packageCharacteristic
Package of thermodynamic and diffusive properties
Extends from CharacteristicEOS (Base thermodynamic package with only the p-v-T relations).
Information
This package is compatible with NASA CEA thermodynamic data [McBride2002] and the virial equation of state [Dymond2002].
Notes regarding the constants:
- Currently,
formulamay not contain parentheses or brackets. - d is the Van der Waals diameter or the diameter for the rigid-sphere ("billiard-ball") approximation of the kinetic theory of gases [Present1958].
- bc: The rows give the coefficients for the temperature intervals bounded by the values in Tlim c. The powers of T increase by column. By default, the powers of T for the first column are each -2, which corresponds to [McBride2002]. In that case, the dimensionalities of the coefficients are {L4.M2/(N2.T4), L2.M/(N.T2), 1, …} for each row, where L is length, M is mass, N is particle number, and T is time. (In FCSys, temperature is a potential with dimension L2.M/(N.T2); see the Units package.)
- Bc: As in bc, the rows correspond to different temperature intervals. The first column is for specific enthalpy and has dimensionality L2.M/(N.T2). The second is for specific entropy and is dimensionless. The integration constants for enthalpy are defined such that the enthalpy at 25 °C is the specific enthalpy of formation at that temperature and reference pressure [McBride2002, p. 2]. The integration constants for specific entropy are defined such that specific entropy is absolute.
- Tlim c: The first and last entries are the minimum and maximum valid temperatures. The intermediate entries are the thresholds between rows of bc (and Bc). Therefore, if there are n temperature intervals (and rows in bc and Bc), then Tlim c must have n + 1 entries.
- The reference pressure is po. In the
NASA CEA data [McBride2002], it is 1 bar for gases and 1 atm for condensed
species. For gases, the reference state is the ideal gas at po.
For example, the enthalpy of a non-ideal (real) gas at 25 °C and po with
ReferenceEnthalpy.zeroAt25degCis not exactly zero. - If the material is gaseous (
phase == Phase.gas), then the first virial coefficient must be independent of temperature. Otherwise, the function for specific enthalpy (h) will be ill-posed. Typically, the first virial coefficient is one (or equivalentlyU.R), which satisfies this requirement.
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Q.PressureAbsolute | p0 (from CharacteristicEOS) | U.bar | <html>Reference pressure (<i>p</i><sup>o</sup>)</html> |
| Integer[2] | n_v (from CharacteristicEOS) | {-1, 0} | <html>Powers of <i>p</i>/<i>T</i> and <i>T</i> for 1<sup>st</sup> row and column of <i>b</i><sub><i>v</i></sub> (<i>n</i><sub><i>v</i></sub>)</html> |
| Real[:,:] | b_v (from CharacteristicEOS) | [1] | <html>Coefficients for specific volume as a polynomial in <i>p</i>/<i>T</i> and <i>T</i> (<i>b</i><sub><i>v</i></sub>)</html> |
| Boolean | isCompressible (from CharacteristicEOS) | anyTrue({anyTrue({abs(b_v[i, j]) > Modelica.Constants.small and n_v[1] + i - 1 <> 0 for i in 1:size(b_v, 1)}) for j in 1:size(b_v, 2)}) | <html><code>true</code>, if density depends on pressure</html> |
| Boolean | hasThermalExpansion (from CharacteristicEOS) | anyTrue({anyTrue({abs(b_v[i, j]) > Modelica.Constants.small and n_v[2] + j - n_v[1] - i <> 0 for i in 1:size(b_v, 1)}) for j in 1:size(b_v, 2)}) | <html><code>true</code>, if density depends on temperature</html> |
| String | formula | Chemical formula | |
| Phase | phase | Material phase | |
| Q.MassSpecific | m | Specific mass | |
| Q.LengthSpecific | d | Specific diameter | |
| Integer | z | charge(formula) | Charge number |
| ReferenceEnthalpy | referenceEnthalpy | ReferenceEnthalpy.enthalpyOfFormationAt25degC | Choice of enthalpy reference |
| Q.PotentialChemical | Deltah0_f | <html>Enthalpy of formation at 298.15 K, <i>p</i><sup>o</sup> (Δ<i>h</i><sup>o</sup><sub>f</sub>)</html> | |
| Q.PotentialChemical | Deltah0 | <html><i>h</i><sup>o</sup>(298.15 K) - <i>h</i><sup>o</sup>(0 K) (Δ<i>h</i><sup>o</sup>)</html> | |
| Q.PotentialChemical | h_offset | 0 | <html>Additional enthalpy offset (<i>h</i><sub>offset</sub>)</html> |
| Integer | n_c | -2 | <html>Power of <i>T</i> for 1<sup>st</sup> column of <i>b</i><sub><i>c</i></sub> (<i>n</i><sub><i>c</i></sub>)</html> |
| Q.TemperatureAbsolute[:] | T_lim_c | {0, Modelica.Constants.inf} | <html>Temperature limits for the rows of <i>b</i><sub><i>c</i></sub> and <i>B</i><sub><i>c</i></sub> (<i>T</i><sub>lim <i>c</i></sub>)</html> |
| Real[size(T_lim_c, 1) - 1,:] | b_c | <html>Coefficients of isobaric specific heat capacity at <i>p</i><sup>o</sup> as a polynomial in <i>T</i> (<i>b</i><sub><i>c</i></sub>)</html> | |
| Real[size(T_lim_c, 1) - 1,2] | B_c | <html>Integration constants for specific enthalpy and entropy (<i>B</i><sub><i>c</i></sub>)</html> |
Contents
| Name | Description |
|---|---|
 omegaprotected | Root mean square of thermal velocity in one dimension as a function of temperature (ω = √ T/m ) |
 c_p | Isobaric specific heat capacity (cp) as a function of temperature and pressure |
 c_v | Isochoric specific heat capacity (cv) as a function of temperature and pressure |
 D | Diffusivity as a function of temperature and specific volume |
 g | Gibbs potential as a function of temperature and pressure |
 h | Specific enthalpy as a function of temperature and pressure |
 s | Specific entropy as a function of temperature and pressure |
 zeta | Continuity (ζ) as a function of temperature |
 eta | Fluidity (η) as a function of temperature |
 theta | Thermal resistivity (θ) as a function of temperature and specific volume |
 tauprime | Phase change interval (τ′) as a function of temperature and specific volume |
 mu | Mobility (μ) as a function of temperature and specific volume |
 nu | Thermal independity (ν) as a function of temperature and specific volume |