On the Scaling of the Visible Lengths of Jet Diffusion Flames

Abstract

Length of jet diffusion flames is of direct importance in many industrial processes and is analyzed by applying scaling method directly to the governing partial differential equations. It is shown that for jet-momentum-dominated diffusion flames, when the buoyancy effects are neglected, the flame length normalized by the burner exit diameter increases linearly with the Reynolds number at the burner exit in the laminar burning regime and decreases in inverse proportion to the Reynolds number in the transitional regime. For turbulent diffusion flames, the normalized flame lengths are independent of the burner exit flow conditions. It is further found that for vertical upward flames, the buoyancy effect increases the flame length in the laminar and transitional regime and reduces the length in the turbulent regime; while for vertical downward flames, the buoyancy effect decreases the flame length in the laminar and transitional regime and increases the length in the turbulent regime, provided that jet momentum is dominated, and there is no flame spreading out and then burning upward like a downward-facing pool fire. Hence, for turbulent flames the flame lengths depend on the Froude number, Fr, and increase (or decrease) slightly as Fr increases for upward (or downward) flames. By comparison, it is found that the foregoing theoretical results are in good agreement with the experimental observations reported in literature.