1 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 Paper No. P024, 27th Symposium (International) on Combustion, Boulder, CO, August 5, 1998 PDR acknowledges support from NASA-LewisNASA-Lewis

2 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 (S L,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 (S L ) increase Flammability limits widen (theoretically no limit)  … but gases, unlike solid particles, emit & absorb only in narrow spectral bands - what will happen ?

3 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 (L P ) ≈ 4 cm for combustion products ≈ cylinder size Atmospheric-pressure furnaces - L P ≈ 1.6 m - comparable to boiler dimensions Exhaust-gas or flue-gas recirculation - absorbing CO 2 & H 2 O present in unburned mixture - reduces L P of reactants & increases reabsorption effects

4 Numerical model  Steady planar 1D energy & species conservation equations  CHEMKIN with pseudo-arclength continuation  18-species, 58-step CH 4 oxidation mechanism (Kee et al.)  Boundary conditions Upstream - T = 300K, fresh mixture composition, inflow velocity S L at x = L 1 = -30 cm Downstream - zero gradients of temperature & composition at x = L 2 = 400 cm  Radiation model CO 2, H 2 O and CO Wavenumbers (  ) 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 CH 4 + {0.21O 2 +(0.79-  )N 2 +  CO 2 } - substitute CO 2 for N 2 in “air” to assess effect of absorbing ambient

5 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

6 Flame structures Flame zone detail Radiation zones (large scale)  Mixture: CH 4 in “air”, 1 atm, equivalence ratio (  ): 0.70;  = 0.30 (“air” = 0.21 O N CO 2 )

7 Radiation effects on burning velocity (S L )  CH 4 -air (  = 0) Minor differences between reabsorption & optically-thin... but S L,lim 25% lower with reabsorption; since S L,lim ~ (radiative loss) 1/2, if net loss halved, then S L,lim should be 1 - 1/√2 = 29% lower with reabsorption S L,lim /S L,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 N 2 replaced by CO 2 ) Massive effect of reabsorption S L much higher with reabsorption than with no radiation! Lean limit much leaner (  = 0.44) than with optically-thin radiation (  = 0.68)

8 Comparisons of burning velocities  = 0 (no CO 2 in ambient)  = 0.30  Note that without CO 2 (left) S L & peak temperatures of reabsorbing flames are slightly lower than non-radiating flames, but with CO 2 (right), S L & T are much higher with reabsorption. Optically thin always has lowest S L & T, with or without CO 2  Note also that all experiments lie below predictions - are published chemical mechanisms accurate for very lean mixtures?

9 Mechanisms of extinction limits  Why do limits exist even when reabsorption effects are considered and the ambient mixture includes absorbers? Spectra of product H 2 O different from CO 2 (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 Absorption spectra of CO 2 & H 2 O at 300K & 1300K

10 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 (πI b = maximum possible flux)

11 Effect of upstream domain length (L 1 ) on limit composition (  o ) & S L for reabsorbing flames. With-out reabsorption,  o = 0.68, thus reabsorption is very important even for the smallest L 1 shown Effect of domain size  Limit  & S L,lim decreases as upstream domain length (L 1 ) increases - less net heat loss  Significant reabsorption effects seen at L 1 = 1 cm even though L P ≈ 18.5 cm because of existence of spectral regions with L(  ) ≈ cm- atm (!)  L 1 > 100 cm required for domain-independent results due to band “wings” with small L(  )  Downstream domain length (L 2 ) has little effect due to small gradients & nearly complete downstream absorption

12 Effect of CO 2 substitution for N 2 on S L Effect of  (CO 2 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 CO 2 (2)  = 0.5: much larger Boltzman number (defined below) (B) (≈127) than  = 1.0 (≈11.3); B ~ potential for radiative preheating to increase S L  Note with reabsorption, only 1% CO 2 addition nearly doubles S L due to much lower net heat loss!

13 Effect of CO 2 substitution on S L,lim /S L,adiabatic Effect of  (continued)  Limit mixture much leaner with reabsorption than optically thin  Limit mixture decreases with CO 2 addition even though C P,CO2 > C P,N2  S L,lim /S L,ad always ≈ e -1/2 for optically thin, in agreement with theory  S L,lim /S L,ad up to ≈ 20 with reabsorption! Effect of CO 2 substitution on flammability limit composition

14 Effect of different radiation models on S L and comparison to theory Comparison to analytic theory  Joulin & Deshaies (1986) - analytical theory  Comparison to computation - poor  Slightly better without H 2 O radiation (mechanism (I) suppressed)  Slightly better still without T broadening (mechanism (II) suppressed, nearly adiabatic flame)  Good agreement when L(  ) = L P = 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!

15 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) CH 4 + (0.21O CO 2 ) (  = 0.79) Counterflow twin flames, extrapolated to zero strain L 1 = L 2 ≈ 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) (CH 4 + 4O 2 ) + CO 2 Expanding spherical flame at µg L 1 = L 2 ≈ 6 cm chosen (≈ flame radius) Optically-thin model over-predicts limit fuel conc. & S L,lim Reabsorption model underpredicts limit fuel conc. but S L,lim well predicted - net loss correctly calculated

16 Conclusions  Reabsorption increases S L & 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 H 2 -O 2 -CO 2 & H 2 -O 2 -SF 6 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