4-Way 3-Position Directional Valve (G)

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

4 way 3 position directional valve g

Description

The 4-Way 3-Position Directional Valve (G) unit is a directional 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 an aperture of variable width. The input signal applied to port S controls the position of the spool valve. The directional control valve closes when the spool closes the orifice.

In a typical system, port P is connected to the pump, port T is connected to the tank, and ports A and B are connected to a double-acting actuator. Opening the P-A and B-T channels allows the pump to pressurise one side of the actuator and the reservoir to depressurise the other. In some systems the actuator shaft extends, in others it retracts. Opening the P-B and A-T channels reverses the pressurised and depressurised sides of the actuator so that the shaft can move in the opposite direction.

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

4 way 3 position directional valve il 1 en

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

Valve positions

The directional control valve is infinitely variable and switches smoothly between one normal and two operating positions.

When the value of the spool movement in port S is zero, the directional control valve returns to the normal position in which it no longer operates. If the spool pistons are not displaced relative to their ports, the directional control valve is fully closed.

The operating positions are the positions to which the valve moves when the spool moves as far as possible in the positive or negative direction from the normal position. In this case, one orifice is normally closed and the other fully open.

Image I shows a valve in which the movement is in the positive direction, ports P-A and B-T are fully open and ports P-B and A-T are fully closed. Image II shows a valve in which the movement is in the negative direction, ports P-A and B-T are fully closed, and ports P-B and A-T are fully open. Image III shows a valve in which the spool is in the neutral position and all orifices are closed.

4 way 3 position directional valve g 1

The spool movement that moves the directional valve to the operating position depends on the displacement of the spool pistons. The parameters under Valve Opening Fraction Offsets set constant values to determine the offset of the spool pistons at the ports.

Valve Opening Fraction Offsets

Between positions of the directional valve, the opening of the port depends on where the spool piston is located relative to the rim. This distance is the orifice opening, and the block normalises this distance so that its value is a fraction of the maximum distance at which the orifice is fully open. The normalised variable is the degree to which the orifice is open.

The degree of opening of the orifice may range from -1 when the directional valve is in the position shown in image I to +1 when the directional valve is in the position shown in image II.

The unit calculates the degree of orifice opening based on the spool movement and the offset of the degree of orifice opening. The displacement and offset are infinitesimal fractions of the maximum piston to orifice distance.

The bore opening ratio P-A is:

The opening degree of the hole B-T is:

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

The opening degree of the hole P-B is:

In these equations:

- the degree of opening of the hole specified by the subscript. If the calculation returns a value outside the [0, 1] range, the block uses the nearest limit;
- orifice opening degree offsets, which are set by the parameters in the Valve Opening Fraction Offsets section. To accommodate unusual spreader configurations, the block does not impose limits on their values, although they are usually between -1 and 1;
- is the normalised spool displacement defined as a scalar on the S port. To compensate for extreme shifts in the degree of opening of the port, the value of the signal is unconstrained. Typically, this value is in the range of -1 to 1.

Hole Opening Degree Offset

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

You can shift the spool piston to simulate a divider valve with partial or full overlap. Partial overlap directional control valves are partially open in the normal position. Full overlap directional control valves are fully closed slightly beyond the normal position. The illustration shows how the opening degrees of the orifice change depending on the movement of the spool valve.

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

4 way 3 position directional valve g 2

Parametrization of the directional control valve

The behaviour of the block depends on the Valve parametrization parameter:

Cv flow coefficient - flow coefficient determines the dependence of flow capacity on pressure drop [2], [3].
Kv flow coefficient - flow coefficient determines the dependence of flow capacity on pressure drop, [2], [3].
Sonic conductance - steady-state acoustic conductance defines the flow capacity at critical flow, the condition at 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 orifice area determines the flow capacity [4].

Orifice characteristic

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

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

Linear' - the flow rate is a linear function of the degree of orifice opening. As the opening degree increases from `0 to 1, the flow rate increases from the specified minimum to the specified maximum.
`Tabulated' - throughput is a general function that can be linear or non-linear with the degree of opening of the orifice. The function is tabulated, with the independent variable specified by the Opening fraction vector parameter.

Numerical smoothing

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

Leakage rate

The leakage rate ensures that no section of the fluid network is isolated. Isolated sections of fluid can reduce the numerical stability of the model, slow down the simulation speed and, in some cases, cause the simulation to fail. 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 on valve parameterization and calculations, see Orifice (G).

Assumptions and limitations

The Sonic conductance value of the Valve parameterization is intended for pneumatic systems. If this parameter is used for gases other than air, it may be necessary to correct the acoustic conductance value by the square root of the specific gravity.
The equation for the `Orifice area' parameterization has less accuracy for gases that are far from ideal.
This block does not model 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
g/cm^3 | kg/m^3 | lbm/gal

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	`g/cm^3` \| `kg/m^3` \| `lbm/gal`
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 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

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` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
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 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

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` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
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 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

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` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
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.