Engee documentation

Translational Mechanical Converter (MA)

Interface between the humid air network and the mechanical progressive network.

blockType: AcausalFoundation.MoistAir.Elements.TranslationalMechanicalConverter

translational mechanical converter (ma)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Translational Mechanical Converter (MA)

Description

The Translational Mechanical Converter (MA) unit represents the interface (converter) between the humid air network and the mechanical progressive network. The unit converts humid air pressure into mechanical force and vice versa. It can be used as a basis for progressive gas actuators.

The converter contains a variable volume of moist air. The pressure and temperature vary according to the compressibility and heat capacity of the moist air. Liquid water condenses out of the moist air volume when it reaches saturation. The Mechanical orientation parameter allows you to specify whether an increase in humid air volume results in a positive or negative displacement of port R relative to port C.

Port A is the humid air port and corresponds to the inverter input. Port H is a thermal port related to the wet air temperature inside the inverter. Ports R and C are mechanical progressive ports corresponding to the inverter stem and housing.

Equations

The block equations use these symbols:

  • The lower indices , and indicate the properties of dry air, water vapour and impurity gas respectively.

  • The lower index indicates the saturation level of water vapour.

  • The lower indices , and indicate the corresponding port.

  • The lower index indicates the internal volume properties of the moist air.

  • - mass flow rate.

  • - energy consumption.

  • - heat flow rate.

  • - pressure.

  • ρ - density.

  • - universal gas constant.

  • - volume of moist air inside the converter.

  • - specific heat capacity at constant volume.

  • - specific enthalpy.

  • - specific internal energy.

  • - mass fraction ( is specific humidity, which is synonymous with water vapour mass fraction).

  • - molar fraction.

  • φ - relative humidity.

  • - humidity coefficient.

  • - temperature.

  • - time.

Conservation of mass and energy

The net flow rate of moist air in the converter volume is:

Where:

  • - condensation flow rate.

  • - is the rate of energy loss by condensed water.

  • - the level of energy added by moisture and impurity gas sources.

  • and are mass flow rates of water and gas respectively through the S port. The values , and are determined by the moisture and impurity gas sources connected to the S port of the converter.

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

ρ

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

ρ

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

ρρ

where

  • - is the volume flow rate of the transducer.

Finally, conservation of energy relates the energy flow rate to the dynamics of 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

Volume of the transducer:

ε

Where:

  • - is the volume of fluid at which the position of the stem is 0.

  • - is the cross-sectional area of the stem.

  • - stem displacement.

  • ε - mechanical orientation coefficient. If the value of the Mechanical orientation parameter Pressure at A causes positive displacement of R relative to C, then ε . If Pressure at A causes negative displacement of R relative to C, then ε .

The stem position is zero if the volume of moist air inside the transducer is equal to . Then, depending on the value of Mechanical orientation, the following is true:

  • If the pressure at A causes a positive displacement of R with respect to C, the stem displacement increases when the volume of moist air increases compared to .

  • If the pressure at A causes a negative displacement of R relative to C, then the stem displacement decreases when the volume of moist air increases compared to .

The balance of forces at the mechanical interface is:

ε ,

where:

  • - the force transmitted from port R to port C.

  • - ambient pressure.

Gas and thermal resistances are not modelled in the converter:

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

φ

Where:

  • φ - Relative humidity at saturation (usually 1).

  • - water vapour saturation pressure corresponding to the temperature .

The condensation rate is equal to:

τρ

where

  • τ - is the value of the Condensation time constant parameter.

Condensed water is subtracted from the volume of moist air as shown in the conservation equations. The energy associated with condensed water is equal to

where

- is the specific enthalpy of vaporisation estimated at .

The quantities of moisture and impurity gases are related to each other as follows:

φ

Assumptions and limitations

  • The housing of the inverter is absolutely rigid.

  • The gas resistance between the transmitter inlet and the wet air volume is not modelled. Connect the Local Restriction (MA) block or Flow Resistance (MA) block to port A to model the pressure loss associated with the inlet.

  • The thermal resistance between port H and the humid air volume is not modelled. Use the thermal library blocks to model the thermal resistance between the moist air mixture and the environment, including any thermal effects of the chamber walls.

  • The movable stem operates without losses.

  • The block does not model mechanical effects such as mechanical constraints, friction, and inertia.

Ports

Non-directional

A - humid air inlet
`humid air

Wet air port, corresponds to the inverter input.

H - temperature inside the thermal converter
heat

Heat port, is related to the temperature of humid air inside the converter.

R - rod
translational mechanics

Mechanical progressive port, corresponds to the stem.

C - housing
translational mechanics

Mechanical progressive port, corresponds to the inverter housing.

S - adding or removing moisture and impurity gases
`moisture and gas impurity'.

Connect this port to the S port of a unit from the Humid Air: Humidity and Gas Impurity Sources library to add or remove moisture and impurity gases.

Output

W is the condensation rate
scalar

A signal output port that contains the value of the condensation rate in the inverter. If Condensation on wall surface is enabled, this port reports the total water vapour condensation rate, which includes condensation from the saturated humid air volume as well as condensation on the inverter wall.

F - information on pressure, temperature, humidity and amount of impurity gases
vector

Output signal port; vector with the following elements: pressure, temperature, humidity level and number of impurity gases inside the component. The Measurement Selector (MA) block is used to decompress the vector signal.

Parameters

Main

Mechanical orientation - orientation of the transducer
Pressure at A causes positive displacement of R relative to C (by default) | `Pressure at A causes negative displacement of R relative `

Sets the orientation of the movement of the mechanical part in relation to the change in the volume of moist air:

  • `Pressure at A causes positive displacement of R relative to C' - an increase in the volume of moist air causes positive displacement of port R relative to port C.

  • `Pressure at A causes negative displacement of R relative to C' - an increase in the volume of moist air causes negative displacement of port R relative to port C.

Initial interface displacement - initial displacement of port R relative to port C
0.0 (By default)

Initial displacement of port R relative to port C. The value 0 corresponds to the initial wet air volume equal to Dead volume.

  • If Mechanical orientation has the value Pressure at A causes positive displacement of R relative to C, the value of the parameter must be greater than or equal to 0.

  • If Mechanical orientation has the value Pressure at A causes negative displacement of R relative to C, the value of the parameter must be less than or equal to 0.

Interface cross-sectional area is the area pressurised by moist air
0.01 m² (by default).

The area over which the moist air exerts pressure to create a translational force.

Dead volume - volume of moist air at zero stem displacement
1e-5 m³ (by default).

Humid air volume at stem displacement equal to 0.

Cross-sectional area at port A - area normal to the flow cross-section at the inlet to the transmitter
0.01 m² (by default)

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

Environment pressure specification - method of specifying the ambient pressure
Atmospheric pressure (by default) | Specified pressure.

Specifies the method of specifying the ambient pressure:

  • Atmospheric pressure - atmospheric pressure.

  • Specified pressure - the value specified by the Environment pressure parameter.

Environment pressure - pressure outside the transmitter
0.101325 MPa (by default).

Pressure outside the converter, counteracting the pressure of the converter wet air volume. A value of 0 indicates that the converter is operating in vacuum.

Dependencies

Available when Environment pressure specification is set to Specified pressure.

Humidity 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 c (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 use 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 unit 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 moisture added or removed corresponds to the enthalpy of water, which is less than the enthalpy of water vapour.

Dependencies

Used when Moisture and trace gas source is 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 connected humid air network. A negative value removes moisture from this network.

Dependencies

Used when Moisture and trace gas source is 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 using the Temperature of added moisture parameter.

Dependencies

It is used if the Moisture and trace gas source parameter is set to Constant.

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

Enter the desired 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 temperature of the connected humid air network.

Dependencies

Used when Added moisture temperature specification is set to Specified temperature.

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

Reflects the mass flow rate of added trace gas through the source. A positive value adds trace gas to the connected humid air volume. A negative value draws impurity gas from that volume.

Dependencies

Used when Moisture and trace gas source is 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 using the parameter Temperature of added trace gas.

Dependencies

It is used if the Moisture and trace gas source parameter is set to Constant.

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

Enter the desired temperature of the added trace gas. This temperature remains constant during the simulation. The block uses this value only to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the removed impurity gas is determined based on the temperature of the connected wet air volume.

Dependencies

Used when the Added trace gas temperature specification is set to Specified temperature.

Examples