Simscape™

Variable Chamber - Simulate hydraulic capacity of variable volume with compressible fluid

Library

Hydraulic Elements

Description

The Variable 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 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:

where

`q`	Flow rate due to fluid compressibility
`V₀`	Initial volume of fluid in the chamber
`V`	Chamber volume change, provided through port V
`E`	Fluid bulk modulus
`E_l`	Pure liquid bulk modulus
`p`	Gauge pressure of fluid in the chamber
`p`_α	Atmospheric pressure
α	Relative gas content at atmospheric pressure, α = `V_G`/`V_L`
`V_G`	Gas volume at atmospheric pressure
`V_L`	Volume of liquid
`n`	Gas-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.

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

The model is based on the following assumptions:

Fluid density remains constant.
Chamber volume can not be less that the dead volume.
Fluid fills the entire chamber volume.

Dialog Box and Parameters

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.
Initial pressure: Initial pressure in the chamber. This parameter specifies the initial condition for use in computing the block's initial state at the beginning of a simulation run. For more information, see Computing Initial Conditions. The default value is 0.

Restricted Parameters

Global Parameters

Fluid bulk modulus: The parameter is determined by the type of working fluid selected for the system under design. Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.
Nondissolved gas ratio: Nondissolved gas relative content determined as a ratio of gas volume to the liquid volume. The parameter is determined by the type of working fluid selected for the system under design. 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.