Thermal Liquid Properties (TL)

Physical properties of thermally conductive liquids connected to the network.

blockType: AcausalFoundation.ThermalLiquid.Properties

Path in the library:

/Physical Modeling/Fundamental/Thermal Liquid/Utilities/Thermal Liquid Properties (TL)

Description

Block Thermal Liquid Properties (TL) sets the physical properties of a liquid for a network of thermally conductive liquid. The properties do not apply to one component, but to all components of the network. Each heat-conducting fluid network in the model must be connected to exactly one instance of this unit.

Properties set in the block Thermal Liquid Properties (TL):

Thermodynamic properties – density, specific internal energy and specific heat.
The derived properties are the modulus of volumetric elasticity and the coefficient of thermal expansion.
Transport properties are kinematic viscosity and thermal conductivity.

Each property of a liquid is set in tabular form depending on temperature and pressure, or only on temperature. Use the option to ignore the pressure dependence if the pressure dependence is insignificant or the pressure in the model will be almost constant, or if only the temperature dependence of the liquid characteristics is known.

Parameterization

Block Thermal Liquid Properties (TL) It contains several parameterizations for independent variables of state, density, and specific internal energy. Parameterization determines the data obtained and the state variables on which the characteristics of the liquid depend. Parameter Setting Table dimensions it affects what parameters you see on other tabs.

Pressure and temperature

Pressure and temperature are the main variables for a thermally conductive liquid. Therefore, they are a natural choice of independent state variables, relative to which all other properties of the liquid are set.

Block Thermal Liquid Properties (TL) It contains two parameterization options based on these state variables. They are available through the parameter Table dimensions:

2D tables based on temperature and pressure (T,p) — indication of tabular data depending on temperature and pressure. The range of permissible temperatures and pressures is set as minimum and maximum values (Figure I) or as a tolerance matrix (Figure II).

Types of confidence areas:
1D vectors based on temperature (T) — specifying tabular data depending on temperature and ignoring any pressure dependencies. The range of permissible temperatures and pressures is set only in terms of minimum and maximum values. The modulus of volumetric elasticity provides a pressure dependence for density and any properties of the liquid calculated based on density.

Density, modulus of bulk elasticity, and coefficient of thermal expansion

Block Thermal Liquid Properties (TL) provides parameterization for density and for two related parameters, the isothermal modulus of bulk elasticity and the isobaric coefficient of thermal expansion.

The parameters include:

specifying tabular data for density, volume modulus, and coefficient of thermal expansion. The data should be specified depending on the temperature and pressure. For the parameter Table dimensions the value must be set to 2D tables based on temperature and pressure (T,p).
indication of tabular density data depending on temperature (and, in the two-dimensional case, pressure). The unit calculates the isothermal modulus of volumetric elasticity and the isobaric coefficient of thermal expansion from tabular data using the finite difference method. Isothermal modulus of volumetric elasticity defined as:

,

where
- — density;
- — temperature;
- — pressure.
  
  Isobaric coefficient of thermal expansion defined as:
.
an indication of the density, the modulus of volumetric elasticity, and the coefficient of thermal expansion at a known temperature (and, in the two-dimensional case, pressure). An analytical expression is used to calculate the density at other temperatures and pressures in the block. The calculation is based on the expression:

,

where — subscript, which indicates the reference value (set in the dialog box of the block).

Specific internal energy

As in the case of density, the block Thermal Liquid Properties (TL) provides three types of parameterization for specific internal energy and specific heat.

The parameters include:

indication of tabular data on specific internal energy and specific thermal coefficient. The data should be specified depending on the temperature and pressure. For the parameter Table dimensions the value must be set to 2D tables based on temperature and pressure (T,p).
indication of tabular data on specific internal energy as a function of temperature (and, in the two-dimensional case, pressure). The unit calculates the specific heat coefficient based on the specific internal energy data. The calculation is based on the expression:

.
indication of tabular data for specific heat capacity depending on temperature (and, in the two-dimensional case, pressure). The unit calculates the specific internal energy based on the specific heat capacity. The calculation is based on the expression:

,

where — subscript, indicates the reference value (set in the dialog box of the block). Meaning It is set to zero because the difference in specific internal energy is important for modeling, not its value. Meaning it may differ from the one given in other sources, for example, in the REFPROP liquid database.

Specific heat at constant volume

Specific heat at constant volume, , must be greater than zero. The unit deduces this value from other properties of the liquid.:

This equation will help you adjust the properties of the liquid to avoid blinking values. during calculations.

Ports

Conserving

# A — connection port
thermal liquid

Details

The port connects the unit to the thermal liquid network, giving it the characteristics of the liquid.

Program usage name

port

Parameters

Temperature and Pressure

# Table dimensions — dimensions of the liquid properties tables
2D tables based on temperature and pressure (T,p) | 1D vectors based on temperature (T)

Details

The dimension of the tables of liquid properties. This parameter determines whether the properties of the liquid are variable or constant depending on the pressure. Select a value 1D vectors based on temperature (T) to ignore the dependence of liquid properties on pressure.

Values	`2D tables based on temperature and pressure (T,p)` \| `1D vectors based on temperature (T)`
Default value	`2D tables based on temperature and pressure (T,p)`
Program usage name	`properties_parameterization`
Evaluatable	No

Details

A vector of temperature values of a thermally conductive liquid, which will be used to search the table for other properties of the liquid.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[273.16:10:373.16…] K`
Program usage name	`T_vector`
Evaluatable	Yes

# Pressure vector — a vector of pressure values for defining the characteristics of a thermally conductive liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A vector of pressure values of a thermally conductive liquid, which will be used together with a vector of temperature values to search for other properties of the liquid in a two-dimensional table.

Dependencies

To use this parameter, set for the parameter Table dimensions the value of `2D vectors based on temperature and pressure (T,p)'.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`[0.01, 0.1, 5:5:50…] MPa`
Program usage name	`p_vector`
Evaluatable	Yes

# Atmospheric pressure — atmospheric pressure for a heat-conducting fluid network
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The absolute pressure of the external environment of the connected network of a heat-conducting liquid. The default value corresponds to normal atmospheric pressure.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_ref`
Evaluatable	Yes

# Valid pressure-temperature region parameterization — a method for setting the permissible pressure and temperature range for a thermally conductive liquid
Specified minimum and maximum values | Validity matrix

Details

Select how the unit sets the allowable pressure and temperature range.:

Specified minimum and maximum values — the values of the Minimum valid temperature, Maximum valid temperature, Minimum valid pressure and Maximum valid pressure parameters are used.
Validity matrix — the parameter is used Pressure-temperature validity matrix to specify valid pressure-temperature pairs.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p).

Values	`Specified minimum and maximum values` \| `Validity matrix`
Default value	`Specified minimum and maximum values`
Program usage name	`validity_parameterization_2D`
Evaluatable	No

Details

The minimum temperature allowed in a thermally conductive liquid during simulation.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T) or set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p), and for the parameter Valid pressure-temperature region parameterization meaning Specified minimum and maximum values.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`273.16 K`
Program usage name	`T_min_2D`
Evaluatable	Yes

Details

The maximum temperature allowed in a thermally conductive liquid during simulation.

Dependencies

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`363.16 K`
Program usage name	`T_max_2D`
Evaluatable	Yes

# Minimum valid pressure — minimum allowable pressure for a thermally conductive liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The minimum pressure of the heat-conducting liquid during the simulation.

Dependencies

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.05 MPa`
Program usage name	`p_min_2D`
Evaluatable	Yes

# Maximum valid pressure — maximum allowable pressure for a thermally conductive liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The maximum pressure allowed in a thermally conductive liquid during simulation.

Dependencies

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`50 MPa`
Program usage name	`p_max_2D`
Evaluatable	Yes

# Pressure-temperature validity matrix — a matrix of acceptable and unacceptable pressure-temperature combinations

Details

A matrix of tolerance values for various temperature and pressure data points. A value of 1 means a valid point, and a value of `0' means an invalid point.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p), and for the Valid pressure-temperature region parameter , the value Validity matrix.

Default value	`[1 1 1 1 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1 1 1 1 1; 1 1 1 1 1 1 1 1 1 1 1 1; 0 1 1 1 1 1 1 1 1 1 1 1; 0 1 1 1 1 1 1 1 1 1 1 1; 0 1 1 1 1 1 1 1 1 1 1 1; 0 1 1 1 1 1 1 1 1 1 1 1; 0 1 1 1 1 1 1 1 1 1 1 1; 0 0 1 1 1 1 1 1 1 1 1 1]`
Program usage name	`validity_matrix`
Evaluatable	Yes

Density

# Density parameterization — a method for setting the density of a liquid depending on temperature and pressure
Density, bulk modulus and thermal expansion tables - rho(T,p), beta(T,p), alpha(T,p) | Density table - rho(T,p) | Reference density

Details

A method for determining the density of a thermally conductive liquid network.

Density can be a function of temperature and pressure.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p).

Values	`Density, bulk modulus and thermal expansion tables - rho(T,p), beta(T,p), alpha(T,p)` \| `Density table - rho(T,p)` \| `Reference density`
Default value	`Density, bulk modulus and thermal expansion tables - rho(T,p), beta(T,p), alpha(T,p)`
Program usage name	`density_parameterization_2D`
Evaluatable	No

# Density parameterization — a method for setting the density of a liquid depending only on temperature
Density vector - rho(T) | Reference density

Details

A method for determining the density of a thermally conductive liquid network.

Density can only be a function of temperature.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T).

Values	`Density vector - rho(T)` \| `Reference density`
Default value	`Density vector - rho(T)`
Program usage name	`density_parameterization_1D`
Evaluatable	No

# Density table, rho(T,p) — table of liquid densities at specified temperatures and pressures
g/cm^3 | kg/m^3 | lbm/gal

Details

A matrix of liquid density values for searching in a two-dimensional table by pressure and temperature.

The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p), and for the parameter Density parameterization meaning Density, bulk modulus and thermal expansion tables - rho(T,p), beta(T,p), alpha(T,p) or Density table - rho(T,p).

Units	`g/cm^3` \| `kg/m^3` \| `lbm/gal`
Default value	[999.7973 999.8431 1002.3216 1004.8218 1007.2930 1009.7358 1012.1506 1014.5379 1016.8979 1019.2311 1021.5380 1023.8188; 999.6579 999.7009 1002.0303 1004.3820 1006.7084 1009.0101 1011.2874 1013.5407 1015.7703 1017.9766 1020.1599 1022.3206; 998.1632 998.2045 1000.4375 1002.6924 1004.9239 1007.1324 1009.3183 1011.4819 1013.6236 1015.7438 1017.8428 1019.9210; 995.6057 995.6458 997.8186 1000.0128 1002.1841 1004.3332 1006.4603 1008.5660 1010.6505 1012.7144 1014.7580 1016.7815; 992.1724 992.2119 994.3513 996.5113 998.6484 1000.7633 1002.8563 1004.9280 1006.9788 1009.0090 1011.0192 1013.0097; 988.0200 988.0299 990.1568 992.3035 994.4268 996.5273 998.6056 1000.6622 1002.6976 1004.7123 1006.7067 1008.6813; 983.1800 983.1901 985.3217 987.4721 989.5983 991.7008 993.7803 995.8374 997.8726 999.8864 1001.8795 1003.8522; 977.7500 977.7583 979.9094 982.0783 984.2216 986.3400 988.4343 990.5050 992.5529 994.5786 996.5825 998.5654; 971.7700 971.7836 973.9673 976.1678 978.3409 980.4876 982.6087 984.7049 986.7768 988.8254 990.8511 992.8545; 965.2600 965.3023 967.5311 969.7753 971.9901 974.1764 976.3354 978.4676 980.5741 982.6556 984.7129 986.7465; 958.6200 958.6315 960.6270 962.9267 965.1944 967.4314 969.6387 971.8173 973.9681 976.0921 978.1900 980.2628] kg/m^3
Program usage name	`rho_matrix_2D_rho_bulk_modulus_alpha`
Evaluatable	Yes

# Isothermal bulk modulus table, beta(T,p) — table of values of the isothermal volume compression modulus for a thermally conductive liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

A matrix of values of the isothermal volume compression module for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Dependencies

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	[1.9649 1.9654 1.9929 2.0213 2.0499 2.0787 2.1078 2.1372 2.1668 2.1966 2.2268 2.2572; 2.0913 2.0918 2.1191 2.1471 2.1752 2.2036 2.2322 2.2610 2.2899 2.3191 2.3485 2.3781; 2.1786 2.1791 2.2067 2.2350 2.2634 2.2919 2.3206 2.3494 2.3784 2.4075 2.4367 2.4661; 2.2332 2.2337 2.2619 2.2908 2.3197 2.3487 2.3778 2.4070 2.4363 2.4657 2.4951 2.5246; 2.2600 2.2605 2.2895 2.3191 2.3487 2.3784 2.4081 2.4378 2.4675 2.4973 2.5272 2.5571; 2.2638 2.2638 2.2936 2.3240 2.3544 2.3848 2.4151 2.4455 2.4758 2.5062 2.5365 2.5669; 2.2472 2.2472 2.2779 2.3092 2.3403 2.3715 2.4025 2.4336 2.4646 2.4955 2.5264 2.5573; 2.2140 2.2140 2.2455 2.2776 2.3096 2.3415 2.3733 2.4050 2.4367 2.4683 2.4998 2.5313; 2.1668 2.1668 2.1992 2.2321 2.2649 2.2976 2.3301 2.3626 2.3949 2.4272 2.4593 2.4914; 2.1081 2.1081 2.1413 2.1750 2.2086 2.2421 2.2754 2.3085 2.3415 2.3744 2.4072 2.4399; 2.0494 2.0494 2.0739 2.1084 2.1428 2.1770 2.2110 2.2449 2.2786 2.3121 2.3455 2.3788] GPa
Program usage name	`bulk_modulus_matrix_2D`
Evaluatable	Yes

Details

A matrix of values of isobaric coefficients of thermal expansion for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Dependencies

Units	`1/K` \| `1/degR` \| `1/deltaK` \| `1/deltadegC` \| `1/deltadegF` \| `1/deltadegR`
Default value	[-0.6790 -0.6760 -0.4900 -0.3070 -0.1300 0.0410 0.2060 0.3650 0.5190 0.6680 0.8110 0.9490; 0.8780 0.8810 0.9980 1.1140 1.2270 1.3370 1.4450 1.5490 1.6510 1.7500 1.8460 1.9390; 2.0680 2.0690 2.1410 2.2130 2.2830 2.3520 2.4200 2.4860 2.5510 2.6140 2.6760 2.7360; 3.0340 3.0350 3.0740 3.1130 3.1520 3.1910 3.2290 3.2670 3.3050 3.3410 3.3770 3.4130; 3.8550 3.8560 3.8700 3.8840 3.8990 3.9140 3.9300 3.9460 3.9610 3.9770 3.9930 4.0090; 4.5780 4.5780 4.5720 4.5660 4.5620 4.5580 4.5550 4.5520 4.5500 4.5490 4.5480 4.5470; 5.2330 5.2330 5.2090 5.1860 5.1650 5.1440 5.1250 5.1070 5.0900 5.0740 5.0590 5.0450; 5.8400 5.8400 5.8010 5.7620 5.7250 5.6910 5.6570 5.6250 5.5950 5.5660 5.5380 5.5120; 6.4140 6.4140 6.3600 6.3070 6.2560 6.2080 6.1610 6.1170 6.0740 6.0330 5.9940 5.9560; 6.9670 6.9670 6.8980 6.8310 6.7660 6.7050 6.6460 6.5890 6.5350 6.4820 6.4320 6.3840; 7.5190 7.5190 7.4230 7.3420 7.2640 7.1890 7.1180 7.0490 6.9830 6.9200 6.8590 6.8000] * 1e-4 1/K
Program usage name	`alpha_matrix_2D`
Evaluatable	Yes

# Reference density — density at known operating condition
g/cm^3 | kg/m^3 | lbm/gal

Details

The density of the heat-conducting fluid network at a known operating point. The block uses this data to obtain an analytical expression for density as a function of pressure and temperature.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T), and for the parameter Density parameterization meaning Reference density.

Units	`g/cm^3` \| `kg/m^3` \| `lbm/gal`
Default value	`998.21 kg/m^3`
Program usage name	`rho_ref_2D`
Evaluatable	Yes

Details

The temperature of the heat-conducting fluid network at a known operating point. The block uses this data to obtain an analytical expression for density as a function of pressure and temperature.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T), and for the parameter Density parameterization meaning Reference density.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.16 K`
Program usage name	`T_ref_2D`
Evaluatable	Yes

# Reference pressure — pressure at known operating condition
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure of the heat-conducting fluid network at a known operating point. The block uses this data to obtain an analytical expression for density as a function of pressure and temperature.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T) or 2D tables based on temperature and pressure (T,p), and for the parameter Density parameterization meaning Reference density.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_ref_2D`
Evaluatable	Yes

# Constant isothermal bulk modulus — isothermal modulus of volumetric elasticity under known operating condition
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Isothermal modulus of volumetric elasticity of a thermally conductive fluid network at a known operating point. The block uses this data to obtain an analytical expression for density as a function of pressure and temperature.

Dependencies

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`2.1791 GPa`
Program usage name	`bulk_modulus_const_2D`
Evaluatable	Yes

Details

Isobaric coefficient of thermal expansion of a heat-conducting fluid network at a known operating point. The block uses this data to obtain an analytical expression for density as a function of pressure and temperature.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T), and for the parameter Density parameterization meaning Reference density.

Units	`1/K` \| `1/degR` \| `1/deltaK` \| `1/deltadegC` \| `1/deltadegF` \| `1/deltadegR`
Default value	`0.00020691 1/K`
Program usage name	`alpha_const_2D`
Evaluatable	Yes

# Density vector, rho(T) — vector of liquid densities at given temperatures
g/cm^3 | kg/m^3 | lbm/gal

Details

Tabular density data is indicated at the temperatures listed in the parameter group Temperature and Pressure. Each element corresponds to its own temperature. The dependence of density on pressure is not taken into account.

Dependencies

To use this parameter, set for the parameter Table dimensions the value is 1D vectors based on temperature, and for the parameter Density parameterization meaning Density vector - rho(T).

Units	`g/cm^3` \| `kg/m^3` \| `lbm/gal`
Default value	`[999.8400, 999.7000, 998.2000, 995.6500, 992.2100, 988.0300, 983.1900, 977.7600, 971.7800, 965.3000, 958.8000] kg/m^3`
Program usage name	`rho_vector_1D`
Evaluatable	Yes

Internal Energy

# Internal energy parameterization — a method for determining the internal energy of a liquid depending on temperature and pressure
Specific internal energy and specific heat tables - u(T,p), cp(T,p) | Specific internal energy table - u(T,p) | Specific heat table - cp(T,p)

Details

A method for determining the internal energy of a heat-conducting liquid network.

Internal energy can be a function of temperature and pressure. It can also be calculated based on the specific heat capacity data that you specify instead of the internal energy.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T).

Values	`Specific internal energy and specific heat tables - u(T,p), cp(T,p)` \| `Specific internal energy table - u(T,p)` \| `Specific heat table - cp(T,p)`
Default value	`Specific internal energy and specific heat tables - u(T,p), cp(T,p)`
Program usage name	`internal_energy_parameterization_2D`
Evaluatable	No

# Specific internal energy table, u(T,p) — table of values of specific internal energies for a thermally conductive liquid
fpm^2 | fps^2 | kph^2 | mph^2 | J/kg | kJ/kg | m^2/s^2 | cm^2/s^2 | ft^2/s^2 | in^2/s^2 | km^2/s^2 | mi^2/s^2 | mm^2/s^2 | Pa/(kg/m^3) | bar/(kg/m^3) | psi/(lbm/ft^3)

Details

A matrix of specific internal energy values for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Units	`fpm^2` \| `fps^2` \| `kph^2` \| `mph^2` \| `J/kg` \| `kJ/kg` \| `m^2/s^2` \| `cm^2/s^2` \| `ft^2/s^2` \| `in^2/s^2` \| `km^2/s^2` \| `mi^2/s^2` \| `mm^2/s^2` \| `Pa/(kg/m^3)` \| `bar/(kg/m^3)` \| `psi/(lbm/ft^3)`
Default value	[0.0002 0.0018 0.0860 0.1588 0.2190 0.2670 0.3034 0.3288 0.3436 0.3483 0.3435 0.3294; 42.0620 42.0600 41.9350 41.8040 41.6680 41.5270 41.3820 41.2330 41.0810 40.9240 40.7630 40.5990; 83.9530 83.9480 83.6510 83.3490 83.0490 82.7490 82.4510 82.1530 81.8560 81.5600 81.2650 80.9710; 125.7700 125.7600 125.3100 124.8600 124.4100 123.9700 123.5300 123.1000 122.6800 122.2500 121.8400 121.4200; 167.5700 167.5600 166.9600 166.3700 165.7900 165.2100 164.6500 164.0900 163.5400 163.0000 162.4600 161.9400; 209.3600 209.3600 208.6300 207.9000 207.1900 206.4800 205.7900 205.1100 204.4500 203.7900 203.1400 202.5000; 251.1900 251.1900 250.3300 249.4700 248.6200 247.7900 246.9800 246.1800 245.3900 244.6200 243.8600 243.1200; 293.0600 293.0600 292.0700 291.0700 290.1000 289.1400 288.2000 287.2800 286.3800 285.4900 284.6200 283.7700; 334.9900 334.9900 333.8600 332.7300 331.6300 330.5400 329.4800 328.4400 327.4100 326.4100 325.4300 324.4600; 377.0000 377.0000 375.7300 374.4600 373.2200 372.0000 370.8100 369.6400 368.5000 367.3800 366.2700 365.1900; 419.0100 419.0100 417.6900 416.2700 414.8900 413.5400 412.2100 410.9100 409.6400 408.4000 407.1700 405.9800] kJ/kg
Program usage name	`u_matrix_2D_u_c_p`
Evaluatable	Yes

# Specific heat at constant pressure table, cp(T,p) — table of specific heat values for a thermally conductive liquid
J/(K*kg) | kJ/(K*kg) | Btu_IT/(lbm*deltadegR)

Details

A matrix of specific heat values for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Units	`J/(Kkg)` \| `kJ/(Kkg)` \| `Btu_IT/(lbm*deltadegR)`
Default value	[4.2199 4.2194 4.1957 4.1726 4.1508 4.1300 4.1103 4.0916 4.0738 4.0569 4.0408 4.0254; 4.1955 4.1951 4.1769 4.1592 4.1422 4.1259 4.1103 4.0954 4.0812 4.0676 4.0545 4.0421; 4.1843 4.1840 4.1690 4.1543 4.1401 4.1264 4.1133 4.1007 4.0885 4.0768 4.0656 4.0548; 4.1801 4.1798 4.1667 4.1538 4.1413 4.1293 4.1177 4.1064 4.0956 4.0851 4.0750 4.0653; 4.1796 4.1794 4.1675 4.1558 4.1444 4.1334 4.1227 4.1123 4.1023 4.0926 4.0832 4.0741; 4.1813 4.1813 4.1702 4.1592 4.1484 4.1380 4.1279 4.1181 4.1086 4.0993 4.0903 4.0816; 4.1850 4.1850 4.1742 4.1636 4.1532 4.1432 4.1334 4.1239 4.1146 4.1056 4.0969 4.0884; 4.1901 4.1901 4.1795 4.1690 4.1588 4.1489 4.1393 4.1299 4.1207 4.1118 4.1032 4.0947; 4.1968 4.1968 4.1862 4.1757 4.1655 4.1555 4.1458 4.1364 4.1273 4.1183 4.1096 4.1012; 4.2052 4.2052 4.1944 4.1837 4.1733 4.1632 4.1534 4.1438 4.1345 4.1255 4.1166 4.1080; 4.2136 4.2136 4.2045 4.1935 4.1828 4.1724 4.1623 4.1524 4.1429 4.1335 4.1245 4.1157] kJ/(K*kg)
Program usage name	`c_p_matrix_2D_u_c_p`
Evaluatable	Yes

# Specific internal energy vector, u(T) — vector of specific internal energy of liquids at given temperatures
fpm^2 | fps^2 | kph^2 | mph^2 | J/kg | kJ/kg | m^2/s^2 | cm^2/s^2 | ft^2/s^2 | in^2/s^2 | km^2/s^2 | mi^2/s^2 | mm^2/s^2 | Pa/(kg/m^3) | bar/(kg/m^3) | psi/(lbm/ft^3)

Details

Tabular data for specific internal energy at temperatures given in the section Temperature and Pressure. Each element corresponds to its own temperature. The dependence of the specific internal energy on pressure is not taken into account.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T), and for the parameter Internal energy parameterization in the value Specific internal energy vector - u(T).

Units	`fpm^2` \| `fps^2` \| `kph^2` \| `mph^2` \| `J/kg` \| `kJ/kg` \| `m^2/s^2` \| `cm^2/s^2` \| `ft^2/s^2` \| `in^2/s^2` \| `km^2/s^2` \| `mi^2/s^2` \| `mm^2/s^2` \| `Pa/(kg/m^3)` \| `bar/(kg/m^3)` \| `psi/(lbm/ft^3)`
Default value	`[0.0018, 42.0600, 83.9480, 125.7600, 167.5600, 209.3600, 251.1900, 293.0600, 334.9900, 377.0000, 418.0100] kJ/kg`
Program usage name	`u_vector_1D`
Evaluatable	Yes

# Specific heat at constant pressure vector, cp(T) — vector of specific heat capacities at specified temperatures
J/(K*kg) | kJ/(K*kg) | Btu_IT/(lbm*deltadegR)

Details

Tabular data for specific heat capacity at temperatures specified in the section Temperature and Pressure. Each row corresponds to a different temperature. The dependence of specific heat on pressure is not taken into account.

Dependencies

Units	`J/(Kkg)` \| `kJ/(Kkg)` \| `Btu_IT/(lbm*deltadegR)`
Default value	`[4.2199, 4.1955, 4.1843, 4.1801, 4.1796, 4.1813, 4.1850, 4.1901, 4.1968, 4.2052, 4.2136] kJ/(K*kg)`
Program usage name	`c_p_vector_1D`
Evaluatable	Yes

Viscosity and Conductivity

# Kinematic viscosity table, nu(T,p) — table of values of kinematic viscosities for a thermally conductive liquid
mm^2/s | St | cSt | newt | m^2/s | in^2/s

Details

A matrix of kinematic viscosity values for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p).

Units	`mm^2/s` \| `St` \| `cSt` \| `newt` \| `m^2/s` \| `in^2/s`
Default value	[1.7917 1.7914 1.7763 1.7615 1.7473 1.7338 1.7208 1.7085 1.6967 1.6854 1.6747 1.6645; 1.3061 1.3059 1.2986 1.2914 1.2845 1.2779 1.2716 1.2656 1.2598 1.2543 1.2491 1.2441; 1.0032 1.0032 0.9995 0.9959 0.9924 0.9891 0.9859 0.9829 0.9801 0.9774 0.9748 0.9724; 0.8006 0.8005 0.7987 0.7970 0.7953 0.7937 0.7922 0.7908 0.7894 0.7881 0.7870 0.7859; 0.6577 0.6577 0.6570 0.6562 0.6555 0.6548 0.6543 0.6537 0.6532 0.6528 0.6523 0.6520; 0.5530 0.5530 0.5529 0.5527 0.5526 0.5525 0.5524 0.5524 0.5524 0.5524 0.5524 0.5525; 0.4739 0.4739 0.4741 0.4743 0.4745 0.4747 0.4750 0.4753 0.4755 0.4758 0.4762 0.4765; 0.4127 0.4127 0.4131 0.4135 0.4139 0.4143 0.4148 0.4152 0.4157 0.4162 0.4167 0.4172; 0.3643 0.3643 0.3648 0.3654 0.3659 0.3665 0.3670 0.3676 0.3682 0.3688 0.3694 0.3700; 0.3254 0.3254 0.3261 0.3267 0.3273 0.3280 0.3286 0.3293 0.3299 0.3306 0.3312 0.3319; 0.2866 0.2866 0.2945 0.2952 0.2959 0.2965 0.2972 0.2979 0.2986 0.2993 0.3000 0.3007] mm^2/s
Program usage name	`nu_matrix`
Evaluatable	Yes

# Kinematic viscosity vector, nu(T) — vector of kinematic viscosities at specified temperatures
mm^2/s | St | cSt | newt | m^2/s | in^2/s

Details

Tabulated data for kinematic viscosity at temperatures specified in the section Temperature and Pressure. Each row corresponds to a different temperature. The dependence of kinematic viscosity on pressure is not taken into account.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T).

Units	`mm^2/s` \| `St` \| `cSt` \| `newt` \| `m^2/s` \| `in^2/s`
Default value	`[1.7917, 1.3061, 1.0032, 0.8006, 0.6577, 0.5530, 0.4739, 0.4127, 0.3643, 0.3254, 0.2866] mm^2/s`
Program usage name	`nu_vector`
Evaluatable	Yes

# Thermal conductivity table, k(T,p) — table of thermal conductivity values for a heat-conducting liquid
W/(m*K) | mW/(K*m) | Btu_IT/(hr*ft*deltadegR)

Details

A matrix of thermal conductivity values for a two-dimensional search in a table based on pressure and temperature. The size of the matrix should correspond to the dimensions of the pressure and temperature vectors. The table rows correspond to the parameter values Temperature vector, and the columns correspond to the values Pressure vector.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 2D tables based on temperature and pressure (T,p).

Units	`W/(mK)` \| `mW/(Km)` \| `Btu_IT/(hrftdeltadegR)`
Default value	[561.0400 561.0900 563.8000 566.5600 569.3200 572.0800 574.8200 577.5400 580.2400 582.9200 585.5700 588.1800; 580.0200 580.0700 582.4500 584.8800 587.3200 589.7500 592.1800 594.6100 597.0200 599.4200 601.8000 604.1600; 598.4400 598.4800 600.7300 603.0300 605.3300 607.6400 609.9400 612.2400 614.5400 616.8200 619.1000 621.3600; 615.4800 615.5200 617.7300 620.0000 622.2600 624.5400 626.8100 629.0700 631.3400 633.6000 635.8500 638.0900; 630.6000 630.6400 632.8700 635.1500 637.4400 639.7200 642.0100 644.2900 646.5700 648.8400 651.1100 653.3600; 643.6100 643.6100 645.8800 648.2100 650.5300 652.8600 655.1800 657.5100 659.8200 662.1400 664.4400 666.7400; 654.3900 654.3900 656.7300 659.1200 661.5000 663.8900 666.2700 668.6500 671.0200 673.3800 675.7400 678.0900; 663.1300 663.1300 665.5400 668.0000 670.4600 672.9100 675.3600 677.8000 680.2400 682.6700 685.0900 687.5000; 670.0200 670.0200 672.5100 675.0500 677.5900 680.1200 682.6400 685.1600 687.6700 690.1700 692.6600 695.1400; 675.2700 675.2700 677.8500 680.4800 683.1100 685.7300 688.3400 690.9400 693.5300 696.1100 698.6800 701.2400; 680.5200 680.5200 681.7700 684.5000 687.2200 689.9400 692.6400 695.3400 698.0200 700.6900 703.3500 706.0000] mW/(K*m)
Program usage name	`k_matrix`
Evaluatable	Yes

# Thermal conductivity vector, k(T) — the vector of thermal conductivity at specified temperatures
W/(m*K) | mW/(K*m) | Btu_IT/(hr*ft*deltadegR)

Details

Tabulated data on thermal conductivity at temperatures specified in the section Temperature and Pressure. Each row corresponds to a different temperature. The dependence of thermal conductivity on pressure is not taken into account.

Dependencies

To use this parameter, set for the parameter Table dimensions meaning 1D vectors based on temperature (T).

Units	`W/(mK)` \| `mW/(Km)` \| `Btu_IT/(hrftdeltadegR)`
Default value	`[561.0400, 580.0200, 598.4400, 615.4800, 630.6000, 643.6100, 654.3900, 663.1300, 670.0200, 675.2700, 680.5200] mW/(K*m)`
Program usage name	`k_vector`
Evaluatable	Yes

Thermal Liquid Properties (TL)

Description

Parameterization

Pressure and temperature

Density, modulus of bulk elasticity, and coefficient of thermal expansion

Specific internal energy

Specific heat at constant volume

Ports

Conserving

Parameters

Temperature and Pressure

Density

Internal Energy

Viscosity and Conductivity

Examples