cefrc combustion summer school...dimensionless quantities in premixed turbulent combustion •...
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Turbulent Premixed Combustion
CEFRC Combustion Summer School
Prof. Dr.-Ing. Heinz Pitsch
2014
Copyright ©2014 by Heinz Pitsch. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Heinz Pitsch.
Example: LES of a stationary gas turbine
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velocity field
flame
Course Overview
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• Turbulence
• Turbulent Premixed Combustion
• Turbulent Non-Premixed
Combustion
• Modelling Turbulent Combustion
• Applications
• Scales of Turbulent Premixed
Combustion
• Regime-Diagram
• Turbulent Burning Velocity
Part II: Turbulent Combustion
Scales of Turbulent Premixed Combustion
• Integral turbulent scales
• Smallest turbulent scales/Kolmogorov scales
• Flame thickness and time, reaction zone thickness
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Energy
Transfer of Energy
Dissipation of Energy
Dimensionless Quantities in Premixed Turbulent Combustion
• Turbulent Reynolds number
• Turbulent Damköhler number
• Karlovitz number (interaction of small-scale turbulence with the flame)
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oxidation layer
preheat zone
Inner layer
Course Overview
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• Turbulence
• Turbulent Premixed Combustion
• Turbulent Non-Premixed
Combustion
• Modelling Turbulent Combustion
• Applications
• Scales of Turbulent Premixed
Combustion
• Regime-Diagram
• Turbulent Burning Velocity
Part II: Turbulent Combustion
Regime Diagram
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Corrugated Flamelet Regime
Regime Diagram: Corrugated Flamelets
• Ka < 1 η > lF
Interaction of a very thin flame with a turbulent flow
Assumption: infinitely thin flame (compared to turbulent scales)
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Buschmann (1996)
OH-radical-distribution in a turbulent premixed flame
premixed flame in isotropic turbulence
Regime Diagramm: Broken Reaction Zones Regime
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Regime Diagramm: Broken Reaction Zones Regime
• Kaδ > 1 η < lδ
Smallest turbulent eddies enter the reaction zones
Turbulent transport radicals are removed from reaction zone
Local extinguishing in the inner reaction zone
• Overall extinguishing of the flame front is possible
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Two-dimensional slices from three-dimensional simulations of low- and high-Karlovitz-supernovae flames, respectively. The left-hand panel in each case is burning rate, and the right-hand panel is temperature.
Ka = 0,1
Ka = 230
Source: A. J. Aspden et al. (JFM 2011)
Burning rate Temp
Regime Diagramm: Thin Reaction Zones Regime
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Regime Diagramm: Thin Reaction Zones Regime
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thin reaction zone
thickened preheat zone
temperature distribution from DNS of a premixed turbulent flame
• Ka > 1 und Kaδ < 1 lδ < η < lF
With lδ ≈ 0,1lF Ka ≈ 100Kaδ
Turbulent mixing inside preheat zone
Assumption: infinitely thin reaction zone (compared to turbulent scales)
Regime Diagram: Résumé
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Source: A. J. Aspden et al. (JFM 2011)
Regime Diagram: Résumé
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Source: A. J. Aspden et al. (JFM 2011)
Course Overview
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• Turbulence
• Turbulent Premixed Combustion
• Turbulent Non-Premixed
Combustion
• Modelling Turbulent Combustion
• Applications
• Scales of Turbulent Premixed
Combustion
• Regime-Diagram
• Turbulent Burning Velocity
Part II: Turbulent Combustion
Turbulent Burning Velocity
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Exemplary measurements in gasoline engine with tumble generator of flame velocity
at spark plug position during full load (Source: Merker, „Grundlagen Verbrennungsmotoren“)
Laminar burning velocity of iso-octane
≈ 15 m/s
< 1 m/s
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Isentropic compression
Comparison: Laminar/Measured Burning Velocity
Comparison: Laminar/Measured Burning Velocity
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Experimental data of sT vs. wrinkled laminar-flame theories of turbulent flame propagation (data from Turns 2000)
≈factor 30
Turbulent Burning Velocity
• Main problem for turbulent premixed combustion: Quantification of turbulent burning velocity sT
• sT: Velocity which quantifies the propagation of the turbulent flame front into unburnt mixture
• Distinction of two limiting cases by Damköhler (1940)
1. Large scale turbulence ↔ corrugated flamelets
2. Small scale turbulence ↔ thin reaction zones
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Turbulent Burning Velocity: Corrugated Flamelets
• Instantaneous flame front
Flame surface area AT
Propagates locally with laminar burning velocity sL into unburnt mixture
• Mean flame front
Mean flame surface area A
Propagates with turbulent burning velocity sT
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„u“ „b“ „u“ „b“
Turbulent Burning Velocity: Corrugated Flamelets
• With the mass flux trough A and AT
• Assume constant density in the unburnt mixture (assumption)
• Wrinkling of the laminar flame (AT↑) increase of sT
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• Turbulence flame surface area ↑
• Using an analogy with a Bunsen flame
• Limit for u‘ 0
• Internal combustion engine:
Engine speed n↑ burning velocity sT↑ due to
→ High engine speed achievable
Turbulent Burning Velocity: Corrugated Flamelets
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Turbulent Burning Velocity: large-scale turbulence
• In experiments often used empirical relation
Constant C experimentally determined
Typical values: 0.5 < n < 1.0
• From experimental data
For small u‘, sT ~ u‘ applies
• Consistent with Damköhler theory
Increase of turbulent intensity
• sT grows linearly
• With further increase less than linear
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Linear
Turbulent Burning Velocity: Thin Reaction Zones
• Reduced increase of turbulent burning velocity second limiting case of Damköhler
• Thin reaction zones/small-scaled turbulence
• In analogy to Damköhler uses
tc: chemical time scale
Dimensional analysis
Constant of proportionality 0.78
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consistent with experimental data
Turbulent Burning Velocity
• Damköhler-limits can be combined to a single formula (Peters, 1999):
constant α = 0,195
• Low turbulence intensity
• High turbulence intensity
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Turbulent Burning Velocity
• By rearranging this formula with Dat = (ltsL)/(lFu‘)
• Limit for high Damköhler number
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comparison with experimental data
Summary
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• Turbulence
• Turbulent Premixed Combustion
• Turbulent Non-Premixed
Combustion
• Modelling Turbulent Combustion
• Applications
• Scales of Turbulent Premixed
Combustion
• Regime-Diagram
• Turbulent Burning Velocity
Part II: Turbulent Combustion