Pressure-Compensated 3-Way Flow Control Valve (IL)

3-way flow control in an isothermal liquid system

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Description

The Pressure-Compensated 3-Way Flow Control Valve (IL) block models constant-pressure flow control. When the control pressure, p_A – p_B, meets or exceeds the Set orifice pressure differential, the relief component of the underlying compensator valve opens to maintain the pressure in the block.

The flow control valve opening and closing is controlled by a physical signal received at port S, which determines the area of the underlying orifice block. A positive signal opens the valve. Port R vents liquid to another part of your network.

For pressure-compensated flow control without venting, see the Pressure-Compensated Flow Control Valve (IL) block.

Orifice Parameterization

You can choose the valve model with the Orifice parameterization setting:

• Linear - area vs. control member position is an analytical formulation that assumes the valve opening area and the valve control member are related linearly.

• Tabulated data - Area vs. control member position is a user-supplied data sheet that relates orifice opening area and the control member position. The block queries between data points with linear interpolation and uses nearest extrapolation for points beyond the table boundaries.

• Tabulated data - Volumetric flow rate vs. control member position and pressure drop is a user-supplied data sheet that relates the control member position, orifice pressure drop, and orifice volumetric flow rate. The block queries between data points with linear interpolation and uses a nearest extrapolation for points beyond the table boundaries.

Numerically-Smoothed Area and Pressure

At the extremes of the orifice area and valve pressure range, you can maintain numerical robustness in your simulation by tuning the block Smoothing factor to a nonzero value less than 1. A smoothing function is applied to all calculated areas and pressures, but primarily influences the simulation at the extremes of these ranges.

The normalized orifice area is calculated as:

$$\widehat{A}=\frac{\left(A-A_{leak}\right)}{\left(A_{\max }-A_{leak}\right)}.$$

where:

• A_leak is the Leakage area.

• A_max is the cushion Maximum orifice area.

The Smoothing factor, f, is applied to the normalized area:

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

The smoothed orifice area is:

$$A_{smoothed}={\widehat{A}}_{smoothed}\left(A_{\max }-A_{leak}\right)+A_{leak}.$$

Similarly, the normalized valve pressure is:

$$\widehat{p}=\frac{\left(p-p_{set}\right)}{\left(p_{\max }-p_{set}\right)}.$$

where:

• p_set is the Set orifice pressure differential.

• p_max is the sum of the Set orifice pressure differential and the Pressure compensator valve regulation range.

Smoothing applied to the normalized pressure is:

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

and the smoothed pressure is:

$$p_{smoothed}={\widehat{p}}_{smoothed}\left(p_{\max }-p_{set}\right)+p_{set}.$$

Block Schematic

The Pressure-Compensated 3-Way Flow Control Valve (IL) is constructed from the Pressure Compensator Valve (IL) and Orifice (IL) blocks.

Three-Way Flow Control Valve Schematic

Ports

Conserving

A — Valve liquid port

isothermal liquid

Liquid entry or exit port to the three-way valve.

B — Orifice liquid port

isothermal liquid

Liquid entry or exit port to the orifice.

R — Reducing valve liquid port

isothermal liquid

Liquid exit port from the reducing valve.

Input

S — Physical signal, in m

physical signal

Orifice opening in m, set as a physical signal.

Parameters

Orifice parameterization — Method of modeling orifice opening

Linear - area vs. control member position (default) | Tabulated data - Area vs. control member position | Tabulated data - Volumetric flow rate vs. control member position and pressure drop

Method of modeling the opening of the orifice. The opening is either parametrized linearly, which correlates the opening area to the control member position; by user-supplied data that correlate the orifice opening area to the control member position; or by an array of data that correlates the valve flow rate to the control member position and valve pressure drop.

Control member position at closed orifice — Control member offset

0 m (default) | scalar

Control member offset when the orifice is fully open. A positive, nonzero value indicates a partially closed orifice. A negative, nonzero value indicates an overlapped orifice that remains open for an initial displacement set by the physical signal at port S.

Control member travel between closed and opened orifice — Maximum control member stroke

5e-3 m (default) | positive scalar

Control member stroke that fully opens the orifice.

Dependencies

To enable this parameter, set Orifice parameterization to Linear - area vs. control member position.

Maximum orifice area — Maximum orifice cross-sectional area

8e-5 m^2 (default) | positive scalar

Cross-sectional area of the orifice in its fully open position. This parameter is used as an upper limit for area-pressure calculations during the simulation.

Dependencies

To enable this parameter, set Orifice parameterization to Linear - area vs. control member position.

Control member position vector — Vector of opening position

[0, .002, .007] m (default) | 1-by-n vector

Vector of orifice opening distances for the tabular parameterization of the orifice opening area. The vector elements must correspond one-to-one with the elements in the Orifice area vector parameter. The elements are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set Orifice parameterization to Tabulated data - Area vs. control member position.

Orifice area vector — Vector of opening areas

[1e-09, 4e-09, 1e-05] 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 Control member position vector parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Orifice parameterization to Tabulated data - Area vs. control member position.

Control member position vector, s — Vector of control member positions

[0, .002, .004, .007, .017] m (default) | 1-by-n vector

Vector of control member positions for the tabular parameterization of the volumetric flow rate. The control member position vector forms an independent axis with the Pressure drop vector, dp parameter for the 3-D dependent Volumetric flow rate table, q(s,dp) parameter. A positive displacement corresponds to valve opening. The values are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set Orifice parameterization to Volumetric flow rate vs. control member position and pressure drop.

Pressure drop vector, dp — Vector of pressure differential values

[.3, .5, .7] MPa (default) | 1-by-n vector

Vector of valve opening areas for the tabular parameterization of the valve opening area. The pressure drop vector forms an independent axis with the Control member position vector, s parameter for the 3-D dependent Volumetric flow rate table, q(s,dp) parameter. The values 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 Orifice parameterization to Volumetric flow rate vs. control member position and pressure drop.

Volumetric flow rate table, q(s,dp) — Array of volumetric flow rate values

[1.7e-05, 2e-05, 2.6e-05; .0035, .0045, .0053; .7, .9, 1.06; 1.96, 2.5, 3; 6, 7.7, 9.13] .* 1e-3 m^3/s (default) | M-by-N array

Array of volumetric flow rates based on independent values of pressure drop and spool travel distance. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the Control member position vector, s parameter.

Dependencies

To enable this parameter, set Orifice parameterization to Volumetric flow rate vs. control member position and pressure drop.

Set orifice pressure differential — Threshold for compensator valve operation

0.6 MPa (default) | positive scalar

Magnitude of pressure differential that triggers valve opening or closing.

Pressure compensator valve regulation range — Area of the fully opened pressure compensator valve

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the valve in its fully open position. This parameter is used as an upper limit for area-pressure calculations during the simulation.

Pressure compensator valve maximum area — Pressure operational region of the pressure compensating valve

0.1 MPa (default) | scalar

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

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 the 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.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Correction factor that accounts for discharge losses in theoretical flows.

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.

Model Examples

Priority Valve Controlling Two Hydraulic Motors

A pressure-compensated 3-way flow control valve. This valve maintains constant flow rate through the main hydraulic motor, which is connected to the pressure-compensated outlet of the flow control valve. It acts as a priority valve, diverting the excess flow to the auxiliary hydraulic motor if the main hydraulic motor receives enough fluid to maintain a preset angular velocity. The auxiliary motor is shut off completely if there is insufficient flow to power the main hydraulic motor.