CEFRC Combustion Summer School...Dimensionless Quantities in Premixed Turbulent Combustion • Turbulent Reynolds number oxidation layer p • Turbulent Damköhler number • Karlovitz

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



Combustion


• Applications


Combustion

• Regime-Diagram



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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Regime Diagram: Résumé

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Course Overview

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• Turbulence



Combustion


• Applications


Combustion

• Regime-Diagram



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


• 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“


• 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


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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


• 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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• 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



Combustion


• Applications


Combustion

• Regime-Diagram



Documents

CEFRC Combustion Summer School...Dimensionless Quantities in Premixed Turbulent Combustion • Turbulent Reynolds number oxidation layer p • Turbulent Damköhler number • Karlovitz