Acknowledgments

L26 : Premixed Turbulent FlamesTurbulent flow.

Effect of turbulence on chemical reaction rates.

Structure of premixed turbulent flames.

Direct numerical simulation of premixed turbulent flames.

School of Mechanical Engineering, Purdue UniversityIntroduction (Brief) to Turbulent FlowCharacterization in terms of mean and fluctuating properties

Length ScalesCharacteristic width of the flow, the macroscale: L

Integral scale or Taylor macroscale: 0 Mean 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.

School of Mechanical Engineering, Purdue UniversityIntroduction (Brief) to Turbulent FlowCharacterization in terms of mean and fluctuating properties

R(r,t)r01

Buoyant Flame MoviesSchool of Mechanical Engineering, Purdue UniversityIntroduction (Brief) to Turbulent FlowLength Scales (cont.)Kolmogorov microscale: K The scale at which molecular dissipation effects are important. Turbulent kinetic energy is dissipated into fluid internal energy at this scale.

School of Mechanical Engineering, Purdue UniversityIntroduction (Brief) to Turbulent FlowAt the Kolmogorov microscale, the time for an eddy of size K to rotate is equal to the momentum diffusion time across the eddy.

Different scales can be related by the turbulence Reynolds numbers:

School of Mechanical Engineering, Purdue UniversityIntroduction (Brief) to Turbulent FlowFrequency or wave-number (1/L)

Viscous dissipation (Kolmogorov Scale)Inertial subrange (Integral Scale)Energy input (Taylor Scale)EnergyEddies are generated at the Taylor length scaleEddies are dissipated into heat at the Kolmogorov length scale

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 inviscidSchool of Mechanical Engineering, Purdue UniversityEffect of Turbulence on the Rates of Chemical ReactionsConsider 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?

School of Mechanical Engineering, Purdue UniversityEffect of Turbulence on the Rates of Chemical ReactionsThe mean reaction rate is given by:

School of Mechanical Engineering, Purdue UniversityEffect of Turbulence on the Rates of Chemical ReactionsWhat is the mean value of k?

Example from Warnatz, Maas, and Dibble, Combustion: Sinusoidal variation of temperature.

School of Mechanical Engineering, Purdue UniversityEffect of Turbulence on the Rates of Chemical Reactions Temporal dependence of T:

T (K)20001250500tSchool of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent FlamesWrinkled Laminar Flame Sheet in a Diverging ChannelTurbulent 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.

Mean Flame Location

School of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames Wirth and Peters, 24th Symposium (International) on Combustion, pp. 493-501 (1992).

School of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames Wirth and Peters, 24th Symposium (International) on Combustion, pp. 493-501 (1992).

School of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames Different flame regimes, the Williams-Klimov criteria:Wrinkled laminar flames:

Flamelets-in-eddies

Distributed reaction regime

dL = laminar flame thicknessSchool of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames The Damkohler number:For premixed flames:

School of Mechanical Engineering, Purdue UniversityStructure 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:

School of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames Alternatively, flow of unburned premixed reactants out of a straight tube:

School of Mechanical Engineering, Purdue UniversityStructure of Premixed Turbulent Flames Wrinkled Laminar Flame Regime:Three models for the turbulent flame speed:

School of Mechanical Engineering, Purdue UniversityBorghi Diagram for Premixed Turbulent Flames

School of Mechanical Engineering, Purdue University