# Constant Volume Pneumatic Chamber

Constant volume pneumatic chamber based on ideal gas law

## Library

None (example custom library)

## Description

Note

As of Release R2016b, the Gas block library replaces the Pneumatic library as the recommended way of modeling pneumatic systems. The former Pneumatic library is now included in the product installation as an example custom library. The pneumatic domain definition is still provided with the software, and all the pneumatic blocks in your legacy models continue to work as before. However, these blocks no longer receive full production support and can be removed in a future release.

The Constant Volume Pneumatic Chamber block models a constant volume pneumatic chamber based on the ideal gas law and assuming constant specific heats.

The continuity equation for the network representation of the constant chamber is

`$G=\frac{V}{RT}\left(\frac{dp}{dt}-\frac{p}{T}\frac{dT}{dt}\right)$`

where

 G Mass flow rate at input port V Chamber volume p Absolute pressure in the chamber R Specific gas constant T Absolute gas temperature t Time

The equivalent circuit of the Constant Volume Pneumatic Chamber block model is shown in the following illustration. Port A is the pneumatic conserving port associated with the chamber inlet. Port A connects both to the gaseous and the thermal circuit. Port H is a thermal conserving port through which heat exchange with the environment takes place. Port H connects only to the thermal circuit.

The diagram shows that the heat flow q to the chamber consists of two components:

• Heat flow qCH, associated with the gaseous process

• Heat flow qHE, associated with the heat exchange with the environment

The heat flow due to gas inflow is

`${q}_{CH}=\frac{{c}_{v}V}{R}·\frac{dp}{dt}$`

where cv is specific heat at constant volume.

The heat exchange with the environment happens through port H, connected to thermal components. To determine the value of the heat exchange flow, the model contains a short-circuit element, resulting in the equation

TA = TH

where both TA and TH represent the gas temperature.

The gas flow and the heat flow are considered positive if they flow into the chamber.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

## Basic Assumptions and Limitations

• The gas is ideal.

• Specific heats at constant pressure and constant volume, cp and cv, are constant.

## Parameters

Chamber volume

Specify the volume of the chamber. The default value is `.001` m^3.

## Ports

The block has the following ports:

`A`

Pneumatic conserving port associated with the chamber inlet.

`H`

Thermal conserving port through which heat exchange with the environment takes place.

## Version History

Introduced in R2009b