Translational Mechanical Converter (MA)
Interface between moist air and mechanical translational networks
Libraries:
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. The Mechanical orientation parameter lets you specify whether an increase in the moist air volume inside the converter results in a positive or 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.
Mass flow rate | |
Φ | Energy flow rate |
Q | Heat flow rate |
p | Pressure |
ρ | Density |
R | Specific gas constant |
V | Volume of moist air inside the converter |
cv | Specific heat at constant volume |
h | Specific enthalpy |
u | Specific internal energy |
x | Mass fraction (xw is specific humidity, which is another term for water vapor mass fraction) |
y | Mole fraction |
φ | Relative humidity |
r | Humidity ratio |
T | Temperature |
t | Time |
The net flow rates into the moist air volume inside the converter are
where:
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. and are the mass flow rates of water and gas, respectively, through port S. The values of , , 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:
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:
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:
where 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:
The equation of state relates the mixture density to the pressure and temperature:
The mixture specific gas constant is
The converter volume is
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
Pressure at A causes positive displacement of R relative to C
, εint = 1. If Mechanical orientation isPressure at A causes negative displacement of R relative to C
, εint = –1.
If you connect the converter to a Multibody joint, use the physical signal input port p to specify the displacement of port R relative to port C. Otherwise, the block calculates the interface displacement from relative port velocities. The interface displacement is zero when the moist air volume inside the converter is equal to the dead volume. Then, depending on the Mechanical orientation parameter value:
If
Pressure at A causes positive displacement of R relative to C
, the interface displacement increases when the moist air volume increases from dead volume.If
Pressure at A causes negative displacement of R relative to C
, the interface displacement decreases when the moist air volume increases from dead volume.
The force balance on the mechanical interface is
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:
When the moist air volume reaches saturation, condensation may occur. The specific humidity at saturation is
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
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
where ΔhvapI is the specific enthalpy of vaporization evaluated at TI.
Other moisture and trace gas quantities are related to each other as follows:
Variables
To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables and Initial Conditions for Blocks with Finite Moist Air Volume.
Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.
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
Input
Output
Conserving
Parameters
Extended Capabilities
Version History
Introduced in R2018a