Inertial-buoyant coupling and bi-directional flow effects on plume deflection in inclined tunnel fires under natural ventilation

• Reveals plume deflection is driven by inertial forces from both airflow sides. • Introduces modified Richardson number ( Ri’ ) for coupling buoyancy with asymmetric inertial forces. • Identifies critical Ri’ = 16.0 ± 1.5 as deflection threshold via buoyancy–inertia interaction. • Develops a robust Ri’ -based model to predict plume deflection angle. • Conventional test configuration is improper in simulating tunnel fire in weak wind scene. Plume deflection in inclined tunnel fires is a critical yet inadequately understood phenomenon that directly influences smoke movement and evacuation safety. This study conducts a series of high-fidelity numerical simulations to investigate the onset conditions and evolution characteristics of plume deflection under natural ventilation. The flow–plume interactions are systematically classified into three regimes based on tunnel slope: (a) symmetric bidirectional flow with vertical plume at low slopes; (b) asymmetric bidirectional flow causing plume deflection at intermediate slopes; and (c) unidirectional flow with pronounced plume deflection at steep slopes, driven by the intensified stack effect. A modified Richardson number Ri’ , representing the ratio of thermal buoyancy to the inertial force difference between high- and low-slope sides, is proposed to characterize the critical transition. The critical threshold for plume deflection is identified as Ri’ =16.0 ± 1.5, which outperforms traditional velocity-based criteria by capturing the counteracting influence of dual-sided airflow. Furthermore, a predictive model relating plume deflection angle to Ri’ is developed, yielding high consistency with experimental and numerical data from previous studies. The proposed framework provides new physical insights into the coupling of buoyancy and inertial forces and offers a reliable predictive tool applicable to tunnels with varied geometries, fire intensities, and ventilation modes.