This document discusses equations governing reacting flows as modeled in ANSYS Fluent. It describes how Fluent solves conservation equations for species mass fractions using a convection-diffusion equation, where the chemical source term Ri accounts for reaction rates. Finite-rate kinetics and turbulence-chemistry interaction models are discussed for determining Ri, including the eddy dissipation model. The Arrhenius equation is also presented for calculating forward reaction rate constants based on pre-exponential factors, temperature exponents, and activation energies specified in the kinetic mechanism.

1. Reactive Flows
Dr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)
Svante August Arrhenius
1859-1927
Jadidi.cfd@gmail.com

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 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.

5. Presented by: Mohammad Jadidi 5
Species Transport Equations-Finite-Rate Kinetics (no TCI)Reactive Flows
When no turbulence-chemistry interaction (TCI) model is used, finite-rate kinetics
are incorporated by computing the chemical source terms using general reaction-
rate expressions
1. laminar flows, where the formulation is exact
2. for turbulent flows using complex chemistry where
either the turbulence time-scales are expected to be
fast relative to the chemistry time scales
3. where the chemistry is sufficiently complex that the
chemistry timescales of importance are highly
disparate.
finite-rate kinetics is recommended for:

6. Presented by: Mohammad Jadidi 6
Reactive Flows
The 𝑟 𝑡ℎ
reaction can be written as
Species Transport Equations-Finite-Rate Kinetics (no TCI)

7. Presented by: Mohammad Jadidi 7
Reactive Flows Species Transport Equations-Finite-Rate Kinetics (no TCI)

8. Presented by: Mohammad Jadidi 8
Reactive Flows Species Transport Equations-Finite-Rate Kinetics (no TCI)

9. Presented by: Mohammad Jadidi 9
Reactive Flows Species Transport Equations-Finite-Rate Kinetics (no TCI)
The forward rate constant for reaction , 𝑘 𝑓,𝑟 , is computed using the Arrhenius expression

10. Presented by: Mohammad Jadidi 10
Reactive Flows The Arrhenius Equation

11. Presented by: Mohammad Jadidi 11
Reactive Flows
if the reaction is reversible, the backward rate constant for reaction r ,
𝑘 𝑏,𝑟 , is computed, by default, from the forward rate constant using
𝐾𝑟 is the equilibrium constant
for the 𝑟 𝑡ℎ reaction
Where ∆𝑆𝑟 and ∆𝐻𝑟 are the entropy and enthalpy of the 𝑖 𝑡ℎ
species evaluated at temperature and atmospheric pressure.
Species Transport Equations-Finite-Rate Kinetics (no TCI)

12. Presented by: Mohammad Jadidi 12
Reactive Flows
ANSYS Fluent also provides the option to explicitly specify the reversible reaction
rate parameters (pre-exponential factor, temperature exponent, and activation
energy for the reaction) if desired
Species Transport Equations-Finite-Rate Kinetics (no TCI)

13. Presented by: Mohammad Jadidi 13
Reactive Flows Species Transport Equations-Finite-Rate Kinetics (no TCI)

14. 14
Thanks
Eddy-dissipation model (EDM)
End of part #2 Next part:
Reactive Flows
https://ir.linkedin.com/in/moammad-jadidi-03ab8399
Jadidi.cfd@gmail.com
Dr. Mohammad Jadidi
(Ph.D. in Mechanical Engineering)
https://www.researchgate.net/profile/Mohammad_Jadidi
https://www.slideshare.net/MohammadJadidi