4-Way Directional Valve (G)
Controlled valve with four ports and four flow paths
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Simscape / Fluids / Gas / Valves & Orifices / Directional Control Valves
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 (P–A and A–T, P–B and B–T). 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 P–A and B–T 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 (P–B and A–T) 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 P–A and B–T orifices are fully open and the P–B and A–T orifices are fully closed (position I in the figure). If it is negative, the P–A and B–T orifices are fully closed and the P–B and A–T 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.
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 P–A orifice is:
Likewise for the B–T orifice:
That of the A–T orifice is:
Lastly for the P–B orifice:
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 0–1, the nearest limit is used. (The orifice opening fractions are said to saturate at
0
and1
.)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
.)
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 P–A and B–T opening fraction offsets are positive and the P–B and the A–T 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 P–A and B–T opening fraction offsets are negative and the P–B and the A–T 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 ofSonic conductance
, the end points of the line are obtained at opening fractions of0
and1
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).