One-way switching valve in an isothermal liquid system
Simscape / Fluids / Isothermal Liquid / Valves & Orifices / Directional Control Valves
The Shuttle Valve (IL) block models a one-way pressure control valve or switching component in an isothermal liquid network. Flow through the valve travels from port A or port A1 to port B. When the pressure differential between A and A1, pAA1, is above a specified threshold pressure, the path between ports A and B is open to flow and the port at A1 closes. The path has been fully changed when the pressure reaches the Pressure at which A-B is fully open and A1-B is fully closed. When pAA1 falls below the threshold pressure, the flow inlet switches to port A1.
Mass is conserved through the valve:
There is no flow between ports A and A1.
The mass flow rate through the valve is calculated as:
Cd is the Discharge coefficient.
Avalve is the valve open area, either between ports A and B or ports A1 and B.
Aport is the Cross-sectional area at ports A and B.
is the average fluid density.
Δp is the valve pressure difference. Depending on the flow path through the valve, this is either pA – pB, pA1 – pB, or the normalized pressure when switching between the two inlet ports, , defined below.
The critical pressure difference, Δpcrit, is the pressure differential associated with the Critical Reynolds number, Recrit, and is also dependent on the flow path through the valve:
The critical Reynolds number is the flow regime transition point between laminar and turbulent flow.
Pressure loss describes the reduction of pressure in the valve due to a decrease in area, and can change if different valve flow paths have different areas. PRloss is calculated as:
Pressure recovery describes the positive pressure change in
the valve due to an increase in area. If you do not wish to capture this increase in
pressure, set the Pressure recovery to
Off. In this case,
PRloss is 1.
The opening area, Avalve, is also impacted by the valve opening dynamics.
The linear parameterization of the valve area depends on the flow path through the valve. The dynamic area is based on a normally open path between ports A and B:
The normalized pressure, , is
when pAA1 is between the parameters Pressure at which A-B is fully closed and A1-B is fully open and Pressure at which A-B is fully open and A1-B is fully closed. If pAA1 is below Pressure at which A-B is fully closed and A1-B is fully open, is 0. If pAA1 is above Pressure at which A-B is fully open and A1-B is fully closed, is 1.
When the valve inlet switches from port A to port A1, the valve opening area is:
If opening dynamics are modeled, a lag is introduced to the flow response to the modeled control pressure. pcontrol becomes the dynamic control pressure, pdyn; otherwise, pcontrol is the steady-state pressure. The instantaneous change in dynamic control pressure is calculated based on the Opening time constant, τ:
By default, Opening dynamics is set to
At the extremes of the control pressure range, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. A smoothing function is applied to every calculated control pressure, but primarily influences the simulation at the extremes of this range.
The Smoothing factor, s, is applied to the normalized pressure, :
and the smoothed pressure is:
A— Liquid port
Entry port to the valve.
A1— Liquid port
Entry port to the valve.
B— Liquid port
Exit port from the valve.
Pressure at which A-B is fully closed and A1-B is fully open— Threshold pressure for fully open inlet A1
-0.01 MPa(default) | scalar
Pressure threshold between ports A and A1, below which the flow path between ports A1 and B is fully open and the flow path between ports A and B is fully closed.
Pressure at which A-B is fully open and A1-B is fully closed— Threshold pressure for fully open inlet A
0.01 MPa(default) | scalar
Pressure threshold between ports A and A1, above which the flow path between ports A and B is fully open and the flow path between ports A1 and B is fully closed.
Maximum opening area— Maximum valve area
1e-4 m^2(default) | positive scalar
Maximum open area of the valve. This value is used to determine the normalized valve pressure and the valve opening area during operation.
Leakage area— Gap area when in fully closed position
1e-10 m^2(default) | positive scalar
Sum of all gaps when the valve is in the fully closed position. Any area smaller than this value is saturated to the specified leakage area. This contributes to numerical stability by maintaining continuity in the flow.
Cross-sectional area at ports A and B— Area at conserving ports
inf m^2(default) | positive scalar
Areas at the entry and exit ports A, A1, and B, which are used in the pressure-flow rate equation that determines the mass flow rate through the valve.
Discharge coefficient— Discharge coefficient
0.64(default) | positive scalar
Correction factor accounting for discharge losses in theoretical flows.
Critical Reynolds number— Upper Reynolds number limit for laminar flow
150(default) | positive scalar
Upper Reynolds number limit for laminar flow through the orifice.
Smoothing factor— Numerical smoothing factor
0.01(default) | positive scalar in the range [0,1]
Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.
Pressure recovery— Whether to account for pressure increase in area expansions
Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area.
Opening dynamics— Whether to introduce flow lag due to valve opening
Whether to account for transient effects to the fluid system due to
opening the valve. Setting Opening dynamics to
On approximates the opening conditions by introducing
a first-order lag in the flow response. The Opening time
constant also impacts the modeled opening dynamics.
Opening time constant— Valve opening time constant
0.1 s(default) | positive scalar
Constant that captures the time required for the fluid to reach steady-state conditions when opening or closing the valve from one position to another. This parameter impacts the modeled opening dynamics.
To enable this parameter, set Opening dynamics to