There are several very reliable medium packages based en multiparameter equations of state; there are also very simple medium packages based in the ideal gas equation for gases, or in constant properties for liquids. But for many products we do not have multiparameter EOS, or we do not need their complexity, but we need a good approximation of physical properties. The TMedia package is based in correlations and offers good accuracy for liquids till say 200 bars pressure and for gases till 20-30 bars.
The medium is designed for liquid, liquid/vapor, or gas phases. For liquid or biphasic states, its application is limited to the higher temperature limits of the liquid heat capacity and vaporization enthalpy correlations used, but temperature should be lower than 0.85 Tc, and pressure not higher than 200 bars, because at higher values the influence of pressure on properties becomes very difficult to correct for. For gas state, it is limited to the maximum pressure which saturation temperature is below the maximum temperature limit of the liquid heat capacity correlation, but should be limited to a maximum of 20-30 bars. It can't work with supercritical states. It extends the Modelica PartialTwoPhaseMedium. It is somewhat similar to the Modelica TableBased medium, but uses specific correlations for each physical property, allows to work with gas phase, and adds a density dependent correlation for the reduced bulk modulus of the liquid, that improves a lot the calculation of liquid density at high pressure, isothermal compressibility, and isobaric expansion coefficient. Improving also the calculation of liquid heat capacity at constant volume (Cv) and the speed of sound. The medium properties are obtained using correlations that are mainly functions of T, but different pressure corrections are also used. It uses the substances data stored in the MediaCommon package.
The use of pressure correction is controlled by the constant Boolean 'highPressure'. Its default value is false. If switched to true, pressure correction will be applied (in plus than to liquid density) to liquid specific enthalpy, specific entropy, heat capacity, viscosity and thermal conductivity. It is interesting to make highPressure=true if we need to work over 20 or 30 bars, but the price is a slower simulation.
The values of enthalpy and entropy are calculated from a reference state. The reference state to use can be selected giving value to the constant string 'refState'. The values can be: 'ASHRAE', 'IIR', 'NBP' or 'User'. Any other value will eliminate any correction for the reference state. When using 'User', the raw values at reference_T will be used as zero for both enthalpy and entropy.
The thermodynamic record contains: p,T,gas fraction, d and h. Care must be taken in limiting the use to the temperature limits of the correlations used, as only few checks are done by the media, in order not to interfere with the solver process.
A constant string 'localInputChoice' has been added to the BaseProperties model in order to specify the independent variables to use in each instance of the BaseProperties model. The default value for this constant is the value given to the constant string 'inputChoice' at package level. The valid alternatives are: 'ph', 'pT', 'dT'.
The global idea has been not to use the Modelica files for the storage of substances data, but to store the data in a database, from which we can recover and use them when needed. A database is provided with more than 400 substances that can be enlarged, and the FreeFluids GUI can retrieve the data from the data base, treat it as needed (for example creating EOS from saturated vapor pressure and/or densities, or creating correlations from the EOS), store the results in the database, and export the data in Modelica format when needed. Nevertheless, in order to make life easier for users, many common substances have been exported, and their packages included in the TMedia.Fluids package.
As a resume: The medium is for fast calculation of liquid phase, condensation, evaporation, and gas phase below the critical point. In the liquid and saturated phases, the results are quite good. In the gas phase, the results are better than the ideal gas approach in density and enthalpy. The medium is compatible with OpenModelica 1.17 old and new frontends. The medium is also compatible, since the addition of derivative functions calculation, with the ThermoPower library and with Modelica.Fluid.
Liquid phase properties
The saturated density is calculated using a dedicated correlation. This density is corrected for pressure influence. If the coefficients for the reduced bulk modulus calculation, as function of density, are available, the correction is done using a very accurate Tait like equation. In other case, a substance specific isothermal compressibility factor (with a default value of 6.667 e-10) is used. The parameters for the reduced bulk modulus correlation (with liquid density as independent variable) are normally not available, but can be calculated from a good equation of state of the multiparameter or SAFT types. This can be done easily with the FreeFluids GUI: you make the calculation with the EOS, transfer the results (density and the natural logarithm of the reduced bulk modulus) to the correlations tab, make the regression of the coefficients, and store the result in the database. It is good to calculate the reduced bulk modulus at a pressure close to 50 bars but, if necessary in order to have liquid phase at the temperature of interest, it can be done at higher pressure. Check that all density data used correspond to the liquid state.
A dedicated correlation is used also for the saturated heat capacity. The use of the saturated liquid Cp correlation, instead of ideal Cp correlation plus vaporization enthalpy, makes possible the use of the medium with substances for which we do not have Cp0 data, and improves the liquid phase thermal properties calculation. This correlation can be also a problem, as many times we only find it with a temperature limit of the normal boiling point. This can be solved using a Cp correlation constructed from a good EOS, using the FreeFluids GUI. It is important not to use data too close to the Tc for the regression (use data till 10 K below the Tc). The best equation for the regression of the liquid heat capacity is the PPDS15 equation. Do not use the ChemSep equations as they are not integrated by the medium to obtain enthalpy or entropy. If highPressure has been made equal to true, a density dependent correction is applied to the Cp.
The liquid enthalpy is calculated from the liquid Cp correlation at saturation. If highPressure has been made equal to true, PV correction is applied. The correction interpolates linearly from full correction below 0.45Tc to none at 0.85Tc.
When going back from liquid enthalpy, or entropy, to temperature, we have two ways: One of them is to fit a correlation that makes this calculation, that can again be made with FreeFluidsGui. The second, that will be used if we left the value of lTfromHsatCorr=0, will calculate in situ the temperature using a solving function, as is done in the IdealGasMedia package.
For water, viscosity is calculated, independent of the phase, using the reference equation as function of temperature and density. For other substances, the saturated liquid viscosity is calculated using a dedicated temperature dependent correlation. Pressure correction, according to Lucas, is applied if highPressure is set to true.
Saturated thermal conductivity is calculated using the corresponding correlation, if available. Otherwise the Latini method is used. If highPressure is set to true, a pressure(in fact density) correction is used.
Surface tension is calculated also by correlation, or using the Sastri-Rao method, if the first is not available.
Gas phase properties
Saturated gas density is calculated using a dedicated correlation. At temperature higher than saturation, for a given pressure, a temperature correction is introduced.
Enthalpy and entropy are calculated from the saturated values at the given pressure (obtained from liquid Cp and vaporization enthalpy correlations), by adding the increase from the saturated temperature to the given temperature, calculated according to the ideal gas Cp, but with a pressure and temperature correction.
Viscosity and thermal conductivity are calculated by correlations or, when not available, by the Chung method. Pressure correction is later applied.
Two phases properties
Transport properties are not calculated for the two phases situation.
| Name | Description |
|---|---|
| TMedium | |
| Fluids | |
| Tests | In Tests Axx are comparing TMedia with multiparameter EOS and ExternalMedia, using a temperature ramp. In Tests Bxx a comparison of the gas phase only also with ideal gas. |