# Tank (TL)

Thermal liquid container with variable fluid volume

## Library

Thermal Liquid/Tanks & Accumulators

## Description

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 has one default inlet, labeled A, and two optional inlets, labeled B and C. 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.

To use the optional tank inlets, right-click the block and select Simscape > Block choices. Then, select Two inlets to add port B or Three inlets to add ports B and C. Port A is always exposed.

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.

### Tank 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.

### Mass Balance

The mass conservation equation in the tank fluid volume is

`$\stackrel{˙}{m}={\stackrel{˙}{m}}_{A},$`
where:

• $\stackrel{˙}{m}$ is the net mass flow rate into the tank.

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate into the tank fluid volume through the inlet A.

### Momentum Balance

The momentum conservation equation in the tank fluid volume is

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

• pA is the fluid pressure at inlet A.

• pRef is the constant tank pressurization.

• pdyn is the dynamic pressure:

`${p}_{dyn}=\left\{\begin{array}{ll}0,\hfill & {\stackrel{˙}{m}}_{A}\ge 0\hfill \\ \frac{{\stackrel{˙}{m}}_{A}^{2}}{2{\rho }_{A}{S}_{A}^{2}},\hfill & {\stackrel{˙}{m}}_{A}<0\hfill \end{array}$`

• ρA is the liquid density at port A.

• SA is the tank inlet area.

• g is the gravitational constant.

• y is the tank level, or height, relative to the tank bottom.

• yA is the tank inlet elevation relative to the tank bottom.

### Energy Balance

The energy conservation equation in the tank fluid volume is

`$m\left({C}_{p}-h\alpha \right)\stackrel{˙}{T}={\varphi }_{A}-{\stackrel{˙}{m}}_{A}h+Q,$`
where:

• Cp is the fluid thermal capacity.

• α is the fluid isobaric bulk modulus.

• T is the fluid temperature.

• ΦA 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.

## Assumptions and Limitations

• 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.

## Parameters

### Parameters Tab

Pressurization specification

Tank pressurization type. Select `Atmospheric pressure` to model a vented tank. Select `Specified pressure` to model a tank at a custom constant pressure.

Tank pressurization

Absolute pressure in the tank. This parameter is visible only when the Pressurization specification parameter is set to `Specified pressure`. The default value, corresponding to atmospheric pressure, is `0.101325` MPa.

Maximum tank capacity

Tank fluid volume in a fully filled state. The default value is `10` m^3.

Tank volume parameterization

Parameterization for calculating the thermal liquid volume as a function of tank level. The default setting is ```Constant cross-sectional area```.

Select `Constant cross-sectional area` to set the thermal liquid volume equal to the product of the tank level and cross-sectional area. Select ```Tabulated data — Volume vs. level``` to directly specify the thermal liquid volume as a function of tank level, e.g., to model a tank of arbitrary geometry.

Tank cross-sectional area

Cross-sectional area for tank fluid volume calculations. This area is assumed uniform along the tank height. This parameter is visible only when the Pressurization specification parameter is set to `Specified pressure`. The default value is `1` m^2.

Liquid level vector

Vector of tank levels at which to specify the thermal liquid volume. The tank level is the thermal liquid height relative to the tank bottom. The block uses this vector to construct a volume-level 1-D lookup table.

This parameter is visible only when the Pressurization specification parameter is set to ```Tabulated data — Volume vs. level```. The default vector is `[0.0,3.0,5.0]`.

Liquid volume vector

Vector of thermal liquid volumes corresponding to the values specified in the Liquid level vector parameter. The block uses this vector to construct a volume-level 1-D lookup table.

This parameter is visible only when the Pressurization specification parameter is set to ```Tabulated data — Volume vs. level```. The default vector is `[0.0,4.0,6.0]`

Inlet height

Tank inlet elevation for elevation head calculations. If the optional ports are exposed, this parameter is a vector with the inlet elevations. The default value is `0.01` m^2.

Inlet cross-sectional area

Flow cross-sectional area of the tank inlets. If the optional ports are exposed, this parameter is a vector with the inlet cross-sectional areas. The default value is `0.01` m^2.

Gravitational acceleration

Gravitational acceleration constant for elevation head calculations. The default value is `9.81` m/s^2.

### Variables Tab

Liquid level

Height of the thermal liquid volume in the accumulator at the start of simulation. The default value is `5` m.

Volume of liquid

Volume of thermal liquid in the accumulator at the start of simulation. The default value is `5` m^3.

Mass of liquid

Mass of thermal liquid in the accumulator at the start of simulation. The default value is `5e+3` kg.

Temperature of liquid volume

Temperature in the thermal liquid chamber at the start of simulation. The default value is `293.15` K.

## Ports

• A — Thermal liquid conserving port representing the tank inlet A

• B — Thermal liquid conserving port representing the optional tank inlet B

• C — Thermal liquid conserving port representing the optional tank inlet C

• H — Thermal conserving port representing heat transfer through the tank wall

• V — Physical signal output port for the tank fluid volume measurement

• L — Physical signal output port for the tank fluid level measurement

• T — Physical signal output port for the tank fluid temperature measurement