Combustion Summer School - Princeton University · Turbulent Premixed Combustion Combustion Summer School Prof. Dr.-Ing. Heinz Pitsch 2018 . Example: LES of a stationary gas turbine

Turbulent Premixed Combustion

Combustion Summer School

Prof. Dr.-Ing. Heinz Pitsch

2018

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

• Turbulent Combustion Modeling

• 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 extinction in the inner reaction zone possible

• Can lead to global flame extinction

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Two-dimensional slices from three-dimensional simulations

Ka = 0,1

Ka = 230

Source: A. J. Aspden et al. (JFM 2011)

Burning rate

Temp

Example: Supernovae flames with transport mechanisms very different from normal flames

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: Summary

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Regime Diagram: Summary

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Regime Diagram: Corrections from Ideal Scaling

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• Usual assumptions:

Sc =1 ν=D

SL lF / ν ≈ 1

lδ ≈ 0,1lF Ka ≈ 100Kaδ

• Example: Methane/air flame, Tu=800K, φ=0.7:

Sc ≈ 1 ν≈ D

but

SL lF / ν ≈ 5

lδ ≈ 0,5lF Ka ≈ 4Kaδ

Lines only for scaling, be careful with absolute values

DNS at Constant Ka for Various Re

16 (from A. Attili et al, 2017)

• Lean methane flame Tu=800K, φ=0.7 (SL=1m/s) • Re variation: constant u’ and increased lt

constant Karlovitz (approximately)

Re 2800 11200 5600 22400

Re 2800 5600 11200 22400

Ka 40 40 40 40

Ubulk 100 m/s 100 m/s 100 m/s 100 m/s

u’ 10 m/s 10 m/s 10 m/s 10 m/s

Jet widths 0.6 mm 1.2 mm 2.4 mm 4.8 mm

Grid points 88 Million 350 Million

2.8 Billion 22 Billion

DNS at Constant Ka for Various Re

red: nominal diagram black: diagram with corrections

Re 2800 5600 11200 22400

Ka 40 40 40 40

Ubulk 100 m/s 100 m/s 100 m/s 100 m/s

u’ 10 m/s 10 m/s 10 m/s 10 m/s

Jet widths 0.6 mm 1.2 mm 2.4 mm 4.8 mm

Grid points 88 Million 350 Million

2.8 Billion 22 Billion

Not clear in which regime the flames are • Thin reaction zone • Broken reaction zone

• Lean methane flame Tu=800K, φ=0.7 (SL=1m/s) • Re variation: constant u’ and increased lt

constant Karlovitz (approximately)

• Reynolds number changed by jet width H • Lt ~ H • h = lt Ret

-3/4 ~ lt1/4, hence h increases slightly with

increasing H

Different Re and constant Ka DNS: regime assessment

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• Strong turbulent mixing in the preheat zone gradient PDF is wide

PDF close to log normal (typical for gradients in turbulence)

far from the gradient in a laminar 1D flame

Preheat zone T = 900K Reaction zone T = 1800K

Laminar value

Laminar value

• Reaction zone not affected by change in turbulence

gradient PDF is narrow

close to the gradient in laminar unstretched 1D flame

The flames are in the thin reaction zone regime

Different Re and constant Ka DNS: flame structure

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Re = 2800

Re = 11200 Re = 5600 Re = 22400

• Flame structure very similar to 1D laminar flame

Conditional mean from DNS agrees well with 1D flame profile

Small scatter

• Reynolds number effects are related to different transport in the preheat zone, not to modifications of the flame structure

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

Turbulent Burning Velocity: Thin Reaction Zones

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20

.5 H

10

H 1

2.9

H

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H

Re 2800 11200 5600 22400

• Decreased length increased flame speed

• Turbulent flame speed increases with increasing Reynolds number

u’ is constant

Increased flame speed due to increased integral scale

(from A. Attili et al, 2017)

800

1000

1200

1400

1600

1800

2000

2200

0 1 2 3 4 5 6 7 8

T (K)

x (cm)

Re = 2800

Re = 5600

Re = 11200

Re = 22400

10

20

40

2800 5800 11200 22400

Lf / H

Re

Flame length vs Reynolds number


• 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



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Combustion Summer School - Princeton University · Turbulent Premixed Combustion Combustion Summer School Prof. Dr.-Ing. Heinz Pitsch 2018 . Example: LES of a stationary gas turbine