CEFRC Combustion Summer School...Dimensionless Quantities in Premixed Turbulent Combustion •...
Transcript of CEFRC Combustion Summer School...Dimensionless Quantities in Premixed Turbulent Combustion •...
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
2
velocity field
flame
Course Overview
3
• 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
4
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)
5
oxidation layer
preheat zone
Inner layer
Course Overview
6
• 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
7
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)
8
Buschmann (1996)
OH-radical-distribution in a turbulent premixed flame
premixed flame in isotropic turbulence
Regime Diagramm: Broken Reaction Zones Regime
9
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
10
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
11
Regime Diagramm: Thin Reaction Zones Regime
12
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
13
Source: A. J. Aspden et al. (JFM 2011)
Regime Diagram: Résumé
14
Source: A. J. Aspden et al. (JFM 2011)
Course Overview
15
• 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
16
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
20
Isentropic compression
Comparison: Laminar/Measured Burning Velocity
Comparison: Laminar/Measured Burning Velocity
17
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
18
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
19
„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
20
• 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
21
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
22
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
23
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
24
Turbulent Burning Velocity
• By rearranging this formula with Dat = (ltsL)/(lFu‘)
• Limit for high Damköhler number
25
comparison with experimental data
Summary
26
• 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