Translational Mechanical Converter (MA)

blockType: AcausalFoundation.MoistAir.Elements.TranslationalMechanicalConverter

Path in the library:

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

Description

The Translational Mechanical Converter (MA) unit is an 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 parameters Mechanical orientation allows you to specify whether an increase in the volume of moist air results in a positive or negative offset of port R relative to port C.

Port A - humid air port, 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 water vapour saturation level;
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;
- 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 the specific humidity, which is synonymous with the mass fraction of water vapour);
- molar fraction;
- 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;
- energy level 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:

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

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

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:

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

The universal gas constant of the mixture is equal to:

Volume of the transducer:

where

- is the volume of liquid at which the position of the rod is equal to 0;
- is the cross-sectional area of the stem;
- stem displacement;
- mechanical orientation coefficient. If the value of the parameters Mechanical orientation Pressure at A causes positive displacement of R relative to C, then . If `Pressure at A causes negative displacement of R relative to C`then .

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

If the pressure at A causes a positive displacement of R with respect to C , then 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:

where

- is the force transmitted from port R to port C;
- is the 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:

where

- is the relative humidity at saturation (usually 1);
- water vapour saturation pressure corresponding to the temperature .

The condensation rate is equal to:

where is the value of the parameters Condensation time constant.

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:

Assumptions and limitations

The inverter enclosure is absolutely rigid.
The gas resistance between the transmitter inlet and the wet air volume is not modelled. Connect the Variable 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

Conserving

# A — humid air inlet
humid air

Details

Humid air port, corresponds to the inverter input.

Program usage name

port

# C — hull
translational mechanics

Details

Mechanical progressive port, corresponds to the inverter housing.

Program usage name

case_flange

# H — internal temperature
`heat

Details

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

Program usage name

thermal_port

# R — stem
translational mechanics

Details

Mechanical progressive port, corresponds to the rod.

Program usage name

rod_flange

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

Details

Connect this port to the S port of the unit from the library Moist Air: Sources to add or remove moisture and impurity gases.

Program usage name

source_port

Output

# F — information on pressure, temperature, humidity and amount of impurity gases
`vector'

Details

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

Data types	`Float64`.
Complex numbers support	No

# W — condensation rate
scalar

Details

A signal output port that contains the value of the condensation rate in the converter. If the Condensation on wall surface parameters are 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.

Data types	`Float64`.
Complex numbers support	No

Input

Parameters

Main

# Mechanical orientation — converter orientation
Pressure at A causes positive displacement of R relative to C | Pressure at A causes negative displacement of R relative to C

Details

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 humid air volume results in a positive displacement of the R port relative to the C port.
Pressure at A causes negative displacement of R relative to C - an increase in the volume of humid air results in a negative displacement of port R relative to port C.

Values	`Pressure at A causes positive displacement of R relative to C` \| `Pressure at A causes negative displacement of R relative to C`
Default value	`Pressure at A causes positive displacement of R relative to C`
Program usage name	`orientation`
Evaluatable	No

# Initial interface displacement — initial offset of port R with respect to port C
m | cm | ft | in | km | mi | mm | um | yd

Details

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

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

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 m`
Program usage name	`delta_p_start`
Evaluatable	Yes

# Interface cross-sectional area — area pressurised by moist air
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The area pressurised by moist air to produce a translational force.

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	`piston_area`
Evaluatable	Yes

# Dead volume — Humid air volume at zero stem displacement
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

Volume of humid air at stem displacement equal to 0.

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	`1.e-5 m^3`
Program usage name	`dead_volume`
Evaluatable	Yes

# Cross-sectional area at port A — area normal to the flow cross-section at the inlet to the transducer
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 transmitter inlet 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_area`
Evaluatable	Yes

# Environment pressure specification — method of setting the ambient pressure
Atmospheric pressure | Specified pressure

Details

Sets the method for setting the ambient pressure:

Atmospheric pressure - atmospheric pressure.
Specified pressure - value set by the parameters Environment pressure.

Values	`Atmospheric pressure` \| `Specified pressure`
Default value	`Atmospheric pressure`
Program usage name	`environment_type`
Evaluatable	No

# Environment pressure — outside pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure outside the transmitter that opposes the pressure of the moist air volume inside the transmitter. A value of 0 indicates that the inverter is operating in vacuum.

Dependencies

Available when parameters Environment pressure specification is set to . Specified pressure.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`environment_pressure`
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 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 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 connected humid air network. A negative value removes moisture 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	`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

Enter the moisture temperature. This temperature remains constant during the simulation. The unit only uses this value 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

To use this parameter, set the parameters Added moisture temperature specification 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

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

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	`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

Enter the desired temperature of the impurity gas to be added. This temperature remains constant during the simulation. The unit only uses this value 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

To use this parameter, set the parameter Added trace gas temperature specification 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 the operation of a pneumatic actuator in a wet environment