Lagrangian Formulation of Turbulent Premixed Combustion

Abstract

The lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with experimental data. In the case of a zero-curvature flame, with a non-markovian parabolic model for turbulent dispersion, the formulation yields the Zimont equation extended to all elapsed times and fully determined by turbulence characteristics. The exact solution of the extended Zimont equation is calculated and analyzed to bring out different regimes.

Modelling wildland fire propagation by tracking random fronts

“…An approach to tracking random fronts (Pagnini and Bonomi, 2011;Pagnini and Massidda, 2012b, a) has been described, re-arranged and analysed to study its suitability for investigating the effects of random processes on wildland fire propagation. Actually, the random fireline is modelled in terms of an average position determined by a level-set model with a certain ROS, and the statistical spread is determined by the PDF of displacements of random contour points marked as active flame holders.…”

“…Equation (11) was originally proposed to model the burned mass fraction in turbulent premixed combustion (Pagnini and Bonomi, 2011). It should be noted that the effective indicator ϕ e introduced here is not an indicator function in the classical sense.…”

“…The approach derived in this section is an improvement of the approach originally formulated for a Lagrangian description of turbulent premixed combustion (Pagnini and Bonomi, 2011), and later extended to the study of wildland fire propagation, including the effects of turbulence (Pagnini and Massidda, 2012a, b). Here, the latter model is developed further in order to include fire spotting phenomena.…”

“…(11), the evolution equation of the effective indicator ϕ e (x, t) reads as (Pagnini and Bonomi, 2011)…”

Front propagation in anomalous diffusive media governed by time-fractional diffusion

“…This approach to the study of random fronts was first proposed -in a context in which anomalous di↵usion was not involved -to investigate the evolution of the burnt mass fraction in turbulent premixed combustion [10], and has recently been applied to wildland fire propagation [11,12,13,14,15]. In these studies, the chosen PDF was the Gaussian density function [10,11,12,13,14,15], or a 25 convolution of the Gaussian with an other PDF [13,14,15].…”