# 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`

, `g`

, and `d`

indicate the
properties of dry air, water vapor, trace gas, and water droplets, 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.

$$\dot{m}$$ | 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 |

c_{p} | Specific heat at constant volume |

h | Specific enthalpy |

u | Specific internal energy |

x | Mass fraction
(x_{w} is specific humidity,
which is another term for water vapor mass fraction) |

y | Mole fraction |

φ | Relative humidity |

r | Humidity ratio |

r_{d} | Mass ratio of water droplets to moist air |

T | Temperature |

t | Time |

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

$$\begin{array}{l}{\dot{m}}_{net}={\dot{m}}_{A}-{\dot{m}}_{condense}+{\dot{m}}_{wS}+{\dot{m}}_{gS}+{\dot{m}}_{d,evap}\\ {\Phi}_{net}={\Phi}_{A}+{Q}_{H}+{\Phi}_{S}-(1-{\lambda}_{d}){\dot{m}}_{condense}{h}_{d}\\ {\dot{m}}_{w,net}={\dot{m}}_{wA}-{\dot{m}}_{condense}+{\dot{m}}_{wS}+{\dot{m}}_{d,evap}\\ {\dot{m}}_{g,net}={\dot{m}}_{gA}+{\dot{m}}_{gS}\\ {\dot{m}}_{d,net}={\dot{m}}_{dA}+{\dot{m}}_{dS}+{\lambda}_{d}{\dot{m}}_{condense}-{\dot{m}}_{d,evap}\end{array}$$

where:

$$\dot{m}$$

_{condense}is the rate of condensation.$$\dot{m}$$

_{d,evap}is the rate of water droplet evaporation.*Φ*_{condense}is the rate of energy loss from the condensed water.*λ*is the value of the_{d}**Fraction of condensate entrained as water droplets**parameter.*Φ*_{S}is the rate of energy added by the sources of moisture and trace gas. $${\dot{m}}_{wS}$$ and $${\dot{m}}_{gS}$$ are the mass flow rates of water and gas, respectively, through port**S**. The values of $${\dot{m}}_{wS}$$, $${\dot{m}}_{gS}$$, and*Φ*_{S}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 humidity level in the internal moist air volume

$$\frac{d{x}_{wI}}{dt}{\rho}_{I}V+{x}_{wI}{\dot{m}}_{net}={\dot{m}}_{w,net}$$

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

$$\frac{d{x}_{gI}}{dt}{\rho}_{I}V+{x}_{gI}{\dot{m}}_{net}={\dot{m}}_{g,net}$$

The water droplets mass conservation equation relates the water droplet mass flow rate to the entrained water droplet dynamics in the internal moist air volume

$$\frac{d{r}_{dI}}{dt}{\rho}_{I}V+{r}_{dI}{\dot{m}}_{net}={\dot{m}}_{d,net}.$$

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:

$$\left(\frac{1}{{p}_{I}}\frac{d{p}_{I}}{dt}-\frac{1}{{T}_{I}}\frac{d{T}_{I}}{dt}\right){\rho}_{I}V+\frac{{R}_{a}-{R}_{w}}{{R}_{I}}\left({\dot{m}}_{w,net}-{x}_{w}{\dot{m}}_{net}\right)+\frac{{R}_{a}-{R}_{g}}{{R}_{I}}\left({\dot{m}}_{g,net}-{x}_{g}{\dot{m}}_{net}\right)+{\rho}_{I}\dot{V}={\dot{m}}_{net}$$

where $$\dot{V}$$ 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:

$$\left({c}_{pI}-{R}_{I}+{r}_{d}{c}_{pd}\right)V{\rho}_{I}\frac{d{T}_{I}}{dt}+{u}_{aI}{\dot{m}}_{MA,net}+\left({u}_{wI}-{u}_{aI}\right){\dot{m}}_{w,net}+\left({u}_{gI}-{u}_{aI}\right){\dot{m}}_{g,net}+{h}_{d}{\dot{m}}_{d,net}={\Phi}_{net}-{p}_{I}\dot{V}$$

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

$${p}_{I}={\rho}_{I}{R}_{I}{T}_{I}$$

The mixture specific gas constant is

$${R}_{I}={x}_{aI}{R}_{a}+{x}_{wI}{R}_{w}+{x}_{gI}{R}_{g}$$

The converter volume is

$$V={V}_{dead}+{S}_{\mathrm{int}}{d}_{\mathrm{int}}{\epsilon}_{\mathrm{int}}$$

where:

*V*_{dead}is the dead volume.*S*_{int}is the interface cross-sectional area.*d*_{int}is the interface displacement.*ε*_{int}is the mechanical orientation coefficient. If**Mechanical orientation**is`Pressure at A causes positive displacement of R relative to C`

,*ε*_{int}= 1. If**Mechanical orientation**is`Pressure at A causes negative displacement of R relative to C`

,*ε*_{int}= –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

$${F}_{\mathrm{int}}=\left({p}_{env}-{p}_{I}\right){S}_{\mathrm{int}}{\epsilon}_{\mathrm{int}}$$

where:

*F*_{int}is the force from port**R**to port**C**.*p*_{env}is the environment pressure.

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

$$\begin{array}{l}{p}_{A}={p}_{I}\\ {T}_{H}={T}_{I}\end{array}$$

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

$${x}_{wsI}={\phi}_{ws}\frac{{R}_{I}}{{R}_{w}}\frac{{p}_{wsI}}{{p}_{I}}$$

where:

*φ*_{ws}is the relative humidity at saturation (typically 1).*p*_{wsI}is the water vapor saturation pressure evaluated at*T*_{I}.

The rate of condensation is

$${\dot{m}}_{condense}=\{\begin{array}{ll}0,\hfill & \text{if}{x}_{wI}\le {x}_{wsI}\hfill \\ \frac{{x}_{wI}-{x}_{wsI}}{{\tau}_{condense}}{\rho}_{I}V,\hfill & \text{if}{x}_{wI}{x}_{wsI}\hfill \end{array}$$

where *τ*_{condense} is the value of the
**Water vapor condensation time constant** parameter.

The rate of evaporation is

$${\dot{m}}_{d,evap}=\frac{{x}_{wsI}-{x}_{wI}}{{x}_{wsI}{\tau}_{evap}}{r}_{dI}{\rho}_{I}V,$$

where *τ*_{evap} is the value of the **Water
droplets evaporation time constant** parameter.

### 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.

## Examples

## Ports

### Input

### Output

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2018a**