Asymmetrical distribution of buoyancy flux and its effect on smoke propagation velocity and backlayering length in inclined tunnel fires

Inclined tunnels are commonly seen in modern society. Compared with horizontal tunnel fires, smoke movement in inclined tunnel fires exhibits noticeable asymmetry. In this study, a series of numerical simulations are conducted to investigate the asymmetrical distribution of source buoyancy flux and its impact on smoke movement in inclined tunnel fires. Because of buoyancy and the stack effect, the proportion of the buoyancy flux of the smoke advancing towards the upper portal, $\eta$, varies with time. When the fire plume impinges the tunnel ceiling, there is an initial distribution of buoyancy flux and the value of $\eta$ is determined by tunnel inclination angle $\alpha$. Subsequently, $\eta$ gradually increases until the steady state is achieved. The growth trajectory of $\eta$ with time is also controlled by $\alpha$, but the steady-state value is dependent on both $\alpha$ and the fire location. Models are established to calculate $\eta$ in different stages. The value of $\eta$ influences smoke flow characteristics. Smoke propagation velocity scales with the cubic root of buoyancy flux per unit width, which can be derived based on $\eta$. Additionally, the backlayering length increases with the steady-state value of $\eta$. The findings contribute to a better understanding of the mechanisms governing the smoke flow in inclined tunnel fires.