Numerical analysis of flame propagation a vertically upward corrugated wall

Corrugated cardboard, a cellulosic material consisting of flat and wavy layers, is widely used in warehouses and packing factories. When a fire occurs in these environments, flame spreading over the wavy surfaces poses significant risks to firefighters' health and the local environment, and can result in substantial economic penalties for building owners and insurance companies. Thus, a detailed understanding of flame spreading on wavy surfaces is crucial for preventing and mitigating fire hazards.

This study developed a simplified model of high-precision direct numerical simulation for flame spreading, utilizing the open-source code Fire Dynamics Simulator version 5.5.3. The model incorporates one-step finite-rate gas-phase combustion, one-step first-order pyrolysis, and gray gas radiation applicable to all gas species. The sample was a cellulose-based material modeled as a "B" flute corrugated cardboard measuring 20.4 cm in length and 2.0 cm in width, with each flute being 8.24 mm long and 3.93 mm high. We hypothesized that the thickness of the flat layer matched that of the wavy layer, with layer thickness ranging from 0.083 to 0.414 mm. The sample was assumed to produce 10% chemically inert char residue and liberate 90% combustible gas vapor. The computational domain is a cuboid measuring 0.10×0.640 8×0.02 m, with a time step set at 1 × 10^-4 s prior to simulation. Flame is defined as a heat release rate exceeding 15, 000 kW/m², with the pyrolysis front identified as the position where the local burning rate exceeds 001 kg/s/m².

The flame characteristics on the corrugated and flat surfaces were compared across five aspects: flame shape, fire spreading speed, flame stationary distance, net heat flow distribution, and local combustion rate. The results indicated that: 1) the flame on the wavy surface split into more flamelets, whereas that on the flat surface tended to remain more cohesive. The flame base on the wavy surface moved more rapidly, reaching the fuel's top end sooner and, consequently, self-extinguishing earlier than the flame on the flat surface. 2) In thermally thin samples of layer thickness less than 0.414 mm, the flame base and pyrolysis front movement rates decreased with increasing thickness. 3) Compared with the flat surface, the wavy surface exhibited a lower peak flame temperature and shorter flame standoff distance, resulting in a larger net heat flux imposed on the wavy surface and an increased pyrolysis rate. 4) Correlations were established between the flame net heat flux and the pyrolysis rate relative to the normalized distance, both showing a decaying trend.

Through the development of a simplified high-precision direct numerical simulation model for flame spreading, the mechanisms behind flame splitting on corrugated surfaces were explored, and the relationship between net heat flow and local combustion rate was analyzed, providing valuable insights for understanding fire behavior on irregular surfaces.