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Turbulent Premixed Combustion

Turbulent Premixed Combustion
Turbulent Premixed Combustion CEFRC Combustion Summer School 2014 Prof. Dr.Ing. Heinz Pitsch 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 velocity field flame 2 Course Overview Part II: Turbulent Combustion • Turbulence • Turbulent Premixed Combustion • Scales of Turbulent Premixed • Turbulent NonPremixed Combustion Combustion • RegimeDiagram • Modelling Turbulent Combustion • Turbulent Burning Velocity • Applications 3 Scales of Turbulent Premixed Combustion • Integral turbulent scales Energy Transfer of Energy • Smallest turbulent scales/Kolmogorov scales Dissipation of Energy • Flame thickness and time, reaction zone thickness 4 Dimensionless Quantities in Premixed Turbulent Combustion • Turbulent Reynolds number oxidation layer preheat zone Inner layer • Turbulent Damköhler number • Karlovitz number (interaction of smallscale turbulence with the flame) 5 Course Overview Part II: Turbulent Combustion • Turbulence • Turbulent Premixed Combustion • Scales of Turbulent Premixed • Turbulent NonPremixed Combustion Combustion • RegimeDiagram • Modelling Turbulent Combustion • Turbulent Burning Velocity • Applications 6 Regime Diagram Corrugated Flamelet Regime 7 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 OHradicaldistribution in a turbulent premixed flame Buschmann (1996) 8 Regime Diagramm: Broken Reaction Zones Regime 9 Regime Diagramm: Broken Reaction Zones Regime • Ka 1  η l δ δ Burning Temp  Smallest turbulent eddies rate enter the reaction zones  Turbulent transport  radicals are removed from reaction zone  Local extinguishing in the inner reaction zone • Overall extinguishing of the Ka = 0,1 flame front is possible Twodimensional slices from threedimensional simulations of low and highKarlovitzsupernovae flames, respectively. The lefthand panel in each case is burning rate, and the righthand panel is Ka = 230 temperature. Source: A. J. Aspden et al. (JFM 2011) 10 Regime Diagramm: Thin Reaction Zones Regime 11 Regime Diagramm: Thin Reaction Zones Regime • Ka 1 und Ka 1  l η l δ δ F  With l ≈ 0,1l  Ka ≈ 100Ka δ F 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 Regime Diagram: Résumé Source: A. J. Aspden et al. (JFM 2011) 13 Regime Diagram: Résumé Source: A. J. Aspden et al. (JFM 2011) 14 Course Overview Part II: Turbulent Combustion • Turbulence • Turbulent Premixed Combustion • Scales of Turbulent Premixed • Turbulent NonPremixed Combustion Combustion • RegimeDiagram • Modelling Turbulent Combustion • Turbulent Burning Velocity • Applications 15 Turbulent Burning Velocity Comparison: Laminar/Measured Burning Velocity Isentropic compression ≈ 15 m/s 1 m/s 20 Exemplary measurements in gasoline engine with Laminar burning velocity tumble generator of flame velocity of isooctane at spark plug position during full load (Source: Merker, „Grundlagen Verbrennungsmotoren“) 16 Comparison: Laminar/Measured Burning Velocity ≈factor 30 Experimental data of s vs. wrinkled T laminarflame theories of turbulent flame propagation (data from Turns 2000) 17 Turbulent Burning Velocity • Main problem for turbulent premixed combustion: Quantification of turbulent burning velocity s T • s : Velocity which quantifies the propagation of the turbulent flame front into T 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 A T  Propagates locally with laminar burning velocity s into unburnt mixture L • Mean flame front  Mean flame surface area A  Propagates with turbulent burning „u“ „b“ „u“ „b“ velocity s T 19 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 ↑)  increase of s T T 20 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 ↑ due to T → High engine speed achievable 21 Turbulent Burning Velocity: largescale turbulence • In experiments often used empirical relation Linear  Constant C experimentally determined  Typical values: 0.5 n 1.0 • From experimental data   For small u‘, s u‘ applies T • Consistent with Damköhler theory  Increase of turbulent intensity • s grows linearly T • With further increase less than linear 22 Turbulent Burning Velocity: Thin Reaction Zones • Reduced increase of turbulent burning velocity  second limiting case of Damköhler • Thin reaction zones/smallscaled turbulence • In analogy to Damköhler uses  t : chemical time scale c consistent with  Dimensional analysis experimental data  Constant of proportionality 0.78 23 Turbulent Burning Velocity • Damköhlerlimits 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 Da = (l s )/(l u‘)  t t L F comparison with experimental data • Limit for high Damköhler number  25 Summary Part II: Turbulent Combustion • Turbulence • Turbulent Premixed Combustion • Scales of Turbulent Premixed • Turbulent NonPremixed Combustion Combustion • RegimeDiagram • Modelling Turbulent Combustion • Turbulent Burning Velocity • Applications 26
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