# Tank (G-IL)

Pressurized tank with variable gas and isothermal liquid volumes

Since R2023b

Libraries:
Simscape / Fluids / Isothermal Liquid / Tanks & Accumulators

## Description

The Tank (G-IL) block models the accumulation of mass and energy in a chamber with separate gas and isothermal liquid volumes. The total fluid volume is fixed, but the individual gas and isothermal liquid volumes can to vary. Two gas ports allow for gas flow and a variable number of isothermal liquid ports, ranging from one to six, allow for isothermal liquid flow. The isothermal liquid ports can be at different elevations.

The tank is pressurized, but the pressurization is not fixed. It changes during simulation corresponding to the pressure in the gas volume. The pressure rises when the pressure of the gas volume rises and falls when the pressure of the gas volume falls. The block assumes that the isothermal liquid volume is at equilibrium with the gas volume and its pressure is the same as that of the gas. The two fluid volumes go not exchange energy with each other, but energy exchanges with other components can occur through the gas ports.

### Isothermal Liquid Ports

You can specify the number of isothermal liquid ports using the Number of inlets parameter:

Number of inletsExposed isothermal liquid ports
`1`Port A2
`2`Ports A2 and B2
`3`Ports A2, B2, and C2
`4`Ports A2, B2, C2, and D2
`5`Ports A2, B2, C2, D2, and E2
`6`Ports A2, B2, C2, D2, E2, and F2

### Fluid Volumes

The total volume of the tank is the sum of the gas and isothermal liquid volumes that it contains,

`${V}_{\text{T}}={V}_{\text{L}}+{V}_{\text{G}},$`

where V is the volume and T, L, and G stand for total, liquid, and gas. Because the total volume is fixed, the time rate of change of the gas volume must be the reverse of the time rate of change for the isothermal liquid volume,

`${\stackrel{˙}{V}}_{\text{G}}=-{\stackrel{˙}{V}}_{\text{L}}.$`

The block calculates the time rate of change of the isothermal liquid volume by differentiating the expression

`${M}_{\text{L}}={\rho }_{\text{L}}{V}_{\text{L}},$`

where M is mass and ρ is density. The differentiation gives the mass flow rate into the isothermal liquid volume,

`${\stackrel{˙}{M}}_{\text{L}}={V}_{\text{L}}{\stackrel{˙}{\rho }}_{\text{L}}+{\stackrel{˙}{V}}_{\text{L}}{\rho }_{\text{L}}.$`

The rate of change of the isothermal liquid volume and, by extension, of the gas volume is

`${\stackrel{˙}{V}}_{\text{G}}=-{\stackrel{˙}{V}}_{\text{L}}\approx {V}_{\text{L}}\frac{{\stackrel{˙}{p}}_{\text{L}}}{{\rho }_{\text{L}}}\frac{d{\rho }_{L}}{dp}|-\frac{{\stackrel{˙}{M}}_{\text{L}}}{{\rho }_{\text{L}}},$`

where p is the pressure.

### Mass Balance

The rate of mass accumulation in each fluid volume is equal to the net mass flow rate into that fluid volume. In the isothermal liquid volume

`${\stackrel{˙}{M}}_{\text{L}}=\sum _{i=\text{A2,B2,}...\text{F2}}{\stackrel{˙}{m}}_{i},$`

where ML is the rate of mass accumulation in the isothermal liquid volume and ${\stackrel{˙}{m}}_{i}$ are the individual mass flow rates into that volume through the isothermal liquid ports A2, B2, C2, D2, E2, or F2.

In the gas volume

MG is the rate of mass accumulation in the gas volume and ${\stackrel{˙}{m}}_{i}$ are the individual mass flow rates into that volume through the gas ports A1 and B1. The rate of mass accumulation for the gas volume contains contributions from pressure, temperature, and volume change,

`${\stackrel{˙}{M}}_{\text{G}}={\frac{dM}{dp}|}_{\text{G}}{\stackrel{˙}{p}}_{\text{G}}+{\frac{dM}{dT}|}_{\text{G}}{\stackrel{˙}{T}}_{\text{G}}+{\stackrel{˙}{V}}_{\text{G}}{\rho }_{\text{G}},$`

where T is the temperature and the pressure and temperature derivatives depend on the type of gas specified in the Gas Properties (G) block. The equations section of the Translational Mechanical Converter (G) page defines the derivatives. The mass balance equation for the gas volume is

### Energy Balance

The rate of energy accumulation in the gas volume is

where:

• U is the total energy of the fluid volume.

• h is the fluid enthalpy.

• Q is the heat flow rate through the thermal port.

• ϕi are the energy flow rates through the fluid inlets.

The pressure and temperature derivatives depend on the type of gas specified in the Gas Properties (G) block. See the equations section of the Translational Mechanical Converter (G) page for the definitions.

### Momentum Balance

The block ignores flow resistance due to friction or other causes in both fluid volumes. The block also ignores the effect of elevation on inlet pressure, but only on the gas side. The gas inlet pressures are equal to each other and to the internal pressure of the gas volume:

`${p}_{\text{A1}}={p}_{\text{B1}}={p}_{\text{G}}.$`

The isothermal liquid inlet pressures are each a function of inlet depth. The internal pressure of the isothermal liquid volume is equal to the gas volume, pL = pG. The block includes dynamic pressures, pi,dyn, at the inlets by using the equation

`${p}_{i}+{p}_{i,\text{dyn}}={p}_{\text{G}}+{\rho }_{\text{L}}\left(y-{y}_{i}\right)g,$`

where y is the elevation of the isothermal liquid surface, yi is the elevation of the isothermal liquid inlet, and g is the gravitational constant. The term y - yi gives the depth of the isothermal liquid inlet with respect to the gas-isothermal liquid boundary. The dynamic pressure at each isothermal liquid inlet depends on the direction of flow at that inlet

where vi is the flow velocity.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables and Initial Conditions for Blocks with Finite Gas Volume.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

### Assumptions and Limitations

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

## Ports

### Output

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Physical signal output port that reports the volume of isothermal liquid in the tank, in m3.

Physical signal output port that reports the height of the isothermal liquid volume relative to the bottom of the tank, in m.

### Conserving

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Gas conserving port associated with the opening through which gas flows into or out of the tank.

Gas conserving port associated with the opening through which gas flows into or out of the tank.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

#### Dependencies

To enable this port, set Number of inlets to `2`, `3`, `4`, `5`, or `6`.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

#### Dependencies

To enable this port, set Number of inlets to `3`, `4`, `5`, or `6`.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

#### Dependencies

To enable this port, set Number of inlets to `4`, `5`, or `6`.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

#### Dependencies

To enable this port, set Number of inlets to `5` or `6`.

Isothermal liquid conserving port associated with the opening through which isothermal liquid flows into or out of the tank.

#### Dependencies

To enable this port, set Number of inlets to `6`.

Thermal conserving port associated with heat transfer at the tank wall for the gas volume.

## Parameters

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Number of isothermal liquid ports for the block.

Aggregate volume of the gas and isothermal liquid portions of the tank.

Choice of parameterization for the isothermal liquid volume. Select `Constant cross-sectional area` to specify a constant tank cross-sectional area. Select ```Tabulated data — volume vs. level``` to compute the isothermal liquid volume by interpolation or extrapolation of tabulated data.

Area of the tank cross-section. The block assumes this value is constant over the allowed range of fluid levels. The block uses this parameter to compute the volume of isothermal liquid inside the tank.

#### Dependencies

To enable this parameter, set Tank volume parameterization to ```Constant cross-sectional area```.

Vector of isothermal liquid levels at which to specify the isothermal liquid volume in the tank. The block uses this vector to construct a one-way lookup table for the isothermal liquid volume as a function of the isothermal liquid level.

#### Dependencies

To enable this parameter, set Tank volume parameterization to ```Tabulated data - volume vs. level```.

Vector of isothermal liquid volumes that correspond to the elements of the Liquid level vector parameter. The block uses this vector to construct a one-way lookup table for the isothermal liquid volume as a function of the isothermal liquid level.

#### Dependencies

To enable this parameter, set Tank volume parameterization to ```Tabulated data - volume vs. level```.

Two-element vector that specifies the flow areas of the gas inlets.

Height of the isothermal liquid inlet.

#### Dependencies

To enable this parameter, set Number of inlets to `1`.

Flow area of the isothermal liquid inlet.

#### Dependencies

To enable this parameter, set Number of inlets to `1`.

Vector of port heights for multiple enabled ports. The parameter name and vector length depend on the value of the Number of inlets parameter. Each element of the vector corresponds to an inlet port, starting with port A2. The default height for each inlet is `.1 m`. Each element of this vector must be greater than or equal to 0.

For example, if Number of inlets is `4`, the name of this parameter is Height vector for inlets A2, B2, C2, and D2 and the default value is `0.1 * ones(1, 4)` m.

#### Dependencies

To enable this parameter, set Number of inlets to `2`, `3`, `4`, `5`, or `6`.

Vector of cross-sectional areas for multiple enabled ports. The parameter name and vector length depend on the value of the Number of inlets parameter. Each element of the vector corresponds to an inlet port, starting with port A2. The default height for each inlet is `.01 m`. Each element of this vector must be greater than 0.

For example, if Number of inlets is `4`, the name of this parameter is Cross-sectional area vector for inlets A2, B2, C2, and D2 and the default value is ```0.01 * ones(1, 4)``` m2.

#### Dependencies

To enable this parameter, set Number of inlets to `2`, `3`, `4`, `5`, or `6`.

Whether to be notified if the tank fluid volume rises above the value of the Total tank volume parameter during simulation. Set this parameter to `Warning` to receive a warning when this occurs during simulation. Set the parameter to `Error` for the simulation to stop when this occurs.

Fill limit of the tank.

#### Dependencies

To enable this parameter, set Liquid volume above max capacity to either `Warning` or `Error`.

Value of the gravitational acceleration at the elevation of the tank. The block assumes this value is constant over the height of the tank.

## Version History

Introduced in R2023b