no slide titleseitzman.gatech.edu/classes/ae6766/ignition.pdf · laser beam (laser-induced...

1

Ignition -1

School of Aerospace Engineering

Copyright © 2004-2005, 2014 by Jerry M. Seitzman. All rights reserved. AE/ME 6766 Combustion

Ignition

Jerry Seitzman

Methane Flame

0

0.05

0.1

0.15

0.2

0 0.1 0.2 0.3

Distance (cm)

Mo

le F

racti

on

0

500

1000

1500

2000

2500

Te

mp

era

ture

(K

)

CH4

H2O

HCO x 1000

Temperature

Ignition -2



Review

• So far, examined

– stable/steady self-sustained propagation of premixed

flames

• how fast: flame speed

• when they will remain stationary: flame

stabilization

• if there is or is not a “stable” flame solution:

flammability and quenching, shape perturbations

• New question

– how do we initiate a flame with an external source

(not the same as the autoignition problem)

2

Ignition -3



Overview

• Need to get reactions “going”

– temperature

– radicals

– (pressure)

• Common approaches

typically start by

putting energy

into “small”

volume

– pilot flame (e.g., match)

– spark plug (lightning for forest fires)

– laser (spark or thermal)

– plasma injector

– shock heating, hot wire

Ignition -4



Spark (Plasma Discharge) Ignition

• Common approach

– IC engines

– home heating/cooking

• Spark

– typically electrical discharge

across electrode gap

– can also produce by focused

laser beam (laser-induced

breakdown)

3

Ignition -5



Questions

• How strong does ignition source have to be?

– how much energy

– how much power (time)

• What are other optimum characteristics?

– e.g., size

• Approach to an answer for premixed reactants

– similar to quenching

– flame can become self-propagating when source of

energy/radicals overcomes losses

Ignition -6



Simple Analysis

• Assume that spark (or other ignition

method) produces an ideal spherical volume

(ignition kernel) in premixed reactants

– initial temperature T1

– after “spark” temperature T2

• Using simple thermal model

– spherical region will only continue to self-

propagate (flame) if

• energy release > losses

flame

surfcondchemAqVq

T2

r

R

T1

23 434 RqRqcondchem

4

Ignition -7



Minimum Ignition Kernel Radius

• Critical Radius

flame

T2

r

R

T1

chem

cond

critq

qR

3

p

L

TRfchemcTT

Shmq

ref 112

2

,2

crit

condR

TTq 12

f

L

critS

R

66

23 434 RqRqcondchem

– at some large enough size,

heat release will exceed losses

– similar to quenching distance in magnitude 8

Ignition -8



Minimum Ignition Energy

• How much energy required to create this

volume of hot gases (assume all energy

input, no chemical heat release)

– calor. perfect gas

flame

T2

r

R

T1

12min

TTVcEp

122

334 TTcRpcrit

122

3

634 TTcRTpSpL

2

12

3

min6.61

T

TT

SR

cpE

L

p

2.55 0.51

O(f)

5

Ignition -9



Minimum Ignition Energy

• Example

– STP methane-air

flame

T2

r

R

T1

2

12

3

min6.61

T

TT

SR

cpE

L

p

3

min180

fpE

335 1010180 mPa

mJ18 Can be 1-2 order of

magnitude less in practice

(e.g., 0.3 mJ value in Turns)

Ignition -10



Pressure Scaling

• Critical size

• Minimum energy

2n

fcritpR

2323

min

n

fppE

221min

11

ppE

Minimum ignition

energy drops at high

pressure

– for hydrocarbons with n=12

Relight of aircraft engine at high altitude?

6

Ignition -11



Spark Ignition - Electric Discharge

• Evolution of voltage and current in a spark igniter

• Breakdown

– nearly

instantaneous

– T rise to

10,000’s K

– little density

change

– large p rise

• Arc and glow discharges: longer duration, more E

Ignition -12



Breakdown Discharge • Most critical phase for spark ignition

– most efficient energy deposition (less losses)

– creates non-equilibrium gas with superequilibrium radical levels

– produces shock wave; behind shock the plasma expands outward quickly

• moves gases away from igniter (away from surface losses)

• more rapidly creates large ignition kernel (higher Vol/Asurf)

– also inside of expanding plasma is colder

• less energy required to create hot shell than hot sphere

8s after

breakdown from A. Lambert

7

Ignition -13


Copyright © 2004-2005, 2014 by Jerry M. Seitzman. All rights reserved.

Nonpremixed Ignition

• Additional issues for igniting nonpremixed systems

– discharge can occur in non-flammable region,

ignition kernel must convect to flammable region

– many things can happen to kernel before reaching

flammable mixture

• recombination of electrons/ions/radicals

• entrainment of (colder) nonflammable mixture

lower temperature kernel

AE/ME 6766 Combustion

Ignition -14


Copyright © 2004-2005, 2014 by Jerry M. Seitzman. All rights reserved.

Nonpremixed Ignition • Simplified geometry

example

• Rapid

entrainment

cooling

AE/ME 6766 Combustion

Flammable Main Flow

Non-Flammable Kernel Flow

splitter plate

Pulsed Igniter

τ transit

from B. Sforzo

~60-100’s s

8

Ignition -15



Thermal Ignition

• Is there a maximum

temperature, beyond

which rapid

combustion

(explosion) occurs in a

fuel/ox. mixture stored

in some container?

– sometimes called

autoignition or

spontaneous ignition

Ignition -16



Thermal Ignition

• Related to chain-

branching explosions we

have seen earlier

– e.g., the lower explosion

limit depends strongly

on container size

• Looking for a tradeoff

– losses to walls (heat or

radicals) versus energy

release/reaction rate

9

Ignition -17



Thermal Ignition Analysis

• Following analysis after Frank-

Kamenetskii (1955)

– focus on thermal approach

– when heat release rate exceeds

losses, reaction rate rapidly climbs

and ignition (explosion) occurs

– does not address slow (low

temperature) reactions that might

occur over long periods of time

chemq

condq

F/O

T

To

Ignition -18



Thermal Ignition Analysis

• Start with simplest case

– infinite parallel plates, no convection

• Differential energy equation

– 1d, thermal conduction only

dx

dT

dx

d

dt

dTcq

pchem

T

To

dx

r

x

– if the conditions are unsafe,

the temperature will continously rise (rapidly)

– if the conditions are safe, there must be a steady-

state (stationary) solution

10

Ignition -19



Steady State Solution

• Steady-state, constant

• Use 1-step/global reaction rate

2

2

dx

Tdq

chem

T

To

r

dt

proddQq

chem

energy released/

mole product

RTEo

eZQ

dx

Td

2

2

RT

Eqp o

eOxFAdt

prodd

Z

2nd order ODE

T=To @ x=r; dT/dx=0 @ x=0

x

Ignition -20



Nondimensionalized Equation

• Normalized coord.

• Normalized temperature

• Normalized size

• Nondimensional ODE

– general geom.

rx

o

e

d

d

2

2

0 1

2

o

oo

RT

TTE o

ooRT

E

RTE

eee

o

oRT

E

o

o

o

eRT

E

T

QZr

2

=0 @ =1

d/d =0 @ =0

e2

11

Ignition -21



Nondimensionalized Solution

• Existence of (steady) solution depends on

– no analtyic solution

– from numerical integ., stable solutions for <critical

(shooting, match BC)

• Critical values – parallel plates

crit=0.878

– cylinder

crit=2.00

– sphere

crit=3.32 0

0.5

1

0 0.5 1

0.9

0.878

0.5

0.1

Ignition -22



Thermal Ignition Limits

• So stable (no thermal ignition) given by following

conditions

• Pressure dependence

• Temperature dependence

critical

RTE

o

o

n

o

o

eRT

EpQZr

2

2 ,

11 nn ppZpQ

o

oRT

E

e

• Decrease safety

– Q, r, To, p,

• r vs. To

– for To<<Eo/2R can show a significant increase in

vessel size does not require much decrease in To

12

Ignition -23



Thermal Ignition Temperatures

• Examples

– H2/O2 833 K

– H2/air 845 K

– CH4/air 810 K

– C2H2/air 578 K

similar kinetics and

lower Q but also lower

high Q and low (least safe)

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