Structure and behavior of diffusion flames in a pressure gradient

Abstract

The structure of a diffusion flame embedded in a flow field parallel to the flame is studied under conditions where this external flow imposes an adverse pressure gradient. It is convenient to think of the physical problem as a flame lying along the flow direction of a divergent channel. The mathematical problem is reduced to a set of ordinary differential equations by (i) employing the Howarth transformation to eliminate the variable density and (ii) introducing a similarity solution somewhat in the manner of the Falkner-Skan treatment of boundary layer flows. Because the low-density gas near the flame responds more readily to the pressure gradient than does the higher density gas, a reverse flow develops in the low density region which severely affects both the structure of the flame and the fuel consumption rate. For a flame with unit stoichiometry, the reverse flow eventually leads to extinction of the flame by separating the two shear layers that bound the fuel and oxidizer streams. For stoichiometry corresponding to methane-air, the flame situates itself near the oxidizer side of the reverse flow and has no tendency toward extinguishment.