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. If **Mechanical orientation** is
set to `Positive`

, then an increase in the
gas volume results in a positive displacement of port R relative to
port C. If **Mechanical orientation** is set to `Negative`

,
then an increase in the gas volume results in a 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`Positive`

,*ε*_{int}= 1. If**Mechanical orientation**is`Negative`

,*ε*_{int}= –1.

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.

Use the **Variables** tab in the block dialog
box (or the **Variables** section in the block Property
Inspector) to set the priority and initial target values for the block
variables prior to simulation. 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.

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