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 parametrization to Linear

Pressure differential vector — Vector of differential pressure values for tabular parametrization

[0.2 : 0.2 : 1.2] MPa (default) | 1-byn vector

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.

Opening area vector — Vector of valve opening areas for tabular parametrization

[1e-05, 8e-06, 6e-06, 4e-06, 2e-06, 1e-10] m^2 (default) | 1-byn vector

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 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 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.

Pressure recovery — Whether to account for pressure increase in area expansions

Off (default) | On

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.

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

Off (default) | On

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.

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.