Translational Mechanical Converter (MA)

Interface between moist air and mechanical translational networks

  • Library:
  • Simscape / Foundation Library / Moist Air / Elements

Description

The Translational Mechanical Converter (MA) block models an interface between a moist air network and a mechanical translational network. The block converts moist air pressure into mechanical force and vice versa. You can use it as a building block for linear actuators.

The converter contains a variable volume of moist air. The pressure and temperature evolve based on the compressibility and thermal capacity of this moist air volume. Liquid water condenses out of the moist air volume when it reaches saturation.

If Mechanical orientation is set to Positive, an increase in the moist air volume inside the converter results in a positive displacement of port R relative to port C. If Mechanical orientation is set to Negative, an increase in the moist air volume results in a negative displacement of port R relative to port C.

The block equations use these symbols. Subscripts a, w, and g indicate the properties of dry air, water vapor, and trace gas, respectively. Subscript ws indicates water vapor at saturation. Subscripts A, H, and S indicate the appropriate port. Subscript I indicates the properties of the internal moist air volume.

m˙Mass flow rate
ΦEnergy flow rate
QHeat flow rate
pPressure
ρDensity
RSpecific gas constant
VVolume of moist air inside the converter
cvSpecific heat at constant volume
hSpecific enthalpy
uSpecific internal energy
xMass fraction (xw is specific humidity, which is another term for water vapor mass fraction)
yMole fraction
φRelative humidity
rHumidity ratio
TTemperature
tTime

The net flow rates into the moist air volume inside the converter are

m˙net=m˙Am˙condense+m˙wS+m˙gSΦnet=ΦA+QHΦcondense+ΦSm˙w,net=m˙wAm˙condense+m˙wSm˙g,net=m˙gA+m˙gS

where:

  • m˙condense is the rate of condensation.

  • Φcondense is the rate of energy loss from the condensed water.

  • ΦS is the rate of energy added by the sources of moisture and trace gas. m˙wS and m˙gS are the mass flow rates of water and gas, respectively, through port S. The values of m˙wS, m˙gS, and ΦS are determined by the moisture and trace gas sources connected to port S of the converter.

Water vapor mass conservation relates the water vapor mass flow rate to the dynamics of the moisture level in the internal moist air volume:

dxwIdtρIV+xwIm˙net=m˙w,net

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

dxgIdtρIV+xgIm˙net=m˙g,net

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

(1pIdpIdt1TIdTIdt)ρIV+RaRwRI(m˙w,netxwm˙net)+RaRgRI(m˙g,netxgm˙net)+ρIV˙=m˙net

where V˙ is the rate of change of the converter volume.

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

ρIcvIVdTIdt+(uwIuaI)(m˙w,netxwm˙net)+(ugIuaI)(m˙g,netxgm˙net)+uIm˙net=ΦnetpIV˙

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

pI=ρIRITI

The mixture specific gas constant is

RI=xaIRa+xwIRw+xgIRg

The converter volume is

V=Vdead+Sintdintεint

where:

  • Vdead is the dead volume.

  • Sint is the interface cross-sectional area.

  • dint is the interface displacement.

  • εint is the mechanical orientation coefficient. If Mechanical orientation is Positive, εint = 1. If Mechanical orientation is Negative, εint = –1.

The force balance on the mechanical interface is

Fint=(penvpI)Sintεint

where:

  • Fint is the force from port R to port C.

  • penv is the environment pressure.

Flow resistance and thermal resistance are not modeled in the converter:

pA=pITH=TI

When the moist air volume reaches saturation, condensation may occur. The specific humidity at saturation is

xwsI=φwsRIRwpIpwsI

where:

  • φws is the relative humidity at saturation (typically 1).

  • pwsI is the water vapor saturation pressure evaluated at TI.

The rate of condensation is

m˙condense={0,if xwIxwsIxwIxwsIτcondenseρIV,if xwI>xwsI

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

The condensed water is subtracted from the moist air volume, as shown in the conservation equations. The energy associated with the condensed water is

Φcondense=m˙condense(hwIΔhvapI)

where ΔhvapI is the specific enthalpy of vaporization evaluated at TI.

Other moisture and trace gas quantities are related to each other as follows:

φwI=ywIpIpwsIywI=xwIRwRIrwI=xwI1xwIygI=xgIRgRIxaI+xwI+xgI=1

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector). For more information, see Set Priority and Initial Target for Block Variables and Initial Conditions for Blocks with Finite Moist Air Volume.

Assumptions and Limitations

  • The converter casing is perfectly rigid.

  • Flow resistance between the converter inlet and the moist air volume is not modeled. Connect a Local Restriction (MA) block or a Flow Resistance (MA) block to port A to model pressure losses associated with the inlet.

  • Thermal resistance between port H and the moist air volume is not modeled. Use Thermal library blocks to model thermal resistances between the moist air mixture and the environment, including any thermal effects of a chamber wall.

  • The moving interface is perfectly sealed.

  • The block does not model the mechanical effects of the moving interface, such as hard stops, friction, and inertia.

Ports

Output

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Physical signal output port that measures the rate of condensation in the converter.

Physical signal output port that outputs a vector signal. The vector contains the pressure (in Pa), temperature (in K), moisture level, and trace gas level measurements inside the component. Use the Measurement Selector (MA) block to unpack this vector signal.

Conserving

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Moist air conserving port associated with the converter inlet.

Thermal conserving port associated with the temperature of the moist air mixture inside the converter.

Mechanical translational conserving port associated with the moving interface.

Mechanical translational conserving port associated with the converter casing.

Connect this port to port S of a block from the Moisture & Trace Gas Sources library to add or remove moisture and trace gas. For more information, see Using Moisture and Trace Gas Sources.

Dependencies

This port is visible only if you set the Moisture and trace gas source parameter to Controlled.

Parameters

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Main

Select the relative orientation of the converter with respect to the volume of moist air inside the converter:

  • Positive — Increase in the moist air volume results in a positive displacement of port R relative to port C.

  • Negative — Increase in the moist air volume results in a negative displacement of port R relative to port C.

The area on which the moist air exerts pressure to generate the translational force.

Translational offset of port R relative to port C at the start of simulation. A value of 0 corresponds to an initial moist air volume equal to Dead volume.

Dependencies

  • If Mechanical orientation is Positive, the parameter value must be greater than or equal to 0.

  • If Mechanical orientation is Negative, the parameter value must be less than or equal to 0.

Volume of moist air when the interface displacement is 0.

Cross-sectional area of the converter inlet, in the direction normal to the air flow path.

Select a specification method for the environment pressure:

  • Atmospheric pressure — Use the atmospheric pressure, specified by the Moist Air Properties (MA) block connected to the circuit.

  • Specified pressure — Specify a value by using the Environment pressure parameter.

Pressure outside the converter acting against the pressure of the converter moist air volume. A value of 0 indicates that the converter expands into vacuum.

Dependencies

Enabled when the Environment pressure specification parameter is set to Specified pressure.

Moisture and Trace Gas

Relative humidity above which condensation occurs.

Characteristic time scale at which an oversaturated moist air volume returns to saturation by condensing out excess moisture.

This parameter controls visibility of port S and provides these options for modeling moisture and trace gas levels inside the component:

  • None — No moisture or trace gas is injected into or extracted from the block. Port S is hidden. This is the default.

  • Constant — Moisture and trace gas are injected into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) blocks become available in the Moisture and Trace Gas section of the block interface. Port S is hidden.

  • Controlled — Moisture and trace gas are injected into or extracted from the block at a time-varying rate. Port S is exposed. Connect the Controlled Moisture Source (MA) and Controlled Trace Gas Source (MA) blocks to this port.

Select whether the block adds or removes moisture as water vapor or liquid water:

  • Vapor — The enthalpy of the added or removed moisture corresponds to the enthalpy of water vapor, which is greater than that of liquid water.

  • Liquid — The enthalpy of the added or removed moisture corresponds to the enthalpy of liquid water, which is less than that of water vapor.

Dependencies

Enabled when the Moisture and trace gas source parameter is set to Constant.

Water vapor mass flow rate through the block. A positive value adds moisture to the connected moist air volume. A negative value extracts moisture from that volume.

Dependencies

Enabled when the Moisture and trace gas source parameter is set to Constant.

Select a specification method for the moisture temperature:

  • Atmospheric temperature — Use the atmospheric temperature, specified by the Moist Air Properties (MA) block connected to the circuit.

  • Specified temperature — Specify a value by using the Temperature of added moisture parameter.

Dependencies

Enabled when the Moisture and trace gas source parameter is set to Constant.

Enter the desired temperature of added moisture. This temperature remains constant during simulation. The block uses this value to evaluate the specific enthalpy of the added moisture only. The specific enthalpy of removed moisture is based on the temperature of the connected moist air volume.

Dependencies

Enabled when the Added moisture temperature specification parameter is set to Specified temperature.

Trace gas mass flow rate through the block. A positive value adds trace gas to the connected moist air volume. A negative value extracts trace gas from that volume.

Dependencies

Enabled when the Moisture and trace gas source parameter is set to Constant.

Select a specification method for the trace gas temperature:

  • Atmospheric temperature — Use the atmospheric temperature, specified by the Moist Air Properties (MA) block connected to the circuit.

  • Specified temperature — Specify a value by using the Temperature of added trace gas parameter.

Dependencies

Enabled when the Moisture and trace gas source parameter is set to Constant.

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

Dependencies

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Introduced in R2018a