Interface between thermal liquid and mechanical translational networks

**Library:**Simscape / Foundation Library / Thermal Liquid / Elements

The Translational Mechanical Converter (TL) block models an interface between a thermal liquid network and a mechanical rotational network. The block converts thermal liquid 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 liquid. The temperature evolves based on the
thermal capacity of this volume. If **Model dynamic compressibility** is set
to `On`

, then the pressure also evolves based on the dynamic
compressibility of the liquid volume. If **Mechanical orientation** is set to
`Positive`

, then an increase in the liquid 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 liquid volume results in a negative displacement of port
**R** relative to port **C**.

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

The mass conservation equation in the mechanical converter volume is

$${\dot{m}}_{\text{A}}=\epsilon \text{\hspace{0.17em}}\rho S\text{\hspace{0.17em}}v+\{\begin{array}{cc}0,& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{off}\\ V\rho \left(\frac{1}{\beta}\frac{dp}{dt}+\alpha \frac{dT}{dt}\right),& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{on}\end{array}$$

where:

$${\dot{m}}_{\text{A}}$$ is the liquid mass flow rate into the converter through port A.

*ε*is the mechanical orientation of the converter (`1`

if positive,`-1`

if negative).*ρ*is the liquid mass density.*S*is the cross-sectional area of the converter interface.*v*is the translational velocity of the converter interface.*V*is the liquid volume inside the converter.*β*is the liquid bulk modulus inside the converter.*α*is the coefficient of thermal expansion of the liquid.*p*is the liquid pressure inside the converter.*T*is the liquid temperature inside the converter.

The momentum conservation equation in the mechanical converter volume is

$$F=-\epsilon \left(p-{p}_{\text{Atm}}\right)S$$

where:

*F*is the force the liquid exerts on the converter interface.*p*_{Atm}is the atmospheric pressure.

The energy conservation equation in the mechanical converter volume is

$$\frac{d(\rho uV)}{dt}={\varphi}_{\text{A}}+{Q}_{H}-pS\epsilon v,$$

where:

*u*is the liquid internal energy.*ϕ*_{A}is the total energy flow rate into the mechanical converter volume through port A.*Q*_{H}is the heat flow rate into the mechanical converter volume.

Converter walls are not compliant. They cannot deform regardless of internal pressure and temperature.

The converter contains no mechanical hard stops. To include hard stops, use the Translational Hard Stop block.

The flow resistance between the inlet and the interior of the converter is negligible.

The thermal resistance between the thermal port and the interior of the converter is negligible.

The kinetic energy of the fluid in the converter is negligible.