# 3-Way Directional Valve (TL)

Valve for routing flow at the junction of three lines

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• Simscape / Fluids / Thermal Liquid / Valves & Orifices / Directional Control Valves

## Description

The 3-Way Directional Valve block models the flow through a directional control valve with three ports (P, T, and A) and two flow paths (the lines P-A and A-T). The ports connect to what in a typical system are a pump (P), a tank (T), and a single-acting actuator (A). The paths each contain a variable orifice that opens in proportion to the displacement of a control member—often a ball, spool, or diaphragm, associated with the signal at port S. This valve serves as a switch by which to partition the flow between the branches of a three-pronged junction.

Typical Valve Setup

### Valve Positions

The valve is continuously variable, which is to say that it shifts smoothly between positions. Of these there are three: one normal and two working. The normal position is that to which the valve reverts when the control member is no longer being actuated. The orifices are both typically closed in this position. The working positions are those to which the valve moves when the control member is maximally actuated. One orifice is typically closed in this position while the other is fully open. The exact opening states of the orifices depend on the opening offsets specified in the block dialog box.

The working positions are shown in the figure in the default case of a valve without opening offsets. One, labeled I, corresponds to the A-T orifice being maximally open and the P-A orifice maximally closed. The other, labeled II, corresponds to the reverse arrangement, with the P-A orifice being maximally open and the A-T orifice maximally closed. At points between the normal and working positions, one orifice is partially open while the other is fully closed. Note that no physical connection exists between ports P and T and therefore that no flow can develop across them.

### Valve Opening

Which position the valve is in depends on the control member coordinates relative to the P-A and A-T orifices—lengths referred to here as the orifice openings. These are calculated during simulation from their opening offsets, each specified as a block parameter in the block dialog box, and from the control member displacement, given by the physical signal at port S. For the P-A orifice:

`${h}_{\text{PA}}={h}_{\text{PA0}}+x,$`

where:

• hPA is the P-A orifice opening.

• hPA0 is the P-A opening offset.

• x is the control member displacement. A control member displacement of zero corresponds to a valve that is in the normal state.

For the A-T orifice:

`${h}_{\text{AT}}={h}_{\text{AT0}}+x,$`

where:

• hAT is the A-T orifice opening.

• hAT0 is the A-T opening offset.

An orifice cracks opens when its calculated opening (variable h) rises above zero. It then continues to widen with a rising opening value. In the case of the P-A orifice, this occurs as the control member is displaced in the positive direction. In the case of the A-T orifice, it occurs as the control member is displaced in the negative direction.

The orifices are each fully open when the opening value is at a specified maximum. In the linear valve parameterization, this maximum is obtained from the Maximum valve opening block parameter. You can set the Area characteristics parameter to ```Different for each flow path``` to specify the Maximum valve opening parameter separately for each orifice. In tabulated valve parameterizations, the maximum opening is obtained from the last breakpoint in the tabulated data.

### Opening Offsets

The valve is by default configured so that it is fully closed when the control member displacement is zero. Such a valve is often described as being zero-lapped. It is possible, by applying an offset to the control member, to model a valve that is underlapped (partially open when the control member displacement is zero) or overlapped (fully closed up to a control member displacement equal to the applied offset). The figure shows the orifice opening as a function of the control member displacement for each case:

• Case I: A zero-lapped valve. The opening offsets are both zero. When the valve is in the normal position, the control member completely covers both orifices. The zero-lapped valve is completely closed when the control member displacement is exactly zero.

• Case II: An underlapped valve. The opening offsets are both positive. When the valve is in the normal position, the control member covers both orifices but neither fully. The underlapped valve is always at least partially open.

• Case III: An overlapped valve. The opening offsets are both negative. The control member completely covers both orifices not only in the normal position but over a small region around it. The overlapped valve is fully closed until the control member crosses the opening offset of either orifice.

### Opening Characteristics

The orifice openings serve during simulation to calculate the mass flow rates through the orifices. The calculation can be a direct mapping from opening to flow rate or an indirect conversion, first from opening to orifice area and then from orifice area to mass flow rate. The calculation, and the data required for it, depend on the setting of the Valve parameterization block parameter:

• `Linear area-opening relationship` — Calculate the valve opening area from the control member position and from it obtain the mass flow rate through the valve. The opening area is assumed to vary linearly with the control member position. The slope of the linear expression is determined from the Maximum valve opening and Maximum opening area block parameters.

• `Tabulated data - Area vs. opening` — Calculate the valve opening area from the control member position and from it obtain the mass flow rate through the valve. The opening area can vary nonlinearly with the control member position. The relationship between the two is given by the tabulated data in the Valve opening vector and Opening area vector block parameters.

• ```Tabulated data - Mass flow rate vs. opening and pressure drop``` — Calculate the mass flow rate directly from the control member position and the pressure drop across the valve. The relationship between the three variables can be nonlinear and it is given by the tabulated data in the Valve opening vector, Pressure drop vector, and Mass flow rate table block parameters.

### Leakage Flow

The primary purpose of the leakage flow rate of a closed valve is to ensure that at no time a portion of the thermal liquid network becomes isolated from the remainder of the model. Such isolated portions reduce the numerical robustness of the model and can slow down simulation or cause it to fail. Leakage flow is generally present in real valves but in a model its exact value is less important than its being a small number greater than zero. The leakage flow rate is determined from the Leakage area block parameter.

### Pressure Loss and Recovery

The pressure drop in the valve is calculated from an empirical parameter known as the discharge coefficient (obtained from the Discharge coefficient block parameter). The calculation captures the effect of flow regime, with the pressure drop being proportional to the mass flow rate when the flow is laminar and to the square of the same when the flow is turbulent. Also captured is the pressure recovery that in real valves occurs between the vena contracta (the narrowest aperture of the valve) and the outlet, which generally lies a small distance away.

### Composite Component Structure

This block is a composite component comprising two Variable Area Orifice (TL) blocks connected as shown in the figure. A single control signal actuates the two blocks simultaneously. The Orifice orientation block parameters are set so that a positive signal acts to open one orifice while closing the other. The opening offsets are applied to the appropriate blocks. Refer to the Variable Area Orifice (TL) block for detail on the opening area calculations.

## Ports

### Input

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Displacement, in m, of the valve control member.

### Conserving

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Opening through which the flow can enter or exit the valve. This port is typically connected to a fluid supply line.

Opening through which the flow can enter or exit the valve. This port is typically connected to a fluid return line.

Opening through which the flow can enter or exit the valve. This port is typically connected to an actuation line.

## Parameters

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Basic Parameters

Assumption to make in the opening characteristics of the valve orifices. The default setting attributes the same opening characteristics to each orifice. The maximum opening area and the orifice opening at which it occurs are then the same for all orifices. Use the alternate setting to specify these parameters separately for each orifice.

Method by which to model the opening characteristics of the valve. The default setting prescribes a linear relationship between the valve opening area and the valve opening. The alternative settings allow for a general, nonlinear relationship to be specified in tabulated form, in one case between the opening area and the control member position (the valve opening), in the other case between the mass flow rate and both the valve opening and the pressure drop between the ports.

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

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Linear area-opening relationship`.

Area normal to the flow path at each port. The ports are assumed to be equal in size. The flow area specified here should match those of the inlets of those components to which the valve connects.

Average distance traversed by the fluid as it travels from inlet to outlet. This distance is used in the calculation of the internal thermal conduction that occurs between the two ports (as part of the smoothed upwind energy scheme employed in the thermal liquid domain).

Ratio of the actual flow rate through the valve to the theoretical value that it would have in an ideal valve. This semi-empirical parameter measures the flow allowed through the valve: the greater its value, the greater the flow rate. Refer to the valve data sheet, if available, for this parameter.

Reynolds number at which the flow is assumed to transition between laminar and turbulent regimes.

Model Parameterization

Value of the orifice opening at which an orifice is considered to be fully open. The opening area of the orifice is then at a maximum. The maximum opening is used to calculate the slope of the linear expression relating the orifice opening area to the orifice opening.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Linear area-opening relationship`.

Opening area of an orifice when its orifice opening has the value specified in the Maximum valve opening block parameter. The maximum opening area parameter is used to calculate the slope of the linear expression relating the orifice opening area to the orifice opening.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Linear area-opening relationship`.

Measure of the amount of smoothing to apply to the opening area function. This parameter determines the widths of the regions to be smoothed, one being at the fully open position, the other at the fully closed position. The smoothing superposes on the linear opening area function two nonlinear segments, one for each region of smoothing. The greater the value specified, the greater the smoothing and the broader the nonlinear segments.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Linear area-opening relationship`.

Vector of control member positions at which to specify—dependent on the valve parameterization—the opening area of the valve or its mass flow rate. The vector elements must increase monotonically from left to right. This vector must be equal in size to that specified in the Opening area vector block parameter or to the number of rows in the Mass flow rate table block parameter.

This data serves to construct a one-way lookup table by which to determine, from the control member position, the opening area of the valve or a two-way lookup table by which to determine, from the control member position and pressure drop, the mass flow rate of the valve. Data is handled with linear interpolation (within the tabulated data range) and nearest-neighbor extrapolation (outside of the data range).

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Tabulated data - Area vs. opening`.

Vector of opening areas corresponding to the breakpoints defined in the Valve opening vector block parameter. The vector elements must increase monotonically from left to right (with increasing control member position). This vector must be equal in size to the number of valve opening breakpoints.

This data serves to construct a one-way lookup table by which to determine from the control member position the opening area of the valve. Data is handled with linear interpolation (within the tabulated data range) and nearest-neighbor extrapolation (outside of the data range).

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to `Tabulated data - Area vs. opening`.

Vector of pressure differentials from port A to port B at which to specify the mass flow rate of the valve. The vector elements must increase monotonically from left to right. This vector must be equal in size to the number of columns in the Mass flow rate table block parameter.

This data serves to construct a two-way lookup table by which to determine, from the control member position and pressure drop, the opening area of the valve. Data is handled with linear interpolation (within the tabulated data range) and nearest-neighbor extrapolation (outside of the data range).

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Matrix of mass flow rates corresponding to the breakpoints defined in the Valve opening vector and Pressure drop vector block parameters. The control member position increases from row to row from top to bottom. The pressure drop increases from column to column from left to right. The mass flow rate must increase monotonically in the same directions (with increasing control member position and increasing pressure drop).

This data serves to construct a two-way lookup table by which to determine, from the control member position and pressure drop, the opening area of the valve. Data is handled with linear interpolation (within the tabulated data range) and nearest-neighbor extrapolation (outside of the data range). Ensure that the number of rows is equal to the size of the Opening area vector block parameter and that the number of columns is equal to the size of the Pressure drop vector block parameter.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Nominal inlet temperature, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the temperature measured during simulation.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Nominal inlet pressure, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the pressure measured during simulation.

#### Dependencies

This parameter is active when the Valve parameterization block parameter is set to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Valve Opening Offsets

Distance by which to offset the valve control member from its centered (zero) position relative to the P-A orifice. This parameter determines the control member displacement, specified via port S, at which the P-A orifice is fully closed. Note that the control member position at which the valve is fully closed is always at zero. Set all opening offsets to positive values to model an underlapped valve or to negative values to model an overlapped valve.

Distance by which to offset the valve control member from its centered (zero) position relative to the A-T orifice. This parameter determines the control member displacement, specified via port S, at which the A-T orifice is fully closed. Note that the control member position at which the valve is fully closed is always at zero. Set all opening offsets to positive values to model an underlapped valve or to negative values to model an overlapped valve.