2-Way Directional Valve (IL)

2-way flow control valve in an isothermal system

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Description

The 2-Way Directional Valve (IL) block models a two-way valve, such as a shut-off valve. Use this block when you need a flow-reducing control element that responds to pressures in another part of the system.

Within an isothermal fluid system, the two-way directional valve provides flow control by a variable orifice. The block controls the flow between ports A and B via a physical signal at port S, which triggers spool motion to open or close the valve. For more details on the calculation of the flow rate through a variable orifice, see Orifice (IL).

Valve Parameterization

The valve opening is parameterized in three ways:

• Linear - area vs. spool travel

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

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

  where:

  • A_orifice is the opening area.

  • ΔS is the spool travel distance.

  • ΔS_max is the Spool travel between closed and open orifice.

  • A_Leak is the Leakage area.

  • A_max is the Maximum orifice area.

  

• Tabulated data - Area vs. spool travel

  Provide spool travel vectors for your system or for individual flow paths between ports A and B. 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 Orifice parameterization is set to Linear - area vs. spool travel and the valve is in near-open or near-closed position, 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:

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

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

S — Spool displacement, m

physical signal

Spool displacement in m, received as a physical signal. A positive displacement opens the valve.

Parameters

Orifice parameterization — Determines opening area relationship

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 flow area. A linear relationship between the opening area and the control member spool is the default parametrization. Additionally, you can provide your own data if the opening relationship is nonlinear, either in terms of opening area and spool travel or in terms of volumetric flow rate, spool travel, and pressure drop over the flow path.

Spool position at maximum orifice area — Spool offset at maximum area

5e-3 m (default) | positive scalar

Position of the spool travel member when the valve is fully open. The default value represents a zero-lapped system. A positive, nonzero value represents an underlapped, or partially closed, system. A negative, nonzero value represents an overlapped system where the valve remains open over a range of displacements.

Spool travel between closed and open orifice — Maximum spool stroke

5e-3 m (default) | positive scalar

Spool offset at the maximum valve opened area.

Dependencies

To enable this parameter, set Orifice parametrization to Linear - area vs. spool travel.

Maximum orifice area — Area of fully opened valve

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

Maximum valve area experienced during simulation. When using Tabulated data - Area vs. spool travel, the maximum valve area is the last element of the Orifice area vector.

Dependencies

To enable this parameter, set Orifice parametrization to Linear - area vs. spool travel.

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 the fully closed position. Any area smaller than this value is maintained at the specified leakage area. This parameter contributes to numerical stability by maintaining continuity in the flow.

Dependencies

To enable this parameter, set Orifice parametrization to Linear - area vs. spool travel.

Cross-sectional area at ports A and B — Valve area at conserving ports

inf m^2 (default) | positive scalar

Cross-sectional area at the entry and exit ports A and B. This area is used in the pressure-flow rate equation that determines the volumetric flow rate through the valve.

Dependencies

To enable this parameter, set Orifice parametrization to:

• Tabulated data - Area vs. spool travel

• Linear - area vs. spool travel

Spool travel vector — Vector of spool opening distance values

[0, .002, .004, .007, .017] m (default) | numerical array

Vector of control member travel distances for the tabular parametrization of the valve opening area. A positive displacement opens the valve. The values in this vector correspond one-to-one to values 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 Orifice parametrization to Tabulated data - Area vs. spool travel.

Orifice area vector — Vector of valve opening area values

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

Vector of valve area values for the tabular parametrization of opening area. The values in this vector correspond one-to-one with the elements in the Spool travel vector parameter. The first element of this vector is the leakage area, and the last element is the maximum valve area. Linear interpolation is employed between table data points.

Dependencies

To enable this parameter, set Orifice parametrization to Tabulated data - Area vs. spool travel.

Spool travel vector, s — Vector of opening values

[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 Orifice parametrization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

Pressure drop vector, dp — Vector of 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 Orifice parametrization to Tabulated data -Volumetric flow rate vs. spool travel 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) | numerical array

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 correlated vectors:

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

• N is the number of vector elements in the Spool travel vector, s parameter.

Dependencies

To enable this parameter, set Orifice parametrization to Tabulated data - Volumetric flow rate vs. spool travel and pressure drop.

Discharge coefficient — Discharge coefficient

0.64 (default) | positive scalar

Discharge loss for a hydraulic structure. The default discharge coefficient for an valve in Simscape™ Fluids™ is 0.64.

Dependencies

To enable this parameter, set Orifice parametrization to:

• Tabulated data - Area vs. spool travel

• Linear - area vs. spool travel

Critical Reynolds number — Upper Reynolds number limit for laminar flow

150 (default) | positive scalar

Upper Reynolds number limit for laminar flow through the valve.

Dependencies

To enable this parameter, set Orifice parametrization to:

• Tabulated data - Area vs. spool travel

• Linear - area vs. spool travel

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range of [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.

Dependencies

To enable this parameter, set Orifice parametrization to Linear - area vs. spool travel.

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

On (default) | Off

Whether to account for pressure increase when the fluid flows from a region of 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.