### 1.5.1. Equation of State/Density

For fixed composition, variable composition, and reacting mixtures, for which mixture density is governed by the `Ideal Mixture` option, the inverse of the mixture density is computed as a mass-fraction-weighted average of specific volumes:

| (1–34)

When the global option for Mixture Properties is set to `Non Ideal Mixture`, you can explicitly set an equation of state for the mixture in the Mixture Properties tab in the Material details view. You may choose one of two options:

- `Mixture Density`

  Sets density as a function of pressure, temperature, and composition.

- `Mixture Pressure`

  Sets pressure as a function of specific volume, temperature, and composition.

For either option, the partial derivatives with respect to temperature and pressure, for `Mixture Density`, or temperature and specific volume, for `Mixture Pressure`, have to be specified. CEL expressions may be used for defining the parameters as functions of the mixture composition and the corresponding properties of the mixture components. The following quantities are available for use in the expressions:

- Density: pressure, temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes

- d(rho)/dp at Const. T: pressure, temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes, component density derivatives with respect to pressure at constant temperature

- d(rho)/dT at Const. p: pressure, temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes, component density derivatives with respect to temperature at constant pressure

- Absolute Pressure: temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes

- dp/dv at Const. Temp.: pressure, temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes, component pressure derivative with respect to volume at constant temperature

- dp/dT at Const. Vol.: pressure, temperature, component mass fractions, component mole fractions, component molar masses, component densities, component specific volumes, component pressure derivative with respect to temperature at constant volume

The text boxes below provide CCL examples for the `Mixture Density` and `Mixture Pressure` options, respectively, for a mixture consisting of four components: H2, O2, H2O, and N2. For simplicity the examples resemble the ideal mixture rule, where for the `Mixture Pressure` option it is additionally assumed that all components are ideal gases.

    EQUATION OF STATE:
      Option = Mixture Density
      Density  = (H2.Mass Fraction/H2.Density + \
                  O2.Mass Fraction/O2.Density + \
                  H2O.Mass Fraction/H2O.Density + \
                  N2.Mass Fraction/N2.Density)^-1
      drhodp t = (H2.Mass Fraction/H2.drhodp t + \
                  O2.Mass Fraction/O2.drhodp t + \
                  H2O.Mass Fraction/H2O.drhodp t + \
                  N2.Mass Fraction/N2.drhodp t)^-1
      drhodt p = (H2.Mass Fraction/H2.drhodt p + \
                  O2.Mass Fraction/O2.drhodt p + \
                  H2O.Mass Fraction/H2O.drhodt p + \
                  N2.Mass Fraction/N2.drhodt p)^-1
    END

    EQUATION OF STATE:
      Option = Mixture Pressure
      Absolute Pressure = (H2.Mass Fraction/H2.Molar Mass + \
                           O2.Mass Fraction/O2.Molar Mass + \
                           H2O.Mass Fraction/H2O.Molar Mass + \
                           N2.Mass Fraction/N2.Molar Mass) * \
                          R*T / Specific Volume
      dpdv t = - (H2.Mass Fraction/H2.Molar Mass + \
                  O2.Mass Fraction/O2.Molar Mass + \
                  H2O.Mass Fraction/H2O.Molar Mass + \
                  N2.Mass Fraction/N2.Molar Mass) * \
                R*T / (Specific Volume^2)
      dpdt v = (H2.Mass Fraction/H2.Molar Mass + \
                O2.Mass Fraction/O2.Molar Mass + \
                H2O.Mass Fraction/H2O.Molar Mass + \
                N2.Mass Fraction/N2.Molar Mass) * \
               R / Specific Volume
    END

It is your responsibility to ensure that the partial derivatives of density or pressure are consistent with the specific heat capacity definition. For details on consistency requirements, see General Equation of State in the CFX-Solver Theory Guide.

Release 18.2 - © ANSYS, Inc. All rights reserved.