Shuttle Valve

Hydraulic valve that allows flow in one direction only

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Directional Valves

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Description

The Shuttle Valve block represents a hydraulic shuttle valve as a data-sheet-based model. The valve has two inlet ports (A and A1) and one outlet port (B). The valve is controlled by pressure differential $$p_c=p_A-p_{A1}$$. The valve permits flow either between ports A and B or between ports A1 and B, depending on the pressure differential p_c. Initially, path A-B is assumed to be opened. To open path A1-B (and close A-B at the same time), pressure differential must be less than the valve cracking pressure (p_cr <=0).

When cracking pressure is reached, the valve control member (spool, ball, poppet, etc.) is forced off its seat and moves to the opposite seat, thus opening one passage and closing the other. If the flow rate is high enough and pressure continues to change, the control member continues to move until it reaches its extreme position. At this moment, one of the valve passage areas is at its maximum. The valve maximum area and the cracking and maximum pressures are generally provided in the catalogs and are the three key parameters of the block.

The relationship between the A-B, A1–B path openings and control pressure p_c is shown in the following illustration.

In addition to the maximum area, the leakage area is also required to characterize the valve. The main purpose of the parameter is not to account for possible leakage, even though this is also important, but to maintain numerical integrity of the circuit by preventing a portion of the system from getting isolated after the valve is completely closed. An isolated or “hanging” part of the system could affect computational efficiency and even cause failure of computation. Therefore, the parameter value must be greater than zero.

The flow rate through each of the orifices is determined according to the following equations:

$$q_{AB}=C_D\cdot A_{AB}\sqrt{\frac{2}{\rho }}\cdot \frac{p_{AB}}{{\left(p_{AB}^2+p_{cr}^2\right)}^{1/4}}$$

$$q_{A1B}=C_D\cdot A_{A1B}\sqrt{\frac{2}{\rho }}\cdot \frac{p_{A1B}}{{\left(p_{A1B}^2+p_{cr}^2\right)}^{1/4}}$$

$$A_{AB}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for }{p}_c\le p_{crack}\hfill \\ A_{leak}+k\cdot \left(p_c-p_{crack}\right)\hfill & \text{for }{p}_{crack}<p_c<p_{crack}+p_{op}\hfill \\ A_{\max }\hfill & \text{for }{p}_c\ge p_{crack}+p_{op}\hfill \end{array}$$

$$A_{A1B}=\{\begin{array}{ll}{A}_{leak}\hfill & \text{for }{p}_c\ge p_{crack}+p_{op}\hfill \\ A_{\max }-k\cdot \left(p_c-p_{crack}\right)\hfill & \text{for }{p}_{crack}<p_c<p_{crack}+p_{op}\hfill \\ A_{\max }\hfill & \text{for }{p}_c\le p_{crack}\hfill \end{array}$$

$$k=\frac{A_{\max }-A_{leak}}{p_{op}}$$

$$p_c=p_A-p_{A1}$$

where

qAB, qA1B	Flow rates through the AB and A1B orifices
pAB, pA1B	Pressure differentials across the AB and A1B orifices
pA, pA1, pB	Gauge pressures at the block terminals
CD	Flow discharge coefficient
ρ	Fluid density
AAB, AA1B	Instantaneous orifice AB and A1B passage areas
Amax	Fully open orifice passage area
Aleak	Closed valve leakage area
pc	Valve control pressure differential
pcrack	Valve cracking pressure differential
pop	Pressure differential needed to fully shift the valve
pcrAB, pcrA1B	Minimum pressures for turbulent flow across the AB and A1B orifices

The minimum pressures for turbulent flow across the AB and A1B orifices, p_crAB and p_crA1B, are calculated according to the laminar transition specification method:

• By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

  p_crAB = (p_avgAB + p_atm)(1 – B_lam)

  p_crA1B = (p_avgA1B + p_atm)(1 – B_lam)

  p_avgAB = (p_A + p_B)/2

  p_avgA1B = (p_A1 + p_B)/2

  where

  pavgAB	Average pressure for orifice AB
  pavgA1B	Average pressure for orifice A1B
  patm	Atmospheric pressure, 101325 Pa
  Blam	Pressure ratio at the transition between laminar and turbulent regimes (Laminar flow pressure ratio parameter value)

• By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:

  $$p_{crAB}=\frac{\rho }{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu }{C_D\cdot D_{HAB}}\right)}^2$$

  $$p_{crA1B}=\frac{\rho }{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu }{C_D\cdot D_{HA1B}}\right)}^2$$

  $$D_{HAB}=\sqrt{\frac{4A_{AB}}{\pi }}$$

  $$D_{HA1B}=\sqrt{\frac{4A_{A1B}}{\pi }}$$

  where

  DHAB, DHA1B	Instantaneous orifice hydraulic diameters
  ν	Fluid kinematic viscosity
  Recr	Critical Reynolds number (Critical Reynolds number parameter value)

By default, the block does not include valve opening dynamics. Adding valve opening dynamics provides continuous behavior that is particularly helpful in situations with rapid valve opening and closing. The orifice passage areas A_AB and A_A1B in the equations above then become steady-state orifice AB and A1B passage areas, respectively. Instantaneous orifice AB and A1B passage areas with opening dynamics are determined as follows:

$$A_{AB\_dyn}(t=0)=A_{AB\_init}$$

$$\frac{d{A}_{AB\_dyn}}{dt}=\frac{A_{AB}-A_{AB\_dyn}}{\tau }$$

$$A_{A1B\_dyn}=A_{\max }+A_{leak}-A_{AB\_dyn}$$

where

AAB_dyn	Instantaneous orifice AB passage area with opening dynamics
AA1B_dyn	Instantaneous orifice A1B passage area with opening dynamics
AAB_init	Initial open area for orifice AB
τ	Time constant for the first order response of the valve opening
t	Time

The block positive direction is from port A to port B and from port A1 to port B. Control pressure is determined as $$p_c=p_A-p_{A1}$$.

Basic Assumptions and Limitations

• Valve opening is linearly proportional to the pressure differential.

• No loading on the valve, such as inertia, friction, spring, and so on, is considered.

Parameters

Maximum passage area

Valve passage maximum cross-sectional area. The default value is 1e-4 m^2.

Cracking pressure

Pressure differential level at which the orifice of the valve starts to open. The default value is -1e4 Pa.

Opening pressure

Pressure differential across the valve needed to shift the valve from one extreme position to another. The default value is 1e4 Pa.

Flow discharge coefficient

Semi-empirical parameter for valve capacity characterization. Its value depends on the geometrical properties of the orifice, 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.

Opening dynamics

Select one of the following options:

• Do not include valve opening dynamics — The valve sets its orifice passage area directly as a function of pressure. If the area changes instantaneously, so does the flow equation. This is the default.

• Include valve opening dynamics — Provide continuous behavior that is more physically realistic, by adding a first-order lag during valve opening and closing. Use this option in hydraulic simulations with the local solver for real-time simulation. This option is also helpful if you are interested in valve opening dynamics in variable step simulations.

Opening time constant

The time constant for the first order response of the valve opening. This parameter is available only if Opening dynamics is set to Include valve opening dynamics. The default value is 0.1 s.

Initial area at port A

The initial open area for orifice AB. This parameter is available only if Opening dynamics is set to Include valve opening dynamics. The default value is 1e-4 m^2.

 Restricted Parameters

When your model is in Restricted editing mode, you cannot modify the following parameter:

• Opening dynamics

All other block parameters are available for modification. The actual set of modifiable block parameters depends on the value of the Opening dynamics parameter at the time the model entered Restricted mode.

Global Parameters

Parameters determined by the type of working fluid:

• Fluid density

• Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

A

Hydraulic conserving port associated with the valve inlet.

A1

Hydraulic conserving port associated with the valve inlet.

B

Hydraulic conserving port associated with the valve outlet.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.