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Variable Hydraulic Chamber

Hydraulic capacity of variable volume with compressible fluid

Library

Hydraulic Elements

Description

The Variable Hydraulic Chamber block models fluid compressibility in variable volume chambers. The fluid is considered to be a mixture of liquid and a small amount of entrained, nondissolved gas. Use this block together with the Translational Hydro-Mechanical Converter block.

    Note   The Variable Hydraulic Chamber block takes into account only the flow rate caused by fluid compressibility. The fluid volume consumed to create piston velocity is accounted for in the Translational Hydro-Mechanical Converter block.

The chamber is simulated according to the following equations (see [1, 2]):

where

qFlow rate due to fluid compressibility
V0Initial volume of fluid in the chamber
VChamber volume change, provided through port V
EFluid bulk modulus
ElPure liquid bulk modulus
pGauge pressure of fluid in the chamber
pαAtmospheric pressure
αRelative gas content at atmospheric pressure, α = VG/VL
VGGas volume at atmospheric pressure
VLVolume of liquid
nGas-specific heat ratio

The main objective of representing fluid as a mixture of liquid and gas is to introduce an approximate model of cavitation, which takes place in a chamber if pressure drops below fluid vapor saturation level. As it is seen in the graph below, the bulk modulus of a mixture decreases at , thus considerably slowing down further pressure change. At high pressure, , a small amount of nondissolved gas has practically no effect on the system behavior.

Cavitation is an inherently thermodynamic process, requiring consideration of multiple-phase fluids, heat transfers, etc., and as such cannot be accurately simulated with Simscape™ software. But the simplified version implemented in the block is good enough to signal if pressure falls below dangerous level, and to prevent computation failure that normally occurs at negative pressures.

If pressure falls below absolute vacuum (–101325 Pa), the simulation stops and an error message is displayed.

Port A is a hydraulic conserving port associated with the chamber inlet. Port V is a physical signal port that provides the chamber volume variation.

The block positive direction is from port A to the reference point. This means that the flow rate is positive if it flows into the chamber.

Basic Assumptions and Limitations

  • Fluid density remains constant.

  • Chamber volume can not be less that the dead volume.

  • Fluid fills the entire chamber volume.

Dialog Box and Parameters

Parameters Tab

Chamber dead volume

Minimal volume of fluid in the chamber. The default value is 1e-4 m^3.

Specific heat ratio

Gas-specific heat ratio. The default value is 1.4.

 Restricted Parameters

Variables Tab

Use the Variables tab to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

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 chamber inlet.

V

Physical signal port that provides the chamber volume variation.

References

[1] Manring, N.D., Hydraulic Control Systems, John Wiley & Sons, New York, 2005

[2] Meritt, H.E., Hydraulic Control Systems, John Wiley & Sons, New York, 1967

See Also

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