### Slide 1

```Non-premixed turbulent combustion
(Flamelet Progress Variable
Approach (FPVA))
Flamelet-based combustion model for
compressible flows
Source term is highly non-linear
The source term:
N sp
N sp

 kj'
 '' 
m i   Wi ij  K fj  X k   K rj  X k  kj 
j 1
k 1
k 1


N reac
with
 E j 
K fj  A fjT exp

 RT 
j

Model algorithm
Transported variables
All other quantities
• EOS
• Mixing rules
NSE
Temperature
• Newton iteration
• Not looked up from
table
Turbulence
Combustion
Tabulated chemistry
• Table lookup
• Pre-computed chemistry
Chemistry does not
account for
compressibility
effects and viscous
heating
Flamelet models for non-premixed combustion
The basic assumption is that the chemical time-scales are short enough so that reactions
occur in a thin layer around stoichiometric mixture on a scale smaller than the small scales
of the turbulence. Physically, the flame structure is locally one-dimensional and depends
only on time and on the coordinate normal to the flame front (or on z).
This has two consequences: the structure of the reaction zone remains laminar, and
diffusive transport occurs essentially in the direction normal to the surface of stoichiometric
mixture. Then, the scalar transport equations can be transformed to a system where the
mixture fraction is an independent coordinate.
A subsequent asymptotic approximation leads to the flamelet equations.
The species mass fractions are related to the mixture fraction Z by the solution of the
steady flamelet equations, parameterized by the scalar dissipation rate.
Z 2
  2D 
x 
Compute flamelet equations
and create chemistry table from the solutions
Step 1:
Step 2:
Goal : Create chemistry table
Inputs : batesgn.therm (thermodata)
batesgn.trans (transportdata)
batesgn.mech (reactions)
1) CreateBinFile
batesgn.therm
batesgn.trans
 thermo.bin
2) ScanMan
thermo.bin
batesgn.mech
 batesgn.pre
3) FlameMaster
batesgn.pre
.in (input file with start profile)
 Flamelet solution
Introducing the assumption of a betafunction sub-filter distribution of the