# 4-Way Directional Valve B

Configuration B of hydraulic continuous 4-way directional valve

## Library

Directional Valves

## Description

The 4-Way Directional Valve B block simulates a configuration of hydraulic continuous 4-way directional valve where port A is permanently connected to port P, and all four ports are interconnected in neutral position. The fluid is pumped in the valve through the inlet line P and is distributed between two outside hydraulic lines A and B (usually connected to a double-acting actuator) and the return line T. The block has four hydraulic connections, corresponding to inlet port (P), actuator ports (A and B), and return port (T), and one physical signal port connection (S), which controls the spool position. The block is built of a Fixed Orifice block in the P-A path and four Variable Orifice blocks, connected as shown in the following diagram.

All Variable Orifice blocks are controlled by the same position signal, provided through the physical signal port S, but the Orifice orientation parameter in the block instances is set in such a way that positive signal at port `S` opens the orifices colored blue in the block diagram (orifices A-T1 and P-B ) and closes the orifices colored yellow (orifices T1-T and B-T). As a result, the openings of the orifices are computed as follows:

`${h}_{AT1}={h}_{AT10}-x$`
`${h}_{PB}={h}_{PB0}-x$`
`${h}_{T1T}={h}_{T1T0}+x$`
`${h}_{BT}={h}_{BT0}+x$`

where

 `hAT1` Orifice opening for the `Variable Orifice A-T1` block `hPB` Orifice opening for the `Variable Orifice P-B` block `hT1T` Orifice opening for the `Variable Orifice T1-T` block `hBT` Orifice opening for the `Variable Orifice B-T` block `hAT10` Initial opening for the `Variable Orifice A-T1` block `hPB0` Initial opening for the `Variable Orifice P-B` block `hT1T0` Initial opening for the `Variable Orifice T1-T` block `hBT0` Initial opening for the `Variable Orifice B-T` block `x` Control member displacement from initial position

For information on the block parameterization options, basic parameter descriptions, assumptions and limitations, global and restricted parameters, see the 4-Way Directional Valve block reference page.

## Parameters

### Basic Parameters Tab

Compared to the Basic Parameters tab of the 4-Way Directional Valve block, there is one additional parameter:

Path P-A passage area

Specify the area of the P-A passage. The parameter value must be greater than zero. The default value is `5e-5` m^2. This parameter is used if Model parameterization is set to `By maximum area and opening`.

The rest of the parameters on this tab are identical to those of the 4-Way Directional Valve block:

Model parameterization

Select one of the following methods for specifying the valve:

• `By maximum area and opening` — Provide values for the maximum valve passage area and the maximum valve opening. The passage area is linearly dependent on the control member displacement, that is, the valve is closed at the initial position of the control member (zero displacement), and the maximum opening takes place at the maximum displacement. This is the default method.

• `By area vs. opening table` — Provide tabulated data of valve openings and corresponding valve passage areas. The passage area is determined by one-dimensional table lookup. You have a choice of two interpolation methods and two extrapolation methods.

• `By pressure-flow characteristic` — Provide tabulated data of valve openings, pressure differentials, and corresponding flow rates. The flow rate is determined by two-dimensional table lookup. You have a choice of two interpolation methods and two extrapolation methods.

Valve passage maximum area

Specify the area of a fully opened valve. The parameter value must be greater than zero. The default value is `5e-5` m^2. This parameter is used if Model parameterization is set to `By maximum area and opening`.

Valve maximum opening

Specify the maximum displacement of the control member. The parameter value must be greater than zero. The default value is `5e-3` m. This parameter is used if Model parameterization is set to `By maximum area and opening`.

Valve opening vector, s

Specify the vector of input values for valve openings as a one-dimensional array. The input values vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for smooth interpolation. The default values, in meters, are ```[-0.002 0 0.002 0.005 0.015]```. If Model parameterization is set to `By area vs. opening table`, the Tabulated valve openings values will be used together with Tabulated valve passage area values for one-dimensional table lookup. If Model parameterization is set to ```By pressure-flow characteristic```, the Tabulated valve openings values will be used together with Tabulated pressure differentials and Tabulated flow rates for two-dimensional table lookup.

Valve passage area vector

Specify the vector of output values for valve passage area as a one-dimensional array. The valve passage area vector must be of the same size as the valve openings vector. All the values must be positive. The default values, in m^2, are ```[1e-09 2.0352e-07 4.0736e-05 0.00011438 0.00034356]```. This parameter is used if Model parameterization is set to ```By area vs. opening table```.

Pressure differential vector, dp

Specify the vector of input values for pressure differentials as a one-dimensional array. The vector must be strictly increasing. The values can be nonuniformly spaced. The minimum number of values depends on the interpolation method: you must provide at least two values for linear interpolation, at least three values for smooth interpolation. The default values, in Pa, are ```[-1e+07 -5e+06 -2e+06 2e+06 5e+06 1e+07]```. This parameter is used if Model parameterization is set to ```By pressure-flow characteristic```.

Volumetric flow rate table, q(s,dp)

Specify the flow rates as an `m`-by-`n` matrix, where `m` is the number of valve openings and `n` is the number of pressure differentials. Each value in the matrix specifies flow rate taking place at a specific combination of valve opening and pressure differential. The matrix size must match the dimensions defined by the input vectors. The default values, in m^3/s, are:

```[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07; -2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05; -0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736; -0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438; -0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]```
This parameter is used if Model parameterization is set to `By pressure-flow characteristic`.

Interpolation method

Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

• `Linear` — Select this option to get the best performance.

• `Smooth` — Select this option to produce a continuous curve (```By area vs. opening table```) or surface (```By pressure-flow characteristic```) with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) and PS Lookup Table (2D) block reference pages.

Extrapolation method

Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

• `Linear` — Select this option to produce a curve or surface with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) and PS Lookup Table (2D) block reference pages.

Flow discharge coefficient

Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the valve, and usually is provided in textbooks or manufacturer data sheets. The default value is `0.7`.

Laminar transition specification

Select how the block transitions between the laminar and turbulent regimes:

• `Pressure ratio` — The transition from laminar to turbulent regime is smooth and depends on the value of the Laminar flow pressure ratio parameter. This method provides better simulation robustness.

• `Reynolds number` — The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the Critical Reynolds number parameter.

Laminar flow pressure ratio

Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is `0.999`. This parameter is visible only if the Laminar transition specification parameter is set to ```Pressure ratio```.

Critical Reynolds number

The maximum Reynolds number for laminar flow. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is `12`, which corresponds to a round orifice in thin material with sharp edges. This parameter is visible only if the Laminar transition specification parameter is set to `Reynolds number`.

Leakage area

The total area of possible leaks in the completely closed valve. The main purpose of the parameter is to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. The parameter value must be greater than 0. The default value is `1e-12` m^2.

### Valve Opening Offsets Tab

Between ports P and B

Orifice opening of the P-B flow path at zero spool displacement. Specify a positive offset to model an underlapped valve or a negative offset to model an overlapped valve. The default value of `0` corresponds to a zero-lapped valve. The default value is `2.5e-3` m.

Between ports B and T

Orifice opening of the B-T flow path at zero spool displacement. Specify a positive offset to model an underlapped valve or a negative offset to model an overlapped valve. The default value of `0` corresponds to a zero-lapped valve. The default value is `2.5e-3` m.

Between ports A and T1

Orifice opening of the A-T1 flow path at zero spool displacement. Specify a positive offset to model an underlapped valve or a negative offset to model an overlapped valve. The default value of `0` corresponds to a zero-lapped valve. The default value is `2.5e-3` m.

Between ports T1 and T

Orifice opening of the T1–T flow path at zero spool displacement. Specify a positive offset to model an underlapped valve or a negative offset to model an overlapped valve. The default value of `0` corresponds to a zero-lapped valve. The default value is `2.5e-3` m.

## Ports

The block has the following ports:

`P`

Hydraulic conserving port associated with the pressure supply line inlet.

`T`

Hydraulic conserving port associated with the return line connection.

`A`

Hydraulic conserving port associated with the actuator connection port.

`B`

Hydraulic conserving port associated with the actuator connection port.

`S`

Physical signal port to control spool displacement.