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Interface between gas and mechanical translational networks

**Library:**Simscape / Foundation Library / Gas / Elements

The Translational Mechanical Converter (G) block models an interface between a gas network and a mechanical translational network. The block converts gas pressure into mechanical force and vice versa. It can be used as a building block for linear actuators.

The converter contains a variable volume of gas. The pressure and temperature evolve based on
the compressibility and thermal capacity of this gas volume. The **Mechanical
orientation** parameter lets you specify whether an increase in the gas
volume results in a positive or negative displacement of port **R**
relative to port **C**.

Port **A** is the gas conserving port associated with the converter inlet.
Port **H** is the thermal conserving port associated with the
temperature of the gas inside the converter. Ports **R** and
**C** are the mechanical translational conserving ports associated
with the moving interface and converter casing, respectively.

Mass conservation equation is similar to that for the Constant Volume Chamber (G) block, with an additional term related to the change in gas volume:

$$\frac{\partial M}{\partial p}\cdot \frac{d{p}_{I}}{dt}+\frac{\partial M}{\partial T}\cdot \frac{d{T}_{I}}{dt}+{\rho}_{I}\frac{dV}{dt}={\dot{m}}_{A}$$

where:

$$\frac{\partial M}{\partial p}$$ is the partial derivative of the mass of the gas volume with respect to pressure at constant temperature and volume.

$$\frac{\partial M}{\partial T}$$ is the partial derivative of the mass of the gas volume with respect to temperature at constant pressure and volume.

*p*_{I}is the pressure of the gas volume. Pressure at port**A**is assumed equal to this pressure,*p*_{A}=*p*_{I}.*T*_{I}is the temperature of the gas volume. Temperature at port**H**is assumed equal to this temperature,*T*_{H}=*T*_{I}.*ρ*_{I}is the density of the gas volume.*V*is the volume of gas.*t*is time.$$\dot{m}$$

_{A}is the mass flow rate at port**A**. Flow rate associated with a port is positive when it flows into the block.

Energy conservation equation is also similar to that for the Constant Volume Chamber (G) block. The additional term accounts for the change in gas volume, as well as the pressure-volume work done by the gas on the moving interface:

$$\frac{\partial U}{\partial p}\cdot \frac{d{p}_{I}}{dt}+\frac{\partial U}{\partial T}\cdot \frac{d{T}_{I}}{dt}+{\rho}_{I}{h}_{I}\frac{dV}{dt}={\Phi}_{A}+{Q}_{H}$$

where:

$$\frac{\partial U}{\partial p}$$ is the partial derivative of the internal energy of the gas volume with respect to pressure at constant temperature and volume.

$$\frac{\partial U}{\partial T}$$ is the partial derivative of the internal energy of the gas volume with respect to temperature at constant pressure and volume.

Ф

_{A}is the energy flow rate at port**A**.*Q*_{H}is the heat flow rate at port**H**.*h*_{I}is the specific enthalpy of the gas volume.

The partial derivatives of the mass *M* and the internal energy
*U* of the gas volume, with respect to pressure and temperature at
constant volume, depend on the gas property model. For perfect and semiperfect gas models,
the equations are:

$$\begin{array}{l}\frac{\partial M}{\partial p}=V\frac{{\rho}_{I}}{{p}_{I}}\\ \frac{\partial M}{\partial T}=-V\frac{{\rho}_{I}}{{T}_{I}}\\ \frac{\partial U}{\partial p}=V\left(\frac{{h}_{I}}{ZR{T}_{I}}-1\right)\\ \frac{\partial U}{\partial T}=V{\rho}_{I}\left({c}_{pI}-\frac{{h}_{I}}{{T}_{I}}\right)\end{array}$$

where:

*ρ*_{I}is the density of the gas volume.*V*is the volume of gas.*h*_{I}is the specific enthalpy of the gas volume.*Z*is the compressibility factor.*R*is the specific gas constant.*c*_{pI}is the specific heat at constant pressure of the gas volume.

For real gas model, the partial derivatives of the mass *M* and the internal
energy *U* of the gas volume, with respect to pressure and temperature at
constant volume, are:

$$\begin{array}{l}\frac{\partial M}{\partial p}=V\frac{{\rho}_{I}}{{\beta}_{I}}\\ \frac{\partial M}{\partial T}=-V{\rho}_{I}{\alpha}_{I}\\ \frac{\partial U}{\partial p}=V\left(\frac{{\rho}_{I}{h}_{I}}{{\beta}_{I}}-{T}_{I}{\alpha}_{I}\right)\\ \frac{\partial U}{\partial T}=V{\rho}_{I}\left({c}_{pI}-{h}_{I}{\alpha}_{I}\right)\end{array}$$

where:

*β*is the isothermal bulk modulus of the gas volume.*α*is the isobaric thermal expansion coefficient of the gas volume.

The gas volume depends on the displacement of the moving interface:

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

where:

*V*_{dead}is the dead volume.*S*_{int}is the interface cross-sectional area.*x*_{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 gas volume 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 gas volume increases from dead volume.If

`Pressure at A causes negative displacement of R relative to C`

, the interface displacement decreases when the gas volume increases from dead volume.

Force balance across the moving interface on the gas volume 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.

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 Gas Volume.

The converter casing is perfectly rigid.

There is no flow resistance between port

**A**and the converter interior.There is no thermal resistance between port

**H**and the converter interior.The moving interface is perfectly sealed.

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