Fractal modelling of turbulent combustion

In a previous paper we proposed a new model for turbulent flows, called the fractal model (FM), which is applicable both to RANS and LES formulations. Here, the model is extended to the reactive case with the goal of simulating turbulent flames, both premixed and non-premixed.

FM is a subgrid model that describes the physics of the small scales of turbulence building on the phenomenological concept of vortex cascade and on fractal theory. The physics of the small scales is summarized by a turbulent ‘viscosity’ μ_t, to be added to the molecular one. μ_t is zero where the flow is laminar and, in particular, goes to zero at solid walls.

The fundamental assumption in treating combustion in this work is that chemical reactions take place only at the dissipative scales of turbulence, i.e. near the so-called ‘fine structures’ (the eddy dissipation concept). FM predicts the growth of dissipative scales due to heat release; therefore, it enables a local DNS in the hot regions of the flow where the dissipative scale may grow up to the cell dimension. FM can also estimate the volume fraction γ* occupied by the ‘fine structures’; this quantity is critical for modelling the reaction rate, and therefore the source terms in the energy and species equations. FM can also estimate the local surface of the reactive ‘fine structures’, that is, the local flame front area. It also takes into account, although in approximate manner, the formation of islands of unburnt mixture. In this paper, the model (in the isotropic formulation (IFM)) is used in conjunction with a time-dependent LES (but with the limitations of an isotropic model) approach and is validated through a three-dimensional axisymmetric diffusion flame studied experimentally by Correa and Gulati and numerically by many researchers. The time-dependent results obtained are in good agreement with the experiments. Moreover, the IFM solution offers a possible explanation for the stabilization process of this flame, which undergoes local stretching of the order of 46 000 s^?1.