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Department of Applied Mechanics A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of A Distinctive Feature of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Turbulent Combustion of Lean Hydrogen Lean Hydrogen- -Air Air Mixtures Mixtures Lean Lean Hydrogen Hydrogen - - Air Air Mixtures Mixtures Andrei N. Lipatnikov Andrei N. Lipatnikov Andrei N. Lipatnikov Andrei N. Lipatnikov Department of Applied Mechanics Chalmers University of Technology Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Contents of the Lecture � Background � Laminar premixed flame � Turbulence � The major physical mechanism of premixed turbulent combustion � Experimental data on turbulent burning velocity � Ordinary hydrocarbon-air mixtures � Lean hydrogen-air mixtures � Why does molecular transport substantially affect turbulent combustion at high Reynolds number? Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Contents of the Lecture � Background � Laminar premixed flame � Turbulence � The major physical mechanism of premixed turbulent combustion � Experimental data on turbulent burning velocity � Ordinary hydrocarbon-air mixtures � Lean hydrogen-air mixtures � Why does molecular transport substantially affect turbulent combustion at high Reynolds number? Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics The Physical Mechanism of Flame Propagation in Premixed Reactants ∂ ∂ ∂ J ( ) ( ) ρ + ρ = − kj + ρ Y u Y w k j k j ∂ ∂ ∂ t x x j j ∂ J ∂ ∂ ( ) Heat release ( ) Tj ρ + ρ = − + ρ T u T w Heat transport j T ∂ ∂ ∂ t x x j j Molecular transport: ∂ ∂ Y T = − ρ = − ρκ J D k ; J kj k Tj ∂ ∂ x x j j From the paper by Williams, F.A., “Progress Θ   in knowledge of flamelet structure and extinction," 1 Progress in Energy and Combustion Science   ∝ − j w exp 26: 657-682 (2000). Chemical Reactions:   j t T   r Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Flame propagation in premixed reactants is caused by the heat release in chemical reactions and the molecular transport of the heat into the unburned mixture. Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics The Physical Mechanism of Flame Propagation in Premixed Reactants ∂ ∂ ∂ J ( ) ( ) ρ + ρ = − kj + ρ Y u Y w k j k j ∂ ∂ ∂ t x x j j ∂ J ∂ ∂ ( ) ( ) δ r Tj ρ + ρ = − + ρ T u T w j T ∂ ∂ ∂ t x x j j Molecular transport: δ T ∂ ∂ Y T = − ρ = − ρκ J D k ; J kj k Tj ∂ ∂ x x j j From the paper by Williams, F.A., “Progress Θ   in knowledge of flamelet structure and extinction," 1 Progress in Energy and Combustion Science   ∝ − j w exp 26: 657-682 (2000). Chemical Reactions: Θ ≈20 000 o K   j t T   r Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics The key peculiarity of premixed combustion is as follows: major chemical reactions that control the heat release are confined to very thin reaction zone! Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Typical Values of Laminar Flame Speed and Thickness κ κ ∝ κ S w δ ∝ ∝ u u L u Tm L w S Tm L Hydrocarbon-air flames: Hydrogen-air flames: • S L ≈2 m/s • S L ≈0.4 m/s • κ u ≈0.05 cm 2 /s • κ u ≈0.02 cm 2 /s • δ r ≈0.02 mm • δ r ≈0.05 mm • δ τ ≈0.2 mm • δ τ ≈0.5 mm Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Laminar Flame Speed CH 4 H 2 Y = F F Y F , St Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Turbulent Flows Photograph by Corke & Nagib Photograph by Dimotakis et al. Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Main Characteristics of Turbulence rms turbulent velocity Integral length scale + u ' ( x ) u ' ( x x ) u u = f ( x ) 0 0 + x u ' ( x ) u ' ( x x ) 0 0 v v + v ' ( x ) v ' ( x x ) x = g ( x ) 0 0 + v ' ( x ) v ' ( x x ) + τ t 0 0 1 ∫ = = η η U ( x ) u ( x , t ) u ( x , ) d ∞ τ ∫ = t L E f ( x ) dx 1 ||  + τ  t 2 1 [ ] 0 ∫ ′ 2 = η − η u u ( x , ) u ( x ) d   τ ∞   ∫ ⊥ = t L E g ( x ) dx 0 Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Turbulence Spectrum From the book by S.B. Pope “Turbulent Flows”, Cambridge University Press, Cambridge, UK, 2000. u ' L = ν >> Re 1 u 3 ' t ε ∝ L − 3 1 η ∝ ν ε ; 4 4 1 1 ′ ∝ ν ε u ; 4 4 η η u ' η = ≈ Re 1 π 2 η ν = k λ Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Effect of Turbulent Velocity on Flame Speed Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Physical Mechanism of the Increase in Flame Speed by Turbulent Velocity Picture from the paper by Fox, M.D. and Weinberg, F.J. “An experimental study of burner stabilized turbulent flames in premixed reactants”, Proceedings of the Royal Society of London, A268:222-239, 1962. S L δ t δ L «δ t Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Physical Mechanism of the Increase in Flame Speed by Turbulent Velocity S L Σ t η << l << L u' 1 S L Σ f 3 − η = ⋅ L Re 4 Σ t f = u ' L U S Re = t L Σ t ν t u u' 2 >u' 1 L Σ f2 > Σ f1 l«L Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Contents of the Lecture � Background � Laminar premixed flame � Turbulence � The major physical mechanism of premixed turbulent combustion � Experimental data on turbulent burning velocity � Ordinary hydrocarbon-air mixtures � Lean hydrogen-air mixtures � Why does molecular transport substantially affect turbulent combustion at high Reynolds number? Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Effect of Laminar Flame Speed on Turbulent Burning Velocity Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Effect of Laminar Flame Speed on Turbulent Burning Velocity � Turbulent burning velocity U t is increased by the laminar flame speed S L , all other things being equal. The larger the laminar flame speed, the higher the rate of the increase in the burning velocity by rms turbulent velocity Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Effect of Laminar Flame Speed on Turbulent Burning Velocity 5 5 5 2 2H 2 +O 2 +12N 2 2H 2 +O 2 +12N 2 2H 2 +O 2 +12N 2 2H 2 +O 2 +9N 2 2H 2 +O 2 +9N 2 2H 2 +O 2 +9N 2 4 4 4 burning velocity, m/s burning velocity, m/s burning velocity, m/s 2H 2 +O 2 +7N 2 burning velocity, m/s 2H 2 +O 2 +7N 2 1.5 2H 2 +O 2 +6N 2 3 3 3 1 2 2 2 2H 2 +O 2 +12N 2 0.5 1 1 1 0 0 0 0 0 2 4 6 0 0 0 2 2 2 4 4 4 6 6 6 r.m.s. turbulent velovity, u’, m/s r.m.s. turbulent velovity, u’, m/s r.m.s. turbulent velovity, u’, m/s r.m.s. turbulent velovity, u’, m/s Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Empirical Parameterization for Turbulent Burning Velocity = + U S u ' t L A linear increase in + burning velocity U t by turbulent velocity u' - dU t ' = const du Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Empirical Parameterization for Turbulent Burning Velocity     δ U u ' u ' ( )     = = = t F ; L F ; Re ; Pr F Da; Ka ; Pr     1 t 3 u ' S L S     L L u ' L S L 2   u ' = ⋅ = ⋅ 1 Re Pr ; Da L ; −   ∝ Ka Re 2   t δ δ S u ' t S   L L L L = const ⋅ ⋅ ⋅ ⋅ ν a b c d U u' L S t L u a+c+d=1; a+b+c+2d=1 Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007

Department of Applied Mechanics Empirical Parameterization for Turbulent Burning Velocity = const ⋅ ⋅ ⋅ ⋅ ν a b c d U u' L S t L u a≈0.5-0.75 c=0.5-0.6 dU t is increased by S L ! du ' Second European Summer School on Hydrogen Safety, Belfast, August 1, 2007