A One-Dimensional Model of a Turbulent Jet Diffusion Flame in an Ambient Atmospheric Flow, Derived from a Three-Dimensional Model

A rigorous deduction of a one-dimensional (ID) model of turbulent jet diffusion flames developed for releases of gaseous fuels is presented. This model considers the presence of a non-uniform incident wind and is derived from a full three-dimensional (3D) formulation of the fluid dynamics equations complemented with models for chemical reaction, thermal radiation and an adaptation of the k-ε-g closure method. To deduce the one-dimensional model, the 3D problem is considered to be parabolic along the center line of the flame and self-similar profiles in planes normal to this line are assumed. New terms, not present in previous works, have been introduced in the ID conservation equations and an alternative approach to derive the production terms of the turbulent kinetic energy and of the mixture fraction variance is proposed. To evaluate the validity and usefulness or the model, its results have been compared with those of the three-dimensional model, developed by the authors, and with available wind-tunnel and full-scale experimental results, and a good agreement is found.