Pressure control valve maintaining preset pressure in system
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 A and the pressure differential p across the valve.
The valve remains closed while pressure at the valve inlet is lower than the valve preset pressure. When the preset pressure is reached, the value 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. Theoretically, the parameter can be set to zero, but it is not recommended.
The model accounts for the laminar and turbulent flow regimes by monitoring the Reynolds number (Re) and comparing its value with the critical Reynolds number (Recr). The flow rate is determined according to the following equations:
|q||Flow rate through the valve|
|p||Pressure differential across the valve|
|pA,pB||Gauge pressures at the block terminals|
|CD||Flow discharge coefficient|
|A(p)||Instantaneous orifice passage area|
|Amax||Fully open valve passage area|
|Aleak||Closed valve leakage area|
|pset||Valve preset pressure|
|pmax||Valve pressure at maximum opening|
|DH||Instantaneous orifice hydraulic diameter|
|ν||Fluid kinematic viscosity|
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.
The transition between laminar and turbulent regimes is assumed to be sharp and taking place exactly at Re=Recr.
Valve passage maximum cross-sectional area. The default value is 1e-4 m^2.
Preset pressure level, at which the orifice of the valve starts to open. The default value is 50e5 Pa.
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 5e5 Pa.
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.
The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is supposed to take place when the Reynolds number reaches this value. The value of the parameter depends on orifice geometrical profile, and the recommendations on the parameter value can be found in hydraulic textbooks. The default value is 12.
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. An isolated or "hanging" part of the system could affect computational efficiency and even cause simulation to fail. Therefore, MathWorks recommends that you do not set this parameter to 0. The default value is 1e-12m^2.
Parameters determined by the type of working fluid:
Fluid kinematic viscosity
The block has the following ports:
The Power Unit with Fixed-Displacement Pump 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.