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L26 : Premixed Turbulent Flames

Turbulent flow. Effect of turbulence on chemical reaction rates. Structure of premixed turbulent flames. Direct numerical simulation of premixed turbulent flames. L26 : Premixed Turbulent Flames. Characterization in terms of mean and fluctuating properties .

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L26 : Premixed Turbulent Flames

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  1. Turbulent flow. Effect of turbulence on chemical reaction rates. Structure of premixed turbulent flames. Direct numerical simulation of premixed turbulent flames. L26 : Premixed Turbulent Flames

  2. Characterization in terms of mean and fluctuating properties Introduction (Brief) to Turbulent Flow • Length Scales • Characteristic width of the flow, the macroscale: L • Integral scale or Taylor macroscale: ℓ0Mean size of the large eddies in a flow. Distance between two points in the flow where the correlation between the fluctuating velocities at two location goes to zero.

  3. Characterization in terms of mean and fluctuating properties Introduction (Brief) to Turbulent Flow R(r,t) 1 0 r Buoyant Flame Movies

  4. Introduction (Brief) to Turbulent Flow • Length Scales (cont.) • Kolmogorov microscale: ℓK The scale at which molecular dissipation effects are important. Turbulent kinetic energy is dissipated into fluid internal energy at this scale.

  5. Introduction (Brief) to Turbulent Flow • At the Kolmogorov microscale, the time for an eddy of size ℓK to rotate is equal to the momentum diffusion time across the eddy. • Different scales can be related by the turbulence Reynolds numbers:

  6. Introduction (Brief) to Turbulent Flow • Eddy break-down occurs through interaction (deforming, folding, squeezing) between eddies of multiple scales • Large eddies feed energy to the smaller eddies and so on until viscous dissipation • The inertial subrange is characterized by a turbulent flow that is roughly isotropic, homogeneous and inviscid Eddies are dissipated into heat at the Kolmogorov length scale Eddies are generated at the Taylor length scale Energy input (Taylor Scale) Inertial subrange (Integral Scale) Viscous dissipation (Kolmogorov Scale) Energy Frequency or wave-number (1/L)

  7. Effect of Turbulence on the Rates of Chemical Reactions • Consider a bimolecular reaction between species A and B. At some point in the flow field we measure the mass fractions of A and B and the temperature T. Are mean measurements adequate for determining the reaction rate between the species?

  8. Effect of Turbulence on the Rates of Chemical Reactions • The mean reaction rate is given by:

  9. Effect of Turbulence on the Rates of Chemical Reactions • What is the mean value of k? • Example from Warnatz, Maas, and Dibble, Combustion: Sinusoidal variation of temperature.

  10. Effect of Turbulence on the Rates of Chemical Reactions T (K) 2000 Temporal dependence of T: 1250 500 t

  11. Structure of Premixed Turbulent Flames • Wrinkled Laminar Flame Sheet in a Diverging Channel Mean Flame Location • Turbulent Flame Speed : • Difficult to determine the mean flame area - experimental measurements of turbulent flame speeds are very difficult and have large error bars. The turbulent flame speed can be much larger than the laminar flame speed.

  12. Structure of Premixed Turbulent Flames Wirth and Peters, 24th Symposium (International) on Combustion, pp. 493-501 (1992).

  13. Structure of Premixed Turbulent Flames Wirth and Peters, 24th Symposium (International) on Combustion, pp. 493-501 (1992).

  14. Structure of Premixed Turbulent Flames • Different flame regimes, the Williams-Klimov criteria: • Wrinkled laminar flames: • Flamelets-in-eddies • Distributed reaction regime dL= laminar flame thickness

  15. Structure of Premixed Turbulent Flames • The Damkohler number: • For premixed flames:

  16. Structure of Premixed Turbulent Flames • Wrinkled Laminar Flame Regime: Most theories of premixed turbulent flames deal with this type of flame. Wrinkling of flame increases the area of contact between hot combustion products and unburned reactants, increasing the rate of consumption of the unburned reactants. • Consider flow of unburned reactants in a diverging channel:

  17. Structure of Premixed Turbulent Flames • Alternatively, flow of unburned premixed reactants out of a straight tube:

  18. Structure of Premixed Turbulent Flames • Wrinkled Laminar Flame Regime: • Three models for the turbulent flame speed:

  19. Borghi Diagram for Premixed Turbulent Flames

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