Engee documentation

Constant Volume Chamber (MA)

A fixed volume tank with a variable number of humid air ports.

blockType: AcausalFoundation.MoistAir.Elements.ConstantVolumeChamber

constant volume chamber (ma)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Constant Volume Chamber (MA)

Description

The Constant Volume Chamber (MA) unit simulates mass and energy storage in a network of moist air. The vessel contains a constant volume of humid air. The vessel can exchange mass and energy with the connected moist air network and exchange heat with the environment, allowing the internal pressure and temperature to vary over time. Pressure and temperature vary with the compressibility and heat capacity of the moist air volume. Water condenses out of the humid air volume when saturation is reached.

Conservation of mass

The following notations are used in the unit equations:

  • - mass flow rate.

  • - energy flow rate.

  • - heat flow rate.

  • - pressure.

  • ρ - density.

  • - universal gas constant.

  • - volume of moist air inside the chamber.

  • - specific heat at constant volume.

  • - specific enthalpy.

  • - specific internal energy.

  • - mass fraction ( - specific humidity, which is otherwise known as the mass fraction of water vapour).

  • - molar fraction.

  • φ - relative humidity.

  • - humidity coefficient.

  • - temperature.

  • - time.

Subline indices: * и - properties of dry air, water vapour and impurity gas, respectively. * - water vapour at saturation. * и - corresponding port. * - properties of the internal volume of moist air.

Then the net flow rates of moist air in the vessel are:

Where:

  • - condensation mass flow rate.

  • - energy loss consumption of condensate.

  • - energy addition flow rate of moisture and impurity gas sources.

  • и - mass flow rates of water and admixture gas through port S respectively.

The values and are determined by the moisture and impurity gas sources connected to the S port of the chamber or by the values of the corresponding parameters.

If the ports are not used, the terms of the equation with the subscript corresponding to the port name are 0.

The water vapour mass conservation equation relates the mass flow rate of water vapour to the dynamics of the humidity level in the internal volume of humid air:

ρ

Similarly, the equation of conservation of admixture gas mass relates the mass flow rate of admixture gas to the dynamics of the level of admixture gas in the internal volume of humid air:

ρ

The mixture mass conservation equation relates the mass flow rate of the mixture to the dynamics of the pressure, temperature, and mass fractions of the internal volume of moist air:

ρ

Finally, the energy conservation equation relates the energy flow rate to the dynamics of changes in pressure, temperature, and mass fractions of the internal volume of moist air:

ρ

The equation of state relates the density of the mixture to pressure and temperature:

ρ

The universal gas constant of the mixture is equal to:

Flow resistance and thermal resistance in the chamber are not modelled:

When the volume of humid air reaches saturation, condensation can occur. The specific humidity at saturation is

φ

where:

  • φ - is the relative humidity at saturation (typically φ ).

  • - saturation pressure of water vapour, estimated at temperature .

The mass flow rate of condensation is:

еслиτρесли

where τ is the value of the parameter Condensation time constant.

Condensate is subtracted from the volume of moist air as shown in the conservation equations. The energy associated with the condensate is equal to:

where is the specific enthalpy of vapour formation, estimated at temperature .

Other parameters of moisture and impurity gas measurement are related to each other by the following relationships:

φ

Assumptions and limitations

  • The walls of the chamber are absolutely rigid.

  • There is no flow resistance between ports A, B, C, D and the interior of the chamber. To model the flow resistance at the inlets to the chamber, use the blocks Local Restriction (MA) and Flow Resistance (MA).

  • There is no thermal resistance between port H and the interior of the chamber. Use the thermal library blocks to model the thermal resistance between the wet air mixture and the environment, including any thermal effects of the chamber wall.

Ports

Non-directional

A - vessel inlet
`moist air

The moist air port corresponding to the vessel inlet.

B - vessel inlet
`humid air

Wet air port corresponding to the second vessel inlet.

Dependencies

This port is used when the Number of ports parameter is set to 2, 3, or 4.

C - vessel inlet
`moist air

Wet air port corresponding to the third vessel inlet.

Dependencies

This port is used when the Number of ports parameters are set to 3 or 4.

D - vessel inlet
`moist air

Wet air port corresponding to the fourth vessel inlet.

Dependencies

This port is used when the Number of ports parameter is set to 4.

H is the temperature inside the vessel
`heat

Heat port related to the wet air temperature inside the vessel.

S - addition or removal of moisture and impurity gas
`moisture and gas impurity'.

Humid Air Source Port. Connect this port to the S port of the humid air final volume unit to add or remove moisture and impurity gas.

Dependencies

This port is used when the Moisture and trace gas source parameters are set to `Controlled'.

Output

W - condensation mass flow rate, kg/s.
scalar

Signal output port that measures the condensation mass flow rate in the chamber.

F - vector signal containing pressure, temperature, humidity and impurity gas level data
vector

Output port that outputs a vector signal. The vector contains the results of pressure, temperature, humidity and impurity gas level measurements inside the component. To decompress this vector signal, use the block Measurement Selector (MA).

Parameters

Chamber volume - volume of moist air in the vessel
`0.001 m³ (by default)

Volume of humid air in the tank. The vessel is rigid, so its volume remains constant during the simulation. It is assumed that the chamber is always completely filled with moist air.

Number of ports - the number of input ports in the vessel
1 (By default)| 2| 3| 4

The number of input ports to the camera. The camera can have one to four ports labelled A to D. When you change the value of the parameters, the corresponding ports are displayed or hidden in the block display.

Cross-sectional area at port A - area normal to the flow path at the vessel inlet
0.01 m² (By default)

The cross-sectional area of the vessel inlet at port A in the direction normal to the wet air flow path.

Cross-sectional area at port B - area normal to the flow path at the vessel inlet
`0.01 m² (By default)

Cross-sectional area of vessel inlet at port B in the direction normal to the wet air flow path.

Dependencies

Used when port B is visible, i.e. when the Number of ports parameters are set to 2, 3 or 4.

Cross-sectional area at port C - area normal to the flow path at the inlet to the vessel
`0.01 m² (by default).

Cross-sectional area of vessel inlet at port C in the direction normal to the wet air flow path.

Dependencies

Used if port C is visible, i.e. if the Number of ports parameters are set to 3 or 4.

Cross-sectional area at port D - area normal to the flow path at the vessel inlet
0.01 m² (by default).

Cross-sectional area of vessel inlet at port D in the direction normal to the wet air flow path.

Dependencies

Used when port D is visible, i.e. when the Number of ports parameter is set to 4.

Moisture and impurity gas

Relative humidity at saturation - relative humidity above which condensation occurs
`1.0 (By default).

Relative humidity above which condensation occurs.

Condensation time constant - condensation time constant
`1e-3 s (by default).

A time scaling factor characterising the time period for the return of an oversaturated volume of humid air to saturation level due to condensation of excess moisture.

Moisture and trace gas source - moisture and trace gas source
None (By default) | Constant | Controlled

This parameter controls the usage of the S port and provides the following options for modelling moisture and trace gas levels within the unit:

  • None - no moisture or impurity gas is introduced into or extracted from the block. The S port is hidden. This value is used by default.

  • Constant - moisture and impurity gas are introduced into or extracted from the block at a constant flow rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) blocks are made available in the block settings. The S port is hidden.

  • `Controlled' - Moisture and impurity gas are introduced into or removed from the block at a time-varying flow rate. The S port is available. Units Moisture Source (MA) and Trace Gas Source (MA) are connected to this port.

Moisture added or removed - add or remove moisture in the form of water vapour or water
Vapor (By default) | Liquid

Select whether the source adds or removes moisture as water vapour or water:

  • Vapor - the enthalpy of moisture added or removed corresponds to the enthalpy of water vapour, which is greater than the enthalpy of water.

  • Liquid - the enthalpy of moisture added or removed corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

Used if the Moisture and trace gas source parameters are set to `Constant'.

Rate of added moisture - constant mass flow rate through the source
0.0 (By default).

Mass flow rate of moisture through the source.

A positive value adds moisture to the chamber. A negative value removes moisture from the chamber.

Dependencies

Used when the Moisture and trace gas source parameters are set to `Constant'.

Added moisture temperature specification - moisture temperature specification method
Atmospheric temperature (by default) | Specified temperature.

Selects the moisture temperature specification method:

  • Atmospheric temperature - atmospheric temperature is used.

  • Specified temperature - the value is set with the parameters Temperature of added moisture.

Dependencies

It is used if the Moisture and trace gas source parameters are set to `Constant'.

Temperature of added moisture - moisture temperature
`293.15 K (by default).

Moisture Temperature. This temperature remains constant during the simulation. The unit uses this value only to estimate the specific enthalpy of added moisture. The specific enthalpy of removed moisture is determined based on the chamber temperature.

Dependencies

Used when the Moisture and trace gas source parameters are set to `Constant' and the Added moisture temperature specification parameters are set to `Specified temperature'.

Rate of added trace gas - constant mass flow rate through the source
0.0 (By default).

Mass flow rate of added trace gas through the source.

A positive value adds impurity gas to the connected humid air network. A negative value removes impurity gas from this network.

Dependencies

Used when the Moisture and trace gas source parameters are set to `Constant'.

Added trace gas temperature specification - method of setting the trace gas temperature specification
Atmospheric temperature (by default) | Specified temperature.

Selects the impurity gas temperature specification method:

  • Atmospheric temperature - atmospheric temperature is used.

  • Specified temperature - the value is set with the parameters Temperature of added trace gas.

Dependencies

It is used if the Moisture and trace gas source parameters are set to `Constant'.

Temperature of added trace gas - temperature of added trace gas
`293.15 K (by default).

Temperature of added trace gas. This temperature remains constant during the simulation. The unit uses this value only to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the removed impurity gas is based on the chamber temperature.

Dependencies

Used when the Moisture and trace gas source parameters are set to `Constant' and the Added trace gas temperature specification parameters are set to `Specified temperature'.

Examples