Flame Surface Density Transport Model Reference

The flame surface density (FSD) is the area of the flame per unit volume. The turbulent flame speed is then proportional to the FSD, as well as the laminar flame speed and the unburnt reactants density.

表 1. Flame Surface Density Transport Model Reference
Theory	See Flame Propagation.
Provided By	[physics continuum] > Models > ECFM Flame Propagation Models
Example Node Path	Continua > Physics 1 > Models > Flame Surface Density Transport
Requires	In Simcenter STAR-CCM+ In-cylinder (open separate add-on): Optional Models:Combustion Combustion Model:ECFM-3Z or ECFM-CLEH In-Cylinder Time: Any Turbulence: Any Any other ICE models that are required. In Simcenter STAR-CCM+, at least the following should be activated: Space: Three Dimensional Material: Multi-Component Gas Reaction Regime: Reacting From In-Cylinder: In-Cylinder Combustion From In-Cylinder: ECFM-3Z or ECFM-CLEH
Properties	Key properties are: Laminar Flame Speed Option, Flame Turbulent Stretch Coefficient, Alpha, Flame Curvature Coefficient Beta. See Flame Surface Density Transport Properties.
Activates	Model Controls	Laminar Flame Properties (Laminar Flame Speed and Laminar Flame Thickness), Turbulence Flame Quenching, and Flame Surface Density Ignition Transition (when using the Large Eddy Simulation model).
	Initial Conditions	Flame Surface Density. See Initial Conditions.
	Field Functions	Laminar Flame Speed, Laminar Flame Thickness. See Field Functions.

Flame Surface Density Transport Model Properties

RANS

Flame Turbulent Stretch Coefficient Alpha: The empirical coefficient $α$ for the production term due to turbulent stretch in the flame surface density transport equation Eqn. (3909).
Flame Curvature Coefficient Beta: The empirical coefficient $β$ for the destruction term due to flame curvature in the flame surface density transport equation Eqn. (3909).
Turbulent Quenching: When activated, enables turbulence flame quenching in broken reaction zones, indicated by a Karlovitz number ${K a}_{δ} > 1$ (see Eqn. (3922)).
LenScQRatio: Length scales quenching ratio $D_{q u e r a t}$ in Eqn. (3916).
Option LgamCor: A coefficient for the $\frac{\partial p}{\partial t}$ term in Eqn. (3909).
LamStrainFactor: Multiplier for laminar strain rate, $F_{l s}$ in Eqn. (3909).
Velocity Divergence Factor: Multiplier for the velocity divergence term $C_{d i v u}$ in Eqn. (3909).
Sigma Production Factor: Multiplier for the overall production term $F_{Σ_{p r o d}}$ in Eqn. (3909).

LES

Parameter for Filter Resolution: $N_{r e s}$ in Eqn. (3900). Adjusts the filter size that is used to filter the species, enthalpy, and flame surface density equations inside the flame.
Turbulent Quenching: When activated, enables turbulence flame quenching in broken reaction zones, indicated by a Karlovitz number ${K a}_{δ} > 1$ (see Eqn. (3922)).
Model Constant c*: $c^{*}$ in Eqn. (3897).
Model Constant Beta: $β$ in Eqn. (3897).
Flame Limit: Minimum value for the progress variable.
Wall Quenching Factor: $q_{w}$ in Eqn. (3901) that is used to control the flame quenching near walls.

Initial Conditions

Flame Surface Density: Allows you to specify an initial profile for the flame surface density $Σ$ in Eqn. (3909).

Field Functions

层流火焰速度: $S_{l, 0}$ （位于 Eqn. (3917) 中）。
层流火焰厚度: $δ_{l}$ （位于 Eqn. (3915) 中）。

Laminar Flame Speed

Method

Provides options for controlling the unstrained laminar flame speed for ECFM combustion.

Method	Corresponding Method Node
Extended Metghalchi-Keck Laminar Flame Speed Uses the Extended Metghalchi-Keck laminar flame speed correlation Eqn. (3917).	Extended Metghalchi/Keck Laminar Flame Speed Provides the properties: First Coefficient for EGR Scaling Exhaust gas recirculation (EGR) scaling coefficient number one. $U_{l a m 1}$ in Eqn. (3917). Second Coefficient for EGR Scaling Exhaust gas recirculation (EGR) scaling coefficient number two. $U_{l a m 2}$ in Eqn. (3917). Coefficient for Pressure Scaling Pressure scaling coefficient $U_{l a m 3}$ in Eqn. (3918). Coefficient for Pressure Scaling Below the Transitional Pressure Value Pressure scaling coefficient when the pressure is below the transitional pressure value. $U_{l a m 3 b e l o w}$ in Eqn. (3918). Normalized Transitional Pressure Value for Pressure Scaling $p_{t r a n s l}$ in Eqn. (3918).
Precomputed LFS Table	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.
Universal Laminar Flame Speed	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.
User Defined Laminar Flame Speed Allows you to provide the unstrained laminar flame speed.	Allows you to define the laminar flame speed profile under the User Defined Laminar Flame Speed > Laminar Flame Speed Profile node. See What is Table (Equivalence Ratio)?

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

Provides options for controlling the laminar flame thickness for ECFM combustion.


Method	Corresponding Method Node
Correlation Laminar flame thickness $δ_{l}$ is calculated according to Eqn. (3915).	None
User Defined Laminar Flame Thickness Allows you to provide the laminar flame thickness.	Allows you to define the laminar flame speed profile under the User Defined Laminar Flame Thickness > Laminar Flame Thickness Profile node.

Turbulence Flame Quenching

Provides options for controlling turbulence flame quenching for ECFM combustion.


Method	Corresponding Method Node
Internal The turbulence flame quenching factor $q$ is calculated according to Eqn. (3921).	Allows you to control flame quenching by setting the Reaction Zone Thickness Multiplier, $δ$ in Eqn. (3922).
User Defined Turbulence Flame Quenching Allows you to define the turbulence flame quenching factor using any of the standard profile methods available in Simcenter STAR-CCM+.	Allows you to specify the turbulence flame quenching factor under the User Defined Turbulence Flame Quenching > Turbulence Flame Quenching Profile node.

Flame Surface Density Ignition Transition

Appears under the Flame Surface Density Transport node when using the Large Eddy Simulation model.

Sector Angle: Angle of the sector mesh.
First Ignition Transition Function Constant: Tuning parameter $α_{1}$ used in the ISSIM flame kernel transition function Eqn. (4007).
Second Ignition Transition Function Constant: Tuning parameter $α_{2}$ used in the ISSIM flame kernel transition function Eqn. (4007).
Turbulent Wrinkling Factor: Turbulent wrinkling factor $Ξ$ used to account for flame stretch during ignition when calculating the flame surface density Eqn. (4005).

Progressive Flame Thickening During Ignition: When activated, uses the transition function $α$ in Eqn. (4007) to progressively thicken the flame (as required by the LES Flame Surface Density) from early kernel development to a fully propagating flame.