Thickened Flame Model Reference

The propagation speed of premixed flame fronts depends on the rate that heat and species diffuse into the flame as well as the subsequent chemical reaction rate. To capture the correct propagation speed with a specified diffusion model and a chemical reaction model, the internal flame structure must be resolved.

Typical premixed flame thicknesses are about 1mm, which is usually smaller than the mesh size. The Thickened Flame Model (TFM) artificially thickens premixed flame fronts to sufficiently resolve the internal flame on the mesh.

The Thickened Flame Model is available with the Complex Chemistry (CC), Eddy Break Up (EBU), and Flamelet Generated Manifold (FGM) models—however, only with Large Eddy Simulation (LES).

Table 1. Thickened Flame Model Reference
Theory	See Thickened Flame.
Provided By	[physics continuum] > Models > Turbulence Chemistry Interactions (when CC is selected) [physics continuum] > Models > Optional Models (when EBU is selected) [physics continuum] > Models > Progress Variable Source (when FGM is selected)
Example Node Path	Continua > Physics 1 > Models > Thickened Flame Model
Requires	Material: Multi-Component Gas Space: Three Dimensional Time: any Unsteady Reaction Regime: Reacting Reacting Flow Models: Flamelet or Reacting Species Transport
	For Flamelet models: Flamelet Models: Flamelet Generated Manifold (FGM) (FGM Reaction and Ideal Gas selected automatically) Progress Variable Source: Thickened Flame Model		For Reacting Species Transport models: Reacting Species Models: Complex Chemistry or Eddy Break-up For Complex Chemistry: Turbulence Chemistry Interactions: Thickened Flame Model For Eddy Break-up: Optional Models: Thickened Flame Model
	Although the TFM is selected, continue to select the LES model:
	Flow: Segregated Flow (Gradients, Segregated Species, and Segregated Fluid Enthalpy selected automatically) Turbulence: Large Eddy Simulation (WALE Subgrid Scale, Wall Distance, and All y+ Wall Treatment selected automatically)
Properties	Number of Cells in Flame and Maximum Flame Thickening Factor. See Thickened Flame Model Properties.
Activates	Model Controls (child nodes)	Efficiency Factor Reaction Zone Sensor Laminar Flame Properties
	Field Functions	Efficiency Factor, Flame Thickening Factor, Reaction Zone Sensor See Field Functions.

Thickened Flame Model Properties

These properties are used for calculating the Flame Thickening Factor.

Number of Cells in Flame: The value $N$ in Eqn. (3465). The default value is 8.
Maximum Flame Thickening Factor: The global maximum flame thickening factor, $F_{\max}$ in Eqn. (3465). The local maximum flame thickening factor $F_{m a x}^{l o c}$ is calculated in every cell. If $F_{m a x}^{l o c}$ exceeds the specified global maximum, the flame thickening factor is clipped to the specified value. $F_{\max}$ has a default value of 20.

Model Controls

Efficiency Factor

Sets the method by which Simcenter STAR-CCM+ computes the efficiency factor. This factor increases the flame speed in order to correct underestimation of the flame front wrinkling.

Method	Corresponding Method Node
Power Law Evaluates the efficiency factor $E$ according to a Power law expression as given by Eqn. (3473).	Power Law Constant Alpha, exponent $α$ , from Eqn. (3473) Constant b, exponent $b$ , from Eqn. (3474) Constant Ck, coefficient $C_{k}$ , from Eqn. (3475) through Eqn. (3477)
Turbulent Flame Speed Evaluates the efficiency factor based on the ratio of turbulent flame speed to laminar flame speed, as specified in Eqn. (3483). See Turbulent Flame Speed.	Turbulent Flame Speed Constant Alpha, the constant multiplier $α$ from Eqn. (3483) Turbulent Flame Speed Option Turbulent Flame Speed - Zimont See Zimont Turbulent Flame Speed. Turbulent Flame Speed - Peters See Peters Turbulent Flame Speed. Turbulent Flame Speed - User-Defined See User Defined Turbulent Flame Speed.
Wrinkling Factor Ratio Evaluates the efficiency factor from the expression in Eqn. (3480).	Wrinkling Factor Ratio Constant cms, coefficient $c_{m s}$

Method

Corresponding Method Node

Power Law

Evaluates the efficiency factor $E$ according to a Power law expression as given by Eqn. (3473).

Power Law

Constant Alpha, exponent $α$ , from Eqn. (3473)
Constant b, exponent $b$ , from Eqn. (3474)
Constant Ck, coefficient $C_{k}$ , from Eqn. (3475) through Eqn. (3477)

Turbulent Flame Speed

Evaluates the efficiency factor based on the ratio of turbulent flame speed to laminar flame speed, as specified in Eqn. (3483).

See Turbulent Flame Speed.

Turbulent Flame Speed

Constant Alpha, the constant multiplier $α$ from Eqn. (3483)
Turbulent Flame Speed Option
- Turbulent Flame Speed - Zimont
  
  See Zimont Turbulent Flame Speed.
- Turbulent Flame Speed - Peters
  
  See Peters Turbulent Flame Speed.
- Turbulent Flame Speed - User-Defined
  
  See User Defined Turbulent Flame Speed.

Wrinkling Factor Ratio

Evaluates the efficiency factor from the expression in Eqn. (3480).

Wrinkling Factor Ratio

Constant cms, coefficient $c_{m s}$

Reaction Zone Sensor

The Thickened Flame Model artificially thickens premixed flame fronts to resolve them on the mesh, by increasing thermal and species diffusivities. Enhanced diffusivities away from the flame front would affect other physics such as mixing, droplet evaporation and wall heat transfer. Hence, thickening is only performed around the flame front, and moves dynamically in time with the flame front. There are several options to calculate this reaction zone sensor.

Method	Corresponding Method Node
Arrhenius Available for the Eddy Break-up model only, as formulated in Eqn. (3468) to Eqn. (3464). Applies to global chemistry schemes.	Arrhenius Constant Beta, coefficient $β$ , from Eqn. (3464) Constant Gamma, coefficient $Γ$ , from Eqn. (3469).
Progress Variable Available for the Flamelet Generated Manifold model only.	Progress Variable Constant Beta, coefficient $β$ , from Eqn. (3466).
Progress Variable Reaction Rate Available for the Flamelet Generated Manifold model only.	Progress Variable Reaction Rate Constant Beta, coefficient $β$ , from Eqn. (3467).
Heat Release Rate Available for the Eddy Break-up model and the Complex Chemistry model only.	Heat Release Rate Constant Beta, coefficient $β$ , from Eqn. (3471).
Reaction Rate Available for the Eddy Break-up model and the Complex Chemistry model only.	Reaction Rate Constant Beta, coefficient $β$ , from Eqn. (3472).
User-Defined Sets the reaction zone sensor.	User-Defined The user scalar profile should be unity inside the flame zone and zero outside.

Laminar Flame Properties

Laminar Flame Speed

Provides options for controlling the laminar flame speed in its properties.

Method	Corresponding Method Node
Flamelet Table Laminar Flame Speed Available when the FGM model is used and the Reactor Type is set to 1D Premixed Freely Propagating.	Uses the laminar flame speed that is stored in the flamelet table generated by the FGM Table Generator. See FGM Table. Activates the Flamelet Table Laminar Flame Speed node.
Gulder Laminar Flame Speed	Uses the Gülder laminar flame speed correlation Eqn. (3579). Activates the Gulder Laminar Flame Speed node which allows you to select a fuel using the Fuel Name property.
Metghalchi Laminar Flame Speed	Uses the Metghalchi laminar flame speed correlation Eqn. (3573). Activates the Metghalchi Laminar Flame Speed node which allows you to select a fuel using the Fuel Name property.
Universal Laminar Flame Speed Available for the Flamelet Generated Manifold model only.	Simcenter STAR-CCM+ identifies the best laminar flame speed correlation for each individual fuel in a mixture of fuels and then uses the Hirasawa method to calculate the laminar flame speed of the blended mixture of fuels that are specified Eqn. (3571). Hydrocarbons, alcohols, hydrogen and ammonia are considered as fuels. Activates the Universal Laminar Flame Speed node.
Precomputed LFS Table Available for the Complex Chemistry model only.	Uses values taken from the Laminar Flame Speed Table that is specified under the Table Generators > LFS Table Generator node. Activates the Precomputed LFS Table node which allows you to select the Laminar Flame Speed Table defined in LFS Table Generator.
User Defined Laminar Flame Speed	Allows you to specify the unstrained laminar flame speed. Activates the User Defined Laminar Flame Speed node.

Flame Speed Multiplier

Available for all Laminar Flame Speed (LFS) methods.

Allows you to multiply the LFS with a scale factor. The flame speed multiplier is applied to

S_{l}

obtained from any of the LFS methods in Flame Speed Calculations.

Increasing the multiplier will increase the LFS and therefore the Turbulent Flame Speed. The recommended value ranges from 0.5 to 2. The default of 1 indicates that no multiplier is applied.

Laminar Flame Thickness

The Laminar Flame Thickness node provides options for controlling the flame thickness.

Method	Corresponding Method Node
Power Law Thermal Diffusivity	Power Law Thermal Diffusivity The laminar flame thickness is calculated using Eqn. (3486).
Sutherland Law Thermal Diffusivity	Sutherland Law Thermal Diffusivity The laminar flame thickness is calculated using Eqn. (3484).
User Defined Laminar Flame Thickness	User Defined Laminar Flame Thickness Sets the laminar flame thickness using its Laminar Flame Thickness Profile sub-node. The options for user defined laminar flame thickness include field functions, tables as functions of equivalence ratio, and user code.

Field Functions

Efficiency Factor: The efficiency factor models an increase in the turbulent flame speed due to eddies smaller than the thickened flame, which are lost in the artificial thickening process. See $E$ in Eqn. (3463).
Flame Thickening Factor: The flame is artificially thickened by $F$ to resolve on the mesh. See $F$ in Eqn. (3465).
Reaction Zone Sensor: The zone around the flame front where diffusivities are increased and reaction rates decreased. See $Ω$ in Eqn. (3463).