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Thermal liquid container with variable fluid volume

**Library:**Simscape / Fluids / Thermal Liquid / Tanks & Accumulators

The Tank (TL) block models a thermal liquid container with a variable fluid volume. The absolute pressure of the tank fluid volume is assumed constant and equal to the value specified in the block dialog box. In the special case that the tank pressurization is equal to atmospheric pressure, the block represents a vented tank.

The tank can exchange energy with its surroundings, allowing its internal temperature and pressure to evolve over time. Heat transfer occurs via convection, as liquid enters or exits the chamber, and conduction, as thermal energy flows through the tank walls and the liquid itself at the tank inlets.

**Tank Schematic**

The tank can have up to six input ports, **A** through
**F**. The pressure at the tank inlets is the sum of the constant
tank pressurization specified in the block dialog box and the hydrostatic pressure due
to the inlet height.

The tank model accounts for heat transfer through the tank wall, associated with
thermal conserving port **H**. The temperature defined at this port is
the temperature of the tank fluid volume.

The tank fluid volume is computed from the total fluid mass at each time step:

$$V=\frac{m}{\rho},$$

where:

*V*is the tank fluid volume.*m*is the tank fluid mass.*ρ*is the tank fluid density.

The mass conservation equation in the tank fluid volume is

$$\dot{m}={\dot{m}}_{A},$$

where:

$$\dot{m}$$ is the net mass flow rate into the tank.

$${\dot{m}}_{A}$$ is the mass flow rate into the tank fluid volume through the inlet

**A**.

The momentum conservation equation in the tank fluid volume is

$${p}_{A}+{p}_{dyn}={p}_{Ref}+\rho g\left(y-{y}_{A}\right),$$

where:

*p*_{A}is the fluid pressure at inlet**A**.*p*_{Ref}is the constant tank pressurization.*p*_{dyn}is the dynamic pressure:$${p}_{dyn}=\{\begin{array}{ll}0,\hfill & {\dot{m}}_{A}\ge 0\hfill \\ \frac{{\dot{m}}_{A}^{2}}{2{\rho}_{A}{S}_{A}^{2}},\hfill & {\dot{m}}_{A}<0\hfill \end{array}$$

*ρ*_{A}is the liquid density at port**A**.*S*_{A}is the tank inlet area.*g*is the gravitational constant.*y*is the tank level, or height, relative to the tank bottom.*y*_{A}is the tank inlet elevation relative to the tank bottom.

The energy conservation equation in the tank fluid volume is

$$m\left({C}_{p}-h\alpha \right)\dot{T}={\varphi}_{A}-{\dot{m}}_{A}h+Q,$$

where:

*C*_{p}is the fluid thermal capacity.*α*is the fluid isobaric bulk modulus.*T*is the fluid temperature.*Φ*_{A}is the energy flow rate into the tank through port**A**.*h*is the fluid enthalpy.*Q*is the thermal energy flow rate into the tank through port**H**.

The tank pressure is constant and uniform throughout the tank volume. The tank elevation head affects only the inlet pressure calculations.

Fluid momentum is lost at the tank inlet due to the sudden expansion into the tank volume.

**Note**

The tank fluid level should remain above the port height at all times. If you have
not set **Liquid level below inlet height** to
`Warn`

or `Error`

and the
liquid level falls below this height, your simulation may return inaccurate results
when fluid flows out of the tank. Connected components in the thermal liquid library
are assumed to be fully filled with liquid throughout the simulation.