Effects of Fire Source Transverse Position and Curvature Radius on the Critical Velocity and Smoke Back-Layering Length in L-Shaped Tunnels

L-shaped tunnels frequently occur in underground coal mines because of geological and operational limitations. Their complex geometry increases ventilation resistance and causes non-uniform airflow, promoting combustible gas accumulation and resulting in a greater fire risk than in straight tunnels. In this work, Fire Dynamics Simulator was employed to quantify the effects of the fire source’s transverse position, curvature radius, heat release rate, and imposed longitudinal ventilation on both the critical velocity and the extent of smoke back-layering. The analysis shows that higher heat-release rates elevate the critical velocity, whereas a centrally located fire yields the lowest value. Shifting the fire toward either sidewall or adopting a larger curvature radius results in a higher critical velocity. In addition, the extent of upstream smoke back-layering increases with curvature, peaking when the ignition point lies close to the convex sidewall. Specifically, with a ventilation velocity of 0.95 m/s and a centerline fire, the back-layering length extends from 23 m (R = 5 m) to 40 m (R = 10 m). Based on theoretical derivation and dimensional analysis, several dimensionless parameters were developed that incorporate both the transverse fire-source position and the curvature radius to modify the dimensionless heat-release rate. Finally, dimensionless predictive models for the critical velocity and back-layering length, incorporating the effects of the curvature radius and the fire transverse position, were developed. These models provide a theoretical foundation and practical framework for fire prevention and ventilation design in L-shaped tunnels.