Akira Miyoshi

Kinetic Modeling for the Insight into Combustion

The 54th Symposium (Japanese) on Combustion (Sendai, Japan) Nov. 23, 2016

1

Department of Chemical Systems Engineering, University of Tokyo

燃焼をわかるための化学反応モデリング

2 Selecting Kinetic Models

hierarchy of combustion kinetic mechanisms

• Fuel ............................

• High-T & Low-T oxidation

• Sub-mechs (NOx, PM/PAH, etc. …)

Flame propagation- need High-T mech only (usually!)- small fuel dependency

Autoignition- require both High-T & Low-T- strong fuel dependency

• Reduction

Nearly automatic down to 1/5~1/10- ANSYS Reaction Workbench(license for which is now included in academic labo license)

Kinetics of Autoignition

3

4 Branched Chain Reactions

H + O2 OH + OO + H2 OH + H

OH + H2 H2O + H—————————

net: 2 H2 + O2 OH + H + H2O

H2-O2 － Typical branched chain reactions (Chain Explosion)

λmax > 0 ... diverging term

zyx

RRRRR

RRR

zyx

321

21

321

0

i

iii

ta esx

Chain carriers cannot be cancelled out

H OOH

branch

exponential growth exp(λmaxt )

• Selfmultiplication of chain carriers Autoacceleration Explosion

x = [H], y = [O], z = [OH],R1 = k1[O2], R2 = k2[H2], R3 = k3[H2]

Jacobian Matrixremains unchanged during the induction period where p, T and x are nearly constants

5 Autoignition Limit : λmax = 0

H + O2 OH + OH + O2 HO2

O + H2 OH + HOH + H2 H2O + H

zyx

RRRRR

RRRR

zyx

321

21

3241

0

λmax < 0slow rxn

λmax > 0explosion

i

iii

ta esx

Autoignition Limit of H2:O2 = 2:1 mixture

Jacobian Matrix

The 1st and 2nd explosion limits can be explained by nearly constant Jacobian matrix

mol

e fra

ctio

ns

mol

e fra

ctio

ns6 Autoignition of Alkanes

Before Cool Flame: Chain-Reaction Controlled (chain explosion)

After Cool Flame: Thermally Controlled (thermal explosion)

Ignition mechanism depends on the condition !

λmax

mol

e fra

ctio

ns

0 1 2t / ms

20 atm, 714.3 K(OH addition)

x0(OH)= 1 10 8 total ra

dicalRO 2

QOOHO 2QOOH

OH

R

HO 2

H 2O 2

total XOOH

KetOOH

Active Species Addition7

• x(OH) ≈ x(total radical) → independent of species added• x(OH) promptly decays to steady state → robust steady state• Additive effect diminishes exponentially with time

Low‐Temperature Oxidation Steady State8

OH R RO2 QOOH O2QOOH

OO

OOH

OOH

OO

OOOH

KetOOH

OO

O

+ OH

+ OH+ OH

+ HO2

+fuel +O2 +O2

HO2

subetantial‘branching’

‘propagation’only

• Reactions up to KetOOH formation are Straight Chain Reactions(No increase in active species)

• Only the decomposition of KetOOH is Chain Branching Reaction

substantial'branching'

Straight Chain ReactionsBranched

Chain Reactions

Livengood‐Wu (L‐W) Integral9

Assumptions: Autoignition occurs when the concentration of "pertinent reaction product

x" reaches the critical value (x)c. The rate of increase of (x)/(x)c is a function of T and p and equal to τ –1(T, p), reciprocal of the ignition delay time, τ(T, p), at this condition. This relation holds for all T and p during the piston compression and

expansion

J. C. Livengood and P. C. Wu, Proc. Combust. Inst., 5, 347–356 (1955).

ign

0 ,d1

t

pTt

2

1

1

(x)(x)c

ignition

2

1

1

(x)(x)c

ignition

2

(x)(x)c

1 ignition

condition-2

(x)(x)c

1

ignition1

condition-1

mol

e fra

ctio

ns

RO 2

QOOHO 2Q

OOH

OHR

mol

e fra

ctio

ns

Integrand of Livengood‐Wu10

• Integrand is log(XOOH)or log(radical) for t < τc .

c> c <(a) τc dominant (b) Δτ dominant

c c

H. Ando, Y. Ohta, K. Kuwahara, and Y. Sakai, Rev. Automotive Eng., 30, 363–370 (2009).

• Integrand is heat for t > τc .

Autoignition of Gasoline/air (p‐dependence)11

• Shifts upper-right with decrease of p• Larger τ2 – τ1 separation at lower p

Difference between const‐p & const‐V12

• Essentially NO difference for τ1• τ2 is slightly shorter for const-V than const-p

Problem in Given‐V Simulation for RCM13

• Cool flame expansion cannot be reproduced in core-gas model• Deviation of from experiments where τ2 – τ1 separation is visible

1.1 1.2 1.3 1.4

10

100

1000 / TEOC(cgm)

exp.sim.

5.51 MPaCH4-C3H8(25%)

= 0.7

adiabatic core

EOCcompression cooling

timepres

sure

end ofcompression

Effect of the Change of Equivalence Ratio14

• Shifts upper-right with decrease of ϕ• Changes mostly τ2 but not so much of τ1

Flame Propagation

15

Laminar Flame Propagation16

0.5 1.0 1.50

10

20

30

40

50

• Laminar flame speed (S L0) decreases with pressure

and increases with temperature

Flame Propagation at High p and T17

puS

u02

1

100 cm s–1 under in-cylinder condition

18 Laminar Flame Structure

• In-cylinder flame thickness： 10~20 μm (require submicron resolution)

— Structure & flame thickness

Flame Propagation vs. Autoignition19

• Autoignition kinetics affects the calculation of laminar flame speedat high temperatures (artefact - NOT true laminar burning velocity)

Flame Propagation vs. Autoignition20

• Small difference between RON~100 S5H (high-octane) & RON~90 S5R (regular)

1.5 mm

xu ignxu =3.5 mm

Summary21

— Flame Propagation

• Autoignition competes under in-cylinder condition

— Kinetics of Autoignition

[before cool flame]• Chain carrier conc. increases exponentially with time, or

log x(radical) increases LINEARLY with time

[after cool flame]• Thermal ignition dominates