3-Way Directional Valve (IL)

3-way flow control valve in an isothermal system

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Description

The 3-Way Directional Valve (IL) block represents a directional control valve with three ports and two positions. For example, this block could provide flow control between a pump, storage tank, and actuator.

Example Valve Configuration

Valve control occurs through the spool, which is connected to a physical signal at port S. In the default configuration, zero displacement indicates a fully closed valve between positions I and II. A negative displacement shifts the spool toward valve position I, and a positive displacement signal shifts the spool toward valve position II.

Fluid can flow between port A and port T (figure I) or between port P and port A (figure II). The block uses the same formulation for flow rate and opening area as the Orifice (IL) block. See Orifice (IL) for more details on flow calculation.

Valve Positions

Opening Area Parameterizations

The Orifice parameterization sets the method for calculating the valve open area. The calculations are based either on the orifice parameters or tabulated data sets specified in the Model Parameterization tab. The block uses the same data for both flow paths if Area characteristics is set to Identical for all flow paths; otherwise, individual equations are applied for the Different for all flow paths setting. The orifice parameterizations are:

• Linear - area vs. spool travel

  The opening area is a linear function of the spool travel distance, the signal received at port S:

  $$A_{orifice}=\frac{\left(A_{\max }-A_{leak}\right)}{\Delta S}\left(S-S_{\min }\right)\epsilon +A_{leak},$$

  where:

  • S_min is the control member position when the orifice is fully closed.

  • ΔS is the Control member travel between closed and open orifice.

  • A_max is the Maximum orifice area.

  • A_leak is the Leakage area.

  • ε is the orifice opening orientation. For the P-A flow path, it is 1. For the A-T flow path, it is -1.

  

• Tabulated data - Area vs. spool travel

  Provide spool travel vectors for your system or for individual flow paths between ports P and A and ports A and T. This data will be used to calculate the relationship between the orifice opening area and spool travel distance. Interpolation is used to determine the opening area between given data points. A_leak and A_max are the first and last parameters of the Opening area vector, respectively.

  

• Tabulated data - Volumetric flow rate vs. spool travel and pressure drop

  Provide spool travel and pressure drop vectors. The volumetric flow rate is calculated based on the relationship between pressure change and the spool travel distance. Interpolation is used to determine flow rate between given data points. The mass flow rate is the product of the volumetric flow rate and the local density.

  

Numerically-Smoothed Valve Area in the Linear Parameterization

When the valve is in a near-open or near-closed position in the linear parameterization, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. A smoothing function is applied to all calculated areas, but primarily influences the simulation at the extremes of the valve area.

The normalized valve area is calculated as:

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

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

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

The smoothed valve area is:

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

Structural Component Diagram

The block is a composite of two Orifice (IL) blocks that are driven by a single physical signal at S. Block Orifice P-A represents the flow path between ports P and A. Block Orifice A-T represents the flow path between ports A and T.

In the diagram below, a positive signal opens Orifice P-A while closing Orifice A-T. A negative signal opens Orifice A-T while closing Orifice P-A.

Valve Structural Diagram

Orifice Openings and Offsets

The initial valve position is determined by the opening offset, or the orifice opening at zero spool displacement. An offset can be due to a change in distance between ports or spool lands. It can also be due to a change in the thicknesses of the spool lands. Orifice opening is determined in the same way as for the Orifice (IL) block.

Assumptions

• Fluid inertia is ignored.

• Spool loading due to inertial, spring, and other forces is ignored.

• All valve orifices are assumed to be identical in size unless otherwise specified.

Ports

Conserving

A — Liquid port

isothermal liquid

Exit point of the valve.

P — Liquid port

isothermal liquid

Entry point to the valve.

T — Liquid port

isothermal liquid

Entry point to the valve.

Input

S — Control member displacement, m

physical signal

Control member displacement in m, received as a physical signal. A positive displacement opens the orifice.

Parameters

Model Parameterization

Area characteristics — Flow equations for orifices

Identical for all flow paths (default) | Different for each flow path

Applies uniform or individual flow equations for the valve orifice area. Identical for all flow paths uses the same orifice and spool geometries, flow rates, pressure, and area vectors for all valve orifices. When using Different for each flow path, different spool offsets and tabulated data are assigned to the orifices between ports P and A and ports A and T. In both cases, ports A, P, and T have the same cross-sectional areas, discharge coefficients, and Reynolds numbers. The same Orifice parameterization is also applied to all flow paths.

Orifice parameterization — Method of calculating opening area

Linear area vs. spool travel (default) | Tabulated data - Area vs. spool travel | Tabulated data - volumetric flow rate vs. spool travel and pressure drop

Method of calculating the valve opening area. In the tabulated data parameterizations, you can provide your own valve area and spool travel data for nonlinear valve opening profiles, or you can provide data in terms of volumetric flow rate, spool travel, and pressure drop over the flow path.

Spool position at maximum P-A orifice area — Spool offset at maximum area between ports P and A

2.5e-3 m (default) | scalar

Initial orifice opening distance between ports P and A. The default represents a zero-lapped system. A positive, nonzero value represents an underlapped, or partially open, system. A negative, nonzero value represents an overlapped system, where the valve remains closed over a range of control member displacements.

Spool position at maximum A-T orifice area — Spool offset at maximum area between ports A and T

5e-3 m (default) | scalar

Initial orifice opening distance between ports A and T. The default represents a zero-lapped system. A positive, nonzero value represents an underlapped, or partially-open, system. A negative, nonzero value represents an overlapped system, where the valve remains closed over a range of control member displacements.

Spool travel between closed and open orifice — Maximum spool stroke

0.005 m (default) | positive scalar

Maximum distance of spool travel. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths.

Maximum orifice area — Maximum orifice opening area

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

Largest open area during operation of valve.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths.

P-A spool travel between closed and open orifice — Maximum stroke for the spool between ports P and A

0.005 m (default) | positive scalar

Maximum distance of spool travel for the orifice between ports P and A. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path.

P-A maximum orifice area — Maximum area between ports P and A

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

Cross-sectional area of the orifice between ports P and A in its fully open position.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Orifice parameterization to Linear - area vs. spool travel.

A-T spool travel between closed and open orifice — Maximum stroke for the spool between ports A and T

0.005 m (default) | positive scalar

Maximum distance of spool travel for the orifice between ports A and T. This value provides an upper limit to calculations so that simulations do not return unphysical values.

Dependencies

To enable this parameter, set Area characteristics type to Different for each flow path.

A-T maximum orifice area — Maximum area between ports A and T

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

Cross-sectional area of the orifice between ports A and T in its fully open position.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Orifice parameterization to Linear - area vs. spool travel.

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 its 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.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Orifice parameterization to Linear - area vs. spool travel.

Spool travel vector — Vector of valve opening distance

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

Vector of control member travel distances for the tabular parameterization of valve area. The vector elements must correspond one-to-one with the elements in the Orifice area vector parameter. 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 Area characteristics to Identical for all flow paths and Orifice parameterization to Tabulated data - Area vs. spool travel.

Orifice area vector — Vector of valve opening areas

[1e-09, 2.0352e-07, 4.0736e-05, .00011438, .00034356] m^2 (default) | 1-byn vector

Vector of opening areas for the tabular parameterization of valve opening area. The vector elements must correspond one-to-one with the elements in the Spool travel vector parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Opening parameterization to Tabulated data - Area vs. spool travel.

P-A orifice spool travel vector — Vector of valve opening distance

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

Vector of control member travel distances for the tabular parameterization of valve area. The vector elements must correspond one-to-one with the elements in the P-A orifice area vector parameter. 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Area vs. spool travel.

P-A orifice area vector — Vector of valve opening areas

[1e-09, 2.0352e-07, 4.0736e-05, .00011438, .00034356] m^2 (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of valve opening area. The vector elements must correspond one-to-one with the elements in the P-A orifice spool travel vector parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Opening parameterization to Tabulated data - Area vs. spool travel.

A-T orifice spool travel vector — Vector of valve opening distances

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

Vector of control member travel distances for the tabular parameterization of valve area. The vector elements must correspond one-to-one with the elements in the A-T orifice area vector parameter. 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Area vs. spool travel.

A-T orifice area vector — Vector of valve opening areas

[1e-09, 2.0352e-07, 4.0736e-05, .00011438, .00034356] m^2 (default) | 1-by-n vector

Vector of opening areas for the tabular parameterization of valve opening area. The vector elements must correspond one-to-one with the elements in the A-T orifice spool travel vector parameter. The elements are listed in ascending order and must be greater than 0.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Opening parameterization to Tabulated data - Area vs. spool travel.

Spool travel vector, s — Vector of valve opening distances

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

Vector of control member travel distances for tabular parametrization of volumetric flow rate. The spool travel 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 Area characteristics to Identical for all flow paths and Orifice parameterization to Volumetric flow rate vs. spool travel and pressure drop.

Pressure drop vector, dp — Vector of valve pressure drop values

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

Vector of pressure drop values for tabular parametrization of volumetric flow rate. The pressure drop vector forms an independent axis with the Spool travel 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 Area characteristics to Identical for all flow paths and Orifice parameterization to Volumetric flow rate vs. spool travel and pressure drop.

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

[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 matrix

M-by-N matrix 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 Spool travel vector, s parameter.

Dependencies

To enable this parameter, set Area characteristics to Identical for all flow paths and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

P-A orifice spool travel vector, s — Vector of valve opening distances

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

Vector of control member travel distances for tabular parametrization of volumetric flow rate. The spool travel vector forms an independent axis with the P-A orifice pressure drop vector, dp parameter for the 3-D dependent P-A orifice 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

P-A orifice pressure drop vector, dp — Vector of pressure drop values over the valve

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

Vector of pressure drop values for tabular parametrization of volumetric flow rate. The pressure drop vector forms an independent axis with the P-A orifice spool travel vector, s parameter for the 3-D dependent P-A orifice 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

P-A orifice volumetric flow rate table, q(s,dp) — Vector of valve volumetric flow rates

[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 matrix

M-by-N matrix 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 P-A orifice pressure drop vector, dp parameter.

• N is the number of elements in the P-A orifice spool travel vector, s parameter.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

A-T orifice spool travel vector, s — Vector of valve opening distances

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

Vector of control member travel distances for tabular parametrization of volumetric flow rate. The spool travel vector forms an independent axis with the A-T orifice pressure drop vector, dp parameter for the 3-D dependent P-A orifice 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

A-T orifice pressure drop vector, dp — Vector of pressure drop values over the valve

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

Vector of pressure drop values for tabular parametrization of volumetric flow rate. The pressure drop vector forms an independent axis with the A-T orifice spool travel vector, s parameter for the 3-D dependent A-T orifice 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 Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

A-T orifice volumetric flow rate table, q(s,dp) — Vector of volumetric flow rate for tabular parameterization - different flow paths

[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 matrix

M-by-N matrix 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 A-T orifice pressure drop vector, dp parameter.

• N is the number of elements in the A-T orifice spool travel vector, s parameter.

Dependencies

To enable this parameter, set Area characteristics to Different for each flow path and Orifice parameterization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

General Parameters

Cross-sectional area at ports A, P and T — Area at valve entry or exit

inf m^2 (default) | positive scalar

Cross-sectional area at the entry and exit ports A, P, and T. These areas are used in the pressure-flow rate equation that determines volumetric flow rate through the valve.

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 based to the flow response when the valve is in near-open and near-closed positions. To increase the stability of your simulation in these regimes, set this parameter to a nonzero value less than one.

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

On (default) | Off

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.

Model Examples

Drill-Ream Actuator

An actuator that drives a machine tool working unit performing a sequence of three technological operations: coarse drilling, fine drilling, and reaming. The actuator speed is controlled by one of three pressure-compensated flow control valves metering out return flow from the cylinder. The selection of an appropriate flow control is performed by directional valves that are activated by a control unit.

Lubrication System

A simplified version of a lubrication system fed with the centrifugal pump. The system consists of five major units: Pump Unit, Scavenge Unit, Heat Exchanger Manifold, Nozzle Manifold, and Control Unit. Both the pump and the scavenge unit are built around the centrifugal pump. The Scavenge Unit collects fluid discharged by nozzles and pumps it back into the reservoir of the Pump Unit. The Control Unit generates commands to bypass either the heat exchanger, represented as a local resistance, or the nozzles block. In a real system, these commands are generated by temperature sensors installed in lubrication cavities.