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D. Bradley, P.H. Gaskell, X.J. Gu, A. Sedaghat, Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity, Combustion and Flame 143 (2005) 227–245.

Combustion and Flame 143 (2005) 227–245


Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity
D. Bradley a,∗, P.H. Gaskell a, X.J. Gub, A. Sedaghat a,1
a School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK
b Department of Computational Science and Engineering, CLRC Daresbury Laboratory, Warrington WA4 4AD, UK
Received 14 October 2004; received in revised form 20 May 2005; accepted 24 May 2005
Available online 27 July 2005
A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in
turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, Pbi, and
the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression
for Pbi are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning
velocity normalised by the effective rms turbulent velocity to Pbi. Evaluation of this last parameter focuses on
problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the
effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame
stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both
the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling,
increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus–Landau thermodiffusive
flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretch
rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered
separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the
effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat
lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and
reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame
to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative
Markstein numbers the predicted values of Pbi and turbulent burning velocity are significantly increased above
the values for positive Markstein numbers. This is confirmed experimentally and these values are close to those
predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the
increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame
instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be
enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.
Keywords: Turbulent burning velocity; Instabilities; Source term
Journal Papers