Presented at the International Conference of Chemical Kinetics, Ghent, Belgium, July, 2015 The qualitative notion that ignition processes have similar behavior, even over an extensive range of starting conditions, is quantitatively demonstrated through the production of a single ’generic’ ignition curve. The key to the production of the generic curve is the recognition that the basic shapes of the species and temperature profiles occurring in the ignition process differ only in their ’timing’. By ’morphing’ the time scale, the profile shapes can be made to align. From the aligned profile shapes, a generic or ’average’ profile can be derived. Synchronizing chemical events modifies the ignition progress times. In addition to fixing the ignition time to have the progress value of one, intermediate ignition events (such as selected profile maxima or inflection points) that occur before ignition are also aligned to have specific ’normalized’ times. With this additional synchronization, a single generic curve, derived from the average of the morphed curves, can be derived. This generic curve represents a kinetic modelers intuitive notion of the mechanism of the process.

1. Characterization Ignition
Behavior through Morphing to
Generic Ignition Curves
Edward S. Blurock

2. Philosophy of work
Zero Dimensional Ignition Process
at
a variety of starting conditions
Quantification of chemical intuition
Focus of this talk
How can we characterize the processes of a
zero-dimensional ignition calculation?

3. This Talk
Ignition Process Characterization (mimic chemical intuition)
Ignition Process Phases
Synchronization of Chemical Events in an ignition process
Generic Ignition Curve over a range of conditions
Progress Variable Definition
Consequences for mixing

4. Chemical Source Terms
ω = f(T,P,Y)
. Zero dimensional adiabatic
constant V (or P) System
Differential Equations
Focus: 0-D adiabatic constant pressure ignition process
Example: Ethanol Mechanism: M.M. Marinov. International Journal of Chemical Kinetics, 31:183–220, 1999.
Behavior under
different starting conditions
Temperature,
Pressure,
Equivalence Ratio

5. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Chemical States in Combustion
In Principle:
given f(T,P,Y)
T,P,Y could be considered independent
n+2 independent variables
Set of Coupled Events
Source of the function is a combustion mechanism
represented as a set of (coupled) differential equations
This coupling is the basis of reduction techniques
(a smaller vector space due to coupling)

6. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Previous Studies:
Quantifying intuitive chemical notions
Intuitive Notion:
An ignition process goes through different phases or regimes
Where the chemical mechanism is different for each regime
Quantification:
A regime can be defined as having similar chemistry
Mathematically, clustering is an algorithm to find similar objects
Describe each progress point in an ignition process is an object
Similar regimes can be clustered together due to the similarity at each point

7. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Chemical regimes through clustering
Object: a point in progress time
Set of objects to be clustered
Several ignition processes with
different starting conditions
(Fuzzy Logic) Description:
• Species composition
• Profile Curvature

8. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Ignition Process Phases
Automatic Characterization of Ignition Processes with Machine Learning
Clustering Techniques,
Blurock, Edward S.; International Journal of Chemical Kinetics, 2006.
Characterizing Complex Reaction Mechanisms using Machine Learning Clustering
Blurock, Edward S., International Journal of Chemical Kinetics, 2004.
Initiation
Equilibrium
Pre-Ignition
Ignition
RadicalBuildup
Data Analysis (clustering) substantiating chemical intuition
Cluster states: (T,P,Y)
Similar states in cluster

9. Synchronizing Chemical Events
Basic Principle:
However, the timing of the states may change:
Time (progress) morphing synchronizes the timing of these states
An ignition process goes through
a similar set of reactive states
(through the same set of reaction process phases)
Regardless (somewhat) of starting conditions
Under a given condition (a given starting condition)
Qualification:
Similarity of mechanistic properties
(follows same pathways: Only the timing of important pathways changes)

10. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Similarities
When a chemist looks at these curves, they have a degree of similarity
Optically we see the similar curvatures
(these same features were used to identify regions)
Steady rise Peak Fast Drop

11. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Synchronization: Core Idea
Synchronize the profiles
so they overlap
Find Events to synchronize
Note:
This technique is not limited to
ignition progres time:
Enthalpy, flame distance, …

12. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Synchronizing Ignition Point
Progress Morphing: Define the ignition event to be at 1.0
Start to see the formation of generic behavior (in line with the chemical intuition)
Many progress variable models synchronize at the ignition point

13. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Further Synchronization
Find
Mathematically well defined points:
Maxima:
1st derivative zero, 2nd derivation negative
Minima:
1st derivative zero, 2nd derivative positive
Inflection Point:
2nd derviative zero.

14. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Multiple Synchronization Events
The events can be chosen from any of the species profiles
And recognizable features within those profiles.

15. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Try to distribute events
throughout combustion process
Initiation
Equilibrium
Pre-Ignition
Ignition
RadicalBuildup
Choice of features to synchronize
Try to evenly distribute over the
entire range
Not always possible

16. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Non-linear Progress
Morphing of time progress compared to just synchronizing at ignition time
Function of temperature Function of equivalence ratio
Line of no deviation
Event occurred earlier
Higher temperature
Event occurred later
Lower Temperatures

17. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Prerequisite and Consequences
Set of events have to occur in same order
On the other hand
This provides a way to characterize different mechanistic beha
vior
This limits the range of the generic curve
A comprehensive mechanism
over
an extensive range of starting conditions
Would be represented
by several generic curves

18. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Towards a Generic Curve
Original Ignition Sync
H2O2 Synchronization
1.0
0.75
0.5
Normalize Maximum of curve

19. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Calculation of Generic Curve
Normalize Maximum of curve Average of profiles to generic curve

20. More Synchronization means Less Deviation
Generic curves and deviation from generic curves
offers a more compact representation of curves over a range of conditions
Average
Deviations

21. Formation of Generic Curves
Generic curves and deviation from generic curves
offers a more compact representation of curves over a range of conditions
Generic Characterization
of Ignition Behavior
Without progress synchronization,
this is not possible

22. Towards Parameterization
Deviations from Generic Curve
Synchronization Points
Compact Representation:
As perturbations
from generic curve
Generic Curve
Synchronization Points
Deviations from curve
(represented as polynomials)

23. Piecewise Polynomial Fit
Error with Polynomial Fit
1-2% error in values
Compact Representation:
As perturbations
from generic curve
Perturbation from ‘average’ values
leads to more accurate results
Mathematical expressions for the
Perturbations are more accurate
(deviations of the deviations)

24. Range of Validity
Simple Criteria:
Order of synchronization points have to be the same
When the order shifts, then another mechanism is at work.
This can be a further characterization of chemical regimes

25. Prerequisites of Progress Variable
Represents the ‘progress’ of the combustion process
Should be Monotone along this progress
A given progress value, under varying conditions,
represents the same state of the ignition process
(important for progress variable models)
Representative of the ‘chemistry’ and ‘thermodynamics of the process
This work:
Given a progress variable
actively
improve its definition to better meet these requirements

26. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Chemical Events
Prerequisite:
A given progress value represents a given chemical event in ignition process
Ethanol Oxygen CO2 H2O
CH4OHOCH2O

27. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Monotonicity Requirement
Non-Monotonic
under equilibrium and rich conditions
Under Lean conditions
(sort of)
Monotonic Behavior

28. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Thermodynamic View of Process
Represents (related to) the inherent ‘energy’
bound up in the molecules
This is released to the environment
through the combustion process
Due to the transformation
from reactants to products
Reactants
Products

29. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Enthalpy as Progress
The use of energy given an indirect indication of chemical compositon
(sum of the energetics of the individual species)
Several SynchronizationsOne SyncOriginal
OH

30. 30
Progress and Mixing
Exchange of
Physical properties (T,P,...)
and
chemical composition ( Y )
Physical Properties
+
Chemical source term ( ὠ )
(Ti,Pi,.., Yi)
(Tl,Pl,.., Yl)
(Tk,Pk,.., Yk)
(Tj,Pj,.., Yj)
(Tm,Pm,.., Ym)
Single Progress Variable models popular in CFD calculations

31. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Mixing Progress unsynchronized states
(extreme case... to show effect of non-matching curves)
Values averaged at each progress (time) point
Mixing unsynchronized states can produce ‘non-physical’ artifacts
Smooth
Curve
Non-physical
Artifact

32. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Mixing Synchronized Progress
Values averaged at each progress point
1. Synchronized only
ignition
II. Multi-point synchronization
A
AA
A
A+BA+B
Under-estimation

33. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Conclusion
Generic ignition process curves:
Mimics chemical intuition of chemical reactivity
Automatic method to mimic chemical intuition
Progress Variables:
Active algorithm to produce a progress representing the same chemistry
More accurate progress representation produces more accurate mixing

34. Edward S. Blurock, REACTION, Sweden
9th International Conference on Chemical Kinetics, 2015
Thank you