Introduction to Reactive Flows modeling using ANSYS FLUENT Eddy-dissipation model (EDM)

1. Reactive Flows
A model boiler. CFD models such as these give utility
engineers greater insight into a boiler's performance and
emissions.
Courtesy: Reaction Engineering InternationalDr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)

2. Presented by: Mohammad Jadidi 2
Equations governing reacting flowsReactive Flows
FLUENT can model the mixing
and transport of chemical species
by solving conservation equations
describing convection, diffusion,
and reaction sources for each
component species.
 Conservation equations
– Continuity equation (conservation of mass)
– Transport of momentum
– Transport of Energy
– Transport of molecular species
 Equation of State
 Turbulence Transport
– Transport of turbulent kinetic energy
– Transport of turbulent dissipation rate
– Transport of turbulent Reynolds stresses
– Transport of moments such as 𝑢′
𝑖 𝑌′
𝑖

3. Presented by: Mohammad Jadidi 3
Species Transport EquationsReactive Flows
To solve conservation equations for chemical species, ANSYS Fluent predicts the
local mass fraction of each species, 𝑌𝑖 , through the solution of a convection-
diffusion equation for the 𝑖 𝑡ℎ species
𝑅𝑖 is the net rate of production of species by chemical reaction
𝑅𝑖 modeling using eddy dissipation model (EDM) is discussed
in details in this presentation
NOTE: Reaction may occur as a volumetric reaction or be a surface reaction.

4. Presented by: Mohammad Jadidi 4
Species Transport Equations-reaction rates modelingReactive Flows
1- finite-rate kinetics: The effect of turbulent fluctuations on
kinetics rates are neglected, and reaction rates are determined by
general finite-rate chemistry directly.
2- Eddy-dissipation model (EDM): Reaction rates are assumed to
be controlled by the turbulence, ignoring the effect of chemistry
timescales
3- Eddy-dissipation-concept (EDC) model: Detailed chemical
kinetics can be incorporated in turbulent flames,
considering timescales of both turbulence and kinetics.
See Previous lecture
(part 2)
Current lecture
(part 3)
See next lecture
(part 4)

5. 5Presented by: Mohammad Jadidi 5
Species Transport Equations-Eddy-dissipation model (EDM)Reactive Flows
2- Eddy-dissipation model (EDM):
Reaction rates are assumed to be
controlled by the turbulence, ignoring
the effect of chemistry timescales
Based on the work of Magnussen
and Hjertager (1976)
Bjørn H. Hjertager
Bjørn F. Magnussen

6. Presented by: Mohammad Jadidi 6
Reactive Flows Eddy-dissipation model (EDM)
Under some combustion conditions, fuels burn quickly and the overall rate of
reaction is controlled by turbulent mixing. For mixed-is-burned approximation,
ANSYS Fluent provides a turbulence-chemistry interaction model called the
Eddy-Dissipation Model

7. Presented by: Mohammad Jadidi 7
Reactive Flows Fast / Slow Chemistry
 Reactions limited by turbulent
mixing
 Selection of turbulence closure model is important
 Combustion in
 Furnaces
 Boilers
 Gas Turbines
 Gasifiers, Incinerators
 Flares, etc.
Fast Chemistry
Da >> 1
Slow Chemistry
Da ~ 1
 Reactions limited by chemistry and turbulence
interactions
 Turbulence/chemistry interactions are important
 Selection of reaction mechanism is important
 Reactions associated with
 Pollutants formation
 Ignition and Extinction
 Chemical Vapor Deposition (CVD)
 Non-Equilibrium Phenomenon
 Air dissociation at hypersonic speed

8. Presented by: Mohammad Jadidi 8
Reactive Flows Eddy-dissipation model (EDM)
Basic idea of EDM: Remove the influence of
chemistry
 A good assumption for fast reacting fuels (Da >> 1)
 Most of the useful fuels are fast burning
Note #1: Brian Spalding (1971) suggested eddy break-up (EBU)
model
 Introduced eddy lifetime ( = 𝑘 / 𝜀)
 Reaction rate is proportional to the inverse of eddy
lifetime
Note #2: F Magnussen and B. H. Hjertager (1976) adapted EBU
and generalized it for non-premixed and partially premixed
combustion
 Eddy dissipation model (EDM)`

9. Da >> 1
 chemical reaction is fast relative to the transport processes in the flow.
 When reactants mix at the molecular level, they instantaneously form products.
 The model assumes that the reaction rate may be related directly to the time required to mix reactants at the molecular level.
 In turbulent flows, this mixing time is dominated by the eddy properties and, therefore, the rate is proportional to a mixing
time defined by the turbulent kinetic energy, 𝑘, and dissipation, 𝜀.
 There is no kinetic control of the reaction process
Presented by: Mohammad Jadidi 9
Reactive Flows
Note: The eddy dissipation model is based on
This concept of reaction control is applicable in many industrial combustion problems where reaction rates are fast compared to reactant
mixing rates.
Eddy-dissipation model (EDM)

10. Presented by: Mohammad Jadidi 10
Reactive Flows
In EDM the net rate of production of species 𝑖 due to reaction 𝑟, 𝑅𝑖,𝑟 , is given by the smaller (that is,
limiting value) of the two expressions below
Eddy-dissipation model (EDM)
In these equations the chemical
reaction rate is governed by the large
eddy mixing time scale, k/𝜺, as in
the eddy-breakup model of Spalding.
Combustion proceeds whenever
turbulence is present (k/𝜺 > 𝟎),
and an ignition source is not required
to initiate combustion.

11. Presented by: Mohammad Jadidi 11
Reactive Flows The Eddy-Dissipation Model for LES
When the LES turbulence model is used, the turbulent mixing rate
,
𝜺
𝒌
,
is replaced by the subgrid-scale mixing rate.
𝝉 𝑺𝑮𝑺
−𝟏
= 𝟐 𝑺𝒊𝒋 𝑺𝒊𝒋

12. Presented by: Mohammad Jadidi 12
Reactive Flows
EDM is computationally cheap, but, for realistic results, only
one or two step heat-release mechanisms should be used.
WHY?
The reason is that multi-step chemical mechanisms are typically based on Arrhenius rates, which differ for each reaction. In the eddy-dissipation model, every reaction has the same, turbulent rate, and therefore the
model should be used only for one-step (reactant → product), or two-step (reactant → intermediate, intermediate → product) global reactions. The model cannot predict kinetically controlled species such as radicals.
Eddy-dissipation model (EDM)

13. Presented by: Mohammad Jadidi 13
Reactive Flows
 Simple and physically based
 Applicable to every flow configuration
Eddy-dissipation model (EDM)
 Rates are independent of temperature
React towards complete products
 Cannot capture detailed chemistry
effects
 Does not predict intermediate
species and dissociation effects
 Temperature over-predicted
 Model constants sometimes require
calibration
DisadvantagesAdvantages

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Reactive Flows Eddy-dissipation model (EDM)

15. Presented by: Mohammad Jadidi 15
Reactive Flows Species Transport tutorial #1

16. 16
Thanks
Eddy-Dissipation-Concept (EDC)
Model
Next part:
Reactive Flows
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Dr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)
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