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:

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

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 have more than one port enabled, the equations below apply to each port. The mass flow rate at the inlet port is:

$${\dot{m}}_{port}=A_{port}\frac{\sqrt{2\rho }}{\sqrt{\xi }}\frac{\Delta p_{port}}{{\left[\Delta p_{port}{}^2+\Delta p_{port,crit}^2\right]}^{1/4}},$$

where:

• A_port is the Inlet cross-sectional area.

• ρ is the fluid density.

• ζ is the Inlet pressure loss coefficient.

The inlet pressure difference due to inlet losses is:

$$\Delta p_{port}=p_{port}-(P+\Delta p_{elev,port}),$$

where:

• p_port is the pressure at the inlet port.

• P is the Tank pressurization if the Pressurization specification parameter is set to Specified pressure. Otherwise, P is the atmospheric pressure.

• Δp_elev,port is the hydrostatic pressure difference at the specified port Inlet height: $$\Delta p_{elev,port}=\rho gL$$, where L is either the difference in height between the fluid level and the inlet height or zero, whichever is larger.

The critical pressure difference, Δp_crit, is the pressure differential associated with the critical Reynolds number, Re_crit, which is the point of transition between laminar and turbulent flow in the fluid:

$$\Delta p_{crit}=\frac{\pi \rho P{R}_{loss}}{8A_{port}}{\left(\nu {\mathrm{Re}}_{crit}\right)}^2,$$

where ν is the fluid kinematic viscosity.

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

Ports

Conserving

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.

Output

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

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

Atmospheric pressure (default) | Specified pressure

Specifies a constant tank pressure. You can define a non-atmospheric pressure by selecting Specified pressure and defining the value in Tank pressurization.

Tank pressurization — User-defined tank pressure

0.101325 MPa (default) | positive scalar

User-defined tank 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 in 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.

Inlet pressure loss coefficient — Loss coefficient for pressure at inlet port

1.2 (default) | positive scalar

Loss coefficient for pressure at inlet port. This value is used for calculating the hydrostatic pressure at the inlet and determining the fluid level minimum conditions.

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.

Pressure loss coefficient vector for inlets A and B — Vector of pressure loss coefficients for tank inlets

[1.2, 1.2] (default) | 1-by-n vector

Vector of pressure loss coefficients for multiple enabled ports. If you have two or more ports enabled, the Pressure loss coefficient parameter becomes a vector of values corresponding to the loss coefficient for each inlet port, 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