A Unified Expression for Vertical Temperature Distribution in Fire-Induced Flows in Tunnels with Rectangular Cross-Sections

Tunnel fires pose serious risks to public safety and lead to significant social and economic losses. A key factor in developing effective fire safety and evacuation strategies is understanding the temperature distribution of fire-induced thermal airflow, which influences smoke movement and tenability conditions. This study proposes a unified function to represent the vertical temperature distribution of fire-induced flow from the ceiling to the floor in the tranquil flow region in tunnels with rectangular cross-sections, under naturally ventilated conditions and with no longitudinal gradient. The function parameters are normalized with respect to the tunnel aspect ratio and expressed as functions of distance from the fire source, incorporating both geometric and thermal effects. The proposed function accurately captures the spatial variation of vertical temperature distributions and is applicable to tunnels with various aspect ratios and heat release rates. It also enables reliable estimation of smoke layer thickness, producing values consistent with experimental data. Comparative analyses using small- and full-scale tunnel experimental data, as well as full-scale tunnel numerical simulation data, confirm that the proposed function reasonably captures the vertical temperature distribution from the ceiling to the mid-height of the tunnel, while also naturally representing the distribution from mid-height to the floor, provided that it is applied under conditions where the Froude number is less than 0.9.