Tank (G-IL)

Pressurized tank with variable gas and isothermal liquid volumes

Since R2023b

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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 inlets	Exposed 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,

$${\dot{V}}_{\text{G}}=-{\dot{V}}_{\text{L}}.$$

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,

$${\dot{M}}_{\text{L}}=V_{\text{L}}{\dot{\rho }}_{\text{L}}+{\dot{V}}_{\text{L}}{\rho }_{\text{L}}.$$

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

$${\dot{V}}_{\text{G}}=-{\dot{V}}_{\text{L}}\approx V_{\text{L}}\frac{{\dot{p}}_{\text{L}}}{{\rho }_{\text{L}}}\frac{d{\rho }_L}{dp}|-\frac{{\dot{M}}_{\text{L}}}{{\rho }_{\text{L}}},$$

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

$${\dot{M}}_{\text{L}}={\displaystyle \sum _{i=\text{A2,B2,}\mathrm{...}\text{F2}}{\dot{m}}_i},$$

where M_L is the rate of mass accumulation in the isothermal liquid volume and $${\dot{m}}_i$$ 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

$${\dot{M}}_{\text{G}}={\displaystyle \sum _{i=\text{A1, B1}}{\dot{m}}_i},$$

M_G is the rate of mass accumulation in the gas volume and $${\dot{m}}_i$$ 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,

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

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

$${\dot{p}}_{\text{G}}{\frac{dM}{dp}|}_{\text{G}}+{\dot{T}}_{\text{G}}{\frac{dM}{dT}|}_{\text{G}}+{\dot{p}}_{\text{G}}\frac{{\rho }_{\text{G}}}{{\rho }_L}{V}_{\text{L}}\frac{d{\rho }_L}{dp}|={\displaystyle \sum _{i=\text{A1, B1}}{\dot{m}}_i}+\frac{{\rho }_{\text{G}}}{{\rho }_{\text{L}}}{\displaystyle \sum _{i=\text{A2, B2,}\mathrm{...}\text{F2}}{\dot{m}}_i},$$

Energy Balance

The rate of energy accumulation in the gas volume is

$${\dot{p}}_{\text{G}}{\frac{dU}{dp}|}_{\text{G}}+{\dot{T}}_{\text{G}}{\frac{dU}{dT}|}_{\text{G}}+{\dot{p}}_{\text{G}}\frac{{\rho }_{\text{G}}}{{\rho }_L}{h}_{\text{G}}{V}_{\text{L}}\frac{d{\rho }_L}{dp}|=Q_{\text{H1}}+{\displaystyle \sum _{i=\text{A1, B1}}{\varphi }_i}+\frac{{\rho }_{\text{G}}}{{\rho }_{\text{L}}}{h}_{\text{G}}{\displaystyle \sum _{i=\text{A2, B2,}\mathrm{...}\text{F2}}{\dot{m}}_i}$$

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.

• ϕ_i 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, p_L = p_G. The block includes dynamic pressures, p_i,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, y_i is the elevation of the isothermal liquid inlet, and g is the gravitational constant. The term y - y_i 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

$$p_{i,\text{dyn}}=\{\begin{array}{cc}\frac{1}{2}{\rho }_i{v}_i^2,& \text{if }{\dot{m}}_i<0\\ 0,& \text{if }{\dot{m}}_i\ge 0\end{array}$$

where v_i 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.

Examples

Electric Vehicle Thermal Management

Model the thermal management system of a battery electric vehicle.

• Open Model

EV Battery Cooling System

This demo shows an Electric Vehicle (EV) battery cooling system. The battery packs are located on top of a cold plate which consists of cooling channels to direct the cooling liquid flow below the battery packs. The heat absorbed by the cooling liquid is transported to the Heating-Cooling Unit. The Heating-Cooling Unit consists of three branches to switch operating modes to cool and heat the battery. The Heater represents an electrical heater for fast heating of the batteries under low temperature conditions. The Radiator uses air-cooling and/or heating when the batteries are operated stably. The Refrigerant system is used for cooling the overheated batteries. The refrigeration cycle is represented by the amount of heat flow extracted from the cooling liquid. The system is simulated under either FTP-75 drive cycle or fast charge scenarios with different environment temperatures.

• Open Model

Ports

Output

V — Isothermal liquid volume, m^3

physical signal

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

L — Isothermal liquid level, m

physical signal

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

Conserving

A1 — Gas inlet

gas

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

B1 — Gas inlet

gas

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

A2 — Isothermal liquid inlet

isothermal liquid

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

B2 — Isothermal liquid inlet

isothermal liquid

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.

C2 — Isothermal liquid inlet

isothermal liquid

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.

D2 — Isothermal liquid inlet

isothermal liquid

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.

E2 — Isothermal liquid inlet

isothermal liquid

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.

F2 — Isothermal liquid inlet

isothermal liquid

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.

H1 — Heat transfer

thermal

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

Parameters

Number of inlets — Number of isothermal liquid ports

1 (default) | 2 | 3 | 4 | 5 | 6

Number of isothermal liquid ports for the block.

Total tank volume — Combined gas and isothermal liquid volume

10 m^3 (default) | positive scalar

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

Tank volume parameterization — Parameterization for isothermal liquid volume

Constant cross-sectional area (default) | Tabulated data — volume vs. level

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.

Tank cross-sectional area — Area of constant tank cross-section

1 m^2 (default) | positive scalar

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.

Liquid level vector — Isothermal liquid levels at which to specify isothermal liquid volume

[0, 3, 5] m (default) | vector

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.

Liquid volume vector — Isothermal liquid volume at specified isothermal liquid levels

[0, 4, 6] m^3 (default) | vector

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.

Cross-sectional area vector for inlets A1 and B1 — Flow areas of gas inlets

[.01, .01] m^2 (default) | vector

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

Inlet height at port A2 — Height of isothermal liquid inlet

0.1 m (default) | positive scalar

Height of the isothermal liquid inlet.

Dependencies

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

Cross-sectional area at port A2 — Flow area of isothermal liquid inlet

0.01 m^2 (default) | positive scalar

Flow area of the isothermal liquid inlet.

Dependencies

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

Height vector for inlets A2 and B2 — Vector of port heights for ports

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

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.

Cross-sectional area vector for inlets A2 and B2 — Vector of inlet areas for ports

[.01, .01] m^2 (default) | 1-by-n vector

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.

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 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.

Maximum tank liquid capacity — Fill limit of 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 or Error.

Gravitational acceleration — Gravitational acceleration constant

9.81 m/s^2 (default) | positive scalar

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

Extended Capabilities

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

Version History

Introduced in R2023b