ABSTRACT
Net escape velocity (NEV) and net escape probability (NEP) are concepts that describe that scalar quantity discharged from a source in an indoor air environment is expressed by the unique velocity scales of the returning and escaping populations. Despite the conceptual description and applications of several numerical simulations, the definitions were not precisely explained using a mathematical formula. Here, we derive rigorous mathematical formulations of the NEV and NEP. These formulations provide us with the physical interpretation of NEV, clarify the sufficient condition of perfect escape, and lead to a further formulation of the transfer probability of the scalar. To justify and apply the derived relationships, two simple problems were numerically solved: One was a diffusion equation, and the other was an advection-diffusion equation. The results of the diffusion problem clearly demonstrate that only the outgoing scalar flux exists on the surface of the control volume, covering the source at any location. In contrast, the advection-diffusion problem reveals that there is a returning population of the scalar in most locations, despite both diffusion and turbulent parts working to remove the scalar. This rigorous formulation contributes to apply NEV as an appropriate air quality index with the clear physical interpretation to determine the local scalar concentration.
Subject(s)
Air Pollution, Indoor , Diffusion , Humans , Models, Theoretical , ProbabilityABSTRACT
Heating, ventilating, and air-conditioning (HVAC) systems usually supply air, which is a mixture of fresh air from the outdoor environment, and return air from rooms via the ventilation ductwork. This air reduces the heat load and cost impact of air conditioning using outdoor air. This recirculation of room air in air-conditioning systems is reasonable in terms of energy saving; however, the deterioration of air quality might be a concern because of the recirculation of contaminated room air. Here, we numerically investigate the effect of pollutant recirculation/return on the formation of concentration distributions of local pollutants in indoor environments when the mixing ratio of recirculated air in the HVAC system changes. We discuss the detailed structure of the formation mechanism of local pollutant concentration distributions using various indices for indoor ventilation efficiency in simplified room models. Among the indices, visitation frequency and net escape probability are the ones that directly assist in evaluating the recirculation/return characteristics of indoor pollutants. As a result, when the proportion of air that is recirculated becomes large, the number of pollutants returning to a target local domain, the visitation frequency, increases exponentially, and the net escape probability-which directly expresses the probability of pollutant discharged from the target domain-is close to zero.