Constant Volume Chamber (MA)

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

blockType: AcausalFoundation.MoistAir.Elements.ConstantVolumeChamber

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 humid 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;
- 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;
- relative humidity;
- humidity coefficient;
- temperature;
- time.

Subline indices:

- properties of dry air, water vapour and impurity gas, respectively;
- water vapour at saturation;
- corresponding port;
- properties of the internal volume of moist air.

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

where

- condensation mass flow rate
- condensate energy loss consumption;
- energy addition flow rate by sources of moisture and impurity gas;
- 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 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:

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

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

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

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

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

where

- is the relative humidity at saturation (usually );
- water vapour saturation pressure, estimated at temperature .

The mass flow rate of condensation is:

where is the value of the parameters 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:

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 Variable 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

Conserving

# A — vessel inlet
`moist air

Details

The moist air port corresponding to the vessel inlet.

Program usage name

port_a

# H — vessel temperature
`heat

Details

Heat port related to the temperature of the moist air inside the vessel.

Program usage name

thermal_port

# S — addition or removal of moisture and impurity gas
`moist air

Details

Wet 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

To use this port, set the parameters Moisture and trace gas source to Controlled.

Program usage name

source_port

# B — vessel inlet
`moist air

Details

The moist air port corresponding to the second vessel inlet.

Dependencies

To use this port, set the Number of ports parameters to . 2, 3 or 4.

Program usage name

port_b

# C — capacitance input
`moist air

Details

The moist air port corresponding to the third vessel inlet.

Dependencies

To use this port, set the Number of ports parameters to 3 or 4.

Program usage name

port_c

# D — vessel inlet
`moist air

Details

The moist air port corresponding to the fourth vessel inlet.

Dependencies

To use this port, set the Number of ports parameters to . 4.

Program usage name

port_d

Output

# W — condensation mass flow rate, kg/s
scalar

Details

Output port of a signal that measures the mass flow rate of condensation in the chamber.

Data types	`Float64`.
Complex numbers support	No

# F — vector signal containing data on pressure, temperature, humidity and level of impurity gases
`vector'

Details

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

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# Chamber volume — volume of moist air in the tank
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

The volume of moist air in the vessel. 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.

Units	`l` \| `gal` \| `igal` \| `m^3` \| `cm^3` \| `ft^3` \| `in^3` \| `km^3` \| `mi^3` \| `mm^3` \| `um^3` \| `yd^3` \| `Nm/Pa` \| `Nm/bar` \| `lbfft/psi` \| `ftlbf/psi`
Default value	`0.001 m^3`
Program usage name	`volume`
Evaluatable	Yes

# Number of ports — number of input ports in the vessel
1 | 2 | 3 | 4

Details

The number of input ports in the chamber. A 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.

Values	`1` \| `2` \| `3` \| `4`
Default value	`1`
Program usage name	`port_count`
Evaluatable	No

# Cross-sectional area at port A — area normal to the flow path at the vessel inlet
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

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

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_a_area`
Evaluatable	Yes

# Cross-sectional area at port B — area normal to the flow path at the vessel inlet
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

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

Dependencies

To use this parameter, set the Number of ports parameters to . 2, 3 or 4.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_b_area`
Evaluatable	Yes

# Cross-sectional area at port C — area normal to the flow path at the vessel inlet
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

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

Dependencies

To use this parameter, set the parameters Number of ports to 3 or 4.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_c_area`
Evaluatable	Yes

# Cross-sectional area at port D — area normal to the flow path at the vessel inlet
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

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

Dependencies

To use this parameter, set the Number of ports parameters to . 4.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_d_area`
Evaluatable	Yes

Moisture and Trace Gas

# Relative humidity at saturation — Relative humidity above which condensation occurs

Details

Relative humidity above which condensation occurs.

Default value	`1.0`
Program usage name	`RH_saturation`
Evaluatable	Yes

# Condensation time constant — condensation time constant
d | s | hr | ms | ns | us | min

Details

A time scale factor characterising the time period for the return of the supersaturated volume of moist air to the saturation level due to condensation of excess moisture.

Units	`d` \| `s` \| `hr` \| `ms` \| `ns` \| `us` \| `min`
Default value	`0.001 s`
Program usage name	`condensation_time_constant`
Evaluatable	Yes

# Moisture and trace gas source — source of moisture and impurity gases
None | Constant | Controlled

Details

This parameter controls the usage of the S port and provides the following options for modelling moisture and impurity 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 fed into or extracted from the unit at a constant flow rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) units are made available in the unit settings. The S port is hidden.
Controlled - Moisture and impurity gas are introduced into or removed from the unit at a time-varying flow rate. Port S is available. Units Moisture Source (MA) and Trace Gas Source (MA) are connected to this port.

Values	`None` \| `Constant` \| `Controlled`
Default value	`None`
Program usage name	`moisture_trace_gas_source`
Evaluatable	No

# Moisture added or removed — add or remove moisture in the form of water vapour or water
Vapor | Liquid

Details

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

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

Dependencies

To use this parameter, set the parameter Moisture and trace gas source to . Constant.

Values	`Vapor` \| `Liquid`
Default value	`Vapor`
Program usage name	`moisture_source_phase`
Evaluatable	No

# Rate of added moisture — constant mass flow rate through the source
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

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

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`0.0 kg/s`
Program usage name	`moisture_mass_flow`
Evaluatable	Yes

# Added moisture temperature specification — Moisture temperature setting method
Atmospheric temperature | Specified temperature

Details

Selects the method for setting the moisture temperature:

Atmospheric temperature - atmospheric temperature is used.
Specified temperature - value is set with the parameters Temperature of added moisture.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`moisture_temperature_type`
Evaluatable	No

Details

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

To use this parameter, set the Moisture and trace gas source parameters to and the parameters to . Constant`and set the Added moisture temperature specification parameters to . `Specified temperature.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`moisture_temperature`
Evaluatable	Yes

# Rate of added trace gas — constant mass flow rate through the source
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Mass flow rate of the impurity 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

To use this parameter, set the parameter Moisture and trace gas source to . Constant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`0.0 kg/s`
Program usage name	`trace_gas_mass_flow`
Evaluatable	Yes

# Added trace gas temperature specification — method for setting the impurity gas temperature
Atmospheric temperature | Specified temperature

Details

Selection of the impurity gas temperature setting method:

Atmospheric temperature - atmospheric temperature is used.
Specified temperature - value is set with the parameters Temperature of added trace gas.

Dependencies

To use this parameter, set the Moisture and trace gas source parameters to . Constant.

Values	`Atmospheric temperature` \| `Specified temperature`
Default value	`Atmospheric temperature`
Program usage name	`trace_gas_temperature_type`
Evaluatable	No

Details

The temperature of the impurity 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

To use this parameter, set the Moisture and trace gas source parameters to and the parameters to . Constant`and set the Added trace gas temperature specification parameters to . `Specified temperature.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`trace_gas_temperature`
Evaluatable	Yes

Examples

Modelling of artificial ventilation system