# 4-Way Directional Valve (G)

Controlled valve with four ports and four flow paths

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## Description

The 4-Way Directional Valve (G) block models a valve with four gas ports (P, A, B, and T) and two sets of flow paths to switch between (PA and AT, PB and BT). The paths each run through an orifice of variable width, its opening being tied to the position of a control member. Think of the control member as a spool with two lands to cover (by degrees) the different orifices. The distance of a land to its appointed orifices determines if, and to what extent, those are open.

(The distances from the lands to the orifices are computed during simulation from the displacement signal specified at port S. They, and all distances related to spool position, are defined as unitless fractions, typically ranging from `-1` to `+1`. The calculations are described in detail under Orifice Opening Fractions.)

The gas ports connect to what, in a representative system, are a pump (P), a tank (T), and a double-sided actuator (A and B). Opening the PA and BT flow paths allows the pump to pressurize one side of the actuator and the tank to relieve the other. The actuator shaft translates (to extend in some systems, to retract in others). Opening the alternate (PB and AT) flow paths flips the pressurized and relieved sides of the actuator so that its shaft can translate in reverse.

The port connections will vary with the system being modeled, but the purpose of the valve—to switch between flow paths and to regulate the flow passing through them—should not.

A Common Use of a 4-Way Directional Valve

The flow can be laminar or turbulent, and it can reach (up to) sonic speeds. This happens at the vena contracta, a point just past the throat of the valve where the flow is both its narrowest and fastest. The flow then chokes and its velocity saturates, with a drop in downstream pressure no longer sufficing to increase its velocity. Choking occurs when the back-pressure ratio hits a critical value characteristic of the valve. Supersonic flow is not captured by the block.

### Valve Positions

The valve is continuously variable. It shifts smoothly between positions, of which it has three: one normal and two working.

The normal position is that to which the valve reverts when it is no longer being operated. The instantaneous displacement of the spool (given at port S) is then zero. Unless the lands of the spool are installed at an offset to their orifices, the valve will be fully closed.

The other two, the working positions, are those to which the valve moves when the spool is maximally displaced from its normal position. That displacement is positive in one case and negative in the other.

If it is positive, the PA and BT orifices are fully open and the PB and AT orifices are fully closed (position I in the figure). If it is negative, the PA and BT orifices are fully closed and the PB and AT orifices are fully open (position II).

What spool displacement puts the valve in a working position depends on the offsets of the lands on the spool. These are generally applied before operation, in a real valve, and before simulation, in a valve model. They are specified in the block as constants (fixed from the start of simulation) in the Valve Opening Fraction Offsets tab.

Orifice Opening Fractions

Between valve positions, the opening of an orifice depends on where, relative to its rim, its land of the spool happens to be. This distance is the orifice opening, and it is normalized here so that its value is a fraction of its maximum (the distance at which the orifice is fully open). The normalized variable is referred to here as the orifice opening fraction.

The orifice opening fractions range from `-1` in working position I to `+1` in working position II (using the labels shown in the figure).

The opening fractions are calculated from the lengths already alluded to: the variable displacement of the control member (applied during operation) and the fixed offsets of its lands (applied during installation). These lengths are themselves defined as unitless fractions of the maximum land–orifice distance. (The offsets are referred to here as the opening fraction offsets.)

The opening fraction of the PA orifice is:

`${h}_{PA}={H}_{PA}+x.$`

Likewise for the BT orifice:

`${h}_{BT}={H}_{BT}+x.$`

That of the AT orifice is:

`${h}_{AT}={H}_{AT}-x.$`

Lastly for the PB orifice:

`${h}_{PB}={H}_{PB}-x.$`

In the equations:

• h is the opening fraction of the orifice denoted by the subscript. If the calculation should return a value outside of the range 01, the nearest limit is used. (The orifice opening fractions are said to saturate at `0` and `1`.)

• H is the opening fraction offset for the orifice denoted by the subscript. The offsets are each specified as a block parameter (in the Valve Opening Fraction Offsets tab). To allow for unusual valve configurations, no limit is imposed on their values, though generally these will fall between `-1` and `+1`.

• x is the normalized instantaneous displacement of the spool, specified as a physical signal at port S. To compensate for equally extreme opening fraction offsets, no limit is imposed on its value (though generally it too will fall in the range of `-1` to `+1`.)

Opening Fraction Offsets

The valve is by default configured so that it is fully closed when the spool displacement is zero. Such a valve is often described as being zero-lapped.

It is possible, by offsetting the lands of the spool, to model a valve that is underlapped (partially open in the normal valve position) or overlapped (fully closed not only in but also slightly beyond the normal position). The figure shows, for each case, how the orifice opening fractions vary with the instantaneous spool displacement:

• Case I: A zero-lapped valve. The opening fraction offsets are all zero. When the valve is in the normal position, the lands of the spool completely cover all four orifices.

• Case II: An underlapped valve. The PA and BT opening fraction offsets are positive and the PB and the AT opening fraction offsets are negative. When the valve is in the normal position, the lands of the spool cover all four orifices, but neither fully.

• Case III: An overlapped valve. The PA and BT opening fraction offsets are negative and the PB and the AT opening fraction offsets are positive. The control member completely covers all orifices not only in the normal position but over a small region (of spool displacements) around it.

### Opening Characteristics

It is common, when picking a valve for throttling or control applications, to match the flow characteristic of the valve to the system it is to regulate.

The flow characteristic relates the opening of the valve to the input that produces it, often spool travel. Here, the opening is expressed as a sonic conductance, flow coefficient, or restriction area (the choice between them being given by the Valve parameterization setting). The control input is the orifice opening fraction (a function of the spool displacement specified at port S).

The flow characteristic is normally given at steady state, with the inlet at a constant, carefully controlled pressure. This (inherent) flow characteristic depends only on the valve and it can be linear or nonlinear, the most common examples of the latter being the quick-opening and equal-percentage types. To capture such flow characteristics, the block provides a choice of opening parameterization (specified in the block parameter of the same name):

• `Linear` — The sonic conductance (C) is a linear function of the orifice opening fraction (h). In the default valve parameterization of `Sonic conductance`, the end points of the line are obtained at opening fractions of `0` and `1` from the Sonic conductance and leakage flow and Sonic conductance at maximum flow block parameters.

• `Tabulated data` — The sonic conductance is a general function (linear or nonlinear) of the orifice opening fraction. The function is specified in tabulated form, with the columns of the table deriving, in the default valve parameterization, from the Opening fraction vector and Sonic conductance vector block parameters.

(If the Valve parameterization setting is other than `Sonic conductance`, the sonic conductance data is obtained by conversion from the chosen measure of valve opening (such as restriction area or flow coefficient). The opening data applies to all orifices equally.)

For controlled systems, it is important that the valve, once it is installed, be approximately linear in its flow characteristic. This (installed) characteristic depends on the remainder of the system—it is not generally the same as the inherent characteristic captured in the block. A pump, for example, may have a nonlinear characteristic that only a nonlinear valve, usually of the equal-percentage type, can adequately compensate for. It is cases of this sort that the `Tabulated data` option primarily targets.

### Leakage Flow

The main purpose of leakage flow is to ensure that no section of a fluid network ever becomes isolated from the rest. Isolated fluid sections can reduce the numerical robustness of the model, slowing down the rate of simulation and, in some cases, causing it to fail altogether. While leakage flow is generally present in real valves, its exact value here is less important than its being a small number greater than zero. The leakage flow area is given in the block parameter of the same name.

### Composite Structure

This block is a composite component comprising two instances of the Variable Orifice ISO 6358 (G) block connected to ports P, A, T, and S as shown below. Refer to that block for more detail on the valve parameterizations and block calculations (for example, those used to determine the mass flow rate through the ports).

## Ports

### Input

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Instantaneous displacement of the control member against its normal (unactuated) position, specified as a physical signal. The displacement is normalized against the maximum position of the control member (that required to open the orifice fully). See the block description for more information. The signal is unitless and its instantaneous value typically (though not always) in the range of `-1``+1`.

### Conserving

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Opening through which flow can enter or exit the valve.

Opening through which flow can enter or exit the valve.

Opening through which flow can enter or exit the valve.

Opening through which flow can enter or exit the valve.

## Parameters

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Basic Parameters

Choice of ISO method to use in the calculation of mass flow rate. All calculations are based on the `Sonic conductance` parameterization; if a different option is selected, the data specified is converted into equivalent sonic conductance, critical pressure ratio, and subsonic index. See the calculations of the Variable Orifice ISO 6358 (G) block for detail on the conversions.

Method by which to calculate the opening area of the valve. The default setting treats the opening area as a linear function of the orifice opening fraction. The alternative setting allows for a general, nonlinear relationship to be specified (in tabulated form).

Area normal to the flow path at the valve ports. The ports are assumed to be of the same size. The flow area specified here should (ideally) match those of the inlets of adjoining components.

Pressure ratio at which the flow transitions between laminar and turbulent flow regimes. The pressure ratio is the fraction of the absolute pressure downstream of the valve over that just upstream of it. The flow is laminar when the actual pressure ratio is above the threshold specified here and turbulent when it is below. Typical values range from `0.995` to `0.999`.

Temperature at standard reference atmosphere, defined as 293.15 K in ISO 8778.

Density at standard reference atmosphere, defined as 1.185 kg/m3 in ISO 8778.

Model Parameterization

Equivalent measure of the maximum flow rate through the valve at some reference inlet conditions, generally those outlined in ISO 8778. The flow is at a maximum when the valve is fully open and the flow velocity is choked (it being saturated at the local speed of sound). This is the value usually reported by manufacturers in technical data sheets.

Sonic conductance is defined as the ratio of the mass flow rate through the valve to the product of the pressure and density upstream of the valve inlet. This parameter is often referred to as the C-value.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Equivalent measure of the minimum flow rate allowed through the valve at some reference inlet conditions, generally those outlined in ISO 8778. The flow is at a minimum when the valve is maximally closed and only a small leakage area—due to sealing imperfections, say, or natural valve tolerances—remains between its ports.

Sonic conductance is defined as the ratio of the mass flow rate through the valve to the product of the pressure and density upstream of the valve inlet. This parameter is often referred to in the literature as the C-value.

This parameter serves primarily to ensure that closure of the valve does not cause portions of the gas network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Ratio of downstream to upstream absolute pressures at which the flow becomes choked (and its velocity becomes saturated at the local speed of sound). This parameter is often referred to in the literature as the b-value. Enter a number greater than or equal to zero and smaller than the Laminar flow pressure ratio block parameter.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Empirical exponent used to more accurately calculate the mass flow rate through the valve when the flow is subsonic. This parameter is sometimes referred to as the m-index. Its value is approximately `0.5` for valves (and other components) whose flow paths are fixed.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance`.

Flow coefficient of the fully open valve, expressed in the US customary units of `ft3/min` (as described in NFPA T3.21.3). This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential. This is the value generally reported by manufacturers in technical data sheets.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Cv coefficient (USCS)`.

Flow coefficient of the maximally closed valve, expressed in the US customary units of `ft3/min` (as described in NFPA T3.21.3). This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential.

The purpose of the leakage value is primarily to ensure that closure of the valve does not cause portions of the gas network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Cv coefficient (USCS)`.

Flow coefficient of the fully open valve, expressed in the SI units of m^3/hr. This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential. This is the value generally reported by manufacturers in technical data sheets.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Kv coefficient (SI)`.

Flow coefficient of the maximally closed valve, expressed in the SI units of m^3/hr. This parameter measures the relative ease with which the gas will traverse the valve when driven by a given pressure differential.

The purpose of the leakage value is primarily to ensure that closure of the valve does not cause portions of the gas network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Kv coefficient (SI)`.

Sum of the gauge pressures at the inlet and pilot port at which the valve is fully open. This value marks the end of the pressure range of the valve (over which the same progressively opens to allow for increased flow).

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Restriction area`.

Opening area of the valve in the maximally closed position, when only internal leakage between the ports remains. This parameter serves primarily to ensure that closure of the valve does not cause portions of the gas network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Restriction area`.

Orifice opening fractions at which to specify the chosen measure of valve opening—sonic conductance, flow coefficient (in SI or USCS forms), or opening area.

This vector must be equal in size to that (or those, in the `Sonic conductance` parameterization) containing the valve opening data. The vector elements must be positive and increase monotonically in value from left to right.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Opening parameterization setting is `Tabulated data`.

Sonic conductances at the breakpoints given in the Opening fraction vector parameter. This data forms the basis for a tabulated function relating the orifice opening fraction, sonic conductance, and critical pressure ratio. Linear interpolation is used within the tabulated data range; nearest-neighbor extrapolation is used outside of it. The two vectors—of sonic conductance and orifice opening fractions—must be of the same size.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance` and the Opening parameterization setting is `Tabulated data`.

Critical pressure rations at the breakpoints given in the Opening fraction vector parameter. This data forms the basis for a tabulated function relating the orifice opening fraction, sonic conductance, and critical pressure ratio. Linear interpolation is used within the tabulated data range; nearest-neighbor extrapolation is used outside of it. The two vectors—of critical pressure ratios and orifice opening fractions—must be of the same size.

The values specified here must each be greater than or equal to zero and smaller than the Laminar flow pressure ratio block parameter.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Sonic conductance` and the Opening parameterization setting is `Tabulated data`.

Flow coefficients, expressed in US customary units of `ft3/min`, at the breakpoints given in the Opening fraction vector. This data forms the basis for a tabulated function relating the two variables. Linear interpolation is used within the tabulated data range; nearest-neighbor extrapolation is used outside of it. The two vectors—of flow coefficients and orifice opening fractions—must be of the same size.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Cv coefficient (USCS)` and the Opening parameterization setting is `Tabulated data`.

Flow coefficients, expressed in SI units of `m^3/hr`, at the breakpoints given in the Opening fraction vector parameter. This data forms the basis for a tabulated function relating the two variables. Linear interpolation is used within the tabulated data range; nearest-neighbor extrapolation is used outside of it. The two vectors—of flow coefficients and orifice opening fractions—must be of the same size.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Kv coefficient (SI)` and the Opening parameterization setting is `Tabulated data`.

Opening areas at the breakpoints given in the Opening fraction vector parameter. This data forms the basis for a tabulated function relating the two variables. Linear interpolation is used within the tabulated data range; nearest-neighbor extrapolation is used outside of it. The two vectors—of opening areas and orifice opening fractions—must be of the same size.

#### Dependencies

This parameter is active and exposed in the block dialog box when the Valve parameterization setting is `Restriction area` and the Opening parameterization setting is `Tabulated data`.

Amount of smoothing to apply to the opening function of the valve. This parameter determines the widths of the regions to be smoothed—one located at the fully open position, the other at the fully closed position.

The smoothing superposes on each region of the opening function a nonlinear segment (a third-order polynomial function, from which the smoothing arises). The greater the value specified here, the greater the smoothing is, and the broader the nonlinear segments become. See the Variable Orifice ISO 6358 (G) block for the impact of the smoothing on the block calculations.

At the default value of `0`, no smoothing is applied. The transitions to the maximally closed and fully open positions then introduce discontinuities (associated with zero-crossings). These can slow down the rate of simulation.

Valve Opening Fraction Offsets

Opening fraction of the PA orifice when the spool displacement is zero. The valve is then in the normal position. The opening fraction measures the distance of a land of the spool to its appointed orifice (here PA), normalized by the maximum such distance. It is unitless and (generally) between `0` and `1`.

Opening fraction of the BT orifice when the spool displacement is zero. The valve is then in the normal position. The opening fraction measures the distance of a land of the spool to its appointed orifice (here BT), normalized by the maximum such distance. It is unitless and (generally) between `0` and `1`.

Opening fraction of the PB orifice when the spool displacement is zero. The valve is then in the normal position. The opening fraction measures the distance of a land of the spool to its appointed orifice (here PB), normalized by the maximum such distance. It is unitless and (generally) between `0` and `1`.

Opening fraction of the AT orifice when the spool displacement is zero. The valve is then in the normal position. The opening fraction measures the distance of a land of the spool to its appointed orifice (here AT), normalized by the maximum such distance. It is unitless and (generally) between `0` and `1`.