Stochastic modeling of scalar dissipation rate fluctuations in non-premixed turbulent combustion

where DZ is the diffusion coefficient of the mixture fraction. The scalar dissipation rate appears in many models for turbulent non-premixed combustion as, for instance, the flamelet model (Peters (1984), Peters (1987)), the Conditional Moment Closure (CMC) model (Klimenko & Bilger (1999)), or the compositional pdf model (O’Brien (1980), Pope (1985)). In common technical applications, it has been found that if the scalar dissipation rates are much lower than the extinction limit, fluctuations of this quantity caused by the turbulence do not influence the combustion process (Kuznetsov & Sabel’nikov (1990), Pitsch & Steiner (2000)). However, it has been concluded from many experimental (Saitoh & Otsuka (1976)) and theoretical studies (Haworth et al. (1988), Mauss et al. (1990), Barlow & Chen (1992), Pitsch et al. (1995)) that there is a strong influence of these fluctuations if conditions close to extinction or auto-ignition are considered. For instance, in a system where the scalar dissipation rate is high enough to prohibit ignition, random fluctuations might lead to rare events with scalar dissipation rates lower than the ignition limit, which could cause the transition of the whole system to a burning state. In this study, we investigate the influence of random scalar dissipation rate fluctuations in non-premixed combustion problems using the unsteady flamelet equations. These equations include the influence of the scalar dissipation rate and have also been shown to provide very reasonable predictions for non-premixed turbulent combustion in a variety of technical applications (Pitsch et al. (1996), Pitsch et al. (1998), Barths et al. (1998)). However, it is clear that these equations are actually not capable of describing all of the features which might occur in turbulent non-premixed flames. For instance, in jet diffusion flames, local extinction events might occur close to the nozzle because of high scalar dissipation rates. These extinguished spots might reignite downstream, not by auto-ignition, but by heat conduction and diffusive mass exchange with the still burning surroundings. It should be kept in mind that the motivation in this work is not to predict actual turbulent reacting flows, but to study the dynamical system defined by the equations described in the following section. The advantage of the present simplified approach allows a study of the extinction process isolated from auto-ignition and re-ignition events.