Real Gas Models Reference

Real Gas models allow you to take into account non-ideal behavior such as compressibility effects, variable specific heat, van der Waals forces, and non-equilibrium thermodynamic effects.

The following Real Gas models are available in STAR-CCM+:

Peng-Robinson—for use at high pressures and low temperatures
Redlich-Kwong—for use at high pressures and low temperatures
Soave-Redlich-Kwong—for more complex treatment of temperature
Modified Soave-Redlich-Kwong—designed to handle phase equilibrium calculations for non-polar molecules ([173], [174])
Van der Waals—designed to handle intermolecular attractive forces
Equilibrium Air—for high temperatures, to handle effects such as ionization. This model is useful for the simulation of hypersonic flows, such as nozzle flows or atmospheric re-entry.
IAPWS-IF97 Steam (for steam)—for this model, the material properties follow the IAPWS-IF97 specification [25], [26], [27].


Model Names and Abbreviations	Peng-Robinson		PR
	Redlich-Kwong		RK
	Soave-Redlich-Kwong		SRK
	Modified Soave-Redlich-Kwong		mSRK
	Van der Waals		VdW
	Equilibrium Air		EA
	IAPWS-IF97 (Steam)		IAPWS-s
Theory	Peng-Robinson Formulation Redlich-Kwong Formulation Soave-Redlich-Kwong Formulation Modified Soave-Redlich-Kwong Formulation Van der Waals Formulation Equilibrium Air Formulation IAPWS-IF97 Models
Provided by	Continua > [physics continuum] > Models > Real Gas Equation of State
Example Node Path	Continua > Physics 1 > Models > Peng-Robinson
Requires	Equation of State: Real Gas
Properties	Density Limiting (PR, RK, SRK, mSRK, VdW, EA)
Activates	Model Controls (child nodes)	Density Limits (PR, RK, SRK, mSRK, VdW, EA)
	Materials	See Real Gas Material Properties.
	Monitors	Vib. Energy
	Field Functions	See Field Functions.

Real Gas Material Properties

This table shows which material properties are used by which real gas models.


	PR	RK	SRK	mSRK	VdW	EA	IAPWS-s
Acentric Factor $ω$	✓		✓	✓
Critical Pressure $p_{c}$	✓	✓	✓	✓	✓		✓
Critical Temperature $T_{c}$	✓	✓	✓	✓	✓		✓
Fugacity Coefficient	✓	✓	✓	✓	✓
Molecular Weight	✓	✓	✓	✓	✓	✓	✓
Saturation Pressure							✓
Saturation Temperature							✓
Specific Heat	✓	✓	✓	✓	✓	✓	✓
Speed of Sound						✓	✓

Acentric Factor

Critical Pressure

Displays the model constant

p_{c}

(read-only).

Critical Temperature

Displays the model constant

T_{c}

(read-only).

Fugacity Coefficient

The ratio of the fugacity and the partial pressure of gas mixture component

i

ϕ_{i}

in Eqn. (81). The coefficient is 1 for ideal gases.

Molecular Weight

Specifies the molecular weight

M

Saturation Pressure

Specifies the saturation pressure.

Saturation Temperature

Specifies the temperature for the corresponding saturation pressure at which the liquid boils into its vapor phase.

Specific Heat

Specifies the fluid-specific heat capacity

C_{p}


Method	Corresponding Method Node
Constant (SRK, mSRK, PR, RK, VdW)	Constant Specifies the specific heat using a scalar profile value.
Equilibrium Air (EA)	Equilibrium Air This node provides no properties.
Fully Excited (TNEq)	Fully Excited This node provides no properties.
Gas Kinetics (SRK, mSRK, PR, RK, VdW) Uses the Gas Kinetics Method for Specific Heat.	Gas Kinetics This node provides no properties. Selecting the Gas Kinetics method adds the following material properties: Electronic Partition Function Specifies the partition function for electronic energy using a Number of Modes with Characteristic Temperatures $θ_{i}$ and Mode Degeneracies $g_{i}$ . See $Q_{e l}$ in Eqn. (163). Molecule Type Describes the molecular structure using the following values: 0: atom 1: linear molecule 2: non-linear molecule Standard State Temperature Specifies the temperature at which the standard state of the fluid is defined. The Standard State Temperature is used to calculate enthalpy. The enthalpy value varies with Standard State Temperature, but in direct proportion, so differences in enthalpy remain the same for different values of Standard State. Vibrational Partition Function For polyatomic molecules, specifies the partition function for vibrational energy using a Number of Modes with Characteristic Temperatures $θ_{i}$ and Mode Degeneracies $g_{i}$ . See $Q_{v i b}$ in Eqn. (163).
IAPWS-IF97 (IAPWS-s)	IAPWS-IF97 This node provides no properties.
Polynomial in T (PR, RK, SRK, mSRK, VdW)	Polynomial in T See Using Polynomial in T. Selecting the Polynomial in T method adds the following material property: Standard State Temperature As for Gas Kinetics.
Table, Cp(T) (PR, RK, SRK, mSRK, VdW) Tabulates specific heat as a function of temperature.	Table, Cp(T) See Using Table(T).
Thermodynamic Polynomial Data (SRK, mSRK, PR, RK, VdW)	Thermodynamic Polynomial Data See Using Thermodynamic Polynomial Data.

Speed of Sound

Specifies the rate of acoustic propagation in the medium using one of the following methods:


Method	Corresponding Method Node
Equilibrium Air (EA)	Equilibrium Air This node provides no properties.
IAPWS-IF97 (IAPWS-s)	IAPWS-IF97 This node provides no properties.

Field Functions

The following table shows which field functions become available for which real gas model:


	PR	RK	SRK	mSRK	VdW	EA	IAPWS-s
Compressibility Factor	✓	✓	✓	✓	✓	✓	✓
Critical Pressure	✓	✓	✓	✓	✓		✓
Critical Temperature	✓	✓	✓	✓	✓		✓
Entropy	✓	✓	✓	✓	✓	✓	✓
Entropy Function	✓	✓	✓	✓	✓
Gas Constant	✓	✓	✓	✓	✓	✓	✓
IAPWS Region ID							✓
Mach Number	✓	✓	✓	✓	✓	✓	✓
Molecular Weight	✓	✓	✓	✓	✓	✓	✓
Ratio of Specific Heats	✓	✓	✓	✓	✓		✓
Real Gas Specific Heat	✓	✓	✓	✓	✓
Reduced Pressure	✓	✓	✓	✓	✓		✓
Reduced Temperature	✓	✓	✓	✓	✓		✓
Relative Mach Number	✓	✓	✓	✓	✓	✓	✓
Saturation Pressure							✓
Saturation Temperature							✓
Speed of Sound	✓	✓	✓	✓	✓	✓	✓

Compressibility Factor

Represents the amount of deviation of the real gas from an ideal gas, expressed as

Z = p / (ρ R T)

. This factor usually takes on values around 1.

For the Equilibrium Air model, the compressibility factor represents the degree of dissociation, which is non-ideal behavior, but has values that vary more widely (approximately between 1 and 6). A simplified formula that applies to the equilibrium air model is given as Eqn. (686).

Critical Pressure

Expressed as

p_{c}

Critical Temperature

Expressed as

T_{c}

Entropy

See Entropy.

Entropy Function

See Entropy Function.

Gas Constant

The specific gas constant.

IAPWS Region ID

Data that Simcenter STAR-CCM+ calculates for a particular IAPWS validity region.

Mach Number

The local Mach number.

Molecular Weight

The molecular weight as specified for the material.

Ratio of Specific Heats

Expressed as:

$γ = \frac{C_{p}}{C_{v}} = \frac{C_{p}}{(C_{p} - R)}$

where $C_{p}$ is specific heat J/(kg K), and $R$ is a specific gas constant J/(kg K).

Real Gas Specific Heat

The value of specific heat at constant pressure of the real gas. This field function accounts for the effects of variations in both temperature and pressure by including the departure from the ideal gas value. The last three terms on the right-hand side of Eqn. (192) give the departure from ideal:

Figure 1. EQUATION_DISPLAY

C_{p} = \begin{matrix} C_{p}^{0} + T \int_{\infty}^{v} {(\frac{\partial^{2} P}{\partial T^{2}})}_{v} d ν \\ - T {(\frac{\partial P}{\partial T})}_{v}^{2} {(\frac{\partial P}{\partial v})}_{T}^{- 1} - R \end{matrix}

(192)

Reduced Pressure

Expressed as

p_{r} = p / p_{c}

Reduced Temperature

Expressed as

T_{r} = T / T_{c}

Relative Mach Number

Saturation Pressure

The saturation pressure as specified for the material.

Saturation Temperature

The saturation temperature as specified for the material.

Speed of Sound

The rate of acoustic propagation in the medium.