Nonlinear damping modeling and computational fluid dynamics analysis of oscillatory flow using instantaneous Reynolds number dynamic partitioning

Traditional Reynolds-averaged Navier–Stokes (RANS) models struggle to accurately predict nonlinear damping in wide-Reynolds-number (Re) oscillatory flows due to dynamic response lag caused by linear vortex–viscosity constitutive relations and time-averaged frameworks. To address this limitation, this paper proposes an instantaneous Re dynamic partitioning damping model (IRDP-Damping). The core innovation lies in establishing the instantaneous Re as an external criterion independent of turbulence variables. This approach enables synchronization of the damping mechanism with the local flow state and adaptive application of nonlinear physical friction laws, thereby fundamentally overcoming the inherent limitations of traditional models. By coupling the IRDP-Damping model with the shear stress transport (SST) turbulence model via a user-defined function, the model is integrated within a computational fluid dynamics framework. Using gas–liquid coupled oscillations in a vertical U-tube as a validation case, the performance of the IRDP-Damping model in free-decaying and forced-resonance oscillations is systematically evaluated. Results demonstrate that, compared to the SST model alone, the IRDP-Damping model improves damping ratio prediction accuracy by 24%–47% and significantly enhances numerical robustness under strongly nonlinear resonance conditions within the validated Re range (up to ∼9000). It also exhibits good agreement with classical U-tube oscillation experiments. This study presents a physically consistent and computationally robust damping modeling approach, validated for oscillatory flow in a U-tube system involving complex flow regime transitions. The framework shows promise for broader applications in oscillatory flows.