Flame spread over flowing fuel under ignition delay: Spread and merging of flame front and fuel flow front

This paper investigates the flame spread over flowing liquid fuel under different ignition delays ( x ig ), substrate slopes ( θ ) and fuel discharge flow rates ( Q ). Focusing on flame front and fuel flow front, their spread and merging behavior, are concerned herein. Results show that: (1) Before two fronts merge, as θ increases, the flame front changes from the oscillating convex-concave shape to concave shape. This may be attributed to wetting and contact line effects near sidewalls, while no-slip boundary conditions and sidewall heat transfer may also play a role. For flame spread rate ( V f ), its variation with θ differs under different Q . In modeling V f , theoretical analysis indicates that, the commonly used method for stationary fuel cases exhibits significant errors. In this work, considering the relative motion between flame and flowing fuel, and by solving the subsurface flow velocity distribution, a correlation of V f is further proposed and verified by experiments. (2) After two fronts merge, compared with the no ignition cases, the burning fuel flows faster than the no-ignition cases under relatively large Q , while burning fuel flows faster initially, gradually slows down and finally becomes slower under lower Q . The discrepancy is attributed to the change of liquid viscosity and thermal expansion induced by temperature variation, and fuel consumed due to combustion. Based on momentum balance, fuel flow velocity ( u ) for no ignition cases is first derived. Further, by quantifying the fuel consumed at different times, and accumulating the fuel left for flowing, the dynamic variation of u is derived. Based on proposed spread rate correlations in (1) and (2), the merging time and location can be calculated, which agrees well with experiments. This work advances fundamental understanding of interaction mechanism between flow and burning of fuel during flame spread, the provided models may help in liquid fire safety. Novelty and significance statement Liquid fuel leakage fires occur worldwide, causing significant property damage and human casualties. Understanding the flame spread behavior in the early stage of such fires is crucial for fire prevention and control. In actual scenarios, the leaked flowing fuel may be ignited at any moment after leakage, i.e., different ignition delay. Despite there are extensive studies on flame spread over stationary fuel, very limited studies have examined the flame spread over flowing fuel under different ignition delays. The key issue is interaction mechanism between flow and combustion of fuel, which is currently unclear. Theoretical analysis indicates that, in modeling flame spread rate over flowing fuel, the method originated from stationary fuel cases demonstrates significant deviations. Based on thermodynamics theories, and attempts to consider the effects of fuel flowing and combustion, the spread and merging of fuel flow front and flame front are well interpreted by the newly proposed theoretical models.