Modeling sinusoidal exhalation: An unsteady Reynolds-averaged Navier–Stokes-based approach for predicting breathing flow dynamics

Accurate modeling of exhalation dynamics is essential in estimating infection rates. In this study, we analyzed the predictive capabilities of three Unsteady Reynolds-Averaged Navier–Stokes (URANS)-based turbulence models: Realizable k–ε, renormalization group (RNG) k–ε, and shear-stress transport (SST) k–ω for sinusoidal exhalation. The exhaled jet flow extends over a distance from the exhalation source, normalized by the exhalation source diameter, and was analyzed across the jet region. Furthermore, this region was divided into three sub-regions: near-field, transitional, and fully developed field for turbulence evaluation. These models were validated against time-resolved particle image velocimetry data and empirical measurements under quiescent ventilation conditions. Results from the centerline velocity decay profiles demonstrated that each model exhibited performance across the sub-regions of the exhaled jet. Using three performance metrics for quantitative validation, the RNG k–ε model demonstrated superior performance overall across the jet flow region. When sectioned into sub-regions, its performance is better in transitional and fully developed regions due to its enhanced strain-term formulation. Meanwhile, the SST k–ω model provides superior accuracy in near-wall shear and boundary–layer interactions. The Realizable k–ε model performs well in the transitional region but underperforms in the near-field and fully developed regions. These results advance the characterization of breath-generated flows, providing insights into airborne transmission dynamics that can inform the optimization of ventilation strategies and mitigation measures in indoor environments. Semi-empirical equations, derived using the best-performing region-specific URANS models, estimate centerline velocities during exhalation (0 < t < 2 s) in developed field regions.