Constant Volume Chamber (P)#

The Constant Volume Chamber (P) block simulates the accumulation of mass and energy in a chamber containing fixed volume of coolant.

The user can specify from 1 to 4 input ports through which the coolant flows.

The coolant volume can exchange heat with heating network, for example, heat exchange with the environment through the Thermal port of the unit.

The medium enters the chamber the pressure upstream the inlet exceeds pressure in the chamber and flows out when pressure drop is reversed.

It is assumed that the flow resistance between the inlet and the chamber internal part is negligible. Thus, pressure inside the chamber is equal to pressure at the inlet ports.

Similarly, thermal resistance between the thermal port and chamber internal part is negligible and temperature inside is equal to temperature in the thermal port.

Mass flow rate calculation

Law of conservation of mass (1):

(1)#\[\dot{m_1}+\dot{m_2}+\dot{m_3}+\dot{m_4}=(\frac{\delta M}{\delta p}\cdot\frac{dp}{dt}+\frac{\delta M}{\delta T} \cdot \frac{dT}{dt})\]

where:

\(\frac{\delta M}{\delta p}\) - partial derivative of gas mass by pressure at constant temperature and volume;

\(\frac{\delta M}{\delta T}\) - partial derivative of gas mass by temperature at constant pressure and temperature;

\(\dot{m_1}\), \(\dot{m_2}\), \(\dot{m_3}\), \(\dot{m_4}\) - mass flow through input ports, [kg/s].

For an ideal gas (2),(3):

(2)#\[\frac{\delta M}{\delta p}=V \cdot \frac{\rho}{p}\]

(3)#\[\frac{\delta M}{\delta T}=-V \cdot \frac{\rho}{T}\]

where:

p - medium pressure in the chamber, [Pa];

T - medium temperature in the chamber, [℃];

ρ - medium density in the chamber, [kg/m\(^3\)];

V - chamber volume, [m\(^3\)];

Energy balance

Law of conservation of energy (4) :

(4)#\[\phi_1+\phi_2+\phi_3+\phi_4+Q=\frac{\delta U}{\delta p} \cdot\frac{dp}{dt}+\frac{\delta U}{\delta T} \cdot\frac{dT}{dt}\]

where:

\(\frac{\delta U}{\delta p}\) - partial derivative of the internal energy of a gas by pressure at constant temperature and volume;

\(\frac{\delta U}{\delta T}\) - partial derivative of the internal energy of a gas by temperature at constant pressure and temperature;

Q - heat flux through the heat port, [W];

\(\phi_1\), \(\phi_2\), \(\phi_3\), \(\phi_4\) - energy fluxes through input ports, [W].

For an ideal gas (5), (6):

(5)#\[\frac{\delta U}{\delta p}=V \cdot (\frac{h}{Z \cdot R \cdot T}-1)\]

(6)#\[\frac{\delta U}{\delta T}=V \cdot \rho \cdot (с_p -\frac{h}{T})\]

where:

Z - compressibility factor;

R - specific gas constant;

h - enthalpy of the medium in the chamber;

\(c_p\) - isobaric mass heat capacity.

Momentum balance

p=p\(_1\)=p\(_2\)=p\(_3\)=p\(_4\)

where p\(_1\), p\(_2\), p\(_3\), p\(_4\) - pressure of input ports, [Pa].

1. Properties#

Property	Default value	Description	Units of measurement
Number of ports: 1; 2; 3; 4	1	-	-
Chamber volume	2.0	-	m\(^3\)
Port 1 cross-sectional area	0.01	-	m\(^2\)
Port 2 cross-sectional area, available when `Number of ports` - `2`, `3` or `4`	0.01	-	m\(^2\)
Port 3 cross-sectional area, available when `Number of ports` - `3` or `4`	0.01	-	m\(^2\)
Port 4 cross-sectional area, available when `Number of ports` - `4	0.01	-	m\(^2\)
Initial temperature of liquid volume	20.0	-	°C
Initial gauge pressure of liquid volume	0.0	-	Pa

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Pneumatics
Input, available when `Number of ports` - `2`, `3` or `4`	Input	-	-	Pneumatics
Input, available when `Number of ports` - `3` or `4`	Input	-	-	Pneumatics
Input, available when `Number of ports` - `4`	Input	-	-	Pneumatics
Thermal port	Input	-	-	Heat exchange

In order to see the connection capabilities of the block, you need to go to page Description of block ports

3. Examples of use#

Examples of using this block can be found in the following sections:

Tutorials;
How-to guides;
Description of Demo.

Tutorials

Library	Tutorial name
`Pneumatics`	Gas outflow to a cylinder through a tube with a narrowing

How-to guides

Section	Guide name
Life support engineering	Development of room thermal state model