premixed flame propagation in hele-shaw cells: what darrieus & landau didn’t tell you

Premixed flame propagation in Hele-Shaw cells: What Darrieus & Landau didnt tell youhttp://ronney.usc.edu/research

Paul D. RonneyDept. of Aerospace & Mechanical EngineeringUniversity of Southern CaliforniaLos Angeles, CA 90089-1453 USA

National Tsing-Hua UniversityOctober 7, 2005

University of Southern CaliforniaEstablished 125 years ago this week!jointly by a Catholic, a Protestant and a Jew - USC has always been a multi-ethnic, multi-cultural, coeducational universityToday: 32,000 students, 3000 faculty2 main campuses: University Park and Health SciencesUSC Trojans football team ranked #1 in USA last 2 years

USC Viterbi School of EngineeringNaming gift by Andrew & Erma ViterbiAndrew Viterbi: co-founder of Qualcomm, co-inventor of CDMA1900 undergraduates, 3300 graduate students, 165 faculty, 30 degree options$135 million external research fundingDistance Education Network (DEN): 900 students in 28 M.S. degree programs; 171 MS degrees awarded in 2005More info: http://viterbi.usc.edu

Paul RonneyB.S. Mechanical Engineering, UC BerkeleyM.S. Aeronautics, CaltechPh.D. in Aeronautics & Astronautics, MITPostdocs: NASA Glenn, Cleveland; US Naval Research Lab, Washington DCAssistant Professor, Princeton UniversityAssociate/Full Professor, USCResearch interestsMicroscale combustion and power generation (10/4, INER; 10/5 NCKU)Microgravity combustion and fluid mechanics (10/4, NCU)Turbulent combustion (10/7, NTHU)Internal combustion enginesIgnition, flammability, extinction limits of flames (10/3, NCU)Flame spread over solid fuel bedsBiophysics and biofilms (10/6, NCKU)

Paul Ronney

IntroductionModels of premixed turbulent combustion dont agree with experiments nor each other!

Introduction - continued...whereas in liquid flame experiments, ST/SL in 4 different flows is consistent with Yakhots model with no adjustable parameters

Motivation (continued)Why are gaseous flames harder to model & compare (successfully) to experiments?One reason: self-generated wrinkling due to flame instabilitiesThermal expansion (Darrieus-Landau, DL)Rayleigh-Taylor (buoyancy-driven, RT)Viscous fingering (Saffman-Taylor, ST) in Hele-Shaw cells when viscous fluid displaced by less viscous fluidDiffusive-thermal (DT) (Lewis number)Needed: simple apparatus for systematic study of DL, RT, ST & DT instabilities & their effects on burning rates

Hele-Shaw flowFlow between closely-spaced parallel platesMomentum eqn. reduces to linear 2-D equation (Darcys law)1000's of referencesPractical application to combustion: flame propagation in cylinder crevice volumes

Joulin-Sivashinsky (CST, 1994) modelLinear stability analysis of flame propagation in HS cells Uses Euler-Darcy momentum eqn. Combined effects of DL, ST, RT & heat loss (but no DT effect - no damping at small l)Dispersion relation: effects of thermal expansion (), viscosity change across front (F) & buoyancy (G) on relationship between scaled wavelength () and scaled growth rate ()Characteristic wavelength for ST = (/6)(uUw2/av): smaller scales dominated by DL (no characteristic wavelength)

ObjectivesMeasurePropagation ratesWrinkling characteristicsof premixed flames in Hele-Shaw cells as a function ofMixture strength (thus SL) (but density ratio () & viscosity change (fb - fu) dont vary much over experimentally accessible range of mixtures) Cell thickness (w)Propagation direction (upward, downward, horizontal)Lewis number (vary fuel & inert type)and compare to JS model predictions

ApparatusAluminum frame sandwiched between Lexan windows40 cm x 60 cm x 1.27 or 0.635 or 0.32 cm test sectionCH4 & C3H8 fuel, N2 & CO2 diluent - affects Le, Peclet #Upward, horizontal, downward orientationSpark ignition (3 locations, plane initiation)Exhaust open to ambient pressure at ignition end - flame propagates towards closed end of cell

Results - video - baseline case6.8% CH4-air, horizontal, 12.7 mm cell

Results - video - upward propagation6.8% CH4-air, upward, 12.7 mm cell

Results - video - downward propagation

6.8% CH4-air, downward, 12.7 mm cell

Results - video - high Lewis number

3.0% C3H8-air, horizontal, 12.7 mm cell (Le 1.7)

Results - video - low Lewis number

8.6% CH4 - 32.0% O2 - 60.0% CO2, horizontal, 12.7 mm cell (Le 0.7)

Results - stoichiometric, baseline thickness

9.5% CH4 - 90.5% air, horizontal, 12.7 mm cell

Results - stoichiometric, thinner cell


Results - stoichiometric, very thin cell


Broken flames at very low Pe, Le < 1

6.0% CH4- air, downward, 6.3 mm cell (Pe 30(!))

Results - qualitativeOrientation effectsHorizontal propagation - large wavelength wrinkle fills cellUpward propagation - more pronounced large wrinkleDownward propagation - globally flat front (buoyancy suppresses large-scale wrinkles); oscillatory modes, transverse wavesThinner cell: transition to single large tulip fingerConsistent with Joulin-Sivashinsky predictionsLarge-scale wrinkling observed even at high LeBroken flames observed near limits for low Le but only rarely & not repeatableFor practical range of conditions, buoyancy & diffusive-thermal effects cannot prevent wrinkling due to viscous fingering and/or thermal expansionEvidence of preferred wavelengths, but selection mechanism unclear

Lewis number effects8.6% CH4 - 34.4% O2 - 57.0% CO2 Horizontal propagation12.7 mm cell, Pe = 856.8% CH4 - 93.2% airHorizontal propagation12.7 mm cell, Pe = 1003.0% C3H8 - 97.0% airHorizontal propagation12.7 mm cell, Pe = 166

Results - propagation rates3-stage propagationThermal expansion - most rapid, propagation rate (u/b)SLQuasi-steady (slower but still > SL)Near-end-wall - slowest - large-scale wrinkling suppressed

Results - quasi-steady propagation ratesHorizontal, CH4-air (Le 1)Quasi-steady propagation rate (ST) always larger than SL - typically ST 3SL even though u/SL = 0!Independent of Pe = SLw/ independent of heat lossSlightly higher ST/SL for thinner cell despite lower Pe (greater heat loss) (for reasons to be discussed later)

Results - quasi-steady propagation ratesHorizontal, C3H8-airVery different trend from CH4-air - ST/SL depends significantly on Pe & cell thickness (why? see next slide)STILL slightly higher ST/SL for thinner cell despite lower Pe (greater heat loss)

Laminar burning velocities

%C3H8phi-C3H8SL-C3H8%CH4phi-CH4SL-CH4

2.810.6920.636.850.7015.76

2.980.7323.957.300.7518.18

3.170.7828.117.770.8024.08

3.320.8230.668.570.8931.28

3.500.8734.149.491.0036.54

3.780.9437.319.891.0537.13

3.960.9838.3510.281.0937.58

4.081.0239.1210.791.1536.13

4.241.0639.9711.201.2031.78

4.631.1639.5711.541.2526.92

4.831.2138.7811.931.2921.28

5.031.2636.9712.411.3515.89

5.161.3032.7912.761.4013.56

5.261.3229.76

5.421.3727.05

5.531.4024.62

Results - quasi-steady propagation ratesC3H8-air (lean): Le 1.7, lower ST/SL C3H8-air (rich): Le 0.9, higher ST/SL ( 3), independent of Pe, similar to CH4-air

Chart1

4.27585022731.74611111111.81998021760

4.51941131621.90888888892.02621167165

4.54827781561.77002967362.0227497527

1.89416419392.0588846618

2.18100890212.2181586341

1.81273200781.5170127892

2.12051228221.480829622

2.16205591861.8524888212

2.60557605581.7939703655

2.69167691681.6380335397

2.22012578622.3780237802

2.14081062191.9848298483

2.88923829491.6789667897

3.02375960871.5387453875

2.30114871162.2875262055

2.93231915552.1408106219

3.02452654462.8728162124

2.60251903932.8169112509

3.88119612072.3014916846

2.91352370692.9984476871

3.06734913793.0620925179

3.60107060922.6130345636

3.31965332653.0932730356

3.45918111033.0553985302

3.72695302693.3054956897

3.67646211473.7836907683

3.21577079113.7899566658

3.50126774853.7351516696

3.1465715014

3.192709661

3.9986072577

3.6105845955

3.0472486315

3.1604724863

3.8697781619

3.9383462979

3.7633038572

3.1270283976

3.0420892495

Stoichiometric

Lean (high Le)

Rich (lower Le)

1/8"

1/4"

1/2"

Fuel % (propane)

ST/SL

Propane, horizontal

Sheet1

test pt.dategapfueldiluentF%Ox%propMax Pressure(atm)final SLST (cm/sec)final ST/SLfinal PeFrnotesTherm.Diffus.ubrhourhobegTadfufbfavST length (cm)FG

5323/20/030.32C3H8O2/N24.03020.155horizontal38.80165.9004.27666.950.000.184

5333/20/030.32C3H8O2/N24.03020.155horizontal38.80175.3504.51966.950.000.184

5343/20/030.32C3H8O2/N24.03020.155horizontal38.80176.4704.54866.950.000.184

1792/16/030.64C3H8O2/N22.7020.40horizontal18.0031.4301.74660.800.000.1880.00001775.96E-051.180.20823529410.1764705882017005.267530535117.739297961411.503414248211.60132574958.28059877330





60.64C3H8O2/N22.920.3horizontal22.3940.581.81375.610.001/4" cell0.1880.00001775.96E-051.180.20823529410.1764705882017005.267530535117.739297961411.503414248214.42824657568.28059877330





173/30/950.64C3H8O2/N23.221horizontal28.6263.542.22097.190.000.1870.00001775.96E-051.180.20823529410.1764705882017005.267530535117.739297961411.503414248218.44610794168.28059877330







163/30/950.64C3H8AIR3.596.5horizontal34.1488.852.603116.550.000.1860.00001775.96E-051.180.20823529410.1764705882017005.267530535117.739297961411.503414248222.00384783828.28059877330
















3873/9/031.27C3H8O2/N22.920.39horizontal22.3933.961.517151.230.001 ignition0.1880.00001775.96E-051.180.20823529410.1764705882017001.31688263384.43482449032.875853562157.71298630228.28059877330

3883/9/031.27C3H8O2/N22.920.39horizontal22.3933.151.481151.230.002 ignitions0.1880.00001775.96E-051.180.20823529410.1764705882017001.31688263384.43482449032.875853562157.71298630228.28059877330






3653/9/031.27C3H8O2/N23.020.37horizontal24.3940.9501.679165.640.001 ignition0.1870.00001775.96E-051.180.20823529410.1764705882017001.31688263384.43482449032.875853562162.87918556218.28059877330









163/31/991.27C3H8AIR3.596.5horizontal34.1489.2092.61233.110.000.1860.00001775.96E-051.180.20823529410.1764705882017001.31688263384.43482449032.875853562188.01539135268.28059877330


















4.030

4.035

Sheet2

Sheet3

Results - quasi-steady propagation ratesHorizontal, CH4-O2-CO2 (Le 0.7)Similar to CH4-air, no effect of PeSlightly higher average ST/SL: 3.5 vs. 3.0, narrow cell again slightly higher


%C3H8phi-C3H8SL-C3H8%CH4phi-CH4SL-CH4

2.810.6920.636.850.7015.76

2.980.7323.957.300.7518.18

3.170.7828.117.770.8024.08

3.320.8230.668.570.8931.28

3.500.8734.149.491.0036.54

3.780.9437.319.891.0537.13

3.960.9838.3510.281.0937.58

4.081.0239.1210.791.1536.13

4.241.0639.9711.201.2031.78

4.631.1639.5711.541.2526.92

4.831.2138.7811.931.2921.28

5.031.2636.9712.411.3515.89

5.161.3032.7912.761.4013.56

5.261.3229.76

5.421.3727.05

5.531.4024.62

Results - quasi-steady propagation ratesUpward, CH4-air (Le 1)Higher ST/SL for thicker cell - more buoyancy effect, increases large-scale wrinkling - no effect of orientation for 1/8 cellMore prevalent at low Pe (low SL) - back to ST/SL 3 for high Pe


%C3H8phi-C3H8SL-C3H8rhoueubT%CH4phi-CH4SL-CH4rhoueubT

2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Results - quasi-steady propagation ratesDownward, CH4-air (Le 1)Higher ST/SL for thinner cell - less buoyancy effect - almost no effect for 1/8 cellMore prevalent at low Pe (low SL) - back to ST/SL 3 for high PeHow to correlate ST/SL for varying orientation, SL, w ???



2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Results - quasi-steady propagation ratesUpward, CH4-O2-CO2 (Le 0.7)Higher ST/SL for thicker cell - more buoyancy effect, increases large-scale wrinkling - less effect of orientation for 1/8 cellMore prevalent at low Pe (low SL) - back to ST/SL 4 for high Pe



2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Results - pressure characteristicsInitial pressure rise after ignitionPressure constant during quasi-steady phasePressure rise higher for faster flames

Slow flameFast flame

Scaling analysisHow to estimate driving force for flame wrinkling?Hypothesis: use linear growth rate () of Joulin-Sivashinsky analysis divided by wavenumber (k) (i.e. phase velocity /k) scaled by SL as a dimensionless growth rateAnalogous to a turbulence intensity)Use largest value of growth rate, corresponding to longest half-wavelength mode that fits in cell, i.e., k* = (2/L)/2 (L = width of cell = 39.7 cm)Small L, i.e. L < ST length = (/6)(uUw2/av)DL dominates - /k = constantPropagation rate should be independent of LLarge L, i.e. L > (/6)(uUw2/av)ST dominates - /k increases with LPropagation rate should increase with LBaseline condition: (6.8% CH4-air, SL = 15.8 cm/s, w = 12.7 mm): ST length = 41 cm > L - little effect of ST

Scaling analysis

ST length smaller (thus more important) for slower flames and smaller w - but these conditions will cause flame quenching - how to get smaller ST length without quenching?ST length = w (/6)(u/av)(1/Pr)Pe for fixed cell width, minimum Pe 40 set by quenching - easier to get smaller ST length without quenching in thinner cells

Effect of JS parameterResults correlate reasonably well with relation ST/SL 1 + 0.64 (/kSL)- suggests dimensionless JS parameter IS the driving force



2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Effect of JS parameterVery similar for CH4-O2-CO2 mixtures



2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Effect of JS parameter but propane far less impressive



2.8160.69020.6301.190.15660235531.80E-056.32E-0518636.850.7015.761.140.16316940251.82E-056.26E-051831.0

2.9800.73023.9501.190.1508227381.80E-056.46E-0519307.300.7518.181.130.15622803041.81E-056.44E-051919.0

3.1700.78028.1101.190.14440850281.79E-056.64E-0520127.770.8024.081.13170.15012760851.81E-056.61E-051996.0

3.3200.82030.6608.570.8931.281.130.14106162981.81E-056.87E-052122.0

3.5000.87034.1409.491.0036.541.120.13377210581.80E-057.08E-052226.0

3.7800.94037.3109.891.0537.131.120.13264358671.80E-057.09E-052233.0

3.9600.98038.35010.281.0937.581.120.13281976361.80E-057.06E-052217.0

4.0801.02039.12010.791.1536.131.120.13397462521.79E-056.96E-052176.0

4.2401.06039.97011.201.2031.781.110.13525028061.79E-056.87E-052137.0

4.6301.16039.57011.541.2526.921.110.13664188891.79E-056.78E-052097.0

4.8301.21038.78011.931.2921.281.110.13780558391.78E-056.71E-052065.0

5.0301.26036.97012.411.3515.891.110.13961410661.78E-056.60E-052018.0

5.1601.30032.79012.761.4013.561.110.14117115591.78E-056.51E-051980.0

5.2601.32029.760

5.4201.37027.050

5.5301.40024.620

C3H8%SL

8.68.826172

Image analysis - flame positionDetermine flame positionVideo frames digitized, scaled to 256 pixels in x (spanwise) directionOdd/even video half-frames separatedFor each pixel column, flame position in y (propagation) direction (yf) is 1st moment of intensity (I) w.r.t. position, i.e.

Contrast & brightness adjusted to obtain good flame trace

Flame front lengthsFront length / cell width - measure of wrinkling of flame by instabilitiesRelatively constant during testHigher/lower for upward/downward propagationFront length / cell width = AT/AL < ST/SL - front length alone cannot account for observed flame acceleration by wrinklingCurvature in 3rd dimension must account for wrinklingAssume ST/SL (AT/AL)(U/SL), where U = speed of curved flame in channel, flat in x-y plane

Flame front lengthsEven for horizontally-propagating flames, AT/AL not constant - decreases with increasing Pe - but (inferred) U/SL increases to make (measured) ST/SL constant!

Flame front lengthsAT/AL similar with propane - but (inferred) U/SL lower at low Pe to make (measured) ST/SL lower!

Flame front lengthsAT/AL correlates reasonably well with JS growth parameter for CH4-air and CH4-O2-CO2Less satisfying for C3H8-air (high Le)Expected trend - AT/AL increases as JS parameter increases but AT/AL > 1 even when JS parameter < 0

Results - wrinkling characteristicsIndividual images show clearly defined wavelength selection

Results - wrinkling characteristicsbut averaging make them hard to see - 1/2 wave mode dominates spectra

Results - wrinkling characteristicsBecause relative amplitudes of modes evolve over time

Results - wrinkling characteristicsShows up better in terms of amplitude x wavenumber

Wrinkling - different mixture strengthsModes 3 - 5 are very popular for a range of SL

Wrinkling - different cell thicknessesCharacteristic wavelength for ST = 103 cm, 26 cm, 6.4 cm in 12.7, 6.35, 3.2 mm thick cells - for thinner cells, ST dominates DL, more nearly monochromatic behavior (ST has characteristic wavelength, DL doesnt)Run 1089.5% CH4-airHorizontal propagation6.35 mm cell

Wrinkling - different orientationsUpward = more wrinkling at large scales (RT encouraged); downward = less wrinkling at large scales; smaller scales unaffected (RT dominant at large wavelengths)

Wrinkling - different fuel-O2-inerts, same SLSlightly broader spectrum of disturbances at low Le, less at high Le

ConclusionsFlame propagation in quasi-2D Hele-Shaw cells reveals effects of Thermal expansion - always presentViscous fingering - narrow channels, high UBuoyancy - destabilizing/stabilizing at long wavelengths for upward/downward propagationLewis number affects behavior at small wavelengths but propagation rate & large-scale structure unaffectedHeat loss (Peclet number) little effect, except U affects transition from DL to ST controlled behavior

RemarkMost experiments conducted in open flames (Bunsen, counterflow, ...) - gas expansion relaxed in 3rd dimension but most practical applications in confined geometries, where unavoidable thermal expansion (DL) & viscous fingering (ST) instabilities cause propagation rates 3 SL even when heat loss, Lewis number & buoyancy effects are negligibleDL & ST effects may affect propagation rates substantially even when strong turbulence is present - generates wrinkling up to scale of apparatus(ST/SL)Total = (ST/SL)Turbulence x (ST/SL)ThermalExpansion ?

RemarkComputational studies suggest similar conclusionsEarly times, turbulence dominates Late times, thermal expansion dominates

H. Boughanem and A. Trouve, 27th Symposium, p. 971.Initial u'/SL = 4.0 (decaying turbulence); integral-scale Re = 18

Future workExamine phase information, mode couplingObstacles of specified wavenumber - examine forced responseLinear growth behavior - need to suppress instabilities until specified time / location (e.g. acoustics, Clanet & Searby PRL 1998)Radial growth from point ignition (Sivashinsky & others)

Thanks toNational Tsing-Hua UniversityProf. C. A. Lin, Prof. T. M. LiouCombustion Institute (Bernard Lewis Lectureship)NASA (research support)

premixed flame propagation in hele-shaw cells: what darrieus & landau didn’t tell you

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