Eddy Dissipation Concept (EDC) Model
Eddy Dissipation Concept (EDC): Theoretical Foundations
Overview
Professor, what does the EDC model stand for?
It stands for Eddy Dissipation Concept, a turbulent combustion model developed by Magnussen as an extension of the Eddy Dissipation Model (EDM). EDM assumed infinitely fast chemical reactions, whereas EDC was extended to handle finite-rate detailed chemical reaction mechanisms in turbulent fields.
So it's a superior replacement for EDM?
Yes. In EDM, the reaction rate is determined by turbulent mixing, like $\dot{\omega} = A\,\rho\,\frac{\varepsilon}{k}\min(Y_F, Y_O/s)$, ignoring Arrhenius kinetics. This is valid when the Damkohler number is large (reactions are sufficiently fast), but it is inaccurate for finite-rate reactions like CO oxidation or NOx formation. EDC overcomes this limitation.
EDC Formulation
Please explain the governing equations for EDC.
EDC considers that chemical reactions proceed within the fine structures of the turbulent field. The volume fraction $\xi^*$ and residence time $\tau^*$ of the fine structures are determined from the turbulence $k$ and $\varepsilon$ as follows.
Here, $C_\xi = 2.1377$, $C_\tau = 0.4082$ (Magnussen's standard constants), and $\nu$ is the kinematic viscosity.
Does the fine structure size correspond to the Kolmogorov scale?
Sharp observation. $\xi^*$ corresponds to the volume fraction of the Kolmogorov scale, and $\tau^*$ is on the order of the Kolmogorov time scale. Physically, the image is that "chemical reactions proceed within the smallest eddies of turbulence."
Reaction Rate Expression
The mean reaction rate for chemical species $i$ can be written as follows.
Here, $Y_i^*$ is the mass fraction within the fine structure, which is the composition after detailed chemical reactions have progressed over $\tau^*$. $Y_i$ is the cell-averaged mass fraction.
How is $Y_i^*$ determined?
It is obtained by time-integrating a constant-volume 0D reactor within the fine structure for $\tau^*$. Stiff ODE solvers like CVODE are used for this 0D integration. In other words, the majority of EDC's computational cost lies in this 0D chemical reaction integration.
So the EDC concept is "solving a 0D reactor within the fine structures of turbulence."
Exactly. The strength of EDC lies in its physically clear model representation of the interaction between turbulence and chemical reactions.
The "Interface of Turbulence and Combustion" Conceived by Magnussen in Norway โ The Background of EDC's Birth
Bjรธrn Magnussen presented EDC at the Norwegian Institute of Technology (NTH) in 1977. At that time, detailed reaction mechanisms could not be solved with available computers. So he devised a model where "reactions occur only within the Kolmogorov-scale eddies of turbulence," successfully describing reactions solely with "fine structure volume fraction" and "turbulent dissipation." Despite its low computational cost, its prediction accuracy for furnaces and burners reached a practical level, quickly drawing attention from the petroleum industry. It was subsequently refined at SINTEF (Norwegian Institute for Industrial Research) and is now standard in Fluent and STAR-CCM+.
Computational Methods for Eddy Dissipation Concept (EDC)
Details of Numerical Methods
What points should I be careful about in the numerical implementation of EDC?
Computational Cost Estimation
Specifically, how much does it cost?
Let me give you a rough estimate.
| Reaction Mechanism | Number of Species | Integration Time per Cell | Total Cost for 1M Cells (1 iteration) |
|---|---|---|---|
| Global 2-step | 5 | 0.01 ms | 10 seconds |
| DRM-19 | 19 | 0.1 ms | 100 seconds |
| GRI-Mech 3.0 | 53 | 1 ms | 1000 seconds (~17 minutes) |
| Detailed C7H16 | 160 | 10 ms | 10000 seconds (~3 hours) |
17 minutes per iteration for GRI-Mech 3.0... For a steady RANS calculation with 3000 iterations, that would take 35 days.
That's precisely why combining it with ISAT is essential. Using ISAT, even GRI-Mech 3.0 can run in practical time. In Fluent, the default recommended setting is the combination of EDC + Stiff Chemistry Solver + ISAT.
Settings in Fluent
Please explain the EDC setup procedure in Fluent.
1. Enable Models > Species > Species Transport
2. Reactions: Select Volumetric and import the reaction mechanism in CHEMKIN format
3. Turbulence-Chemistry Interaction: Select Eddy Dissipation Concept
4. EDC Model Constants: Usually OK with default values ($C_\xi = 2.1377$, $C_\tau = 0.4082$)
5. ODE Solver: Enable ISAT, error tolerance $10^{-4}$
6. Solution Controls: Set Species Under-Relaxation to 0.8-0.9
Implementation in OpenFOAM
What about in OpenFOAM?
In OpenFOAM's reactingFoam solver, specify EDC in combustionProperties.
```
combustionModel EDC;
EDCCoeffs
{
version v2005;
C1 2.1377;
C2 0.4082;
}
```
OpenFOAM's EDC implementation also supports v2005 (Magnussen's 2005 revised version). The revised version includes Reynolds number-dependent $\xi^*$ correction, improving accuracy in low Re number regions.
Sensitivity of EDC Constants
How do the results change if I modify the EDC constants $C_\xi$, $C_\tau$?
Increasing $C_\xi$ increases the fine structure volume, raising the reaction rate. Increasing $C_\tau$ extends the residence time, also advancing the reaction. Usually, default values are sufficient, but there are research reports adjusting $C_\xi$ by about ยฑ20% for flame lift-off height tuning. However, this adjustment is case-dependent, and there is no universal recommended value.
So in practice, the key to EDC implementation is combining it with ISAT.
Yes. EDC calculations without ISAT are extremely time-consuming even for research purposes. Tune it along with ISAT's accuracy settings.
Combining EDC with Strang Splitting โ The Wisdom of Implementation to "Split" Reaction and Diffusion
A technique often used in the numerical implementation of the EDC model is "Strang Splitting." The time scales of the reaction source term (chemical time scale: microseconds) and turbulent mixing (fluid time scale: milliseconds) differ by orders of magnitude, so solving both as the same ODE causes stiffness to explode. The splitting method solves alternately at each time step: "first the chemical reaction step with a CHEMKIN solver in an inner loop โ then the transport step." This dramatically reduces the stiffness of each sub-step. OpenFOAM's reactingFoam also adopts this implementation, with reports of speedups of over 1.5 times just by selecting the order of Strang Splitting.
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