characterization ignition behavior through morphing to generic ignition curves edward s. blurock

Characterization Ignition Behavior through Morphing

toGeneric Ignition Curves

Edward S. Blurock

Philosophy of work

Zero Dimensional Ignition Processat

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?

This TalkIgnition Process Characterization (mimic chemical intuition)Ignition Process PhasesSynchronization of Chemical Events in an ignition processGeneric Ignition Curve over a range of conditionsProgress Variable DefinitionConsequences for mixing

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 processExample: Ethanol Mechanism: M.M. Marinov. International Journal of Chemical Kinetics, 31:183–220, 1999.

Behavior under different starting conditions

Temperature,Pressure,

Equivalence Ratio

Edward S. Blurock, REACTION, Sweden9th International Conference on Chemical Kinetics, 2015

Chemical States in CombustionIn 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 mechanismrepresented as a set of (coupled) differential equations

This coupling is the basis of reduction techniques(a smaller vector space due to coupling)


Previous Studies:Quantifying intuitive chemical notions

Intuitive Notion:An ignition process goes through different phases or regimesWhere 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


Chemical regimes through clustering

Object: a point in progress time

Set of objects to be clusteredSeveral ignition processes with different starting conditions

(Fuzzy Logic) Description:• Species composition• Profile Curvature


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 TechniquesBlurock, Edward S., International Journal of Chemical Kinetics, 2004.

Initiation

Equilibrium

Pre-Ignition Ignition

Radical B

uildup

Data Analysis (clustering) substantiating chemical intuition

Cluster states: (T,P,Y) Similar states in cluster

Synchronizing Chemical EventsBasic 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)


SimilaritiesWhen 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


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, …


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


Further SynchronizationFindMathematically well defined points:Maxima:1st derivative zero, 2nd derivation negative

Minima:1st derivative zero, 2nd derivative positive

Inflection Point:2nd derviative zero.


Multiple Synchronization Events

The events can be chosen from any of the species profilesAnd recognizable features within those profiles.


Try to distribute eventsthroughout combustion process

Initiation

Equilibrium

Pre-Ignition Ignition

Radical B

uildup

Choice of features to synchronize

Try to evenly distribute over the entire range

Not always possible


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


Prerequisite and ConsequencesSet of events have to occur in same order

On the other handThis provides a way to characterize different mechanis-

tic behavior

This limits the range of the generic curve

A comprehensive mechanismover

an extensive range of starting conditionsWould be represented

by several generic curves


Towards a Generic Curve

Original Ignition Sync

H2O2 Synchronization

1.0

0.75

0.5

Normalize Maximum of curve


Calculation of Generic Curve

Normalize Maximum of curve Average of profiles to generic curve

More Synchronization means Less Deviation

Generic curves and deviation from generic curvesoffers a more compact representation of curves over a range of

conditions

Average

Deviations

Formation of Generic Curves

Generic curves and deviation from generic curvesoffers a more compact representation of curves over a range of

conditions

Generic Characterization of Ignition Behavior

Without progress synchronization,

this is not possible

Towards Parameterization

Deviations from Generic Curve

Synchronization Points

Compact Representation: As perturbations

from generic curve

Generic CurveSynchronization PointsDeviations from curve (represented as polynomials)

Piecewise Polynomial Fit

Error with Polynomial Fit

1-2% error in values

Compact Representation: As perturbations

from generic curvePerturbation from ‘average’ values

leads to more accurate results

Mathematical expressions for the Perturbations are more accurate

(deviations of the deviations)

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

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

activelyimprove its definition to better meet these

requirements


Chemical EventsPrerequisite:

A given progress value represents a given chemical event in ignition process

Ethanol Oxygen CO2 H2O

CH4OHOCH2O


Monotonicity Requirement

Non-Monotonic under equilibrium and rich conditions

Under Lean conditions(sort of)

Monotonic Behavior


Thermodynamic View of ProcessRepresents (related to) the inherent ‘energy’

bound up in the molecules

This is released to the environmentthrough the combustion process

Due to the transformationfrom reactants to products

Reactants

Products


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

Progress and Mixing

Exchange ofPhysical properties (T,P,...)

andchemical 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


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

SmoothCurve

Non-physicalArtifact


Mixing Synchronized ProgressValues averaged at each progress point

1. Synchronized only ignition

II. Multi-point synchronization

A

AA

A

A+BA+B

Under-estimation


Conclusion

Generic ignition process curves:

Mimics chemical intuition of chemical reactivityAutomatic method to mimic chemical intuition

Progress Variables:

Active algorithm to produce a progress representing the same chemistryMore accurate progress representation produces more accurate mixing


Thank you

characterization ignition behavior through morphing to generic ignition curves edward s. blurock

Documents

chemical states

dimensional ignition

chemical regimes

chemical mechanism

blurock slide

generic ignition curves

chemical source terms

set of reaction process