Exploring Ventilation Efficiency through Scalar Transport Equations with existing and new CFD-based indices

In practical ventilation design for contamination control, it is commonly assumed that perfectly mixed or well-mixed conditions exist. However, due to the complex fluid dynamics within indoor environments, the actual distribution of indoor scalar concentrations is often heterogeneous. Ventilation efficiency indices provide valuable insights into the mechanisms that lead to heterogeneous distributions. In CFD-based ventilation efficiency studies, once a steady-state flow field is established, various ventilation efficiency analyses can be conducted by coupling the steady-state flow field with scalar transport equations. This study focuses on CFD-based ventilation efficiency indices to explore the correlation between ventilation efficiency and the number of scalar transport equations required for their calculations. In addition to the ventilation efficiency indices proposed to date, a new index, the average return time, was introduced as a time scale for scalars recirculating within the source point. Furthermore, we provide deeper insights into ventilation efficiency by decomposing the average staying time of scalars within a room into three distinct components: recirculation, staying, and direct exhaust. The results of these ventilation efficiency analyses offer valuable information for describing fresh/clean air supply, scalar removal, recirculation, and dispersion within indoor spaces.