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ORIGINAL   DISTORTED  

Corner  handles  

Good

 prin

/ng  qu

ality

 

Bad  prin/n

g  qu

ality

 

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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.

Abstract  

Synchroniza@on  

Time  Devia@ons  from  Linear  

Mul@ple  Synchroniza@ons  

Generic  Curves  The inherent assumption is that a given progress value, regardless of its origin, should represent a given stage of the ignition process. In terms of species profiles, for example, this means that a given species reaches a maxima at the same progress value regardless of starting conditions. The one assumption is that relatively the same mechanistic steps are involved. Different mechanistic steps would imply another generic curve.

Edward  S.  Blurock,  REACTION,  Sweden  

Characterizing  Igni@on  behavior  through  morphing  to  generic  curves  

 

This work exploits the similarities of an ignition process

to produce generic ignition curves, uniting ignition curves,

each with different starting conditions, into one common behavior

using one single progress variable.

0 0.0005 0.001 0.0015Ignition Process Time (s)

1000

1500

2000

2500

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Tem

per

atu

re (

Kel

vin

)

0 0.0005 0.001Ignition Process Time (s)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Mas

s F

ract

ion o

f S

pec

ies

CH2O

H2O2

HO2

CHO

0 1 2Normalized Time (Ignition at 1.0)

1000

1500

2000

2500

3000

Tem

per

ature

(K

elv

in)

0.50

0.75

1.00

0 0.5 1Normalized Time (Ignition at 1.0)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Spec

ies

Mas

s F

ract

ions

CH2O

H2O2

HO2

CHO

0 0.2 0.4 0.6 0.8 1Normalized Time (both with T and H2O2 max)

0

0.0005

0.001

0.0015

0.002

Mas

s F

ract

ion

s

O.50

0.75

1.00

Equivalence Ratio

H2O2 Max Time Norm

0 0.2 0.4 0.6 0.8 1Normalized Time (with both T and H2O2 Max)

0

0.2

0.4

0.6

0.8

1

No

rmal

ized

Mas

s F

ract

ion

0.50

0.75

1.00

Equivalence Ratio

All  figures  show  a  range  of  condi/ons,  with  3  star/ng  temperatures  (1200,  1250,  1300  Kelvin),  two  star/ng  pressures  (1,11  atm)  and  three  different  equivalence  ra/os  (0.50,  0.75,  1.00.  The  first  is  a  plot  of  the  H2O2  with  a  /me  normaliza/on  at  both  the  maximum  of  the  H2O2  mole  frac/on  (derived  from  the  average  of  the  set,  0.745)  and  at  the  igni/on  /me  (1.0).The  second  is  with  the  H2O2  maximum  normalized  to  1.0.  

A  set  of  igni/on  curves  where  the  /me  is  normalized  to  be  at  the  point  of  igni/on.  The  first  curve  is  /me  versus  temperature  with  5  different  star/ng  temperatures  from  1200  to  1300  and  three  different  equivalence  ra/os  (see  legend).  The  second  curve  shows  the  evolu/on  of  intermediate  species  at  ten  star/ng  temperatures  between  1200  and  1300  Kelvin.  Only  values  several  (20  /mes  10{-­‐5)  past  igni/on  were  calculated.  For  some  star/ng  condi/ons,  the  equilibrium  was  not  reached.  

0 0.2 0.4 0.6 0.8 1

Normalized Time

-0.02

-0.01

0

0.01

0.02

0.03

Devia

tion

0.5

0.6

0.7

0.8

0.9

1.0

0 0.2 0.4 0.6 0.8 1

Normalized Time

-0.05

0

0.05

Devia

tion

1200K

1210K

1220K

1230K

1240K

1250K

1260K

1270K

1280K

1290K

1300K

The  devia/on  from  linear  progression  based  only  on  igni/on  /me.  Four  events  (see  text)  were  chosen  as  /me  normaliza/on  points.  The  graphs  show  the  devia/ons  along  the  normalized  /me  for  a  (le]  graph)  a  range  of  temperatures,  1200K  to  1300K  (1  atmosphere  pressure  and  equivalence  ra/o  of  1.0),  and  (right  graph)  a  range  of  equivalence  ra/os,  0.5  to  1.0  (Temperature  130  and  pressure  1  atmosphere).}  

0 0.2 0.4 0.6 0.8 1Temperature Normalized Progress

0

0.2

0.4

0.6

0.8

1

CH

2O

No

rmal

ized

to

Max

imu

m

0.50

0.75

1.00

0 0.2 0.4 0.6 0.8 1Time Normalized (T, H2O2 Max)

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1

No

rmal

ized

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Max

imu

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0 0.2 0.4 0.6 0.8 1Time Normalized (T, H2O2 Max, CH2O Max)

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1

No

rmal

ized

to

Max

imu

m

0.50

0.75

1.00

1 atm

11 atm

The  effect  of  progression  of  /me  normaliza/on  on  the  maximum  normalized  mass  frac/on  curves  of  CH2O  are  shown.    With  each  addi/onal  normaliza/on,  the  spread  of  curves  diminishes.  From  just  igni/on  /me  (le]),  adding  H2O2  maximum  (center),  to  adding  both  H2O2  and  HO2  maximum  (right).    All  figures  show  a  range  of  condi/ons,  with  3  star/ng  temperatures  (1200,  1250,  1300  Kelvin),  two  star/ng  pressures  (1,11  atm)  and  three  different  equivalence  ra/os  (0.50,  0.75,  1.00).  

0 0.2 0.4 0.6 0.8 1

Normalized Time

0

0.2

0.4

0.6

0.8

1

Norm

ali

zed H

2O

2

0 0.2 0.4 0.6 0.8 1

Normalized Time

0

0.2

0.4

0.6

0.8

1

Norm

ali

zed H

O2

Range  of  Validity  and  the  Choice  of  Events  A  single  generic  curve  is  produced  by  morphing  the  individual  curves  to  coincide  at  specified  sequen/al  chemical  events.  This  is  a  mathema/cal  descrip/on  of  the  statement  that  the  set  of  igni/on  curves  have  the  same  mechanis/c  chemistry.  A  combus/on  process  undergoing  a  different  set  of  mechanis/c  events  should  be  described  by  a  different  generic  curve.  In  this  formula/on  a  different  set  of  mechanis/c  events  is  defined  as  being  a  set  of  curves  in  which  the  set  of  chemical  events  occur  and  occur  in  the  same  order.  This  can  be  used  as  a  criteria  for  differen/a/ng  combus/on  events  with  different  mechanis/c  steps.  A  complete  descrip/on  of  a  combus/on  process  over  the  complete  set  of  ranges  would  be  described  by  a  set  of  generic  curves.  

0 0.2 0.4 0.6 0.8 1Normalized Time

-0.2

-0.1

0

0.1

0.2

Dif

fere

nce

Fro

m A

ver

age

0 0.2 0.4 0.6 0.8 1Normalized Time

-0.02

-0.01

0

0.01

0.02

0.03

Dif

fere

nce

Fro

m P

iece

wis

e P

oly

no

mia

l

The  le]  plot  shows  the  difference  between  the  average  generic  curve  and  the  actual  curves  of  the  individual  star/ng  condi/ons.  The  le]  plot  shows  differences  between  the  piecewise  second  degree  polynomial  approxima/on  of  the  curve  differences.  The  solid  lines  denote  minimum  and  maximum  values  and  the  doaed  lines  between  are  the  difference  values.  

Towards  Parameteriza@on  

Average,  maximum  and  minimum  value  plots  of  HO2  (le])  and  H2O2  (right)  under  a  wider  range  of  pressures  (1,11,21,31  atms),  temperatures  (1200-­‐1300K  at  10K  intervals)  and  equivalence  ra/os  (0.5,0.75  and  1.00)  are  shown.  The  solid  lines  are  /me  normalized  with  four  fixed  points,  including  igni/on  /me  and  the  doaed  lines  is  normalized  /me  with  respect  to  just  igni/on  /me.  

0.5 0.6 0.7 0.8 0.9 1Equivalence Ratio

-0.02

-0.01

0

0.01

0.02

0.03

Dev

iati

on

0.77

0.21

0.86

0.94

1200 1220 1240 1260 1280 1300Starting Temperature

-0.05

0

0.05

Dev

iati

on

0.23

0.78

0.880.93

The  devia/on  from  linear  progression  based  only  on  igni/on  /me.  Four  events  (see  text)  were  chosen  as  /me  normaliza/on  points.  The  graphs  show  the  devia/ons  along  the  normalized  /me  for  a  (le]  graph)  a  range  of  temperatures,  1200K  to  1300K  (1  atmosphere  pressure  and  equivalence  ra/o  of  1.0),  and  (right  graph)  a  range  of  equivalence  ra/os,  0.5  to  1.0  (Temperature  1300  and  pressure  1  atmosphere).