4-Way 3-Position Directional Valve (G)

Four-line three-position distribution valve in the gas network.

blockType: EngeeFluids.Gas.Valves.DirectionalControl.FourWayThreePosition

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Description

Block 4-Way 3-Position Directional Valve (G) It is a distribution valve with four gas ports (P, A, B and T) and channels between them P-A, A-T, P-B and B-T. Each of the channels passes through a hole of variable width. The input signal applied to port S controls the position of the spool. The distribution valve closes when the spool covers the opening.

In a typical system, port P is connected to a pump, port T to a reservoir, and ports A and B to a two—way actuator. Opening the channels P-A and B-T allows the pump to create pressure on one side of the drive, and the tank to relieve pressure on the other. In some systems, the drive shaft is extended, in others it is retracted. Opening the channels P-B and A-T unfolds the drive sides, which are under pressure and unloaded, so that the shaft can move in the opposite direction.

An example of a distribution valve configuration is shown in the figure.

4 way 3 position directional valve g 1 en

The flow can be laminar or turbulent and can reach sonic velocities. The maximum speed is reached at the mouth of the valve opening, where the flow is narrowest and fastest. The flow becomes critical when the ratio of outlet pressure to inlet pressure reaches a critical value characteristic of the valve. The unit does not calculate supersonic flow.

Valve positions

The control valve is steplessly adjustable and switches smoothly between one normal and two operating positions.

When the value of the movement of the spool in port S is zero, the distribution valve returns to its normal position, in which it no longer operates. If the pistons of the spool are not displaced relative to their openings, the distribution valve is completely closed.

The operating positions are the positions to which the valve moves when the spool is maximally moved in a positive or negative direction from the normal position. In this case, one hole is usually closed and the other is completely open.

The image I shows a valve in which movement occurs in the positive direction, the holes P-A and B-T are fully open, and the holes P-B and A-T are completely closed. Image II shows a valve in which movement occurs in the negative direction, the openings P-A and B-T are completely closed, and the openings P-B and A-T are completely open. The image III shows a valve in which the spool is in the neutral position and all openings are closed.

4 way 3 position directional valve g 2

The movement of the spool, which moves the distribution valve to the operating position, depends on the displacement of the spool pistons. The parameters in the Valve Opening Fraction Offsets section set constant values for determining the displacement of the spool pistons at the ports.

The stage of opening the hole

In the intervals between the positions of the distribution valve, the opening of the hole depends on where the piston of the spool is located relative to the rim. This distance is an open hole, and the unit normalizes this distance so that its value is a fraction of the maximum distance at which the hole is fully open. The normalized variable is the degree of opening of the hole.

The degree of opening of the hole may vary from -1 when the distribution valve is in the position shown in the image I, until +1 when the distribution valve is in the position shown in image II.

The unit calculates the degree of opening of the hole based on the movement of the spool and the displacement of the degree of opening of the hole. Displacement and displacement are infinitesimal fractions of the maximum piston—hole distance.

The degree of opening of the hole P-A is:

The degree of opening of the hole B-T is:

The degree of opening of the hole A-T is:

The degree of opening of the hole P-B is:

In these equations:

— the degree of opening of the hole indicated by the subscript. If the calculation returns a value outside the range [0, 1], then the block uses the nearest limit;
— offsets of the opening degree of the hole, which are set by the parameters in the Valve Opening Fraction Offsets section. To account for the unusual configurations of the distributors, the block does not impose restrictions on their values, although they are usually between -1 and 1;
— this is the normalized displacement of the spool, set as a scalar on the port S. To compensate for extreme shifts in the degree of opening of the hole, the signal value is unlimited. This value is usually in the range of -1 before 1.

The displacement of the opening degree of the hole

By default, the control valve is completely closed when its control displacement is zero. In this state, the valve has zero overlap.

The piston of the spool can be displaced to simulate a distribution valve with incomplete or complete shut-off. The partial shut-off valves are partially open in the normal position. The full-shut-off control valves are completely closed slightly further than the normal position. The figure shows how the opening degrees of the hole vary depending on the movement of the spool.

Image I: distribution valve without overlap. The offset of the opening degree is zero. When the valve is in the normal position, the piston of the spool completely covers the opening.
Image II: A distribution valve with incomplete shut-off. The offset of the degree of opening P-A and B-T holes is positive, and the offset of the degree of opening P-B and A-T holes is negative. When the valve is in the normal position, the piston of the spool partially covers the four holes.
Image III: closed distribution valve. The offset of the degree of opening of P-A and B-T holes is negative, and the offset of the degree of opening of P-B and A-T holes is positive. The piston of the spool completely closes all the holes not only in the normal position, but also in the small area of movement of the spool around it.

4 way 3 position directional valve g 3

Parameterization of the distribution valve

The block behavior depends on the Valve parametrization parameter:

Cv flow coefficient — expense ratio determines the dependence of the throughput on the pressure drop [2], [3].
Kv flow coefficient — expense ratio determines the dependence of throughput on pressure drop, [2], [3].
Sonic conductance — steady-state acoustic conductivity determines the throughput at critical flow, a condition in which the flow velocity is equal to the local speed of sound. The flow becomes critical when the ratio of outlet pressure to inlet pressure reaches a value called the critical pressure ratio [1].
Orifice area — the area of the hole determines the throughput [4].

Hole Characteristic

The flow characteristic relates the opening of the distribution valve to the inlet value, which is often the stroke of the spool. The unit calculates the hole through acoustic conductivity, flow coefficient, or the cross-sectional area of the hole, depending on the setting of the Valve parameterization parameter. The control input is the degree of opening of the hole, which is a function of the movement of the spool set on the port S.

The flow characteristic is usually given in steady-state mode, when the inlet pressure is constant, carefully controlled. The flow characteristic depends only on the valve and can be linear or non-linear. To select a flow characteristic, use the Opening characteristic parameter.:

Linear — throughput is a linear function of the degree of opening of the hole. As the degree of opening of the hole increases from 0 before 1, the throughput indicator increases from the specified minimum to the specified maximum.
Tabulated — throughput is a general function that can be linear or non-linear depending on the degree of opening of the hole. The function is set in tabular form, with the independent variable being set by the Opening fraction vector parameter.

Numerical smoothing

If the Opening characteristic parameter is set to Linear, and the Smoothing factor parameter is set to a non-zero value, then numerical smoothing is applied to the degree of hole opening. Smoothing helps to maintain the numerical stability of the simulation.

Leakage rate

The leakage rate ensures that no section of the liquid network is isolated. Isolated areas of fluid can reduce the numerical stability of the model, slow down the simulation speed and, in some cases, lead to simulation failure. The Leakage flow fraction parameter represents the leakage area as a small number greater than zero.

Composite structure

This block is a composite component consisting of four blocks Orifice (G) connected to ports P, A, B, T and S. For more information about valve parameterization and calculations, see Orifice (G).

Assumptions and limitations

Meaning Sonic conductance The Valve parameterization parameter is intended for pneumatic systems. If this parameter is used for gases other than air, it may be necessary to adjust the acoustic conductivity value by the square root of the specific gravity.
The equation for parameterization Orifice area it has lower accuracy for gases that are far from ideal.
This block does not simulate supersonic flow.

Ports

Conserving

# A — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_a

# B — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_b

# P — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_p

# T — gas inlet or outlet
gas

Details

Non-directional port, corresponds to flow in or flow out.

Program usage name

port_t

Input

# S — control signal
scalar

Details

The instantaneous displacement of the actuating element relative to its normal non-operating position, specified as a scalar. The unit normalises the displacement relative to the maximum position of the actuating element required to fully open the hole. The scalar has no unit of measurement and its instantaneous value is normally in the range -1 to 1.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Valve parameterization — method of specifying the flow characteristic through the orifice
Cv flow coefficient | Kv flow coefficient | Sonic conductance | Orifice area

Details

The method of mass flow calculation is based on:

Cv flow coefficient - flow coefficient .
Kv flow coefficient - flow coefficient , which is defined as .
Sonic conductance - steady-state acoustic conductance.
Orifice area - orifice area.

Values	`Cv flow coefficient` \| `Kv flow coefficient` \| `Sonic conductance` \| `Orifice area`
Default value	`Cv flow coefficient`
Program usage name	`valve_parameterization`
Evaluatable	No

# Opening characteristic — method for calculating valve opening characteristics
Linear | Tabulated

Details

The method that the unit uses to calculate the valve opening area:

`Linear' - the opening area is a linear function of the degree of opening of the orifice.
Tabulated - a general non-linear relationship that is specified in tabular form.

Values	`Linear` \| `Tabulated`
Default value	`Linear`
Program usage name	`opening_characteristics`
Evaluatable	No

# Maximum Cv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

Flow coefficient value , when the orifice cross-sectional area is maximum.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Cv flow coefficient and the Opening characteristic parameter to Linear.

Default value	`4.0`
Program usage name	`C_v_max`
Evaluatable	Yes

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Cv coefficient vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Cv coefficient vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to Tabulated and the Orifice parameterization parameter to Cv flow coefficient.

Default value	`[0:0.2:1...]`
Program usage name	`opening_fraction_vector_C_v`
Evaluatable	Yes

# Cv flow coefficient vector — vector of flow coefficient values

Details

Vector of flow coefficients . The values must be specified in ascending order. The dimensionality of the vector corresponds to that of the Opening fraction vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to `Tabulated' and the Orifice parameterization parameter to `Cv flow coefficient'.

Default value	`[1e-6, 0.8, 1.6, 2.4, 3.2, 4.0]`
Program usage name	`C_v_vector`
Evaluatable	Yes

# xT pressure differential ratio factor at choked flow — critical differential pressure ratio

Details

The ratio between the inlet pressure and the outlet pressure , defined as , at which the flow becomes critical. If this value is not known, it can be found in Table 2 in ISA-75.01.01 [3]. By default the value 0.7 is suitable for many valves.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Cv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_C_v`
Evaluatable	Yes

# Maximum Kv flow coefficient — flow coefficient corresponding to the maximum orifice area

Details

The value of the flow coefficient is , when the value of the control signal at port L is 1 and the orifice area is maximum.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Kv flow coefficient and the Opening characteristic parameter to Linear.

Default value	`3.6`
Program usage name	`K_v_max`
Evaluatable	Yes

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Kv coefficient vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Kv coefficient vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to Tabulated and the Orifice parameterization parameter to Kv flow coefficient.

Default value	`[0:0.2:1...]`
Program usage name	`opening_fraction_vector_K_v`
Evaluatable	Yes

# Kv flow coefficient vector — vector of flow coefficient values

Details

Vector of flow coefficients . The values must be specified in ascending order. The dimensionality of the vector corresponds to that of the Opening fraction vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to `Tabulated' and the Orifice parameterization parameter to `Kv flow coefficient'.

Default value	`[1e-6, 0.72, 1.44, 2.16, 2.88, 3.6]`
Program usage name	`K_v_vector`
Evaluatable	Yes

# xT pressure differential ratio factor at choked flow — critical differential pressure ratio

Details

Dependencies

To use this parameter, set the Orifice parameterization parameter to Kv flow coefficient.

Default value	`0.7`
Program usage name	`delta_p_ratio_K_v`
Evaluatable	Yes

# Maximum sonic conductance — acoustic conductivity corresponding to the maximum aperture area
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

The value of acoustic conductivity when the value of the control signal on the L port is 1 and the orifice cross-sectional area is maximised.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance' and the Opening characteristic parameter to `Linear'.

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`12.0 l/(bar*s)`
Program usage name	`C_max`
Evaluatable	Yes

# Critical pressure ratio — critical pressure ratio

Details

The ratio of pressures at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound. The ratio between the outlet pressure and the inlet pressure : .

Dependencies

To use this parameter, set the Orifice parameterization parameter to Sonic conductance and the Opening characteristic parameter to Linear.

Default value	`0.3`
Program usage name	`B_critical_linear`
Evaluatable	Yes

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the throughput measure Sonic conductance vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Sonic conductance vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to Tabulated and the Orifice parameterization parameter to Sonic conductance.

Default value	`[0:0.2:1...]`
Program usage name	`opening_fraction_vector_C`
Evaluatable	Yes

# Sonic conductance vector — vector of acoustic conductivity values
l/(bar*s) | gal/(min*psi) | m^3/(Pa*s)

Details

Vector of acoustic conductivity values. The values should be specified in ascending order. The dimensionality of the vector corresponds to the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance' and the Opening characteristic parameter to `Tabulated'.

Units	`l/(bars)` \| `gal/(minpsi)` \| `m^3/(Pa*s)`
Default value	`[1e-5, 2.4, 4.8, 7.2, 9.6, 12.0] l/(bar*s)`
Program usage name	`C_vector`
Evaluatable	Yes

# Critical pressure ratio vector — vector of critical pressure ratio values

Details

Vector of critical pressure ratios. The critical pressure ratio is the ratio of the outlet pressure to the inlet pressure at which the flow becomes critical and the flow velocity reaches a maximum determined by the local speed of sound. The dimensionality of the vector corresponds to that of the Opening fraction vector.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance' and the Opening characteristic parameter to `Tabulated'.

Default value	`0.3 * ones(6)`
Program usage name	`B_critical_vector`
Evaluatable	Yes

# Subsonic index — degree value used to calculate the mass flow rate in subsonic flow regime

Details

An empirical value used to more accurately calculate the mass flow rate in subsonic flow regime.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance'.

Default value	`0.5`
Program usage name	`m`
Evaluatable	Yes

Details

The temperature in the standard reference atmosphere in ISO 8778.

The values of the ISO reference parameters only need to be adjusted if acoustic conductivity values obtained with different reference values are used.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance'.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_reference`
Evaluatable	Yes

# ISO reference density — reference density according to ISO 8778
kg/m^3 | g/m^3 | g/cm^3 | g/mm^3 | lbm/ft^3 | lbm/gal | lbm/in^3

Details

Density in a standard reference atmosphere in ISO 8778.

The values of the ISO reference parameters need only be adjusted if acoustic conductivity values obtained with different reference values are used.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Sonic conductance'.

Units	`kg/m^3` \| `g/m^3` \| `g/cm^3` \| `g/mm^3` \| `lbm/ft^3` \| `lbm/gal` \| `lbm/in^3`
Default value	`1.185 kg/m^3`
Program usage name	`rho_reference`
Evaluatable	Yes

# Maximum orifice area — flow cross-sectional area corresponding to the maximum orifice area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Maximum flow area when the value of the control signal at port L is 1.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Orifice area' and the Opening characteristic parameter to `Linear'.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`1e-4 m^2`
Program usage name	`max_restriction_area`
Evaluatable	Yes

# Opening fraction vector — values of the control signal for the opening degree

Details

The vector of control signal values at which the capacity measure Orifice area vector is set. The control signal value is equal to the opening degree only in the range from 0 to 1.

The values must be specified in ascending order. The dimensionality of the vector corresponds to the dimensionality of the Orifice area vector.

Dependencies

To use this parameter, set the Opening characteristic parameter to Tabulated and the Orifice parameterization parameter to Orifice area.

Default value	`[0:0.2:1...]`
Program usage name	`opening_fraction_vector_area`
Evaluatable	Yes

# Orifice area vector — vector of hole area values
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

Vector of the areas of the hole cross-section. The dimensionality of the vector corresponds to the Opening fraction vector. The first element of this vector is the leakage area and the last element is the maximum orifice area.

Dependencies

To use this parameter, set the Orifice parameterization parameter to `Orifice area' and the Opening characteristic parameter to `Tabulated'.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`[1e-10, 0.2e-4, 0.4e-4, 0.6e-4, 0.8e-4, 1e-4] m^2`
Program usage name	`restriction_area_vector`
Evaluatable	Yes

# Discharge coefficient — flow coefficient

Details

The correction factor is the ratio of the actual mass flow rate to the theoretical mass flow rate.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Orifice area.

Default value	`0.64`
Program usage name	`C_d`
Evaluatable	Yes

# Leakage flow fraction — cost ratio

Details

The ratio of the flow rate through a closed orifice to that through an open orifice.

Dependencies

To use this parameter, set the Orifice parameterization parameter to Orifice area.

Default value	`1e-6`
Program usage name	`leakage_fraction`
Evaluatable	Yes

# Smoothing factor — numerical smoothing factor

Details

A continuous smoothing factor that ensures smooth opening by correcting the orifice characteristic in the nearly open and nearly closed positions.

Dependencies

To use this parameter, set Opening characteristic to `Linear'.

Default value	`0.01`
Program usage name	`smoothing_factor`
Evaluatable	Yes

# Laminar flow pressure ratio — pressure ratio at which the flow transitions between laminar and turbulent regimes

Details

The ratio of outlet pressure to inlet pressure at which the flow transitions between laminar and turbulent flow regimes.

Typical values range from 0.995 to 0.999.

Default value	`0.999`
Program usage name	`B_laminar`
Evaluatable	Yes

# Cross-sectional area at ports A, B, P, and T — inlet or outlet area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

This area is used when calculating the mass flow rate through the ports.

The ports are all the same size. The value of this parameter must match the inlet port area of the component to which the unit is connected.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

Valve Opening Fraction Offsets

# Between ports P and A — degree of opening of the P-A orifice at zero offset signal

Details

The degree of opening of P-A orifice when the value of input signal S is zero. In this case, the valve is in the normal position. The opening degree measures the distance from the spool piston to the P-A orifice normalised to the maximum permissible opening. The opening degree has no unit of measurement and usually has a value between 0 and 1.

Default value	`0.0`
Program usage name	`offset_pa`
Evaluatable	Yes

# Between ports B and T — degree of opening of the B-T orifice at zero offset signal

Details

The degree of opening B-T of the orifice when the value of the input signal S is zero. In this case, the valve is in the normal position. The opening degree measures the distance from the spool piston to the B-T orifice normalised to the maximum permissible opening. The opening degree has no unit of measurement and usually has a value between 0 and 1.

Default value	`0.0`
Program usage name	`offset_bt`
Evaluatable	Yes

# Between ports P and B — degree of opening of the P-B orifice at zero offset signal

Details

The degree of opening of P-B orifice when the value of input signal S is zero. In this case, the valve is in the normal position. The opening degree measures the distance from the spool piston to the P-B orifice normalised to the maximum permissible opening. The opening degree has no unit of measurement and usually has a value between 0 and 1.

Default value	`0.0`
Program usage name	`offset_pb`
Evaluatable	Yes

# Between ports A and T — degree of opening of the A-T orifice at zero offset signal

Details

The degree of opening A-T of the orifice when the value of the input signal S is zero. In this case, the valve is in the normal position. The opening degree measures the distance from the spool piston to the A-T orifice normalised to the maximum permissible opening. The opening degree has no unit of measurement and usually has a value between 0 and 1.

Default value	`0.0`
Program usage name	`offset_at`
Evaluatable	Yes

Literature

[1] ISO 6358-3. "Pneumatic fluid power – Determination of flow-rate characteristics of components using compressible fluids – Part 3: Method for calculating steady-state flow rate characteristics of systems". 2014.

[2] IEC 60534-2-3. "Industrial-process control valves – Part 2-3: Flow capacity – Test procedures". 2015.

[3] ANSI/ISA-75.01.01. "Industrial-Process Control Valves – Part 2-1: Flow capacity – Sizing equations for fluid flow underinstalled conditions". 2012.

[4] P. Beater. Pneumatic Drives. Springer-Verlag Berlin Heidelberg. 2007.