Mode transition of interacting buoyant non-premixed flames

The dynamic behavior, especially in the transition to oscillation mode (in-phase and anti-phase), of two interacting non-premixed methane-air jet flames was investigated experimentally. A well-controllable experimental system for the present purpose was constructed and key parameters; such as fuel flowrate ( Q ), burner diameter ( d ), and burner separation distance ( L ), were varied systematically. A well-known periodic motion of the flame was observed and the frequency monitored by thermocouples mounted adjacent to the burner exit. Time-variation of flame shape was recorded by a high speed camera associated with the optical imaging visualization. It was found that the flickering frequency was insensitive to the fuel flowrate, Q , implying that inertia played secondary role in the transition. Instead, the burner critical separation distance for the transition ( 𝐿 𝑐𝑟𝑡 ) varied when various burner diameters were used, confirming that the difference in distance played an important role in the transition. It was found that the critical condition could be summarized by an updated correlation as 𝑑 × 𝐿 𝑐𝑟𝑡3 ~𝑐𝑜𝑛𝑠𝑡. This is slightly different from the one recently proposed by Yang et al. (2019), which was given under a narrower range of the fire scale. Accordingly, the critical condition can also be described by the critical value of the updated global parameter, such as 𝛼 3 𝐺𝑟 4/3 , where 𝛼 and 𝐺𝑟 denote the length ratio ( 𝐿 𝑐𝑟𝑡 / d ) and Grashof number based on the burner diameter, respectively. “flame flickering (or flame puffing)” and the frequency is an important characteristic, as well as the quantity. Previous studies (Hamins et al., 1992; Cetegen and Ahmed, 1993; Cetegen and Dong, 2000), have confirmed the prominent scaling relation, f ~ d -1/2 , in a wide range of fire scales ( d ) irrespective of the kinds of fuel. Cetegen and Ahmed (1993) developed a mathematical model to predict the dynamic frequency based on the convective time scale of flame flickers. Since the main convective flow is induced by the buoyancy, the burner scale acts as representative scale to control the magnitude of buoyancy-induced flow velocity. From a fluid dynamics point of view, the buoyancy-induced flow forms the shedding toroidal vortex along the flame. In this way, the relation between the fire scale and dynamic frequency of the flame is correlated as described. Most recently, Xia et al. (2018) introduced vortex-dynamical principles and attempted to observe the relation between flame and vortex dynamics. According to their work, the total vorticity (circulation) of the toroidal vortex shows independency on the geometric shape of burner port; rather it is dictated by the vertical length of vortex sheet. This is consistent with the experimental observation that the pinching-off length of the flame is nearly identical. When two buoyant flames are positioned close to each other, the interaction of inner-side shear layer, where the