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# Rotational Mechanical Converter (MA)

Interface between moist air and mechanical rotational networks

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

## Description

The Rotational Mechanical Converter (MA) block models an interface between a moist air network and a mechanical rotational network. The block converts moist air pressure into mechanical torque and vice versa. You can use it as a building block for rotary 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 rotation 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.

 $\stackrel{˙}{m}$ 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 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

`$\begin{array}{l}{\stackrel{˙}{m}}_{net}={\stackrel{˙}{m}}_{A}-{\stackrel{˙}{m}}_{condense}+{\stackrel{˙}{m}}_{wS}+{\stackrel{˙}{m}}_{gS}\\ {\Phi }_{net}={\Phi }_{A}+{Q}_{H}-{\Phi }_{condense}+{\Phi }_{S}\\ {\stackrel{˙}{m}}_{w,net}={\stackrel{˙}{m}}_{wA}-{\stackrel{˙}{m}}_{condense}+{\stackrel{˙}{m}}_{wS}\\ {\stackrel{˙}{m}}_{g,net}={\stackrel{˙}{m}}_{gA}+{\stackrel{˙}{m}}_{gS}\end{array}$`

where:

• $\stackrel{˙}{m}$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. ${\stackrel{˙}{m}}_{wS}$ and ${\stackrel{˙}{m}}_{gS}$ are the mass flow rates of water and gas, respectively, through port S. The values of ${\stackrel{˙}{m}}_{wS}$, ${\stackrel{˙}{m}}_{gS}$, 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:

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

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:

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

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:

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

where $\stackrel{˙}{V}$ 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:

`${\rho }_{I}{c}_{vI}V\frac{d{T}_{I}}{dt}+\left({u}_{wI}-{u}_{aI}\right)\left({\stackrel{˙}{m}}_{w,net}-{x}_{w}{\stackrel{˙}{m}}_{net}\right)+\left({u}_{gI}-{u}_{aI}\right)\left({\stackrel{˙}{m}}_{g,net}-{x}_{g}{\stackrel{˙}{m}}_{net}\right)+{u}_{I}{\stackrel{˙}{m}}_{net}={\Phi }_{net}-{p}_{I}\stackrel{˙}{V}$`

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 depends on the rotation of the moving interface:

`$V={V}_{dead}+{D}_{\mathrm{int}}{\theta }_{\mathrm{int}}{\epsilon }_{\mathrm{int}}$`

where:

• Vdead is the dead volume.

• Dint is the interface volume displacement.

• θint is the interface rotation.

• εint is the mechanical orientation coefficient. If Mechanical orientation is ```Pressure at A causes positive rotation of R relative to C```, εint = 1. If Mechanical orientation is ```Pressure at A causes negative rotation of R relative to C```, εint = –1.

If you connect the converter to a Multibody joint, use the physical signal input port q to specify the rotation of port R relative to port C. Otherwise, the block calculates the interface rotation from relative port angular velocities. The interface rotation 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 rotation of R relative to C```, the interface rotation increases when the moist air volume increases from dead volume.

• If ```Pressure at A causes negative rotation of R relative to C```, the interface rotation decreases when the moist air volume increases from dead volume.

The torque balance on the mechanical interface is

`${\tau }_{\mathrm{int}}=\left({p}_{env}-{p}_{I}\right){D}_{\mathrm{int}}{\epsilon }_{\mathrm{int}}$`

where:

• τint is the torque from port R to port C.

• penv 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:

• 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

`${\Phi }_{condense}={\stackrel{˙}{m}}_{condense}\left({h}_{wI}-\Delta {h}_{vapI}\right)$`

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

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

`$\begin{array}{l}{\phi }_{wI}=\frac{{y}_{wI}{p}_{I}}{{p}_{wsI}}\\ {y}_{wI}=\frac{{x}_{wI}{R}_{w}}{{R}_{I}}\\ {r}_{wI}=\frac{{x}_{wI}}{1-{x}_{wI}}\\ {y}_{gI}=\frac{{x}_{gI}{R}_{g}}{{R}_{I}}\\ {x}_{aI}+{x}_{wI}+{x}_{gI}=1\end{array}$`

### 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

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Input physical signal that passes the position information from a Simscape™ Multibody™ joint. Connect this port to the position sensing port q of the joint. For more information, see Connecting Simscape Networks to Simscape Multibody Joints.

#### Dependencies

To enable this port, set the Interface rotation parameter to ```Provide input signal from Multibody joint```.

### 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 rotational conserving port associated with the moving interface.

Mechanical rotational 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 alignment of moving interface with respect to the volume of moist air inside the converter:

• ```Pressure at A causes positive rotation of R relative to C``` — Increase in the moist air volume results in a positive rotation of port R relative to port C.

• ```Pressure at A causes negative rotation of R relative to C``` — Increase in the moist air volume results in a negative rotation of port R relative to port C.

Select method to determine rotation of port R relative to port C:

• ```Calculate from angular velocity of port R relative to port C``` — Calculate rotation from relative port angular velocities, based on the block equations. This is the default method.

• ```Provide input signal from Multibody joint``` — Enable the input physical signal port q to pass the rotation information from a Multibody joint. Use this method only when you connect the converter to a Multibody joint by using a Rotational Multibody Interface block. For more information, see How to Pass Position Information.

Rotational 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

Enabled when the Interface rotation parameter is set to ```Calculate from angular velocity of port R relative to port C```.

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

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

Displaced moist air volume per unit rotation of the moving interface.

Volume of moist air when the interface rotation is 0.

Cross-sectional area of the converter inlet, in the direction normal to the moist 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`.

## Version History

Introduced in R2018a