Reacting flow computations with detailed mechanisms can be computationally demanding, even with the speedup provided by ISAT. Chemistry agglomeration (CA) provides additional run-time improvement, with a corresponding additional decrease in accuracy. The idea behind chemistry agglomeration is to collect cells (or particles for the Lagrangian PDF Transport model) that are close in composition space, average these to a single composition, call the reaction step integrator, then map this reaction step back to the cells. In summary:
Just before the reaction step, bin CFD cells that are close in composition space.
Average their compositions.
Call ISAT to perform the chemistry integration with the single, averaged composition.
Map this reaction step back to the cells in the group.
The number of calls to the relatively costly chemistry integration routine (ISAT) is less than the number of cells in the domain. Chemistry agglomeration is hence similar to Reactor Network, or Multi-Zone models, which calculate reaction on a smaller number of zones than the number of cells in the CFD simulation.
A reaction mapping is represented as,
 | (7–173) |
where 
and 
are
the thermo-chemical compositions (temperature, pressure, and species
fractions) before and after reaction, respectively. By default, Ansys Fluent loops
over all cells (or particles for the Lagrangian PDF Transport model)
and calculates the reaction mapping.
Chemistry agglomeration loops through all CFD cells before reaction and bins those that are ‘close’ in composition space to within a specified tolerance. The composition in each bin is averaged as,
 | (7–174) |
where 
represents the agglomerated composition, subscript 
is an index over the cells
in the bin, and 
and 
denote the
density and volume of the 
th cell, respectively.
After agglomeration, the ISAT reaction mapping routine is called,
 | (7–175) |
Finally, the reacted cluster composition is mapped back to all the CFD cells in the corresponding bin,
 | (7–176) |
for every cell 
within the bin.
To ensure an iso-enthalpic reaction, the enthalpy of each cell
after reaction, 
, is set according to:
 | (7–177) |
where 
denotes the enthalpy of cell 
before the reaction step, 
is the formation enthalpy of species 
, 
is
the mass fraction after reaction for the cell cluster, and 
is the cell mass fraction
before reaction.
To learn how to enable Chemistry Agglomeration, see Using Chemistry Agglomeration in the User's Guide.
For more information, see the following section:
A uniform Cartesian mesh is used to bin cells at every reaction
step. The composition space has 
dimensions, where 
are the number of species and the additional two
dimensions are temperature and pressure. To reduce the cost of tabulating
in 
-dimensions, a subset of 
representative composition space
coordinates is selected.
For tabulation purposes, each coordinate 
of the 
-dimensional reduced composition
space is normalized as,
 | (7–178) |
where 
and 
are the minimum and maximum of composition space
variable 
in the CFD computational domain. Hence, the reduced
composition space binning mesh extends from zero to one in each of
the 
coordinates. The hyper-cube is discretized into 
uniform intervals along each of the species
or pressure coordinates and 
uniform temperature intervals.
Here, 
(dimensionless) and 
(units of Kelvin) are user specified CA tolerances
that indicate maximum bin sizes for species and temperature dimensions,
respectively. All CFD cell compositions that fall within a reduced
composition space bin are agglomerated.
Since most of the bins in the 
-dimensional hyper-cube are likely
to be empty, a dynamic hash table [30] is employed to efficiently store the bins. The hash table maps
a unique bin index in the 
-dimensional hyper-cube to a 1D line. Since the reduced
space hyper-cube is discretized into equi-spaced bins, a unique index
for every bin can be defined as,
 | (7–179) |
where 
is the bin index in the 
th dimension.
The hash table maps 
to a 1D table of size 
, which is much smaller than the
number of entries in the reduced space hyper-cube, 
. A simple
hash mapping function is the modulo function:
 | (7–180) |
Different 
-space indices 
may have the same hash mapping index 
, which results in collisions.
In the dynamic hash table, the number of collisions, as well as the
number of empty hash table entries are monitored, and the hash table
size, 
, is adjusted at each iteration to set these to be
within acceptable limits.
The 
compositions representing the reduced space coordinates
are selected from the 
dimensional
composition space as follows. By default, temperature is included
and pressure is excluded. The current algorithm orders the species
with largest total mass in the computational domain. For example, 
is typically first in this list for combustors using
air as the oxidizer. The first 
species of this list are
selected as the reduced composition space variables.
By selecting species with the largest mass, minor species are invariably neglected. Since CO and OH are of interest in many practical applications, CO and OH are inserted at the front of the list if they exist in the computational domain. It was found that inclusion of these species in the table coordinates consistently provided increased accuracy for all thermo-chemical variables.
In summary, the default coordinate algorithm selects 
as a reduced space coordinate, then OH (if OH is present in the CFD domain),
then CO (if CO is present in the CFD domain), followed by the species with largest mass in the
domain until 
variables are reached (with 
=4 as default). The default reduced table size (
) and species list should be suitable for most reacting flow applications, but
can be changed. Contact your technical support engineer to learn how to make the changes.