Turbulent Premixed Combustion

Transcription

1 Turbulent Premixed Combustion Combustion Summer School 2018 Prof. Dr.-Ing. Heinz Pitsch

2 Example: LES of a stationary gas turbine velocity field flame 2

3 Course Overview Part II: Turbulent Combustion Turbulence Turbulent Premixed Combustion Turbulent Non-Premixed Combustion Turbulent Combustion Modeling Applications Scales of Turbulent Premixed Combustion Regime-Diagram Turbulent Burning Velocity 3

4 Scales of Turbulent Premixed Combustion Integral turbulent scales Energy Smallest turbulent scales/kolmogorov scales Transfer of Energy Dissipation of Energy Flame thickness and time, reaction zone thickness 4

5 Dimensionless Quantities in Premixed Turbulent Combustion Turbulent Reynolds number oxidation layer preheat zone Turbulent Damköhler number Inner layer Karlovitz number (interaction of small-scale turbulence with the flame) 5

6 Course Overview Part II: Turbulent Combustion Turbulence Turbulent Premixed Combustion Turbulent Non-Premixed Combustion Turbulent Combustion Modeling Applications Scales of Turbulent Premixed Combustion Regime-Diagram Turbulent Burning Velocity 6

7 Regime Diagram Corrugated Flamelet Regime 7

8 Regime Diagram: Corrugated Flamelets Ka < 1 η > l F Interaction of a very thin flame with a turbulent flow Assumption: infinitely thin flame (compared to turbulent scales) premixed flame in isotropic turbulence OH-radical-distribution in a turbulent premixed flame Buschmann (1996) 8

9 Regime Diagramm: Broken Reaction Zones Regime 9

10 Regime Diagramm: Broken Reaction Zones Regime Ka δ > 1 η < l δ 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 Example: Supernovae flames with transport mechanisms very different from normal flames Burning rate Ka = 0,1 Temp Two-dimensional slices from three-dimensional simulations Burning rate Ka = 230 Temp 10 Source: A. J. Aspden et al. (JFM 2011)

11 Regime Diagramm: Thin Reaction Zones Regime 11

12 Regime Diagramm: Thin Reaction Zones Regime Ka > 1 und Ka δ < 1 l δ < η < l F With l δ 0,1l F Ka 100Ka δ Turbulent mixing inside preheat zone Assumption: infinitely thin reaction zone (compared to turbulent scales) thin reaction zone thickened preheat zone temperature distribution from DNS of a premixed turbulent flame 12

13 Regime Diagram: Summary Source: A. J. Aspden et al. (JFM 2011) 13

14 Regime Diagram: Summary Source: A. J. Aspden et al. (JFM 2011) 14

15 Regime Diagram: Corrections from Ideal Scaling Usual assumptions: Sc =1 ν=d S L l F / ν 1 l δ 0,1l F Ka 100Ka δ Example: Methane/air flame, T u =800K, φ=0.7: Sc 1 ν D but S L l F / ν 5 l δ 0,5l F Ka 4Ka δ 15 Lines only for scaling, be careful with absolute values

16 DNS at Constant Ka for Various Re Lean methane flame T u =800K, φ=0.7 (S L =1m/s) Re variation: constant u and increased l t constant Karlovitz (approximately) Re Ka U bulk 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 (from A. Attili et al, 2017) Re

17 DNS at Constant Ka for Various Re Lean methane flame T u =800K, φ=0.7 (S L =1m/s) Re variation: constant u and increased l t constant Karlovitz (approximately) red: nominal diagram black: diagram with corrections Re Ka U bulk 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 Reynolds number changed by jet width H L t ~ H h = l t Re t -3/4 ~ l t 1/4, hence h increases slightly with increasing H Not clear in which regime the flames are Thin reaction zone Broken reaction zone

18 Different Re and constant Ka DNS: regime assessment Preheat zone T = 900K Laminar value Reaction zone T = 1800K Laminar value 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 18 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

19 Different Re and constant Ka DNS: flame structure Re = 2800 Re = 5600 Re = Re = 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 19

20 Course Overview Part II: Turbulent Combustion Turbulence Turbulent Premixed Combustion Turbulent Non-Premixed Combustion Turbulent Combustion Modeling Applications Scales of Turbulent Premixed Combustion Regime-Diagram Turbulent Burning Velocity 20

21 Turbulent Burning Velocity Comparison: Laminar/Measured Burning Velocity Isentropic compression 15 m/s < 1 m/s 20 Laminar burning velocity of iso-octane Exemplary measurements in gasoline engine with tumble generator of flame velocity at spark plug position during full load (Source: Merker, Grundlagen Verbrennungsmotoren ) 21

22 Comparison: Laminar/Measured Burning Velocity factor 30 Experimental data of s T vs. wrinkled laminar-flame theories of turbulent flame propagation (data from Turns 2000) 22

23 Turbulent Burning Velocity Main problem for turbulent premixed combustion: Quantification of turbulent burning velocity s T s T : 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 23

24 Turbulent Burning Velocity: Corrugated Flamelets Instantaneous flame front Flame surface area A T Propagates locally with laminar burning velocity s L into unburnt mixture Mean flame front Mean flame surface area A Propagates with turbulent burning velocity s T u b u b 24

25 Turbulent Burning Velocity: Corrugated Flamelets With the mass flux trough A and A T Assume constant density in the unburnt mixture (assumption) Wrinkling of the laminar flame (A T ) increase of s T 25

26 Turbulent Burning Velocity: Corrugated Flamelets Turbulence flame surface area Using an analogy with a Bunsen flame Limit for u 0 Internal combustion engine: Engine speed n burning velocity s T due to High engine speed achievable 26

27 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, s T ~ u applies Consistent with Damköhler theory Increase of turbulent intensity s T grows linearly With further increase less than linear Linear 27

28 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 t c : chemical time scale Dimensional analysis Constant of proportionality 0.78 consistent with experimental data 28

29 10 H 17 H 12.9 H 20.5 H Turbulent Burning Velocity: Thin Reaction Zones Flame length vs Reynolds number T (K) L f / H x (cm) Re = 2800 Re = 5600 Re = Re = (from A. Attili et al, 2017) Re Decreased length increased flame speed Turbulent flame speed increases with increasing Reynolds number u is constant Re Increased flame speed due to increased integral scale 29

30 Turbulent Burning Velocity Damköhler-limits can be combined to a single formula (Peters, 1999): constant α = 0,195 Low turbulence intensity High turbulence intensity 30

31 Turbulent Burning Velocity By rearranging this formula with Da t = (l t s L )/(l F u ) Limit for high Damköhler number comparison with experimental data 31

32 Summary Part II: Turbulent Combustion Turbulence Turbulent Premixed Combustion Turbulent Non-Premixed Combustion Turbulent Combustion Modeling Applications Scales of Turbulent Premixed Combustion Regime-Diagram Turbulent Burning Velocity 32