Effects of radiative emission and
absorption on the propagation
and extinction of premixed gas
flames
Yiguang Ju and Goro Masuya
Department of Aeronautics & Space Engineering
Tohoku University, Aoba-ku, Sendai 980, Japan
Paul D. Ronney
Department of Aerospace & Mechanical
Engineering
University 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
1
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 (AbbudMadrid & 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?
2
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
3
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 (w) 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-g)N2+ g CO2} - substitute CO2 for
N2 in “air” to assess effect of absorbing ambient
4
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
5
Flame structures
q (reabsorption)
q (optically thin)
1500
1000
Convective-loss zone
(optically thin)
6
-1 10
7
3
-5 10
0
-0.5
0
0.5
Spatial coordinate (cm)
Flame zone detail

)
adiabatic
reabsorption
optically thin
500
1
Reabsorbing fla me:
max . T > adiaba tic flame
1600
Temperature (K)
0
2000
Radiative power (W/m
Reabsorption
zone (negative
los s region)
2500
Temperature (K)
2000
5 10 6
3000
Reabsorbing fla me:
slow downstream loss
1200
800
Reabsorbing fla me:
convec tive radia tive zone
Optica lly thin:
rapid dow nstrea m loss
400
-30
-20
-10
0
10
20
30
40
Spatial coordinate (cm)
Radiation zones (large scale)
Mixture: CH4 in “air”, 1 atm, equivalence ratio (f): 0.70;
g = 0.30 (“air” = 0.21 O2 + .49 N2 + .30 CO2)
6
Radiation effects on burning velocity (SL)


CH4-air (g = 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
g = 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 (f = 0.44) than with optically-thin
radiation (f = 0.68)
7
Comparisons of burning velocities
g = 0 (no CO2 in ambient)


g = 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
8
mixtures?
-1
atm
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
-1

)
Mechanisms of extinction limits
Absorption spectra
of CO2 & H2O at
300K & 1300K
9
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)
10
Effect of domain size

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Limit f & 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(w) ≈ 0.025 cmatm (!)
L1 > 100 cm required for
domain-independent results
due to band “wings” with
small L(w)
Downstream domain length
(L2) has little effect due to
small gradients & nearly
complete downstream
absorption
Effect of upstream domain
length (L1) on limit composition
(fo) & SL for reabsorbing
flames. With-out reabsorption,
fo = 0.68, thus reabsorption is
very important even for the
smallest L1 shown
11
Effect of g (CO2 substitution level)


f = 1.0: little effect of radiation;
f = 0.5: dominant effect - why?

(1) f = 0.5: close to radiative
extinction limit - large benefit
of decreased heat loss due to
reabsorption by CO2

(2) f = 0.5: much larger
Boltzman number (defined
below) (B) (≈127) than f = 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!
Effect of CO2 substitution
for N2 on SL
Tad4  To4  
Blackbody radiative heat flux at ad. flame temp. ln( SL )
E
B

; 
Convective enthalpy flux through flame front ln( Tad ) o SL,adCPTad 2
RTad
12
Effect of g (continued)
Effect of CO2 substitution on
flammability limit composition

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Effect of CO2 substitution
on SL,lim/SL,adiabatic
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!
13
Comparison to analytic theory

Joulin & Deshaies (1986) analytical theory
 SL   SL 

ln 
  B
S
S
 L,ad   L,ad 




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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(w) = 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!
Effect of different radiation
models on SL and
comparison to theory
14
Comparison with experiment


No directly comparable expts., BUT...
Zhu, Egolfopoulos, Law (1988)

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CH4 + (0.21O2 + 0.79 CO2) (g = 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
Comparison of computed
results to experiments
where reabsorption effects
may have been important
15
Conclusions
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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
16