D. Bradley*, P. H. Gaskella A. Sedaghat, X. J. Gu, Generation of PDFS for flame curvature and for flame stretch rate in premixed turbulent combustion, Combustion and Flame 135 (2003) 503–523.
Combustion and Flame 135 (2003) 503–523
Generation of PDFS for flame curvature and for flame stretch rate in premixed turbulent combustion
D. Bradleya,*, P. H. Gaskella, A. Sedaghata, X. J. Gub
aSchool of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, England
bDepartment of Computational Science and Engineering, CLRC Daresbury Laboratory, Warrington WA4 4AD, England
Received 15 February 2003; received in revised form 26 June 2003; accepted 16 July 2003
Experimentally derived pdfs of turbulent, premixed, flame curvatures from a variety of sources, for a wide
range of conditions are surveyed and a suitable expression sought to generalize these. This proves to be one based
on the Damko¨hler number, Da. This is tantamount to normalizing the curvature by multiplying it by the Taylor
scale of turbulence. It enables the distribution of flame curvature when normalized by the laminar flame thickness,
to be expressed in terms of the Karlovitz stretch factor, K, and the turbulent Reynolds number, Rl. The value of
the pdf at zero curvature is linearly related to Da1/2.
The pdf expressions of Yeung et al.  obtained from numerical simulations are used for the strain rate
distribution and, on the assumption that these and that for flame curvature are statistically independent, values of
flame stretch rate pdfs are generated numerically. It is necessary to define an appropriate surface to define the
burning velocity, flame stretch rate, and appropriate Markstein numbers. Two surfaces are considered and
employed in the computations, one located at the start of the preheat zone, the other at the start of the reaction
zone. The latter seems more rational and gives the better generalisation of the pdfs of flame stretch rate.
An assumed linearity of laminar burning velocity with flame stretch rate, extending over both positive and
negative stretch rates, enables flame stretch rate pdfs to be generated. It is concluded that negative values of
burning velocity are unlikely and that burning velocities should tend to zero rather than attain negative values.
This modifies the derivation of flame stretch rate pdfs. These depend on the Markstein number, Karlovitz stretch
factor and turbulent Reynolds number. Computations suggest that, for values of K above 0.1 and of Rl above 100,
the pdf of stretch rate is similar to that of strain rate. At very low values of K and negative values of Markstein
number, pronounced flamelet instability might be anticipated. © 2003 The Combustion Institute. All rights
Keywords: Turbulent combustion; Probability density function; Stretch rate