Pressure-Compensated Flow Control Valve (IL)

Flow control with pressure regulation in an isothermal liquid system

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Description

The Pressure-Compensated Flow Control Valve (IL) block provides constant-pressure flow control through an Orifice (IL) block via a Pressure Compensator Valve (IL) connected in series. When the control pressure over the orifice, p_A – p_B, meets or exceeds the Set orifice pressure differential, the reducing valve in the pressure compensator component begins to close, which maintains the pressure in the orifice. For systems with venting or redirection of fluid to another part of the system, see the Pressure-Compensated 3-Way Flow Control Valve (IL) block.

The valve opening and closing is controlled by a physical signal received at port S. A positive signal opens the valve.

Flow Control Valve Schematic

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 adjusting the block Smoothing factor. 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:

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

Orifice Parameterization

Setting Orifice parameterization to:

• Linear - area vs. control member position assumes that the spool position and the orifice opening area are related linearly.

• Tabulated data - Area vs. control member position interpolates user-provided data between the orifice opening area and the control member position with a potentially nonlinear relationship.

• Tabulated data - Volumetric flow rate vs. control member position and pressure drop interpolates the orifice volumetric flow rate directly from user-provided data between the control member position, orifice pressure drop, and orifice volumetric flow rate.

Ports

Conserving

A — Liquid port

isothermal liquid

Liquid entry or exit point to the valve.

B — Liquid port

isothermal liquid

Liquid entry or exit point to the valve.

Input

S — Physical signal, in m

physical signal

Orifice opening in m, returned as a physical signal. A positive signal opens the orifice.

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 travel between closed and open valve — 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 travel.

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 travel.

Control member position at closed valve — Control member offset

0 m (default) | positive 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.

Dependencies

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

Control member position vector — Vector of control member travel distances

[0, .002, .007] (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 displacements

[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) | scalar

Magnitude of pressure differential that triggers valve opening or closing.

Pressure compensator valve regulation range — 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.

Pressure compensator valve maximum area — Area of the fully opened pressure compensator valve

1.5 * 8e-5 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.

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

Hydraulic Flow Rectifier Circuit

A flow rectifier circuit with four check valves and a flow control valve. It is used to allow a single flow control valve to control fluid flow in both directions. Similar to a Graetz circuit implemented with diodes, the check valves are arranged in such a way that flow always passes through the flow control valve in the same direction. In the Orifices subsystem, there are two more check valves that are used to select the orifice that the flow passes through depending on the flow direction.