### 1.4.3. Equation of State

Equations of state can be modeled in the following ways in CFX:

- Setting Density directly

- Using the built in Ideal Gas equation

- Using the built in Real Gas equations

- Using the built in IAPWS equation

- Reading properties from a CFX-TASCflow RGP table. For details, see Real Fluid Properties.

All properties except density and specific heat capacity, can be modeled using any valid expressions containing CFX System Variables.

#### 1.4.3.1. Option

##### 1.4.3.1.1. Value

This selection gives a fair amount of flexibility in modeling the variation in density. For example, it can be used to model a variety of different fluid types:

- Constant

- Variation with temperature and pressure not available as a built-in model

Variation with temperature and pressure can be set up using analytic CEL expressions or CEL user functions. Many of the popular thermal equations of state (for example van der Waals, Peng-Robinson, Beattie-Bridgemann,...) are explicit in pressure, rather than density. So, if the built-in Redlich Kwong equation is not suitable, then you will need to either create your own RGP table, or use a CEL user function to define your equation of state. Simply pass pressure and temperature into your user CEL function and then use a root finder to come up with values of density. For details, see Real Gas Property (RGP) File Format.

The constitutive relation is set by specifying specific heat at constant pressure. Again, this can be a constant or enabled to vary as a function of temperature and pressure the same as density.

Transport properties can also be specified in the same ways as density and specific heat, but can additionally depend on other CFX System Variables, not just temperature and pressure.

The special dependency of density and specific heat capacity on local pressure or temperature can be set using the Density Dependency and Specific Heat Dependency forms. For details, see Density and Specific Heat Dependencies.

##### 1.4.3.1.2. Ideal Gas

For many situations involving compressible flow, the thermodynamic properties for real fluids can be closely approximated using the relationships for an ideal gas. The Ideal Gas model uses the Ideal Gas law to calculate the local density variation in the fluid. The density is automatically computed using the specified molecular weight. For details, see Dynamic Viscosity.

The relationships are especially suited to compressible gas flows at low density under the following conditions:

- At low pressures (~ 1 bar), regardless of temperature.

- At high pressures (>> 1 bar), providing the temperature is also reasonably high (that is, > 2 x critical temperature for the gas). At temperatures lower than this, together with relatively low pressures (such as atmospheric), significant deviations from the ideal gas approximations may exist.

##### 1.4.3.1.3. Real Gas

The real gas option enables you to use the Redlich Kwong [85] or Peng Robinson [157] equations of state. These are three parameter state equations that can be used to model for gas density, and additionally, liquid density with the Peng Robinson equation. Minimal input is required. You need to enter the critical temperature, pressure and volume as well as the acentric factor for the pure substance. These equations are suitable for modeling subcritical gas phases and supercritical properties. Only the Peng Robinson equation will provide reasonably accurate results for subcritical liquid phase materials.

When you select a cubic equation of state the flow solver automatically generates a table of values for density at a range of temperatures and pressures. The default range is T = 100 K - 1000 K and p = 0.01 bar - 2 bar. You can change this range by selecting the table generation option and setting minimum and maximum temperature and pressure limits to what makes sense for your model.

In order to accurately model the influence of the vapor dome, the critical volume and acentric factor are provided. This enables the CFX-Solver to calculate where the vapor pressure curve cuts through the default temperature and pressure range or the range you have supplied.

Finally, to provide a default reference temperature and pressure the flow solver also requires the Boiling Temperature of the fluid at one atmosphere.

For details on real gases, see Real Gas Properties in the CFX-Solver Theory Guide.

##### 1.4.3.1.4. IAPWS Library

The IAPWS equation of state is specific for water. If your model set-up requires subcooled water or superheated steam, especially with phase change, then this is the best option available.

The library materials are grouped into several temperature and pressure ranges for convenience, but you can define new materials with custom temperature and pressure ranges.

For specific temperature and pressure limitations, see IAPWS Equation of State in the CFX-Solver Theory Guide. For details on importing library data, see Library Materials in the CFX-Pre User's Guide.

#### 1.4.3.2. Molar Mass

For all pure substances CFX requires that you provide the Molar Mass (relative molecular mass). The molecular mass of an element or compound is defined as the average mass of its molecules on a scale where one atom of C12 (isotope of carbon) has a mass of 12 units.

For an Ideal Gas or the Redlich Kwong equation of state, it is essential to set the correct Molar Mass because it is always used by the CFX-Solver. When you specify density directly using Option=Value, the Molar Mass is used only in certain situations:

- When the fluid is involved in a chemical reaction.

- When species transfer occurs for a multiphase-multicomponent simulation. For details, see Interphase Species Mass Transfer.

In other cases, it is not essential to specify an accurate Molar Mass. However, for a multicomponent flow, the derived solution variables `<component>.Molar Concentration` and `<component>.Molar Fraction` will not be accurate unless the correct Molar Mass is set.

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