Evaluation of a Scalar Probability Density Function Approach for Turbulent Jet Nonpremixed Flames

A scalar probability density function (PDF) method considering a detailed chemical kinetics is applied to a diluted hydrogen turbulent jet nonpremixed flame to evaluate the performance. The flame is formed on a nozzle of an inner diameter of D=6mm, with a fuel exit velocity of 30m/s, surrounded by two annular pipes issuing airs of higher and lower velocities of 30m/s and 3m/s, respectively. The hydrogen as a fuel is diluted by one third volumetrically by the nitrogen, giving a stoichiometric mixture fraction of 0.46. The flow field has been solved on the basis of the k-ε two equation model. A modelled scalar PDF equation has been solved by an Eulerian Monte Carlo method developed by Pope [1]. The PDF transport term due to turbulent velocity fluctuations involved in the PDF equation is modelled based on the gradient diffusion concept. The molecular mixing term is modelled by the modified Curl model. On the other hand, reactions are dealt exactly in the PDF method and a twentystep reaction, eight species kinetic mechanism for hydrogen-oxygen combustion is employed here. Each joint scalar PDF is described as an ensemble of stochastic particles of thousand at each node. Each PDF is transported through each stochastic process of the turbulent diffusion, the molecular mixing, and the convection, and through the exact chemical reaction process. In order to evaluate the performance of the present PDF method, calculation results are compared with those of two flamelet calculations, which are the conventional laminar flamelet model method and a scalar PDF method based on the conserved scalar approach. The present PDF method can reproduce the extinction and reignition phenomena, which cannot be easily predicted by the conserved scalar approaches. Variations in the nonpremixed flame structure due to the flame stretch, which were experimentally confirmed by Barlow et al.[2], have been also reproduced.