A new mathematical quantification of wind-blown flame tilt angle of hydrocarbon pool fires with a new global correlation model

Abstract

A new mathematical methodology is brought forward in this paper to objectively quantify the flame tilt angle based on flame appearance intermittency spatial distribution obtained from the flame images series recorded in the experiments, in counteracting the uncertainty in traditional method due to the fact of extensive vibration nature of the flame in a wind. The flame tilt angle is determined based on a proposed sum function of the product of multiplication of p(x, y) as probability of flame appearance at each pixel, by D(x, y) as perpendicular distance from the pixel to a threshold line originated from the flame base center. The flame tilt angle is solved mathematically as the angle of the threshold line when the above sum function at the two sides of the threshold line in the flame intermittency distribution contour are early equal. Experiments are carried out for ethanol and heptane square pool fires with dimensions of 10cm, 15cm, 20cm and 25cm in wind speed of 0–2.5m/s. The tilt angles of the flames in the experiments determined by above mathematical method are compared with previous models reported in the literatures. A new dimensionless global parameter, equating the wind speed by a characteristic uprising velocity of the flame supported by the buoyancy strength of the pool fire, is further proposed, which is shown to better converge and correlate the flame tilt angle data than previous models.