# Constant Volume Pneumatic Chamber

Constant volume pneumatic chamber based on ideal gas law

## Library

Pneumatic Elements

## Description

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.

## Basic Assumptions and Limitations

• The gas is ideal.

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

## Dialog Box and Parameters

### Parameters Tab

Chamber volume

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

### Variables Tab

Use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector) 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.

## 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.