Thermal Liquid Settings (TL)

Physical properties of a thermal liquid

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Libraries:
Simscape / Foundation Library / Thermal Liquid / Utilities

Description

The Thermal Liquid Settings (TL) block provides the physical properties of a fluid to a thermal liquid network. The properties are global: they apply not to one component but to all those that comprise the network. Every thermal liquid network in a model must connect to exactly one instance of this block. Among the properties specified in this block are:

• Thermodynamic properties — Density, specific internal energy, and specific heat

• Derivative properties — Bulk modulus and thermal expansion coefficient

• Transport properties — Kinematic viscosity and thermal conductivity

Each fluid property is specified in tabulated form against both temperature and pressure or against temperature alone. Use the option to ignore pressure-induced changes if those changes are known to be negligible, if pressure is expected to be nearly constant, or if fluid property data is accessible in terms of temperature only.

Data Visualization

The block provides the option to plot the specified fluid properties over their temperature and pressure domains. To create the plots, right-click the block and select Foundation Library > Plot Fluid Properties. Use the drop-down list located at the top of the plot to select the fluid property to visualize. Click the Reload button to regenerate a plot following a block parameter update.

Use the plots to visualize the dependences of the fluid properties on pressure and temperature—for example, to more easily catch anomalies in the specified data. Most fluid properties are shown as variable over pressure only if they are specified as functions of pressure. Exceptions include density, which derives a pressure dependence from the bulk modulus and thermal expansion coefficient, and any properties calculated from density, such as specific heat.

Thermal Liquid Properties Plot

Parameterizations

The block provides several parameterizations for the independent state variables, density, and specific internal energy. The parameterization that you select for each determines the data that you must obtain and the state variables with respect to which you must specify it. The setting of the Table dimensions parameter affects which parameters you see in other tabs.

Pressure and Temperature

Pressure and temperature are the across variables of the thermal liquid domain. As such, they are the natural choice of independent state variables against which to specify all other fluid properties. The block provides two parameterizations based on these state variables. They are available through the Table dimensions parameter:

• 2D tables based on temperature and pressure — Provide tabulated data against both temperature and pressure. The region of valid temperatures and pressures is specified in terms of minimum and maximum values (I in the figure) or in terms of a validity matrix (II).

  Validity Region Types

  

• 1D vectors based on temperature — Provide tabulated data against temperature and ignore any dependences on pressure. The region of valid temperatures and pressures is specified in terms of minimum and maximum values only. The bulk modulus provides a pressure dependence to density and to any fluid properties calculated from density.

Density and Derivatives

The block provides three types of parameterizations for density and for the two derivative parameters that the density calculation often depends on—the isothermal bulk modulus and the isobaric thermal expansion coefficient. Options include:

• Density, bulk modulus, and thermal expansion coefficient tables — Provide tabulated data for density, the bulk modulus, and the thermal expansion coefficient. The data must be specified against both temperature and pressure. The Table dimensions parameter must be set to 2D tables based on temperature and pressure.

• Density table/vector — Provide tabulated data for density against temperature (and, in the 2D case, pressure). The block computes the isothermal bulk modulus and isobaric thermal expansion coefficient from the tabulated data using the finite-difference method. The isothermal bulk modulus β is defined as:

  $$\frac{1}{\beta }=\frac{1}{\rho }{\left(\frac{\partial \rho }{\partial p}\right)}_T,$$

  where ρ is density, T is temperature, and p is pressure. The isobaric thermal expansion coefficient α is defined as:

  $$\alpha =-\frac{1}{\rho }{\left(\frac{\partial \rho }{\partial T}\right)}_p.$$

• Reference Density — Provide the density, bulk modulus, and thermal expansion coefficient at a known temperature (and, in the 2D case, pressure). The block uses an analytical expression to calculate the density at other temperatures and pressures. The calculation is based on the expression:

  $$\text{ln}\left(\frac{\rho }{{\rho }_{\text{R}}}\right)=-\alpha \left(T-T_{\text{R}}\right)+\frac{p-p_{\text{R}}}{\beta },$$

  where the subscript R denotes a reference quantity (specified in the block dialog box).

Specific Internal Energy

As in the case of density, the block provides three types of parameterization for the specific internal energy and for a related quantity from which it can be computed—the specific heat. Options include:

• Specific internal energy and specific heat tables — Provide tabulated data for the specific internal energy and the specific heat coefficient. The data must be specified against both temperature and pressure. The Table dimensions parameter must be set to 2D tables based on temperature and pressure.

• Specific internal energy table/vector — Provide tabulated data for the specific internal energy against temperature (and, in the 2D case, pressure). The block computes the specific heat coefficient from the specific internal energy data. The calculation is based on the expression:

  $$c_p\left(T,p\right)={\left(\frac{\partial u}{\partial T}\right)}_p+\frac{p\alpha }{\rho },$$

  where c_p is the specific heat coefficient, and u is the specific internal energy.

• Specific heat coefficient table/vector — Provide tabulated data for the specific heat coefficient against temperature (and, in the 2D case, pressure). The block computes the specific internal energy from the specific heat coefficient data. The calculation is based on the expression:

  $$u\left(T,p\right)={\displaystyle {\int }_{T_R}^T\left(c_p\left(T,p\right)-\frac{p\alpha \left(T,p\right)}{\rho \left(T,p\right)}\right)dT+u_R},$$

  where the subscript R denotes a reference quantity. The value of u_R is set to zero, a suitable choice because it is the difference in specific internal energy, rather than its value, that is relevant for simulation. The value of u can differ from that provided in other sources, such as the REFPROP fluids database.

Specific Heat at Constant Volume

Specific heat at constant volume, c_v, must be greater than zero. The block derives this quantity from the other fluid properties:

$$c_v=c_p-\frac{T{\alpha }^2\beta }{\rho }.$$

If you get a warning that specific heat at constant volume must be greater than zero, this equation can help you understand how to avoid negative c_v values by adjusting the fluid properties that you provide to the block.

You can also use data visualization plots. Right-click the block, select Foundation Library > Plot Fluid Properties, and then, from the drop-down list at the top of the plot, select Specific Heat at Constant Volume (kJ/(K*kg)). If c_v is negative only in a small pressure and temperature region of the plot and you are not simulating the model in that region, you can cut out these pressure and temperature ranges from the fluid property tables.

Examples

Engine Cooling System

Model a basic engine cooling system using custom thermal liquid blocks. A fixed-displacement pump drives water through the cooling circuit. Heat from the engine is absorbed by the water coolant and dissipated through the radiator. The system temperature is regulated by the thermostat, which diverts flow to the radiator only when the temperature is above a threshold.

• Open Model

Optimal Pipeline Geometry for Heated Oil Transportation

Model shows the opposing effects of viscous warming and conductive cooling on the temperature of a buried pipeline segment for heated oil transportation. A requirement for these systems is for the crude oil to stay well above the pour point to provide a continuous steady flow. The system is modeled using the Thermal Liquid Foundation Library. Crude oil thermodynamic properties are stored in workspace matrices and are used to populate the Thermal Liquid Settings block mask parameters.

• Open Model

Ports

Conserving

A — Thermal liquid network connector

thermal liquid

Port identifying the thermal liquid network to which the specified fluid properties apply.

Parameters

Temperature and Pressure

Table dimensions — Dimensions of the fluid property tables

2D tables based on temperature and pressure (T,p) (default) | 1D vectors based on temperature (T)

Dimensions of the fluid property tables. This parameter determines whether the fluid properties are variable or constant with pressure. Select 1D vectors based on temperature (T) to ignore the pressure dependences of the fluid properties.

Temperature vector — Reference temperatures at which to specify the fluid properties

[273.1600 : 10 : 373.16]' K (default) | M-element column vector with units of temperature

Vector of temperatures at which to specify the values of the fluid properties. Each temperature corresponds to a row of a fluid property table.

Pressure vector — Reference pressures at which to specify the fluid properties

[0.01, 0.1, 5 : 5 : 50] MPa (default) | N-element row vector with units of pressure

Vector of pressures at which to specify the values of the fluid properties. Each pressure corresponds to a column of a fluid property table.

Dependencies

This parameter is active only when the Table dimensions parameter is set to 2D vectors based on temperature and pressure (T,p).

Atmospheric pressure — Absolute pressure of the thermal liquid network environment

0.101325 MPa (default) | scalar with units of pressure

Absolute pressure of the outside environment of the attached thermal liquid network. The default value corresponds to the earth's standard atmospheric pressure.

Valid pressure-temperature region parameterization — Specification method for the pressure-temperature validity region

Specified minimum and maximum values (default) | Validity matrix

Specification method for the pressure-temperature validity region. You can specify the limits of a square pressure-temperature region or a matrix of validity values for an arbitrarily shaped pressure-temperature region.

Dependencies

This parameter is active only when the Table dimensions parameter is set to 2D vectors based on temperature and pressure (T,p).

Minimum valid temperature — Lowest temperature allowed in a model

273.16 K (default) | scalar with units of temperature

Lowest temperature that the attached thermal liquid network is allowed to reach during simulation.

Maximum valid temperature — Highest temperature allowed in a model

363.16 K (default) | scalar with units of temperature

Highest temperature that the attached thermal liquid network is allowed to reach during simulation.

Minimum valid pressure — Lowest pressure allowed in a model

0.05 MPa (default) | scalar with units of pressure

Lowest pressure that the attached thermal liquid network is allowed to reach during simulation.

Maximum valid pressure — Highest pressure allowed in a model

50 MPa (default) | scalar with units of pressure

Highest pressure that the attached thermal liquid network is allowed to reach during simulation.

Pressure-temperature validity matrix — Matrix of allowed and disallowed pressure-temperature conditions

11-by-12 matrix of zeros and ones (default) | unitless M-by-N matrix

Matrix of validity values for the various temperature-pressure data points. A value of 1 denotes a valid point and a value of 0 denotes an invalid point.

Dependencies

This parameter is active only when the Valid pressure-temperature region parameterization parameter is set to Validity matrix.

Pressure and temperature outside valid range — Whether to notify when pressure or temperature are outside valid range

Error (default) | Warning | None

Select what happens if the fluid pressure or temperature go beyond the valid range during simulation:

• None ― The block does not return an error if the properties go out of range.

• Warning ― The block issues a warning, but continues the simulation.

• Error ― The block returns an error and stops the simulation.

Density

Density parameterization — Specification method for the fluid density

Density, bulk modulus and thermal expansion tables - rho(T,p), beta(T,p), alpha(T,p) (default) | Density table - rho(T,p) | Reference density | Density vector - rho(T)

Specification method for the density of the thermal liquid. The density can be a function of temperature and pressure or as a function of temperature alone.

Density table, rho(T,p) — Matrix of fluid densities at the specified temperatures and pressures

11-by-12 matrix (default) | M-by-N matrix with units of mass/volume

Tabulated density data specified at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Density vector, rho(T) — Vector of fluid densities at the specified temperatures

11-element column vector (default) | M-element vector with units of mass/volume

Tabulated density data specified at the temperatures provided in the Temperature and Pressure section. Each element corresponds to a different temperature. The dependence of density on pressure is ignored.

Isothermal bulk modulus table, beta(T,p) — Matrix of isothermal bulk moduli at the specified temperatures and pressures

11-by-12 matrix (default) | M-by-N matrix with units of pressure

Tabulated data for the isothermal bulk modulus at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Isobaric thermal expansion coefficient table, alpha(T,p) — Matrix of isobaric thermal expansion coefficients at the specified temperatures and pressures

11-by-12 matrix (default) | M-by-N matrix with units of 1/temperature

Tabulated data for the isobaric thermal expansion coefficient at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Reference density — Density at a known operating condition

998.21 kg/m^3 (default) | scalar with units of mass/volume

Density of the thermal liquid at a known operating point. The block uses this data to arrive at an analytical expression for density as a function pressure and temperature.

Reference temperature — Temperature at a known operating condition

293.16 K (default) | scalar with units of temperature

Temperature of the thermal liquid at a known operating point. The block uses this data to arrive at an analytical expression for density as a function pressure and temperature.

Reference pressure — Pressure at a known operating condition

0.101325 MPa (default) | scalar with units of pressure

Pressure of the thermal liquid at a known operating point. The block uses this data to arrive at an analytical expression for density as a function pressure and temperature.

Constant isothermal bulk modulus — Isothermal bulk modulus at a known operating condition

2.1791 GPa (default) | scalar with units of pressure

Isothermal bulk modulus of the thermal liquid at a known operating point. The block uses this data to arrive at an analytical expression for density as a function pressure and temperature.

Constant isobaric thermal expansion coefficient — Isobaric thermal expansion coefficient at a known operating condition

2.0691e-4 1/K (default) | scalar with units of 1/temperature

Isobaric thermal expansion coefficient of the thermal liquid at a known operating point. The block uses this data to arrive at an analytical expression for density as a function pressure and temperature.

Internal Energy

Internal energy parameterization — Specification method for the fluid internal energy

Specific internal energy and specific heat tables - u(T,p), cp(T,p) (default) | Specific internal energy table - u(T,p) | Specific heat table - cp(T,p)

Specification method for the internal energy of the thermal liquid. The internal energy can be a function of temperature and pressure or as a function of temperature alone. It can also be calculated from specific heat data that you specify in the place of internal energy.

Specific internal energy table, u(T,p) — Matrix of internal energies at the specified temperatures and pressures

11-by-12 matrix (default) | M-by-N matrix with units of energy/mass

Tabulated data for the specific internal energy at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Specific internal energy vector, u(T) — Vector of internal energies at the specified temperatures

11-element vector (default) | M-element vector with units of energy/mass

Tabulated data for the specific internal energy at the temperatures provided in the Temperature and Pressure section. Each element corresponds to a different temperature. The dependence of the specific internal energy on pressure is ignored.

Specific heat at constant pressure table, cp(T,p) — Matrix of specific heats at the specified temperatures and pressures

11-by-12 matrix (default) | M-by-N matrix with units of energy/(mass*temperature)

Tabulated data for the specific heat at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Specific heat at constant pressure vector, u(T) — Vector of specific heats at the specified temperatures

11-element vector (default) | M-element vector with units of energy/(mass*temperature)

Tabulated data for the specific heat at the temperatures provided in the Temperature and Pressure section. Each row corresponds to a different temperature. The dependence of the specific heat on pressure is ignored.

Viscosity and Conductivity

Kinematic viscosity table, nu(T,p) — Matrix of kinematic viscosities at the specified temperatures and pressures

11-element vector (default) | M-element vector with units of area/time

Tabulated data for the kinematic viscosity at the temperatures and pressures provided in the Temperature and Pressure tab. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Thermal conductivity table, K(T,p) — Matrix of thermal conductivities at the specified temperatures and pressures

11-element vector (default) | M-element vector with units of power/(length*temperature)

Tabulated data for the thermal conductivity at the temperatures and pressures provided in the Temperature and Pressure section. Each row corresponds to a different temperature and each column corresponds to a different pressure.

Kinematic viscosity vector, nu(T) — Vector of kinematic viscosities at the specified temperatures

11-by-12 matrix (default) | M-by-N matrix with units of area/time

Tabulated data for the kinematic viscosity at the temperatures provided in the Temperature and Pressure section. Each row corresponds to a different temperature. The dependence of the kinematic viscosity on pressure is ignored.

Thermal conductivity vector, K(T) — Vector of thermal conductivities at the specified temperatures

11-by-12 matrix (default) | M-by-N matrix with units of power/(length*temperature)

Tabulated data for the thermal conductivity at the temperatures provided in the Temperature and Pressure section. Each row corresponds to a different temperature. The dependence of the thermal conductivity on pressure is ignored.

Extended Capabilities

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

Version History

Introduced in R2013b

R2023a: Control block behavior when fluid properties go out of range during simulation

Previously, if fluid properties went beyond the valid range during simulation, the block would return an error. You can now use the new Pressure and temperature outside valid range parameter to control the block behavior if fluid properties go out of range during simulation.