Flamelet Generated Manifold Model Reference

FGM Model

For simulations involving combustion, it is often important to include a detailed reaction mechanism, which has many reactions and many species. Inclusion of such a mechanism in a CFD simulation with realistic geometries, however, inevitably leads to a large computational cost.

In the FGM model, the effects of detailed chemistry on combustion are stored in a Flamelet table and the required values are retrieved during the CFD simulation. A progress variable is used to facilitate interactions between CFD computation and the Flamelet table.

Table 1. FGM Model Reference
Theory	See Flamelet Generated Manifold.
Provided By	[physics continuum] > Models > Flamelet Models
Example Node Path	Continua > Physics 1 > Models > Flamelet Generated Manifold (FGM)
Requires	Material: Multi-Component Gas Reaction Regime: Reacting Reacting Flow Models: Flamelet
Properties	Key properties are: FGM Constant, Alpha. See FGM Model Properties.
Activates	Physics Models	FGM Reaction and Ideal Gas Equation of State for FGM
	Model Controls (child nodes)	Mixture Fraction Variance Progress Variable Variance See Model Controls
	Material Properties	See Materials and Methods
	Initial Conditions	Mixture Fraction Profile and Mixture Fraction Variance Profile. See Initial Conditions.
	Boundary Settings	Wall Combustion Scalar Option. See Boundary Settings.
	Region Settings	Active Reactions Option, Flamelet Sources Option. See Region Settings.
	Other Continuum Nodes	FGM Table. See FGM Table Reference. The Ignitors node provides the right-click option to create a Progress Variable Ignitor. See Ignitors.
	Solvers	FGM Combustion
	Field Functions	Chemistry Heat Release Rate Indicator, Combustion Scalar Diffusion Coefficient, Heat Loss Ratio, Mach Number, Mixture Fraction 0, Mixture Fraction Variance 0, Progress Variable. See Field Functions.
	Simulation Operations	See Run Flamelet Table Generator.

Flamelet Generated Manifold (FGM) 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.

FGM Constant, Alpha

A scaling factor multiplying the progress variable source term.

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, diffusion is calculated across the flow boundary for all combustion scalars (for example, mixture fraction, mixture fraction variance, and progress variable).

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.

Model Controls

Mixture Fraction Variance

Available when the Large Eddy Simulation (LES) turbulence model is selected, and when the Maximum Number of Grid Points property within the FGM Table Generator > Parameters > 0D Ignition Numerical Settings > Table Dimensions > Mixture Fraction Variance node is set to a value greater than 1.

Method	Corresponding Method Node
Transport Equation Computes the mixture fraction variance using the standard Simcenter STAR-CCM+ calculations.	None.
Algebraic Relationship Computes the mixture fraction variance using Eqn. (3505).	Algebraic Relationship—allows you to specify the model constant, $c_{v}$ , in Eqn. (3505).

Progress Variable Variance

Available when the Large Eddy Simulation (LES) turbulence model is selected, and when the Maximum Number of Grid Points property, within the FGM Table Generator > Parameters > 0D Ignition Numerical Settings > Table Dimensions > Progress Variable Variance node, is set to a value greater than 1.

Method	Corresponding Method Node
Transport Equation Computes the progress variable variance using a transport equation, Eqn. (3537).	None.
Algebraic Relationship Computes the progress variable variance using Eqn. (3536).	Algebraic Relationship—allows you to specify the Cv model constant, $c_{v}$ , in Eqn. (3536).

Materials and Methods

Molecular Weight: The Molecular Weight Method is set to Flamelet Table by default. This setting specifies that all values for Molecular Weight are taken from the values in the FGM Flamelet Table.
Specific Heat: The Specific Heat Method is set to Flamelet Table by default. This setting specifies that all values for Specific Heat are taken from the values in the FGM Flamelet Table.
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).
Turbulent Schmidt Number for Progress Variable: Available when the Flamelet Generated Manifold (FGM) model property Separate Turbulent Schmidt Number is activated.; Allows you to specify the turbulent Schmidt number $σ_{t, y}$ that is specifically applied to the unnormalized progress variable $y$ transport equation Eqn. (3533).
Turbulent Schmidt Number for Progress Variable Variance: Available when the Flamelet Generated Manifold (FGM) model property Separate Turbulent Schmidt Number is activated.; Allows you to specify the turbulent Schmidt number $σ_{t, y_{var}}$ that is specifically applied to the unnormalized progress variable variance $y_{var}$ transport equation Eqn. (3537).

Initial Conditions

Mixture Fraction

The mixture fraction is the atomic mass fraction that originated from the fuel stream. 1.0 is equal to 100%. To initialize with pure oxidizer, maintain the default of 0.0. For inflows where the mixture is unburnt, the Mixture Fraction Profile is the mass fraction of the fuel.

Mixture Fraction Variance

The mixture fraction variance is a measure of turbulent fluctuations in the local mixture fraction values. It is a scalar quantity whose initial and boundary condition values are entered in the Properties window as a scalar array profile. In simulations that use the Large Eddy Simulation (LES) model, you can select one of two methods for mixture fraction variance:

Transport Equation: Uses standard Simcenter STAR-CCM+ calculations.
Algebraic Relationship: Activates the Algebraic Relationship node which allows you to set values for the model constant, $C_{v}$ in Eqn. (3537), and the Internal Dissipation Constant, $C_{d}$ in Eqn. (3538).

Boundary Settings

Wall

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

Region Settings

Applies to any region:

Active Reactions Option

Activates or deactivates chemical reactions in this 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
Progress Variable Source Option
Progress Variable Variance Source Option

Progress Variable 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.
Add to Built-In Source Term	Progress Variable User Source Allows you to add a new source term to the existing sources in the progress variable transport equation. Progress Variable User Source Jacobian Allows you to add a new source term linearization to the existing sources in the progress variable transport equation.
Replace Built-In Source Term	Progress Variable User Source Allows you to define a new source term to replace the existing source term in the progress variable transport equation. Progress Variable User Source Jacobian Allows you to define a new source term linearization to replace the existing source term linearization in the progress variable transport equation.

Progress Variable 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.
Add to Built-In Source Term	Progress Variable Variance User Source Allows you to add a new source term to the existing sources in the progress variable variance transport equation. Progress Variable Variance User Source Jacobian Allows you to add a new source term linearization to the existing sources linearization in the progress variable variance transport equation.
Replace Built-In Source Term	Progress Variable Variance User Source Allows you to define a new source term to replace the existing source term in the progress variable variance transport equation. Progress Variable Variance User Source Jacobian Allows you to define a new source term linearization to replace the existing source term linearization in the progress variable variance transport equation.

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.

FGM 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).

URF for Progress Variable: Appears only when the flamelet solver property Separate URF Numbers is activated.; Under-relaxation factor for the progress variable $y_{}$ in Eqn. (3532).

URF for Progress Variable Variance: Appears only when the flamelet solver property Separate URF Numbers is activated, and if using the Flamelet Generated Manifold model, the model property Progress Variable Variance is set to Transport Equation.; Under-relaxation factor for the progress variable variance $y_{var}$ in Eqn. (3537).

URF for Flame Area Density: Available only with the Coherent Flame Model model.; Appears only when the flamelet solver property Separate URF Numbers is activated.; Under-relaxation factor for the flame area density variance $Σ$ in Eqn. (3563).
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, URF for Mixture Fraction Variance, and URF for Progress Variable Variance.

Field Functions

Chemistry Heat Release Rate Indicator: The chemistry heat release rate is $\dot{h}$ in Eqn. (3367).
Combustion Scalar Diffusion Coefficient: $Γ_{y}$ in Eqn. (3534)—for the unnormalized progress variable.
Progress Variable: The progress variable, $c$ in Eqn. (3535).