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 9 th 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 9 th 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 9 th 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 9 th 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 Techniques Blurock, Edward S., International Journal of Chemical Kinetics, 2004. Initiation Equilibrium Pre-Ignition Ignition Radical Buildup 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 9 th 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 risePeak Fast Drop

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

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

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

17. Edward S. Blurock, REACTION, Sweden 9 th 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 9 th 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 9 th 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 9 th International Conference on Chemical Kinetics, 2015 Chemical Events Prerequisite: A given progress value represents a given chemical event in ignition process EthanolOxygen CO 2 H2OH2O CH 4 OHO CH 2 O

27. Edward S. Blurock, REACTION, Sweden 9 th 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 9 th 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 9 th 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 ) (T i,P i,.., Y i ) (T l,P l,.., Y l ) (T k,P k,.., Y k ) (T j,P j,.., Y j ) (T m,P m,.., Y m ) Single Progress Variable models popular in CFD calculations

31. Edward S. Blurock, REACTION, Sweden 9 th 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 9 th 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+B Under-estimation

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