Chemical Equilibrium Model Reference

In this model, a few parametric variables such as the mean mixture fraction (and in non-adiabatic cases, the mean enthalpy) are tracked on the grid. The mean species concentrations, temperature, and density are obtained as functions of the mean parametric variables, after an averaging process around a presumed probability distribution (PPDF) that is considered to represent turbulent fluctuations.

Table 1. Chemical Equilibrium Model Reference
Theory	See Chemical Equilibrium.
Provided By	[physics continuum] > Models > Flamelet Models
Example Node Path	Continua > Physics 1 > Models > Chemical Equilibrium
Requires	Material: Multi-Component Gas Reaction Regime: Reacting Reacting Flow Models: Flamelet
Properties	Key properties are: Active Species, Dissipation Constant, Number of Streams. See Chemical Equilibrium Model Properties.
Activates	Physics Models	Equation of State: Ideal Gas Energy Option: Non-Adiabatic*
	Reference Values	Minimum Allowable Temperature, Maximum Allowable Temperature. See Reference Values.
	Boundary Settings	Wall Combustion Scalar Option
	Region Settings	See Region Settings
	Material Properties	See Materials and Methods
	Other Continuum Nodes	Chemical Equilibrium Table Generator. See Chemical Equilibrium Table Reference.
	Monitors	MixFrac0: Mixture Fraction 0 MixFracVar0: Mixture Fraction Variance 0
	Solvers	PPDF Combustion See also: CFM Combustion Solver Properties and TFC Combustion Solver Properties
	Field Functions	Chemistry Heat Release Rate Indicator, Mixture Fraction 0, Mixture Fraction Variance 0. See Field Functions.
	Simulation Operations	See Run Flamelet Table Generator.

*The Non-Adiabatic model is selected by default when the Chemical Equilibrium model is selected with Auto-select recommended models activated. If required, you can deselect Non-Adiabatic and select Adiabatic instead. Both the Non-Adiabatic and Adiabatic models provide properties that relate to the Chemical Equilibrium model. See Adiabatic and Non-Adiabatic Model Properties.

Chemical Equilibrium Model Properties

Active Species: Read only. Displays, from the species that are available for post-processing in the flamelet table, a sub-set of species that are accessed, used, or interpolated during the simulation. For example, species that are used in plots, reports, monitors, scenes, or custom field functions. The remaining post-processing species in the flamelet table that are not accessed during the simulation are inactive.

Dissipation Constant: Represents the ratio of velocity and chemical species fluctuations.

Reference Values

Minimum Allowable Temperature

The smallest temperature value that is permitted anywhere in the continuum.

The Energy models (Coupled Energy, Coupled Solid Energy, Segregated Solid Energy, Segregated Fluid Enthalpy, Segregated Fluid Temperature) limit temperature corrections such that the corrected value does not go below this minimum. If this occurs, a message is printed to the Output window.

Maximum Allowable Temperature

The largest temperature value that is permitted anywhere in the continuum.

The Energy models (Coupled Energy, Coupled Solid Energy, Segregated Solid Energy, Segregated Fluid Enthalpy, Segregated Fluid Temperature) limit temperature corrections such that the corrected value does not exceed this maximum. If this occurs, a message is printed to the Output window.

Boundary Settings

Wall Combustion Scalar: Selects the scalars for the wall combustion calculation.; See Wall Combustion Scalar Option.

Region Settings

Applies to any region:

Flamelet Sources Option

Provides the Flamelet Sources Term property which when activated creates the following physics conditions:

Mixture Fraction Source Option
Mixture Fraction Variance Source Option

Mixture Fraction Source Option

Available when the region condition Flamelet Sources Option has the property Flamelet Sources Term activated.


User Source Term	Corresponding Physics Values Nodes
None No source term is defined.	None.
Add to Built-In Source Term	Mass Source Allows you to define a new source term for the mass fraction that is associated with the mixture fraction. This source term is added to the existing source term in the mixture fraction transport equation. Mass Source Pressure Derivative Allows you to define a new source term to represent the derivative of the Mass Source with respect to pressure. This source term is added to the existing source term linearization in the mixture fraction transport equation. Mixture Fraction User Source Allows you to define a new source term to add to the existing source term in the mixture fraction transport equation. Mixture Fraction User Source Jacobian Allows you to define a new source term linearization to add to the existing source term linearization in the mixture fraction transport equation.
Replace Built-In Source Term	Mass Source Allows you to define a new source term for the mass fraction that is associated with the mixture fraction. This source term replaces the existing source term in the mixture fraction transport equation. Mass Source Pressure Derivative Allows you to define a new source term to represent the derivative of the Mass Source with respect to pressure. This source term linearization replaces the existing source term linearization in the mixture fraction transport equation. Mixture Fraction User Source Allows you to define a new source term to replace the existing source term in the mixture fraction transport equation. Mixture Fraction User Source Jacobian Allows you to define a new source term linearization to replace the existing source term linearization in the mixture fraction transport equation.

Mixture Fraction Variance Source Option

Available when the region condition Flamelet Sources Option has the property Flamelet Sources Term activated.


User Source Term	Corresponding Physics Values Nodes
None No source term is defined.	None.
Add to Built-In Source Term	Mixture Fraction Variance User Source Allows you to add a new source term to add to the existing sources in the mixture fraction variance transport equation. Mixture Fraction Variance User Source Jacobian Allows you to add a new source term linearization to add to the existing sources linearization in the mixture fraction variance transport equation.
Replace Built-In Source Term	Mixture Fraction Variance User Source Allows you to define a new source term to replace the existing source term in the mixture fraction variance transport equation. Mixture Fraction Variance User Source Jacobian Allows you to define a new source term linearization to replace the existing source term linearization in the mixture fraction variance transport equation.

Materials and Methods

Turbulent Schmidt Number: $σ_{t}$ in all applicable scalar transport equations, except when the Adiabatic or Non-Adiabatic model property, Separate Turbulent Schmidt Number is activated. If values are specified separately (for Turbulent Schmidt Number for Mixture Fraction, or Turbulent Schmidt Number for Mixture Fraction Variance), this Turbulent Schmidt Number property setting applies to all instances of the turbulent Schmidt number other than those that are specified separately.
Turbulent Schmidt Number for Mixture Fraction: Available when the Adiabatic or Non-Adiabatic model property Separate Turbulent Schmidt Number is activated.; Allows you to specify the turbulent Schmidt number $σ_{t, Z}$ that is specifically applied to the mixture fraction $Z$ transport equation Eqn. (3494).
Turbulent Schmidt Number for Mixture Fraction Variance: Available when the Adiabatic or Non-Adiabatic model property Separate Turbulent Schmidt Number is activated.; Allows you to specify the turbulent Schmidt number $σ_{t, Z_{var}}$ that is specifically applied to the mixture fraction variance $Z_{var}$ transport equation Eqn. (3495).

PPDF Combustion Solver Properties

Under-Relaxation Factor: In order to promote convergence, this property is used to under-relax changes of the solution during the iterative process. If residuals show solution divergence or do not decrease, reduce the under-relaxation factor.
URF for Mixture Fraction: Appears only when the solver property Separate URF Numbers is activated.; Under-relaxation factor for the mixture fraction $Z$ in Eqn. (3494).
URF for Mixture Fraction Variance: Appears only when the solver property Separate URF Numbers is activated.; Under-relaxation factor for the mixture fraction variance $Z_{var}$ in Eqn. (3495).
Solver Frozen: When On, the solver does not update any quantity during an iteration. It is Off by default. This is a debugging option that can result in non-recoverable errors and wrong solutions due to missing storage. See Finite Volume Solvers Reference for details.
Reconstruction Frozen: When On, Simcenter STAR-CCM+ does not update reconstruction gradients with each iteration, but rather uses gradients from the last iteration in which they were updated. Activate Temporary Storage Retained in conjunction with this property. This property is Off by default.
Reconstruction Zeroed: When On, the solver sets reconstruction gradients to zero at the next iteration. This action means that face values used for upwinding (Eqn. (905)) and for computing cell gradients (Eqn. (917) and Eqn. (918)) become first-order estimates. This property is Off by default. If you turn this property Off after having it On, the solver recomputes the gradients on the next iteration.
Temporary Storage Retained: When On, Simcenter STAR-CCM+ retains additional field data that the solver generates during an iteration. The particular data retained depends on the solver, and becomes available as field functions during subsequent iterations. Off by default.

Separate URF Numbers: When activated, the Under-Relaxation Factor property for the solver is removed and replaced by separate URF properties for each relevant transport equation. For example, URF for Mixture Fraction and URF for Mixture Fraction Variance.

Field Functions

Chemistry Heat Release Rate Indicator: The chemistry heat release rate is $\dot{h}$ in Eqn. (3370) for the partially-premixed Chemical Equilibrium model, and is not available for the non-premixed Chemical Equilibrium model.
Mixture Fraction 0: Represents the atomic mass fraction that originated from the fuel stream.
Mixture Fraction Variance 0: Represents the turbulent fluctuations in the fuel mixture fraction values.

Adiabatic and Non-Adiabatic Model Properties

Convection

In transport equations, you can choose from a range of schemes that calculate the convection term at a cell face. This calculation requires Simcenter STAR-CCM+ to compute the face value of a quantity from the surrounding cell values. The method used for computing this face value has a profound effect on the stability and accuracy of the numerical scheme. For guidance on selecting a convection scheme, see Convective Flux.

1st-order: First-order convection scheme.
2nd-order: Second-order convection scheme.

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

On: Default value. Solves for interior and boundary types of secondary gradient.
Off: Does not solve for either type of secondary gradient.
Interior Only: Solves for the interior secondary gradients only.
Boundaries Only: Solves for the boundary secondary gradients only.

Flow Boundary Diffusion

When activated, this property includes the flow-boundary diffusion fluxes (or viscous fluxes for flow models) as given by Eqn. (899). This property is activated by default.

Separate Turbulent Schmidt Number

When activated, allows you to specify a different turbulent Schmidt number for each flamelet transport equation that is applicable—such as the transport equations for unnormalized progress variable

y

Eqn. (3533), unnormalized progress variable variance

y_{var}

Eqn. (3537), mixture fraction

Z

Eqn. (3494), and mixture fraction variance

Z_{var}

Eqn. (3495).

It is only possible to specify custom turbulent Schmidt numbers for

y_{var}

and

Z_{var}

when the relevant flamelet table contains multiple points in the

y_{var}

and

Z_{var}

table dimensions—and additionally, if the Transport Equation method is used to calculate them.