Pressure control valve maintaining preset pressure in system
Pressure Control Valves
The Pressure Relief Valve block represents a
hydraulic pressure relief valve as a data-sheet-based model. The following
figure shows the typical dependency between the valve passage area
the pressure differential
p across the
The valve remains closed while pressure at the valve inlet is lower than the valve preset pressure. When the preset pressure is reached, the valve control member (spool, ball, poppet, etc.) is forced off its seat, thus creating a passage between the inlet and outlet. Some fluid is diverted to a tank through this orifice, thus reducing the pressure at the inlet. If this flow rate is not enough and pressure continues to rise, the area is further increased until the control member reaches its maximum. At this moment, the maximum flow rate is passing through the valve. The value of a maximum flow rate and the pressure increase over the preset level to pass this flow rate are generally provided in the catalogs. The pressure increase over the preset level is frequently referred to as valve steady state error, or regulation range. The valve maximum area and regulation range are the key parameters of the block.
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.
By default, the block does not include valve opening dynamics, and the valve sets its opening area directly as a function of pressure:
Adding valve opening dynamics provides continuous behavior that is more physically realistic, and is particularly helpful in situations with rapid valve opening and closing. The pressure-dependent orifice passage area A(p) in the block equations then becomes the steady-state area, and the instantaneous orifice passage area in the flow equation is determined as follows:
In either case, the flow rate through the valve is determined according to the following equations:
|pA, pB||Gauge pressures at the block terminals|
|CD||Flow discharge coefficient|
|A||Instantaneous orifice passage area|
|A(p)||Pressure-dependent orifice passage area|
|Ainit||Initial open area of the valve|
|Amax||Fully open valve passage area|
|Aleak||Closed valve leakage area|
|pset||Valve preset pressure|
|pmax||Valve pressure at maximum opening|
|τ||Time constant for the first order response of the valve opening|
|pcr||Minimum pressure for turbulent flow|
The minimum pressure for turbulent flow, pcr, is calculated according to the laminar transition specification method:
By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:
pcr = (pavg + patm)(1 – Blam)
pavg = (pA + pB)/2
|pavg||Average pressure between the block terminals|
|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:
|DH||Valve instantaneous hydraulic diameter|
|ν||Fluid kinematic viscosity|
|Recr||Critical Reynolds number (Critical Reynolds number parameter value)|
The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B and the pressure differential is determined as .
Valve opening is linearly proportional to the pressure differential.
No loading on the valve, such as inertia, friction, spring, and so on, is considered.
Valve passage maximum cross-sectional area. The default value
Preset pressure level, at which the orifice of the valve starts
to open. The default value is
Pressure increase over the preset level needed to fully open
the valve. MathWorks recommends using values less than 0.2 of the Valve
pressure setting parameter value. The default value is
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
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.
Pressure ratio at which the flow transitions between laminar
and turbulent regimes. The default value is
This parameter is visible only if the Laminar transition
specification parameter is set to
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. This parameter is visible
only if the Laminar transition specification parameter
is set to
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
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.
The time constant for the first order response of the valve
opening. This parameter is available only if Opening dynamics is
Include valve opening dynamics.
The default value is
The initial opening area of the valve. This parameter is available
only if Opening dynamics is set to
valve opening dynamics. The default value is
Parameters determined by the type of working fluid:
Fluid kinematic viscosity
The block has the following ports:
Hydraulic conserving port associated with the valve inlet.
Hydraulic conserving port associated with the valve outlet.
The Closed-Loop Pump Control with Flexible Drive Shaft example illustrates the use of the Pressure Relief Valve block in hydraulic systems. The valve is set to 75e5 Pa and starts diverting fluid to tank as soon as the pressure at its inlet reaches this value.