Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity

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 thermo-diffusive 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.