Analytical Modeling of Flame Kernel Formation and Development in SI

Engines

Hamed Aghajani

Nasser S. Mehdizadeh

Sadegh Tabejamaat

Amirkabir University of Technology-Aerospace Engineering Department-Tehran-Iran

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Topics

Published Work Categories Goals in Modeling Most Important Researches Spark Discharge Model Description (assumption) Validation Results

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Published Works Categories

Phenomenology Electrical spark ignition Reaction kinetics Modeling of flame kernel

formation

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Goals in Modeling

Reducing the fuel consumption

Reducing the exhaust emissions

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Most Important Researches

Champion 1986 Sloane 1989-1990-1992 Ko 1991 Akram 1996 Yashar 2001

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Spark Discharge

Pre-breakdown phase Breakdown phase Arc phase Glow phase

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Model Description (assumptions)

Calculations start at 1 s after the breakdown Ideal gas law is applicable Temperature inside the kernel is uniform Kernel to assumed to be spherical Ignition flame kernel separates the burned and

unburned gas Flame kernel volume is much smaller than the

combustion chamber volume

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Model Description

Increase in flame kernel mass ptku

kk

kk

kkk ssA

dt

dV

dt

dV

dt

Vdm

Utilizing the ideal gas law

dt

dP

Pdt

dT

TVSsA

dt

dV k

kkplk

k

uk 11

By normalizing the volume increase

dt

dP

Pdt

dT

TA

VSs

dt

dr k

kk

kpl

k

uk 11

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Model Description

The Energy balance for the control volume

CV

kuCV dt

dVpmh

dt

dEQ

..

Change in flame kernel internal energy

kkk

kkk mU

dt

dUm

dt

Umd

dt

dE

Change in volume work

ptk

uk

kk

CV

ssprdt

drpr

dt

dVp

22 44

Add of 3 above equations

pt

k

ukkukk

kkhtchspk sspAmhmUdt

dUmQQQ

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Model Description Turbulent flame speed calculated by Herweg’s equation

21

210

2121

2100 exp1exp1

l

Gk

ll

t

s

uTt

l

r

su

uII

s

s

Characteristic time scale

lG su

lT

0

Effect of strain on the kernel development

k

u

k

F

l

F

r

l

s

u

l

lI

2

2321

0 215

1

Laminar burning velocity using Metghalchi’s equation

RPTssss k

l 1.2110013.1298

1

52

12

321

2121

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Validation Validation of model has been demonstrated regarding Maly’s experimental

Result

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Results

Ignoring the initial step, there is good agreement between the model and experimental data.

Developed zero dimensional thermodynamic model predicts correctly linear trend from the beginning to the finishing radius of flame kernel radius.

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006

Thanks

Any Question?

2nd International Conference “From Science Computing to Computational Engineering”, 5-8 July 2006