Thermal Liquid Settings (TL)

Physical properties of a thermal liquid

• Library:
• 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 cp 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:

`$u\left(T,p\right)={\int }_{{T}_{R}}^{T}\left({c}_{p}\left(T,p\right)-\frac{p\alpha \left(T,p\right)}{\rho \left(T,p\right)}\right)dT+{u}_{R},$`

where the subscript R denotes a reference quantity. The value of uR 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.

Ports

Conserving

expand all

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

Parameters

expand all

Temperature and Pressure

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.

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

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)```.

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

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)```.

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

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

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

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

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`.

Density

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.

Tabulated density data specified 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.

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

Tabulated data for the isothermal bulk modulus 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.

Tabulated data for the isobaric thermal expansion coefficient 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.

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.

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.

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.

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.

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

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.

Tabulated data for the specific internal energy 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.

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

Tabulated data for the specific heat 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.

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

Viscosity and Conductivity

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.

Tabulated data for the thermal conductivity 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.

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

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

Version History

Introduced in R2013b