Pressure-Reducing 3-Way Valve (IL)
Combined pressure-relief and pressure-reducing valve in isothermal
system
Description
The Pressure-Reducing 3-Way Valve (IL) is a combination of a pressure-relief and
pressure-reducing valve. It maintains pressure at the valve outlet, port
A, by restricting the inflow area at port
P and venting the flow at port T.
Valve Functionality
Valve operation is triggered by comparing the pressure difference between port
T and port A to a threshold, the set
pressure. When the pressure between T and
A, Pcontrol,
exceeds this set pressure, Pset,reducing,
port P begins to close. A transition pressure range defines the
pressures the valve experiences when both valves at ports P and
T are closed. When the pressure difference between ports
A and T exceeds the pressure
transition range, port T opens. That is, The Pressure regulation range is specified
for both the pressure-reducing and the pressure-relief valves. The valve parameters,
such as Leakage Area and Maximum Opening
Area, are the same for all ports.
To simulate pressure relief or pressure reduction with respect to another system
element, see Pressure
Compensator Valve (IL). To simulate pressure reduction between
the valve outlet and atmosphere, see the Pressure-Reducing
Valve (IL). To simulate pressure relief with respect to a valve
or between the valve outlet and atmospheric pressure, see Pressure Relief
Valve (IL).
Pressure Control
When Pcontrol,
PA –
PT, exceeds the threshold pressure,
Pset,reducing, the valve at port
P begins to close. When the Pressure transition
range is exceeded, or when
Pcontrol >
Pset,relief, the valve at port
T begins to open. Both valve closing and opening are
parameterized in two ways:
When Set Pressure control is set to
Controlled
, connect a pressure signal to
port Ps, set the constant Pressure
regulation range, and set the constant Pressure
transition range. The pressure-reducing valve begins to
close when Pcontrol is greater
than Pset,reducing and below
Pmax,reducing. The relief
valve response is triggered when
Pcontrol is greater than
Pset,relief and below
Pmax,relief.
Pmax,relief is the sum of
the Pressure regulation range and
Pset,relief.
When Set Pressure control is set to
Constant
, valve closing at port
P is continuously regulated by either a linear
or tabular parameterization. Similarly, relief valve opening at port
T is parameterized linearly or by table lookup.
An example of linear parameterization of the reduction valve (solid
line) and relief valve (dotted line) is shown below.
When the Tabulated data
option
is selected, Pset,reducing and
Pmax,reducing are the
first and last parameters of the Pressure differential vector
for reducing valve, respectively, and
Pset,relief and
Pmax,relief are the first
and last parameters of the Pressure differential vector for
relief valve, respectively. An example of tabular
parameterization of both the reducing and relieving valves are shown
below.
Mass Flow Rate Equation
Momentum is conserved through the valve:
The mass flow rate through the valves is calculated as:
where:
Cd is the
Discharge coefficient.
A is the instantaneous valve open area between
ports Aand P or
A and T, as indicated by
the subscript.
Aport is the
Cross-sectional area at ports A, P &
T.
is the average fluid density.
Δp is the valve pressure difference:
pA –
pB.
The critical pressure difference,
Δpcrit, is the pressure differential
associated with the Critical Reynolds number,
Recrit, the flow regime transition
point between laminar and turbulent flow, which corresponds to either the
pressure-reducing or pressure relief component of the valve:
where A is either
APA or
AAT, corresponding to the reducing or
relief component of the valve, respectively.
Pressure loss describes the reduction of pressure in the
valve due to a decrease in area. 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 Pressure recovery to
Off
. In this case,
PRloss is 1.
The opening area A is determined by the opening
parameterization (for Constant
valves only) of the
reducing valve (P to A) or relief valve
(A to T) and the valve opening
dynamics.
Opening and Closing parameterization
Linear parameterization of the valve area for the reducing valve is
and for the relief valve is
The normalized pressure, , is
where the set and maximum pressures are the respective reducing
or relief valve settings.
For tabular parameterization of the valve area in its operating range,
Aleak,PA and
Amax,PA are the first and last
parameters of the Opening area vector reducing valve,
respectively, and Aleak,AT and
Amax,AT are the first and last
parameters of the Opening area vector for relief valve,
respectively.
Opening Dynamics
If Opening dynamics are modeled, a lag is introduced to the
flow response to valve opening. Avalve
becomes the dynamic opening or closing area,
Adyn; otherwise,
Avalve is the steady-state opening
area. This area is specific to the reducing and relief components of the valve,
APA or
AAT, respectively. The instantaneous
change in dynamic opening area is calculated based on the Opening time
constant, τ:
By default, Opening dynamics is set to
Off
.
Steady-state dynamics and valve opening are set by the same parameterization and
are based on the control
pressure.
Assumptions and Limitations
Friction between the valve and fluid, the hydraulic force of the fluid on the
valve components, and the effect of fluid inertia are neglected.
Ports
Conserving
expand all
A
— Liquid port
isothermal liquid
Liquid exit port of the valve.
P
— Liquid port
isothermal liquid
Liquid entry port to the valve.
T
— Liquid port
isothermal liquid
Liquid relief port of the valve.
Input
expand all
Ps
— Controlled pressure differential
physical signal
Varying-signal set pressure for controlled valve operation.
Dependencies
To enable this port, set Set pressure control
to Controlled
.
Parameters
expand all
Set pressure control
— Valve operation method
Constant
(default) | Controlled
Valve operation method. A Constant
valve opens
or closes linearly over a fixed pressure regulation range and pressure
transition or in accordance with tabulated pressure and opening area data
that you provide. A Controlled
valve opens or
closes according to a variable set pressure signal at port
Pset over a fixed pressure regulation and pressure
transition range. The selected setting applies both to the reducing and
relief valve operation.
Opening parameterization
— Type of opening parameterization
Linear
(default) | Tabulated data
Method of modeling the valve opening or closing. Valve opening is either
parametrized linearly, which correlates the opening area to the provided
pressure range, or by a table of values you provide that correlate the valve
opening area to pressure differential data.
Dependencies
To enable this port, set Set pressure control to
Constant
.
Set pressure differential for reducing valve
— Set pressure for valve closing at port P
0.6
MPa (default) | scalar
Pressure differential between port T and port
A. When this set pressure differential is
surpassed, the valve at port P begins to close. The
closing is parametrized linearly or by lookup table as defined in the
Opening parameterization.
Pressure regulation range
— Valve operational pressure range
3e-2
MPa (default) | scalar
Operational pressure range of the reducing valve. The pressure regulation
range lies between the Set pressure differential and
the maximum valve operating pressure. At the end of the Pressure
regulation range, the pressure-reducing valve is closed and
the Pressure transition range begins.
Dependencies
To enable this parameter, set
Set pressure control to
Controlled
, or
Set pressure control to
Constant
and
Opening parameterization to
Linear
.
Pressure transition range
— Pressure range of valve with ports P and T closed
2e-2
MPa (default) | scalar
Pressure range of the 3-way valve. This parameter defines the pressure
range, which begins at the end of the Pressure regulation
range, over which both ports P and
T are closed. Below this range, the reducing valve
at port P is open to flow, and above this range, the
relief valve at port T opens.
Dependencies
To enable this parameter, set either:
Maximum opening area
— Maximum opening area of ports
1e-4
m^2 (default) | positive scalar
Cross-sectional area of the valve
(P-A or
A-T) in its fully-open
position.
Dependencies
To enable this parameter, set either:
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 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.
Dependencies
To enable this parameter, set either:
Pressure differential vector for reducing valve
— Differential pressure values for tabular parameterization of reducing valve
0.6 : 0.02 : 0.7
MPa (default) | 1-by-n vector
Vector of pressure differential values for the tabular parameterization of
opening area. The vector elements correspond one-to-one to the values in the
Opening area vector reducing valve parameter.
Pressure differential vector values are listed in ascending order and must
have the same number of elements as the Opening area vector
reducing valve parameter. Linear interpolation is employed
between table data points.
Dependencies
To enable this parameter, set Set pressure
control to Constant
and
Opening parameterization to
Tabulated data
.
Opening area vector reducing valve
— Vector of valve opening areas for tabular parameterization of reducing valve
[1e-05, 8e-06, 6e-06, 4e-06, 2e-06, 1e-10]
m^2 (default) | 1-by-n vector
Vector of opening area values for the tabular parameterization of opening
area. The vector elements must correspond one-to-one to the values in the
Pressure differential vector for reducing valve
parameter. Areas are listed in descending order. Linear interpolation is
employed between table data points.
Dependencies
To enable this parameter, set Set pressure
control to Constant
and
Opening parameterization to
Tabulated data
.
Pressure differential vector for relief valve
— Differential pressure values for tabular parameterization of relief valve
0.68 : 0.02 : 0.78
MPa (default) | 1-by-n vector
Vector of pressure differential values for the tabular parameterization of
opening area. The vector elements correspond one-to-one to the values in the
Opening area vector relief valve parameter.
Pressure differential vector values are listed in ascending order and must
have the same number of elements as the Opening area vector relief
valve parameter. Linear interpolation is employed between
table data points.
Dependencies
To enable this parameter, set Set pressure
control to Constant
and
Opening parameterization to
Tabulated data
.
Opening area vector for relief valve
— Valve opening areas for tabular parameterization of relief valve
[1e-10, 2e-06, 4e-06, 6e-06, 8e-06, 1e-05]
m^2 (default) | 1-by-n vector
Vector of opening area values for the tabular parameterization of opening
area. The vector elements must correspond one-to-one to the values in the
Pressure differential vector for relief valve
parameter. Areas are listed in ascending order. Linear interpolation is
employed between table data points.
Dependencies
To enable this parameter, set Set pressure
control to Constant
and
Opening parameterization to
Tabulated data
.
Cross-sectional area at ports A, P & T.
— Orifice area at conserving ports
inf
m^2 (default) | positive scalar
Cross-sectional area at the entry and exit ports A,
P, and T. This area is used in
the pressure-flow rate equation that determines the mass flow rate through
the orifice.
Discharge coefficient
— Discharge coefficient
0.64
(default) | positive scalar
Correction factor accounting for discharge losses in theoretical flows.
The default discharge coefficient for a valve in Simscape™
Fluids™ is 0.64.
Critical Reynolds number
— Upper Reynolds number limit for laminar flow
150
(default) | positive scalar
Upper Reynolds number limit for laminar flow through the valve.
Pressure recovery
— Whether to account for pressure increase in area expansions
Off
(default) | On
Accounts for pressure increase when fluid flows from a region of smaller
cross-sectional area to a region of larger cross-sectional area. This
increase in pressure is not captured when Pressure
recovery is set to Off
.
Opening dynamics
— Whether to introduce flow lag due to orifice opening
Off
(default) | On
Accounts for transient effects to the fluid system due to the valve
opening. 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.
Reducing valve initial opening area
— Open area at port P at the start of the simulation
1e-4
m^2 (default) | positive scalar
Initial cross-sectional area at port P at the time of
dynamic opening. This value is used to calculate the instantaneous opening
area for the dynamic opening between P and
A at the following time step.
Dependencies
To enable this parameter, set Opening dynamics to
On
.
Relief valve initial opening area
— Open area at port T at the start of the simulation
1e-10
m^2 (default) | positive scalar
Initial cross-sectional area at port T of opening at
the time of dynamic opening. This value is used to calculate the
instantaneous opening area for the dynamic opening between
A and T at the following time
step.
Dependencies
To enable this parameter, set Opening dynamics to
On
.
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 when opening or closing the valve from one position to another.
This parameter impacts the modeled opening dynamics.
Dependencies
To enable this parameter, set Opening dynamics to
On
.
Introduced in R2020a