Constant Volume Chamber (TL)
Chamber with fixed coolant volume and variable number of ports.
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Description
The Constant Volume Chamber (TL) unit simulates the mass and energy storage of a thermal fluid in a fixed volume chamber. The chamber can have one to four ports, labelled A, B, C, D, through which fluid can flow. The fluid volume may exchange heat with a thermal network, such as a network representing the surrounding space of the chamber, through thermal port H.
The mass of fluid in the chamber varies with density, which in a thermal liquid typically depends on pressure and temperature. The fluid enters the chamber when the pressure in front of the port rises above the pressure in the chamber, and flows out when the pressure gradient is reversed. The effect in the model is often to smooth out abrupt pressure changes, similar to the way an electrical capacitor smooths out voltage.
The resistance to flow between the port and the interior of the chamber is considered negligible. Therefore, the pressure inside the chamber is equal to the inlet pressure.
Similarly, the thermal resistance between the thermal port and the interior of the chamber is considered negligibly small. The temperature inside the chamber is equal to the temperature at the heat port.
Conservation of mass
Fluid can flow in and out of the chamber through ports A, B, C and D. The volume of the chamber is fixed, but due to the compressibility of the fluid, its mass can vary with pressure and temperature.
The rate of mass accumulation in the chamber must be exactly equal to the mass flow rate through ports A, B, C and D:
where:
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- pressure inside the vessel;
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- temperature;
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- isothermal bulk modulus of elasticity;
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- isobaric thermal expansion coefficient;
-
- mass flow rate of liquid.
Conservation of energy
Energy can enter and leave the chamber in two ways: fluid flow through ports A, B, C and D and heat flow through port H. No work is done on the liquid inside the chamber. Therefore, the rate of energy accumulation in the internal volume of liquid must be equal to the sum of energy flows through ports A, B, C, D and H:
where:
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- enthalpy;
-
- density;
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- specific heat;
-
- chamber volume;
-
- energy flow;
-
- heat flux.
Conservation of momentum
The pressure drop due to viscous friction between the individual holes and the interior of the chamber is considered negligible. Gravity and other volumetric forces can be neglected. Therefore, the pressure in the internal volume of the fluid must be equal to the pressure at ports A, B, C and D:
Assumptions and limitations
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The chamber contains a fixed volume of liquid.
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The flow resistance between the inlet and the interior of the chamber is negligible.
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The thermal resistance between the heat port and the interior of the chamber is negligibly small.
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Kinetic energy of liquid in the chamber is negligibly small.
Ports
Non-directional
A - thermal liquid port
thermal liquid
Thermal liquid port, corresponds to the inlet of the tank.
B - thermal liquid port.
thermal liquid
Thermal liquid port, corresponds to the second inlet of the tank.
Dependencies
This port is visible when the Number of port parameters are set to 2, 3 or 4.
C - thermal liquid port
``thermal liquid''.
Thermal liquid port, corresponds to the third inlet of the tank.
Dependencies
This port is visible when the Number of port parameters are set to 3 or 4.
D - thermal liquid port
`thermal liquid'.
Thermal liquid port, corresponds to the fourth inlet of the tank. If the reservoir has four inlets, it can be used as a joint in a cross-connection.
Dependencies
This port is visible when the Number of port parameters are set to 4.
H - heat port
heat
Through this port the fluid in the chamber exchanges heat with the heat network.
Parameters
Chamber volume - volume of liquid inside the tank
`0.001 m^3 (by default)
The volume of liquid inside the tank. This volume is constant during the simulation.
Number of ports - number of inlet ports in the tank
1 (by default) | 2 | 3 | 4
Number of inlet ports in the tank.
The tank can have one to four ports labelled A, B, C, D.
When the parameters value is changed, the corresponding ports are opened or hidden in the block icon.
Cross-sectional area at port A - area of the input port A normal to the flow direction
0.01 m^2 (by default).
The area of the inlet port A normal to the direction of flow.
Cross-sectional area at port B - area of inlet port B normal to the direction of flow
0.01 m^2 (by default).
The area of inlet port B normal to the direction of flow.
Dependencies
Enabled if port B is visible, that is, if the Number of ports parameters are set to 2, 3 or 4.
Cross-sectional area at port C - area of inlet port C normal to the direction of flow
0.01 m^2 (by default).
The area of the inlet port C normal to the direction of flow.
Dependencies
Enabled if the C port is visible, that is, if the Number of ports parameter is set to 3 or 4.
Cross-sectional area at port D - area of inlet port D normal to the direction of flow
0.01 m^2 (by default).
The area of the inlet port D normal to the direction of flow.
Dependencies
Enabled if the D port is visible, that is, if the Number of ports parameter is set to 4.