Tank (IL)

Tank in an isothermal liquid system

Since R2020a

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

Description

The Tank (IL) block models a container with up to six input ports, A through F, within an isothermal liquid system. The tank outputs fluid volume at port V and fluid level at port L as physical signals. The block models the hydrostatic pressure difference between the liquid surface and the inlet height level. The tank can be pressurized to a constant, user-specified value or to atmospheric pressure.

Fluid Volume

The volume of fluid in the tank is determined from the total mass flow into the tank:

$V = \frac{M}{ρ},$

where:

M is the total mass in the tank supplied by all ports.
ρ is the fluid density.

Due to the constant pressure in the tank, the liquid volume inside the tank changes based on mass flow rate. Note that the converse is true for pipes, where pressure is a function of fixed fluid volumes.

If the tank fluid volume exceeds the specified capacity of the tank, you can choose to be notified. Set the Liquid volume above max capacity parameter to Warning if you would like to receive a warning when this occurs during simulation. Set the parameter to Error if you would like the simulation to stop when this occurs.

Fluid Level

If Tank volume parameterization is set to Constant cross-section area, the fluid level in the tank is determined from the fluid volume V, due to the constant cross-sectional area of the tank. Otherwise, the fluid level can be specified as tabulated data in the Tabulated data - volume vs. level option.

When the level in the tank falls below the inlet height, the assumption that fluid entirely fills the volume of the connecting blocks may not be valid. Connections to a Pipe (IL) block, which is based on this assumption, may in this case return unphysical results. If you expect to model tank fluid levels below tank inlet height(s), connect the Tank (IL) block to your system with a Partially Filled Pipe (IL) block instead.

Like the Liquid volume above max capacity parameter, you can be notified if the tank fluid level falls below the height of the inlet port(s) during your simulation by changing the Liquid level below inlet height parameter setting.

Mass Flow Rate

If you set Number of inlets to a number greater than 1, the equations below apply to each port. The dynamic pressure for an inlet port, i, is

$p_{i, dyn} = {\begin{matrix} \frac{1}{2} ρ_{i} v_{i}^{2}, & if {\dot{m}}_{i} < 0 \\ 0, & if {\dot{m}}_{i} \geq 0 \end{matrix}$

where:

ρ_i is the fluid density.
v_i is the flow velocity.
${\dot{m}}_{i}$ is the mass flow rate into the tank fluid volume through the port.

The total pressure is

$p_{t o t a l} = P + p_{d y n} + Δ p_{e l e v, p o r t},$

where:

P is the value of the Tank pressurization parameter if the Pressurization specification parameter is Specified pressure. Otherwise, P is the atmospheric pressure.
Δp_elev,port is the hydrostatic pressure difference at the specified port Inlet height: $Δ p_{e l e v, p o r t} = ρ g L$ , where L is either the difference in height between the fluid level and the inlet height or zero, whichever is larger.

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.

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.

Examples

Partially Filled Pipe

The Partially Filled Pipe (IL) block used to model the emptying and filling of a tank in multiple configurations. You can use the live script provided with this example to understand the effect of different configurations.

Open Model

Assumptions and Limitations

When you set the Pressurization specification parameter to Variable pressure, the block assumes that variation in pressure occurs slowly and there is no pressure derivative in the mass and energy balance equations.

Ports

Conserving

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A — Liquid port
isothermal liquid

Tank inlet.

B — Liquid port
isothermal liquid

Optional tank inlet.

Dependencies

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

C — Liquid port
isothermal liquid

Optional tank inlet.

Dependencies

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

D — Liquid port
isothermal liquid

Optional tank inlet.

Dependencies

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

E — Liquid port
isothermal liquid

Optional tank inlet.

Dependencies

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

F — Liquid port
isothermal liquid

Optional tank inlet.

Dependencies

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

Input

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P — Tank pressure, `MPa`
physical signal

Tank pressure, specified as a physical signal input, in MPa.

Dependencies

To enable this port, set Pressurization specification to Variable pressure.

Output

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V — Liquid volume, `m^3`
physical signal

Liquid volume inside the tank in m^3, specified as a physical signal.

L — Liquid level, `m`
physical signal

Liquid level inside the tank in m, specified as a physical signal.

Parameters

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Number of inlets — Number of inlet ports
`1` (default) | positive integer between 1 and 6

Number of inlet ports. Setting this parameter to 2 or more exposes additional input ports.

Pressurization specification — Tank pressure specification method
`Atmospheric pressure` (default) | `Specified pressure` | `Variable pressure`

Method to specify the tank pressure. To define a non-atmospheric constant pressure, set this parameter to Specified pressure and specify the value with the Tank pressurization parameter. To specify a variable tank pressure, set this parameter to Variable pressure and supply the tank pressure as a physical signal at port P.

Tank pressurization — User-defined tank pressure
`0.101325 MPa` (default) | positive scalar

User-defined tank pressure.

Dependencies

To enable this parameter, set Pressurization specification to Specified pressure.

Tank volume parameterization — Tank area characteristics
`Constant cross-section area` (default) | `Tabulated data - volume vs. level`

Specifies tank area characteristics. This parameter is used to determine the fluid level in the tank. If you would like to model a tank with a variable cross-sectional area, you can provide data for tank volume and fluid level with the Tabulated data - volume vs. level option.

Tank cross-sectional area — Tank cross-sectional area
`1 m^2` (default) | positive scalar

Tank cross-sectional area.

Dependencies

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

Liquid level vector — Vector of tank fluid levels
`[0, 3, 5] m` (default) | 1-by-n vector

Vector of tank fluid levels for the tabular parameterization of a non-constant tank area. The values in this vector correspond one-to-one to values in the Volumetric flow rate vector parameter. Its elements are listed in ascending order. The elements must be positive and the first element must be 0.

Dependencies

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

Liquid volume vector — Vector of tank fluid volumes
`[0, 4, 6] m^3` (default) | 1-by-n vector

Vector of tank fluid volumes for the tabular parameterization of a non-constant tank area. The values in this vector correspond one-to-one to values in the Liquid level vector parameter. Its elements are listed in ascending order. The elements must be positive and the first element must be 0.

Dependencies

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

Inlet height — Height of inlet port
`0.1 m` (default) | positive scalar

Height of inlet port. The value must be greater than or equal to 0.

Dependencies

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

Inlet cross-sectional area — Cross-sectional area of the port inlet
`0.01 m^2` (default) | positive scalar

Cross-sectional area of the port inlet. This value must be greater than 0.

Height vector for inlets A and B — Vector of port heights for multiple enabled ports
`[.1, .1]` m (default) | 1-by-n vector

Vector of port heights for multiple enabled ports. If you have two or more ports enabled, the Inlet height parameter becomes a vector of values that correspond to the height of each inlet port, starting with port A. The parameter name and vector length depend on the value of the Number of inlets parameter. The default height for each inlet is .1 m. Each element of this vector must be greater than or equal to 0.

Dependencies

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

Cross-sectional area vector for inlets A and B — Vector of inlet areas for two enabled ports
`[.01, .01] m^2` (default) | 1-by-n vector

Vector of cross-sectional areas for multiple enabled ports. If you have two or more ports enabled, the Inlet cross-sectional area parameter becomes a vector of values that correspond to the cross-sectional area of each inlet, starting with port A. The parameter name will include all enabled ports. Each element of this vector must be greater than 0.

Dependencies

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

Liquid level below inlet height — Whether to be notified of low tank levels
`Error` (default) | `None` | `Warning`

Whether to be notified if the tank fluid level falls below the port inlet height during simulation. Set this parameter to Warning if you would like to receive a warning when this occurs during simulation. Set the parameter to Error if you would like the simulation to stop when this occurs.

Liquid volume above max capacity — Whether to be notified of high tank volume
`None` (default) | `Warning` | `Error`

Whether to be notified if the tank fluid volume rises above the tank maximum capacity during simulation. Set this parameter to Warning if you would like to receive a warning when this occurs during simulation. Set the parameter to Error if you would like the simulation to stop when this occurs.

Maximum tank capacity — Fill limit of the tank
`10 m^3` (default) | positive scalar

Fill limit of the tank.

Dependencies

To enable this parameter, set Liquid volume above max capacity to either:

Warning
Error

Gravitational acceleration — Acceleration of gravity constant
`9.81 m/s^2` (default) | positive scalar

Constant for the acceleration of gravity.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

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R2023b: Specify variable pressure

You can now specify variable tank pressurization for the Tank (IL) block. When you set Pressurization specification to Variable pressure, the block uses the values from the physical signal at port P in the dynamic pressure equation.

R2023b: Tank (IL) block calculates dynamic pressure directly

The Tank (IL) block no longer uses the Inlet pressure loss coefficient or Pressure loss coefficient vector parameters to calculate pressure loss. The block now calculates the dynamic pressure directly. If your model previously used values greater than 1 for the Inlet pressure loss coefficient or Pressure loss coefficient vector parameters, connect a Local Resistance (IL) block to the tank inlet or outlet to maintain the model behavior. Set the loss coefficient for the Local Resistance (IL) block to the value of the previous tank loss coefficient minus 1. If your model previously used values less than 1 for the Inlet pressure loss coefficient or Pressure loss coefficient vector parameters, the Tank (IL) block cannot recreate this behavior.

The block does not model inlet losses. Do not connect these blocks directly to a Tank (IL) block:

Tank (IL) blocks
Constant Volume Chamber (IL) blocks
Spring-Loaded Accumulator (IL) blocks
Gas-Charged Accumulator (IL) blocks

There must always be flow resistance, which can be modeled by blocks such as pipes, orifices, and local resistances, between two fluid volumes.

Tank (IL)

Description

Fluid Volume

Fluid Level

Mass Flow Rate

Variables

Examples

Partially Filled Pipe

Assumptions and Limitations

Ports

Conserving

A — Liquid port isothermal liquid

B — Liquid port isothermal liquid

Dependencies

C — Liquid port isothermal liquid

Dependencies

D — Liquid port isothermal liquid

Dependencies

E — Liquid port isothermal liquid

Dependencies

F — Liquid port isothermal liquid

Dependencies

Input

P — Tank pressure, MPa physical signal

Dependencies

Output

V — Liquid volume, m^3 physical signal

L — Liquid level, m physical signal

Parameters

Number of inlets — Number of inlet ports 1 (default) | positive integer between 1 and 6

Pressurization specification — Tank pressure specification method Atmospheric pressure (default) | Specified pressure | Variable pressure

Tank pressurization — User-defined tank pressure 0.101325 MPa (default) | positive scalar

Dependencies

Tank volume parameterization — Tank area characteristics Constant cross-section area (default) | Tabulated data - volume vs. level

Tank cross-sectional area — Tank cross-sectional area 1 m^2 (default) | positive scalar

Dependencies

Liquid level vector — Vector of tank fluid levels [0, 3, 5] m (default) | 1-by-n vector

Dependencies

Liquid volume vector — Vector of tank fluid volumes [0, 4, 6] m^3 (default) | 1-by-n vector

Dependencies

Inlet height — Height of inlet port 0.1 m (default) | positive scalar

Dependencies

Inlet cross-sectional area — Cross-sectional area of the port inlet 0.01 m^2 (default) | positive scalar

Height vector for inlets A and B — Vector of port heights for multiple enabled ports [.1, .1] m (default) | 1-by-n vector

Dependencies

Cross-sectional area vector for inlets A and B — Vector of inlet areas for two enabled ports [.01, .01] m^2 (default) | 1-by-n vector

Dependencies

Liquid level below inlet height — Whether to be notified of low tank levels Error (default) | None | Warning

Liquid volume above max capacity — Whether to be notified of high tank volume None (default) | Warning | Error

Maximum tank capacity — Fill limit of the tank 10 m^3 (default) | positive scalar

Dependencies

Gravitational acceleration — Acceleration of gravity constant 9.81 m/s^2 (default) | positive scalar

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

R2023b: Specify variable pressure

R2023b: Tank (IL) block calculates dynamic pressure directly

See Also

A — Liquid port
isothermal liquid

B — Liquid port
isothermal liquid

C — Liquid port
isothermal liquid

D — Liquid port
isothermal liquid

E — Liquid port
isothermal liquid

F — Liquid port
isothermal liquid

P — Tank pressure, `MPa`
physical signal

V — Liquid volume, `m^3`
physical signal

L — Liquid level, `m`
physical signal

Number of inlets — Number of inlet ports
`1` (default) | positive integer between 1 and 6

Pressurization specification — Tank pressure specification method
`Atmospheric pressure` (default) | `Specified pressure` | `Variable pressure`

Tank pressurization — User-defined tank pressure
`0.101325 MPa` (default) | positive scalar

Tank volume parameterization — Tank area characteristics
`Constant cross-section area` (default) | `Tabulated data - volume vs. level`

Tank cross-sectional area — Tank cross-sectional area
`1 m^2` (default) | positive scalar

Liquid level vector — Vector of tank fluid levels
`[0, 3, 5] m` (default) | 1-by-n vector

Liquid volume vector — Vector of tank fluid volumes
`[0, 4, 6] m^3` (default) | 1-by-n vector

Inlet height — Height of inlet port
`0.1 m` (default) | positive scalar

Inlet cross-sectional area — Cross-sectional area of the port inlet
`0.01 m^2` (default) | positive scalar

Height vector for inlets A and B — Vector of port heights for multiple enabled ports
`[.1, .1]` m (default) | 1-by-n vector

Cross-sectional area vector for inlets A and B — Vector of inlet areas for two enabled ports
`[.01, .01] m^2` (default) | 1-by-n vector

Liquid level below inlet height — Whether to be notified of low tank levels
`Error` (default) | `None` | `Warning`

Liquid volume above max capacity — Whether to be notified of high tank volume
`None` (default) | `Warning` | `Error`

Maximum tank capacity — Fill limit of the tank
`10 m^3` (default) | positive scalar

Gravitational acceleration — Acceleration of gravity constant
`9.81 m/s^2` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.