Simulation of turbulent mode of combustion of gas jets

The diffusion mode of combustion of fuel jets in an oxygen-containing atmosphere occurs very widely both in nature and in engineering. In so doing, a glowing flame is formed, whose geometric dimensions define the energy efficiency of combustion of fuel.
The hydrodynamic structure of the flame exhibits a number of differences from the classical jet flows, in particular, from well-studied subsonic turbulent jets [1]. The flames are characterized by a high degree of hydrodynamic instability; however, at the same time, the flame height clearly follows the phenomenon such as the change of laminar mode for turbulent one; by the way, this phenomenon presents a difficult problem for investigation in flows of other types.
The diffusion mode of jet combustion is of further interest because of the presence of "scaling" effect, i.e., the dependence of the relative flame height both on the Reynolds number (which is typical of all flows with laminarto-turbulent transition) and on the dimensionless nozzle diameter $(d_0/d^*)$; in so doing, the threshold value of $d^*$ divides the entire diversity of dimensions into regions with the presence and absence of this effect.
These and other features of burning fuel jets present a serious problem for mathematical simulation of burners and combustors.
The paper contains analysis of a number of relations used in different models of turbulent combustion.