# Pressure Compensator

Hydraulic pressure compensating valve

## Library

Pressure Control Valves

## Description

The Pressure Compensator block represents a hydraulic pressure compensating valve, or pressure compensator. Pressure compensators are used to maintain preset pressure differential across a hydraulic component to minimize the influence of pressure variation on a flow rate passing through the component. The following illustration shows typical applications of a pressure compensator, where it is used in combination with the orifice installed downstream (left figure) or upstream (right figure). The compensator can be also used in combination with metering pumps, flow dividers, and so on.

The block is implemented as a data-sheet-based model, based on parameters usually provided in the manufacturer's catalogs or data sheets.

Pressure compensator is a normally open valve. Its opening is proportional to pressure difference between ports X and Y and the spring force. The following illustration shows typical relationship between the valve passage area A and the pressure difference `pxy`.

The orifice remains fully open until the pressure difference is lower than valve preset pressure determined by the spring preload. When the preset pressure is reached, the valve control member is forced off its stop and starts closing the orifice, thus trying to maintain pressure differential at preset level. Any further increase in the pressure difference causes the control member to close the orifice even more, until the point when the orifice if fully closed. The pressure increase that is necessary to close the valve is referred to as regulation range, or pressure compensator static error, and usually is provided in manufacturer's catalog or data sheets.

The main parameters of the block are the valve maximum area and regulation range. In addition, you need to specify the leakage area of the valve. Physically, it represents a possible clearance in the closed valve, but 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 failure of computation.

By default, the block does not include valve opening dynamics, and the valve sets its opening area directly as a function of pressure:

$A=A\left(p\right)$

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:

$A\left(t=0\right)={A}_{init}$

$\frac{dA}{dt}=\frac{A\left(p\right)-A}{\tau }$

In either case, the flow rate through the valve is determined according to the following equations:

$q={C}_{D}\cdot A\sqrt{\frac{2}{\rho }}\cdot \frac{p}{{\left({p}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$

$p={p}_{A}-{p}_{B}$

${p}_{cr}=\frac{\rho }{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu }{{C}_{D}\cdot {D}_{H}}\right)}^{2}$

${D}_{H}=\sqrt{\frac{4A}{\pi }}$

$k=\frac{{A}_{\mathrm{max}}-{A}_{leak}}{{p}_{reg}}$

${p}_{xy}={p}_{x}-{p}_{y}$

where

 q Flow rate p Pressure differential across the valve pxy Pressure differential across valve control terminals pA, pB Gauge pressures at the valve main terminals px, py Gauge pressures at the valve control terminals pset Valve preset pressure pmax Pressure needed to fully close the orifice preg Regulation range A Instantaneous orifice passage area A(p) Pressure-dependent orifice passage area Ainit Initial open area of the valve Amax Orifice maximum area Aleak Closed orifice leakage area CD Flow discharge coefficient DH Instantaneous orifice hydraulic diameter ρ Fluid density ν Fluid kinematic viscosity τ Time constant for the first order response of the valve opening t Time pcr Minimum pressure for turbulent flow Recr Critical Reynolds number

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 $p={p}_{A}-{p}_{B}$. The control pressure differential is measured as ${p}_{xy}={p}_{x}-{p}_{y}$, and it creates a force acting against the spring preload.

## 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.

• Flow consumption associated with the spool motion is neglected.

## Dialog Box and Parameters

Maximum passage area

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

Valve pressure setting

Pressure difference that must be maintained across an element connected to ports X and Y. At this pressure the valve orifice starts to close. The default value is `3e6` Pa.

Valve regulation range

Pressure increase over the preset level needed to fully close the valve. Must be less than 0.2 of the Valve pressure setting parameter value. The default value is `1.5e5` Pa.

Flow discharge coefficient

Semi-empirical parameter for orifice 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`.

Critical Reynolds number

The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. 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`.

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. 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-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

The initial opening area of the valve. This parameter is available only if Opening dynamics is set to ```Include valve opening dynamics```. The default value is `1e-12` m^2.

## 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.

`B`

Hydraulic conserving port associated with the valve outlet.

`X`

Hydraulic conserving port associated with the pressure control terminal that opens the orifice.

`Y`

Hydraulic conserving port associated with the pressure control terminal that closes the orifice.