Pinch-off in forced and non-forced, buoyant laminar jet diffusion flames

Abstract

This paper investigates the conditions under which flame pinch-off occurs in forced and non-forced, buoyant laminar jet diffusion flames. The fuel jet emerges into a stagnant air atmosphere at temperature T 0, with a velocity that varies periodically in time with non-dimensional frequency ω l and amplitude A = 0.5. We use the formulation developed by Liñán and Williams [1] based on the combination of the mass fraction and energy conservation equations to eliminate the reaction terms, that are substituted by the mixture fraction Z and the excess-enthalpy H scalar conservations equations. With this formulation, valid for arbitrary Lewis numbers, the flame lies on the stoichiometric mixture fraction level surface Z = Z s and its temperature can be easily calculated as T e ′ / T 0 = 1 + γ ( 1 + H s ) , where Z s = 1/(1 + S), γ is the non-dimensional heat release parameter, S is the air needed to burn the unit mass of fuel and H s is the value of the excess enthalpy at the flame surface. Non-modulated flames ω l = 0 subjected to a gravity field g are known to flicker at a non-dimensional frequency ω l,0 that depends on the Froude number Fr l . The surface of the flame is deformed by the buoyancy-induced oscillations and, for Froude numbers below a certain critical value Fr l , c ∞ , the flame breaks repeatedly in two different combustion regions (pinch-off). The first one remains attached to the burner and constitutes the main flame. The second region detaches from the tip of the flame, forming a pocket of hot gas surrounded by a flame that travels along the downstream coordinate z with velocity u ¯ ∼ ( γ z / Fr l 2 ) 1 / 2 until the fuel inside the pocket is depleted. Pinch-off is affected by the modulation of the velocity of the jet, changing the critical Froude number of pinch-off Fr l, c as the excitation frequency ω l is modified. Very large ω l / ω l,0 ≫ 1 or very small ω l / ω l,0 ≪ 1 excitation frequencies do not modify Fr l, c and it remains equal to Fr l , c ∞ . For ω l / ω l,0 ∼ O(1), the response of the flame is determined by the ratio l/ x g = γ/ Fr l , where l represents the flame length and x g is the distance at which buoyancy effects become important. A strong resonance is observed at ω l ∼ ω l,0 if the flame is sufficiently long, giving Fr l, c that could be thirty times larger than Fr l , c ∞ . Short flames do not present that peak and Fr l, c remains almost independent of ω l .