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