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Effects of radiative Effects of radiative emission and absorption on emission and absorption on

the propagation and the propagation and extinction of premixed gas extinction of premixed gas

flamesflamesYiguang Ju and Goro Masuya

Department of Aeronautics & Space Engineering

Tohoku University, Aoba-ku, Sendai 980, Japan

Paul D. RonneyDepartment of Aerospace & Mechanical

EngineeringUniversity of Southern California

Los Angeles, CA 90089-1453

Paper No. P024, 27th Symposium (International) on Combustion, Boulder,

CO, August 5, 1998

PDR acknowledges support from NASA-Lewis

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Background Microgravity experiments show importance of radiative

loss on flammability & extinction limits when flame stretch, conductive loss, buoyant convection eliminated – experiments consistent with theoretical predictions of Burning velocity at limit (SL,lim) Flame temperature at limit Loss rates in burned gases

…but is radiation a fundamental extinction mechanism? Reabsorption expected in large, "optically thick” systems

Theory (Joulin & Deshaies, 1986) & experiment (Abbud-Madrid & Ronney, 1993) with emitting/absorbing blackbody particles Net heat losses decrease (theoretically to zero) Burning velocities (SL) increase Flammability limits widen (theoretically no limit)

… but gases, unlike solid particles, emit & absorb only in narrow spectral bands - what will happen?

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Background (continued) Objectives

Model premixed-gas flames computationally with detailed radiative emission-absorption effects

Compare results to experiments & theoretical predictions

Practical applications Combustion at high pressures and in large

furnaces• IC engines: 40 atm - Planck mean absorption

length (LP) ≈ 4 cm for combustion products ≈ cylinder size

• Atmospheric-pressure furnaces - LP ≈ 1.6 m - comparable to boiler dimensions

Exhaust-gas or flue-gas recirculation - absorbing CO2 & H2O present in unburned mixture - reduces LP of reactants & increases reabsorption effects

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Numerical model Steady planar 1D energy & species conservation

equations CHEMKIN with pseudo-arclength continuation 18-species, 58-step CH4 oxidation mechanism (Kee et al.) Boundary conditions

Upstream - T = 300K, fresh mixture composition, inflow velocity SL at x = L1 = -30 cm

Downstream - zero gradients of temperature & composition at x = L2 = 400 cm

Radiation model CO2, H2O and CO Wavenumbers () 150 - 9300 cm-1, 25 cm-1 resolution Statistical Narrow-Band model with exponential-tailed

inverse line strength distribution S6 discrete ordinates & Gaussian quadrature 300K black walls at upstream & downstream

boundaries Mixtures CH4 + {0.21O2+(0.79-)N2+ CO2} - substitute

CO2 for N2 in “air” to assess effect of absorbing ambient

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Results - flame structure Adiabatic flame (no radiation)

The usual behavior Optically-thin

Volumetric loss always positive Maximum T < adiabatic T decreases “rapidly” in burned gases “Small” preheat convection-diffusion zone - similar to

adiabatic flame With reabsorption

Volumetric loss negative in reactants - indicates net heat transfer from products to reactants via reabsorption

Maximum T > adiabatic due to radiative preheating - analogous to Weinberg’s “Swiss roll” burner with heat recirculation

T decreases “slowly” in burned gases - heat loss reduced

“Small” preheat convection-diffusion zone PLUS “Huge” convection-radiation preheat zone

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Flame structures

Flame zone detail Radiation zones (large scale)

Mixture: CH4 in “air”, 1 atm, equivalence ratio (): 0.70; = 0.30 (“air” = 0.21 O2 + .49 N2 + .30 CO2)

0

500

1000

1500

2000

2500

3000

-1 10 7

-5 10 6

0

5 10 6

-0.5 0 0.5 1

adiabaticreabsorptionoptically thin

q (reabsorption)q (optically thin)

Spatial coordinate (cm)

Reabsorptionzone (negativeloss region)

Convective-loss zone(optically thin)

400

800

1200

1600

2000

-30 -20 -10 0 10 20 30 40

Spatial coordinate (cm)

Reabsorbing flame: convective-

radiative zone

Reabsorbing flame: max. T > adiabatic flame

Optically thin: rapid downstream loss

Reabsorbing flame: slow downstream loss

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Radiation effects on burning velocity (SL) CH4-air ( = 0)

Minor differences between reabsorption & optically-thin ... but SL,lim 25% lower with reabsorption; since SL,lim ~

(radiative loss)1/2, if net loss halved, then SL,lim should be 1 - 1/√2 = 29% lower with reabsorption

SL,lim/SL,ad ≈ 0.6 for both optically-thin and reabsorption models - close to theoretical prediction (e-1/2)

Interpretation: reabsorption eliminates downstream heat loss, no effect on upstream loss (no absorbers upstream); classical quenching mechanism still applies

= 0.30 (38% of N2 replaced by CO2) Massive effect of reabsorption SL much higher with reabsorption than with no

radiation! Lean limit much leaner ( = 0.44) than with optically-

thin radiation ( = 0.68)

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Comparisons of burning velocities

= 0 (no CO2 in ambient) = 0.30

Note that without CO2 (left) SL & peak temperatures of reabsorbing flames are slightly lower than non-radiating flames, but with CO2 (right), SL & T are much higher with reabsorption. Optically thin always has lowest SL & T, with or without CO2

Note also that all experiments lie below predictions - are published chemical mechanisms accurate for very lean mixtures?

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Mechanisms of extinction limits Why do limits exist even

when reabsorption effects are considered and the ambient mixture includes absorbers? Spectra of product H2O

different from CO2 (Mechanism I)

Spectra broader at high T than low T (Mechanism II)

Radiation reaches upstream boundary due to “gaps” in spectra - product radiation that cannot be absorbed upstream

0.1

1

10

100

1000 1300K300K

CO2

0.1

1

10

100

1000 10000

1300K300K

Wavenumber (cm -1 )

H2O

Absorption spectra of CO2 & H2O at 300K & 1300K

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Mechanisms of limits (continued) Flux at upstream boundary

shows spectral regions where radiation can escape due to Mechanisms I and II - “gaps” due to mismatch between radiation emitted at the flame front and that which can be absorbed by the reactants

Depends on “discontinuity” (as seen by radiation) in T and composition at flame front - doesn’t apply to downstream radiation because T gradient is small

Behavior cannot be predicted via simple mean absorption coefficients - critically dependent on compositional & temperature dependence of spectra

Spectrally-resolved radiative flux at upstream boundary for a reabsorbing flame

(πIb = maximum possible flux)

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Effect of upstream domain length (L1) on limit composition (o) & SL for reabsorbing flames. With-out reabsorption, o = 0.68, thus reabsorption is very important even for the smallest L1 shown

Effect of domain size Limit & SL,lim decreases

as upstream domain length (L1) increases - less net heat loss

Significant reabsorption effects seen at L1 = 1 cm even though LP ≈ 18.5 cm because of existence of spectral regions with L() ≈ 0.025 cm-atm (!)

L1 > 100 cm required for domain-independent results due to band “wings” with small L()

Downstream domain length (L2) has little effect due to small gradients & nearly complete downstream absorption

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Effect of CO2 substitution for N2 on SL

Effect of (CO2 substitution level)

= 1.0: little effect of radiation; = 0.5: dominant effect - why? (1) = 0.5: close to

radiative extinction limit - large benefit of decreased heat loss due to reabsorption by CO2

(2) = 0.5: much larger Boltzman number (defined below) (B) (≈127) than = 1.0 (≈11.3); B ~ potential for radiative preheating to increase SL

Note with reabsorption, only 1% CO2 addition nearly doubles SL due to much lower net heat loss!

B ≡ . .Blackbody radiative heat flux at ad flame temp

Convective enthalpy flux through flame front ∂ln(SL)∂ ln(Tad )

=σ Tad

4 − To4

( )

ρoS L,adCPTad

β

2; β ≡

E

RTad

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Effect of CO2 substitution on SL,lim/SL,adiabatic

Effect of (continued)

Limit mixture much leaner with reabsorption than optically thin Limit mixture decreases with CO2 addition even though CP,CO2 > CP,N2

SL,lim/SL,ad always ≈ e-1/2 for optically thin, in agreement with theory SL,lim/SL,ad up to ≈ 20 with reabsorption!

Effect of CO2 substitution on flammability limit composition

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Effect of different radiation models on SL

and comparison to theory

Comparison to analytic theory Joulin & Deshaies (1986) -

analytical theory

Comparison to computation - poor Slightly better without H2O

radiation (mechanism (I) suppressed)

Slightly better still without T broadening (mechanism (II) suppressed, nearly adiabatic flame)

Good agreement when L() = LP = constant - emission & absorption across entire spectrum rather than just certain narrow bands.

Note drastic differences between last two cases, even though both have no net heat loss and have the same Planck mean absorption lengths!

SLSL,ad

⎛

⎝ ⎜ ⎞

⎠ ⎟ln

SLSL ,ad

⎛

⎝ ⎜ ⎞

⎠ ⎟ =B

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Comparison of computed results to experiments where reabsorption effects may have been important

Comparison with experiment No directly comparable expts., BUT... Zhu, Egolfopoulos, Law (1988)

CH4 + (0.21O2 + 0.79 CO2) ( = 0.79) Counterflow twin flames, extrapolated

to zero strain L1 = L2 ≈ 0.35 cm chosen since 0.7 cm

from nozzle to stagnation plane No solutions for adiabatic flame or

optically-thin radiation (!) Moderate agreement with reabsorption

Abbud-Madrid & Ronney (1990) (CH4 + 4O2) + CO2 Expanding spherical flame at µg L1 = L2 ≈ 6 cm chosen (≈ flame radius) Optically-thin model over-predicts limit

fuel conc. & SL,lim Reabsorption model underpredicts limit

fuel conc. but SL,lim well predicted - net loss correctly calculated

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Conclusions Reabsorption increases SL & extends limits, even in

spectrally radiating gases Two loss mechanisms cause limits even with reabsorption

(I) Mismatch between spectra of reactants & products (II) Temperature broadening of spectra

Results qualitatively & sometimes quantitatively consistent with theory & experiments

Behavior cannot be predicted using mean absorption coefficients!

Can be important in practical systems Future work

“Flame balls” in H2-O2-CO2 & H2-O2-SF6 mixtures - comparison of computation & experiment indicates reabsorption important

Spherically expanding flames Elevated pressures - pressure (collisional) broadening

would lead to even greater reabsorption effects Exhaust-gas & flue-gas recirculation