Burning Rate, Kinetic Coupling,and Mechanism Reduction

Yiguang Ju Mechanical and Aerospace Engineering

Princeton University

2007 AFOSR MURI Kick-Off MeetingGeneration of Comprehensive Surrogate Kinetic

Models andValidation Databases for Simulating Large

Molecular WeightHydrocarbon Fuels

Holiday Inn, Princeton100 Independence Way

Princeton, NJ 08540

September 17, 2007

Outline

•Identification of research problems

•Research targets

•Experimental and analytical methods

ParaffinsIso-paraffins Cycloparaffins Aromatics Naphthalenes

Fuel Component SelectionLimited understanding

DetailedModel B

DetailedModel C

DetailedModel D

DetailedModel A

Thermodynamic/Transport/Reaction -Rate Parameter Determination

Experimental Data• Ignition (RCM,ST)• Speciation (FR, ST)• Flames (HP/HT)

burning rateignitionextinctiondiffusion

• Soot characteristics (HPDC)

Minimization / Optimization / Validation

Greater understanding

Kinetic Coupling

Density Ignition criteriaViscosity C/H Ratio

Heat Release RateHeat Capacity

Flame TemperatureSooting Character

etc …

Surrogate Composition Formulation(emulation of physical/chemical properties)

JetFuels

SURROGATE FUEL

Validation

SingleComponents

Single Componentsand

Mixtures

Comparison

REDUCED MECHANISMSFor specificapplications

II

III

I

VI

V

IV

•Burning rate•Diffusion-Kinetic coupling•Mechanism reduction

Research Targets &

Where We Fitin The Roadmap

Problems: Burning Rates at High Pressures

ms.flow speed

lengtht

msSα

dflame speeyDiffusivitt

r

Lf

3100

30

11

102

3

22

===

====−

DME, Ф = 0.77, 10 atm Kobayashi et al. 10 atmQin & Ju, 2005

Yuan, Ju & Law, 2005

Relevant to ICE?

KaMSS

au

u −=10

Research Tasks

• Accurate measurements of flame speeds at elevated pressures by using spherical flames

• Understanding and modeling of transport-kinetic coupling

• Development of efficient reduced mechanism by considering transport-kinetic coupling

Experimental Methods: Flame Speed Measurements

• Challenges and methodologies to measure flame speeds at high pressures and temperatures accurately

Flame Speed Measurement: Spherical Flames1.

Constant volume method:

(High pressure & high temperature)without stretch correction but large pressure increase

Lewis (1934), Metghalchi (1980), Farrell (2004)…Assumption: Non-flame curvature (stretch) effect!

)3()()(

1)(3

/10

0

200

dtdP

PP

PPRRRS u

efu

γ

−=

)4()(11123/1

/10

000

0 −

⎥⎦

⎤⎢⎣

⎡−−

−⎟⎟⎠

⎞⎜⎜⎝

⎛+−≈

− γ

γγ PP

PPPP

PP

RL

SSS

e

eeu

u

uu

What if the stretch effect is not zero?Flame speed error will be:

Lu

: Markstein length from pressure history

Constant Volume Method:Stretch Corrected Flame Speed (SCFS) (H2 /air)

Chen et al. 2007

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1Normalized flame radius, Rf /R0

Flam

e sp

eeds

nom

arliz

ed b

y S

L0 PREMIXwithout stretch correctionstretch corrected flame speed

1.0 1.01 1.02 1.05 1.1 1.2 1.5 2 3 4 5

Normalized pressure, P/P0

(Su0)

(Su)(SL)

Flame Speed Measurement: Spherical Flames:12.

Constant pressure method

(High pressure)

What if the burned gas velocity is not zero?Flame speed error will be:

with stretch correction & small pressure increase

Bradley (1972), Faeth (1992), Law (2000), Ju (2005), Peterson (2007)…

)1(/ ubfu VS ρρ=

)2(ˆˆ

f

b

u

uu

Vu

SSS

=−

≡ε

Assumption: Burned gas velocity is zero!

What causes non-zero burned gas velocity?Compression, non-symmetric flow, radiation…Q U

b

Constant Pressure Method: Compression Induced Burned Gas Velocity

Chen & Ju 2007

Q Ub

Nomalized spatial coordinate, r/R0

Nor

mal

ized

flow

velo

city

,a*U

/SL

0 0.25 0.5 0.75 1-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Velocity distribution V(r)

-30%

-20%

-10%

0%

10%

to Rf/R0

S u0 /S

L-1

from =0.1from =0.2from =0.3

0.2 0.3 0.4 0.5

use "Su=a*dRf/dt"neglect the compression effect

compression corrected flame speeduse "Su=a*(dRf/dt-Ub)"

Rf/R0

Rf/R0

Rf/R0

Constant Pressure Method:

Compression Corrected Flame Speed (CCFS)

Flame speed correction:

What If a Cylindrical Chamber is Used?

Princeton 8.3 cm 8.3 cm diadia. by 13 cm length,. by 13 cm length,10 cm dia. by 15 cm length,10 cm dia. by 15 cm length,

Outer Chamber

Inner Chamber

Mercury Lamp

Focus Lens

Collimating Lens

Decollimating Lens

Pinhole

High-Speed VideoCamera

Knife Edge

Permanentmagnet

Gas Releasing HolesQuartz Window

Tungsten Wire

Iron Plate

Pressure Sensor & GaugesOuter Chamber

Inner Chamber

Mercury Lamp

Focus Lens

Collimating Lens

Decollimating Lens

Pinhole

High-Speed VideoCamera

Knife Edge

Permanentmagnet

Gas Releasing HolesQuartz Window

Tungsten Wire

Iron Plate

Pressure Sensor & Gauges

Non-symmetrical flow induced burned gas velocity!

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Axial direction, z (cm)

Rad

ial d

irect

ion,

r (c

m)

What If a Cylindrical Chamber is Used?

High Pressure Flame Speed (Su

) MeasurementEffect of non-spherical flow, ub

≠0

?)1(*

=Δ⋅−=

−

f

f

u

uu

uu

sss σ

0

50

100

150

200

250

0 1000 2000 3000 4000Stretch (1/s)

Flame speed (cm/s)

0.5 cm

1.01.52.02.53.0

3.5

4.0

How to Improve Measurements: Potential Flow Model

Potential flow:

Ring source

Point source

{ } γγηγηπ

φπ

dzyx

tqr

tm⋅

+⋅−+⋅−+

⋅= ∫

2

02/1222 )]sin([)]cos([

)(4

)(

Prediction of Fame Speed Using Potential Flow

0

50

100

150

200

250

0 1000 2000 3000 4000Stretch (1/s)

Flame speed (cm/s)

Cylindrical Model (Rw=5 cm)

Cylindrical Experiment (Rw=5 cm)

Unconfined ModelUnconfined Model

Cylindrical Model

Rw = 5 cm

Cylindrical Experiment

Rw = 5 cm

Stretch (s-1)

Flam

e Sp

eed

(cm

-s-1

)

Flow-Corrected Flame Speed

M.P. Burke, Y. Ju, F.L. Dryer, Eastern States Meeting, Virginia 2007

150160170180190200210220230240250

0 500 1000 1500 2000 2500 3000 3500Stretch (1/s)

Cal

cula

ted

flam

e sp

eed

(cm

/s)

Uncorrected

Flow Corrected

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅= b

f

u

bu u

dtdr

sρρ

dtdr

s f

u

bu ⋅=

ρρ

wfw rrr 5.01.0 <<

H2

-air, Φ=3.0,1atm

X

Y

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

X

Y

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Le=0.25 Le=2.0

•1D steady-state and transient simulation of counterflow flames

•2D direct simulation of transient spherical flame propagation

Modeling Approaches

How to Improve Measurements (Radiation Effects): One-Dimensional Direct Modeling

Temperature distribution Radiation heat loss distribution

Flame

Improving Measurements (Multi-Dimensional Effect):Adaptive Direct Modeling

X (mm)

Y(m

m)

-10 -5 0 5 10-10

-5

0

5

10

X (mm)

Y(m

m)

-10 -5 0 5-10

-5

0

5

10

Q3.75E+103.50E+103.25E+103.00E+102.75E+102.50E+102.25E+102.00E+101.75E+101.50E+101.25E+101.00E+107.51E+095.00E+092.50E+09

A

B

D

C

a. Adaptive unstructured grid b. Grids for spherical flames

c. Spherical flame propagation

Research Goal

• Measure the flame speeds and Markstein lengths of surrogate fuel components up to 30 atm in a wide range of equivalence ratios

2. Models for Transport-Kinetic Coupling

Transport-coupling regimes:• Diffusion of reactants modifies fuel flux

n-heptane, n-dodecane, oxygen…• Diffusion of intermediate species

modifies local C/H ratio, e.g. H2

,CH4

,C2

H4• Diffusion of radicals modifies kinetic

reaction rate (via H abstraction)e.g. H, O, …

Kinetic coupling between straight chain and aromatic molecules

Sensitivity of Transport Properties: Flame Temperature

0 20 40 60 80 100 120

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

nC7H16 C6H5CH3

iC4H8

iC8H18

C3H6pC3H4

C2H6

C2H2C2H4

CH4

CO2

CO

O

H2O

H

Sen

sitiv

ity o

f fla

me

tem

pera

ture

on

diffu

sivi

ty

Species number

O2

Extinction of PRF + Toluene

Lewis Number, Le

Crit

ical

Igni

tion

Pow

er,Q

c

0.5 1 1.5 2 2.510-2

10-1

100

101

102

103

h=0.00h=0.01

(a)

Q ?

Lewis Number, Le

Crit

ical

Igni

tion

Pow

er,Q

c

0.5 1 1.5 2 2.510-2

10-1

100

101

102

103

h=0.00h=0.01

(a)

Q ?

Effect of Reactant Transport on Minimum Ignition Energy

Fuel molecular size

Experimental Measurements Using Steady StateCounterflow Flames

• Extinction limit & temperature• Species (reactants, intermediate species, and radicals (O, H, OH)

Understanding of transport-kinetic coupling

Numerical modeling

Modeling of Transport-Kinetic Coupling inTransient Mixing & Ignition Process

Tem

pera

ture

, spe

cies

, and

vel

ocity

0 L

T

YO

YF

V

0 L

T

YOYF

V

0 L

T

YO

YF

V

a.Homogeneous ignition b. Frozen diffusionignition

c. diffusion ignition

•Kinetic ignition delay•Transport-kinetic coupling (No mixing delay time)

Transport-kinetic coupling (with mixing delay time)

Mechanism Reduction

Current strategies• Reaction Rate Analysis (Peters et al.)• Graph relation analysis (Lu et al.)• Intrinsic Low Dimension Method (Mass & Pope)• Computational Singular Perturbation (Lam et al.)• High Dimensional Fitting

(Franklach et al.)

•Lead to similar size of reduced mechanism•Reduced mechanism remains large•Homogeneous system, diffusion flux is not included

Our Approach

Path analysis (including diffusion flux, forspecies & reaction reduction)

CSP time scale analysis (fast & slow species)

In-situ adaptive HDMR (fitting)

High Dimensional Modeling Representation: Piecewise Reusable Implementation of Solution

Mapping

))(( 11 nnr

nn t SySyy +Δ+= ++

nnHDMR

n ttf Syy Δ+Δ=+ ),(1

)x,...,x,x()x,(xf)(xf+ f = (x)f N21..12i

jijii

ii0HDMR Nj

f++∑∑≥

Explicit time marching: need to calculate minor species

HDMR fitting:

Time (s)

Tem

pera

ture

(K)

0.0E+00 2.0E-04 4.0E-04

1000

1500

2000

2500

HDMRODE

Example: Ignition of Methane-Air

Li, Chen, Ju, Rabitz et al., 2007

Conclusions• Accurate measurement of flame speeds at high

pressures by using a spherical bomb remains challenging. Physical processes such as flow compression, non-symmetrical flow motion, stretch, and radiation need to be included for accurate measurements.

• There are three different types of transport-kinetic couplings. New models to describe mixing and transport-kinetic coupling in non-premixed and transient ignition process are needed. Advanced computation methods and experimental data are needed to gain quantitative understanding of transport-

kinetic coupling.• New methodologies to generate computationally

efficient reduced mechanisms are needed. Adaptive HDMR and time splitting method are attractive approaches.