A Physical Model for Flame Height Intermittency

In this paper, a simple physical model for flame height intermittency in buoyant diffusion flames is proposed. We use dimensional analysis to link existing relations for the pulsation period of diffusion flames and the burnout time of discrete volumes of gaseous fuel. From this analysis, relationships for flame height and intermittency as a function of the ratio of pulsation to burnout timescales is presented. To test these concepts, an automated method to measure flame height from digital images was developed. For a sequence of images, the flame is isolated from its surroundings using a popular histogram-based image segmentation algorithm. Spatial accuracy is obtained through automation of a common photogrammetric technique. The physical model and measurement methods are tested using four methane burners with equivalent diameters ranging from 23 cm to 81 cm and heat release rates ranging from 10 kW to 1500 kW. A total of 64 burner/HRR combinations were observed. 50th percentile flame heights ranging from 0.25 m to 3.5 m were measured. A statistical analysis of the automated flame height measurements showed total spatial error rates of less than 10% for even the least optimal camera setups. The experimental results show that flame intermittency (relative to 50th percentile flame length) scales with dimensionless heat release rate (Q* (D) ) to the - 1/5 power when the ratio of burnout to fire pulsation timescales is > 1. When this ratio is less than one, the relative flame intermittency rapidly approaches unity since only a single flame pulse exists in the plume.