Constant Volume Chamber (G)
Tank with one inlet and fixed gas volume.
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Description
The Constant Volume Chamber (G) unit simulates mass and energy storage in a gas network. The chamber contains a constant volume of gas. The enclosure can exchange mass and energy with the connected gas network and exchange heat with the environment, allowing the internal pressure and temperature to vary over time. The pressure and temperature change depending on the compressibility and heat capacity of the gas volume.
Conservation of mass
The law of conservation of mass relates mass flow rate to the dynamics of pressure and temperature changes of the internal unit representing a volume of gas:
,
where:
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- is the partial derivative of the mass of the gas in terms of pressure at constant temperature and volume.
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- is the partial derivative of the gas mass by temperature at constant pressure and volume.
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- gas pressure. The pressure at port A is assumed to be equal to this pressure, .
-
- gas temperature. The temperature at port H is assumed to be equal to this temperature, .
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- time.
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- mass flow rate at port A. The flow rate associated with the port is positive when the gas flows into the block.
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- mass flow rate at port B. The flow rate associated with the port is positive when gas flows into the block.
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- mass flow rate at port C. The flow rate associated with the port is positive when gas flows into the block.
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- mass flow rate at port D. The flow rate associated with the port is positive when gas flows into the block.
Energy balance
The law of conservation of energy relates the expenditure of energy and heat to the dynamics of pressure and temperature changes of an internal unit representing a volume of gas:
,
where:
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- is the partial derivative of the internal energy of the gas in pressure at constant temperature and volume.
-
- is the partial derivative of the internal energy of the gas in terms of temperature at constant pressure and volume.
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- energy flux through port A.
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- energy flow through port B.
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- power flow through port C.
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- power flow through port D.
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- heat flow through port H.
Partial derivatives for ideal and semi-ideal gas models
The partial derivatives of the mass M and internal energy U of a volume of gas in terms of pressure and temperature at constant volume depend on the model properties of the gas. For the ideal and semi-ideal gas models, the equations are as follows:
Where:
- is the density of the gas.
- is the volume of the gas.
- specific enthalpy of a gas.
- compressibility coefficient.
- universal gas constant.
- specific heat capacity at constant pressure of a volume of gas.
Partial derivatives for the real gas model
For the real gas model, the partial derivatives of the mass M and internal energy U of a volume of gas with respect to pressure and temperature at constant volume are equal:
Where:
- isothermal volume modulus of gas compression.
- isobaric coefficient of thermal expansion of gas.
Ports
Non-directional
A - chamber entrance
gas
Gas port, corresponds to the chamber entrance.
B - chamber inlet
gas
Gas port, corresponds to the second chamber entrance.
Dependencies
This port is used when Number of ports is set to 2, 3 or 4.
C - camera input
gas
Gas port, corresponds to the third chamber inlet.
Dependencies
This port is used when Number of ports is set to 3 or 4.
D - camera input
gas
Gas port, corresponds to the fourth chamber entrance.
Dependencies
This port is used if the Number of ports parameter is set to 4.
H - temperature inside the chamber
heat
Heat port related to the gas temperature inside the chamber.
Parameters
Chamber volume - volume of gas in the chamber
`0.1 m³ (by default)
The volume of gas in the chamber. The chamber is rigid, so its volume remains constant during the simulation. It is assumed that the chamber is always completely filled with gas.
Number of ports - number of inlet ports in the chamber
1 (by default)| 2 | 3 | 4
The number of inlet ports in the chamber. The chamber can have one to four ports, labelled A to D. When you change the value of a parameter, the corresponding ports are displayed or hidden on the block icon.
Cross-sectional area at port A - area normal to the flow path at the inlet to the chamber
0.01 m² (by default).
Cross-sectional area of the chamber inlet at port A in the direction normal to the gas flow path.
Cross-sectional area at port B - area normal to the flow path at the chamber inlet
0.01 m² (by default).
Cross-sectional area of the chamber inlet at port B in the direction normal to the gas flow path.
Dependencies
This parameter is used when Number of ports is set to 2, 3 or 4.
Cross-sectional area at port C - area normal to the flow path at the chamber inlet
0.01 m² (by default).
Cross-sectional area of the chamber inlet at port C in the direction normal to the gas flow path.
Dependencies
This parameter is used when Number of ports is set to 3 or 4.
Cross-sectional area at port D - area normal to the flow path at the chamber inlet
0.01 m² (by default).
Cross-sectional area of the chamber inlet at port D in the direction normal to the gas flow path.
Dependencies
This parameter is used when Number of ports is set to 4.
Initial value of pressure of gas volume - initial value of gas pressure
0.101325 MPa (by default).
Initial value of gas pressure.
Initial value of temperature of gas volume - initial value of gas temperature
`293.15 K (by default).
Initial value of gas temperature.
Initial value of density of gas volume - initial value of gas density
1.2 kg/m³ (by default).
Initial value of gas density.