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Returning characteristics of pollutants for a local domain in the presence of returning and recirculating airflow in indoor environments

Abstract 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.

air will be repeatedly mixed with the air in the supply inlet. Previous studies have reported calculation methods for pollutant concentration characteristics in ventilation systems with return air. [5][6][7][8][9] Li et al.
proposed an algorithm for calculating indoor contaminant distribution in complex different ventilation systems with recirculation. 5 Hiyama et al. proposed a calculation method using the concentration response factor as the time serial to calculate the three-dimensional concentration transport in an air-conditioned room. 6 Li et al. proposed a versatile numerical method to determine the pollutant distribution of a ventilation system with recirculation at steady state based on ventilation systems with supply air and a contaminant source. 7 Waters and Simons studied the effect of ventilation effectiveness parameters, for example, the mean age of air and contaminant removal effectiveness, on the recirculation of air in a room with recirculation by the multizonal method. 8  When considering indoor ventilation efficiency, particularly in local domains such as an occupied zone or a breathing zone, the presence of return air means that old-aged air or pollutants are recirculated. 10 A part of the conditioned air that is exhausted out of the room through the exhaust outlets (containing a part of the pollutants generated indoors) is exhausted outside the HVAC system, and the remaining part, a certain percentage, is returned to the room as "return air." When the air-conditioning airflow rate and the exhaust airflow rate are constant, that is, mass-balanced, and therefore, the flow field can be assumed to be in a steady state, the pollutants contained in the air-conditioning airflow from the supply inlet must be uniformly distributed in the room according to the law of mass conservation and linear superposition.
When the proportion of return air is zero, i.e., all fresh air/outdoor air is being conditioned, a non-uniform concentration distribution is formed by pollutants that are heterogeneously distributed, and a nonuniform flow pattern is formed in the room. In case of a steady-state flow field, the pollutant transport equation becomes a linear equation, and then, the pollutant concentration distributions containing multiple pollutant sources can be calculated by linear superposition.
In other words, the indoor pollutant concentration field in the presence of "return air" in the HVAC system is determined by the uniform pollutant concentration owing to the existence of return air and the non-uniform concentration distribution formed in the room by heterogeneous pollutant sources and the non-linear flow pattern produced when there is zero return air. When considering indoor ventilation efficiency, especially when discussing the formation of a concentration field focusing on the recirculation of pollutants by an HVAC system with return air, comprehensive evaluations of the formation structure of the pollutant concentration distribution and transport mechanism are essential because the proportion of return air has a dominant impact on indoor pollutant concentration levels.
Studies on indoor ventilation efficiency have been conducted for many decades, beginning with that by Sandberg et al, and various fruitful indices for evaluating ventilation efficiency in indoor environments have been proposed and used in the practical ventilation designs. [11][12][13] For example, local purging flow rate (L-PFR), visitation frequency (VF), and average residence time proposed by Sandberg et al. [12][13][14][15] and Kato et al. 16,17 have been used to investigate the structure of local pollutant concentration formation not only in indoor environments but also in urban outdoor ventilation. [18][19][20][21][22][23][24] We have proposed new ventilation efficiency concepts, NEV and NEP, which are indicators that can evaluate ventilation efficiency at a local point in the room. Using these indices, it is possible to obtain the distribution of ventilation efficiency at a local area in the room. [25][26][27][28] In this context, Lim et al. 25,26 and Chung et al. 27 proposed using more constructive concepts, such as net escape velocity (NEV) and net escape probability (NEP), as indices to define the ventilation efficiency at a certain point in an enclosed space and investigated the basic properties of pollutant mixture via numerical analysis. Lim et al. also reported the results of evaluating the concentration field formation in indoor air using the concept of NEV considering air-phase chemical reactions. 28 Against this background, the purpose of this study is to investigate the applicability of ventilation efficiency indices, for example, NEV, NEP, VF, and L-PFR, to a heterogeneous pollutant mixing field where "return air" from an HVAC system exists and to discuss quantitatively the formation mechanism of pollutant concentration distributions in the local domain in indoor environments. We discuss the impact of the proportion of return air on indoor ventilation performance based on computational fluid dynamics (CFD) analysis, the prediction accuracy of which is discussed and verified.

| VENTIL ATI ON EFFI CIEN C Y IND I CE S
To understand the ventilation process, it is necessary to elucidate the transport and formation mechanism of pollutant concentrations by distinguishing between the action caused by the two populations: a

Practical implications
• Returning of pollutants at a local point in a room results from circulation of indoor airflow and returning air from the room via the ventilation ductwork of the HVAC system. Assuming a steady-state flow field, the pollutant transport equation becomes a linear system, and the pollutant concentration value of the local point is determined by superimposing the concentration distributions.
• The ventilation efficiency indices, for example, visitation frequency (VF), local purging flow rate (L-PFR), net escape velocity (NEV), and net escape probability (NEP), allow for quantitative evaluation of an exponential increase of pollutant concentration at a local domain or a local point that correlates with an increase in the proportion of air recirculated through the HVAC system. population ventilating the space, that is, leaving the space and never returning to the domain, and a population returning (recirculating) to the domain, thereby spreading the contaminants. The following information is essential: (a) the number of times the pollutants generated in the target local domain return to the domain after leaving. This is quantified by the visitation frequency (VF), which is related to the population of air/contaminant returning, and the net escape probability (NEP), which denotes the probability that the contaminant is transported directly to the exhaust outlet without re-visiting the target point along the flow path. They reflect the state of the flow, for example, whether the flow is unidirectional or not. 29 (b) The amount of fresh air used to dilute and discharge the pollutants in the local domain. This is quantified by the local purging flow rate (L-PFR) and the corresponding velocity, which is the net escaper velocity (NEV).
These concepts are related to the population leaving and never returning. In this study, we performed CFD analysis with Reynolds averaged Navier-Stokes (RANS) modeling and solved the transport equation of an ensemble-averaged scalar quantity numerically.
Here, p represents the volume-averaged pollutant concentration (kg m −3 ) in the target control volume (CV), U j represents the ensemble-averaged scalar quantity of advection velocity in the j direction, and S represents the generation rate of the pollutant. The effective diffusivity constant D eff is given by Equation (2), where Sc t represents the turbulent Schmidt number, t is the turbulent viscosity, and D represents the molecular diffusivity.

| Net escape velocity
In our previous studies, we developed a ventilation efficiency index for analyzing the structure of the formation of a pollutant concentration field at a point as a local domain in an indoor environment. We also discussed the physical meaning of the concentration formation when the target local region was minimized. 25,26 To quantitatively discuss the essential velocity scale that directly determines the pollutant concentration of a point, we proposed two definitions of NEV as follows: NEV j represents the vector quantity of j direction of NEV defined by the difference of outflow flux and inflow flux on the target CV. NEV * j represents the vector quantity of j direction of NEV defined by the outflow flux on the target CV. In CFD, the minimum resolution corresponds to the CV for discretization, and NEV is defined and obtained by overlapping the effect of the diffusion flux with the effect of the advection flux in each CV. NEV shows that the driving force for ventilation and scalar transportation is not only due to the timeaveraged advection velocity at that point but also due to the instantaneous fluctuating air velocity component (this fluctuating effect corresponds to molecular and turbulent diffusion).

| Net escape probability
According to the context of NEV, we also defined two probabilistic indices for determining the recirculation of pollutants, that is, the returning probability α, which represents the probability that a pollutant returns to the target point (here, CV) as a local domain under the condition that a contaminant is generated in the CV, and the NEP, which denotes the probability that the contaminant is transported directly to the exhaust outlet without re-visiting the target CV along the flow path. 27 By definition, the sum of NEP and α is equal to 1.0.
They can be defined as follows: Here, F of and A of denote the total outflow flux (convective and diffusive flux) from the target CV (kg m −2 s −1 ) and the area through the outflow flux in the target CV (m 2 ), respectively. qV CV is the total amount of contaminant generated in the CV (kg s −1 ).

| Local purging flow rate
pollutant in the local domain (s one staying −1 ), q p is the parcels/pollutant generation rate per unit time (kg s −1 ), and C p represents the local domain-averaged concentration (kg m −3 ).

| Visitation Frequency
VF represents the number of times a particle enters and passes through the local domain. VF =1 means that after being generated, a particle appears in the local domain only once, and then, after leaving the local domain, never returns. 12 VF =2 means a particle enters the local domain for the first time, is transported to the outside, and then returns again to the local domain because of the recirculating flow only one time. VF can be calculated using Equation (9).
where J p is the amount of parcels/pollutants, visiting (returning to) the target local domain per unit time (Particle s −1 ), M p is the amount of parcels/pollutants generated in the local domain (Particle s −1 ), Δq p is the inflow rate of parcels/pollutants into the local domain per unit time (kg s −1 ), and q p denotes the particle generation rate per unit time (kg s −1 ).

| Normalized concentration at local domain
The average pollutant concentration can provide fundamental and essential information regarding the ventilation efficiency, and then, the normalized pollutant concentration at a local domain becomes dimensionless with the representative concentration, that is, perfect mixing concentration defined simply by pollutant generation rate and ventilation rate, usually adopted for ventilation design.
Here, C p is the mean concentration at local domain P (kg m −3 ), C e is the mean concentration at the exhaust outlet (kg m −3 ), C n is the normalized concentration at local domain P (-), and Q in is the airflow rate from the supply inlet opening (kg m −3 ).
In this study, these ventilation efficiency indices are numerically analyzed in the simplified room models described next.

| NUMERIC AL ME THODS
We used two simplified room cases forming a large internal circulating flow in spaces with different aspect ratios and different air mixing conditions: a simple square room model (two-dimensional analysis) and a simple rectangular room model (three-dimensional analysis), which is the IEA Annex benchmark test case with detailed measurement data. The geometries of the two room model cases were set in order to investigate the effect of the differences in the aspect ratio of the room on the change in ventilation efficiency distribution at local domains. The temperature conditions were assumed to be isothermal. To avoid discussing the dependence of the influence of Reynolds number (Re) of the flow field, a constant and fixed supply airflow rate through the supply inlet of the HVAC system was assumed, and the proportion of return air in the supply airflow rate was gradually increased from zero (0%) to 90%. The 0% return air condition represents an all fresh air supply. In the case of 100% return air, fresh outdoor air is not supplied in the room; consequently, the pollutant concentration in the room becomes infinity because the pollutants generated in the enclosed space are not diluted. To analyze the ventilation efficiency, room models were divided into upper and lower parts, and the lower part of each room model was assumed to be a target local domain, for example, occupied space. We assumed the area below y = 5.6L in in the square case and y = 0.5H in the rectangular case as local domains for including strong airflow along the wall surface and the stagnant area.
These values represent the height through the area where the velocity is almost zero in the center of recirculating flow.
The amount of supply air is set constantly, and when there was return air in the HVAC system, the ratio of outdoor fresh air included in the supply air was gradually changed, and the scalar (pollutant) concentration included in the supply air was determined by the ratio of return air. The returning pollutant rate was set by the ratio of return air. If the ratio of return air to supply air in the room is assumed to be "γ", the ratio of outdoor air to supply air will be "1γ". Here, the returning pollutant rate included in supply air q' (kg s −1 ) is written as follows: where q represents the pollutant generation rate per unit time in a target local domain (kg s −1 ) and q' represents the returning pollutant rate included in supply air per unit time (kg s −1 ).
Assuming n is infinite, q' is given by the following equation via an infinite series.
If the returning pollutant rate q' is assumed to represent a pollutant generation source in the target room, the total pollutant generation rate will be q + q � as follows: Flow fields were analyzed using the standard kε model with a generalized log law for wall function. In the scalar advection and  Table 1. The supply inlet openings were located on the wall near the floor, the non-dimensional air velocity U in =1.0 (-) was set, and the turbulence intensity was set to 30%.

| Numerical analysis conditions for the rectangular room model (three-dimensional case)
The IEA Annex 20 test case, which was used as the rectangular room model, is shown in Figure 3. 30- 36 The numerical and boundary conditions are summarized in Table 2. The supply inlet opening was located on the wall near the ceiling, and the supply velocity U in =0.455 m s −1 was adopted. The turbulence intensity was set to 4% in accordance with experimental results. We conducted a preliminary CFD analysis to determine the independent grid design and numerical analysis conditions for reproducing experimental results with sufficient accuracy.

| Validation and quality control of CFD
In the CFD analyses structured grid designs were adopted to en-

| Airflow distribution
The airflow distributions for the square room model (2D case) are shown in Figure 4. Figure 4A shows the streamline for the square room case, and Figure 4B shows the distribution of air velocity normalized by the velocity of the supply air for the square room case.  Figure 5. Figure 5A shows the airflow vector distribution in the room, Figure 5B shows the airflow scalar distribution, and Figure 5C shows          Figure 9B. The L-PFR/Q in values in 80% return air condition compared to the 0% return air condition increased by 62.0% and 42.0%

| Ventilation efficiency distributions
in the square room and rectangular room cases, respectively. Figure 11 shows the distributions of normalized NEV using the supply air velocity (here, NEV) as function of the percentage of return air (%). Figure 11A     x/ H (-) Square Rectangular x/ H (-) Square Rectangular (B) (C) Figure 13 shows the distributions for the normalized NEV*, NEV*/U in , by advection velocity, NEV*/U, at each CV as function of the percentage of return air (%). Figure 13A shows

| DISCUSS ION
In this study, we considered the return air of an HVAC system and as- x/ H (-)  simple boundary conditions were adopted in this study and the analyses assumed an isothermal condition. Therefore, the effects of the temperature distribution or the thermal plume on the pollutant transport were ignored.
The target model rooms in this study were very simple rectangular shapes used to obtain universal results; they were not intended to be an exact reproduction of the actual buildings and there was no reproduction of furniture and residents. The HVAC system was also simplified and the removal of pollutants by filters and deposition of pollutants in ducts was not included in this study. Pollutants used in the ventilation efficiency analysis were also assumed to be passive scalars and the specific characteristic of pollutants, for example, gas and particle phase, particle size, and Schmidt number, were not taken into account. These simplifications indicate that this study was conducted under very limited conditions; however, we believe that these simplifications make the formation mechanism of the pollutant concentration distributions clearer. An application-focused study targeting actual building spaces and ventilation design will be an importance issue to address in the future.

| CON CLUS IONS
In general, the air in a ventilated space consists of two populations.
• A population ventilating the space, that is, leaving the space and never returning to the domain.
• A population returning (recirculating) and thereby spreading the contaminates.
The two populations are generated by the air distribution system itself because air is entrained into the airflow supplied to the room. The final result is that the air distribution system generates a flow rate within the room that is larger than the supplied airflow rate. However, air is extracted from the room at the same rate as it is supplied. This implies that the surplus air must return (recirculate) to the room. It recirculates several times within the room before it finally leaves. To understand the formation mechanism of pollutant concentration distributions under the existence of "return air" of an HVAC system and large recirculating flow indoors, the returning characteristics of pollutants were investigated by ventilation efficiency indices, for example, NEV, NEP,VF, and L-PFR, under conditions in which the proportion of the return air in the HVAC system was changed from 0% to 90%.
The numerical investigation findings can be summarized as follows: • The pollutant concentration and VF increased and NEV, NEP, and L-PFR decreased as the proportion of return air increased. When the proportion of return air exceeded 50%, the pollutant concentration and VF increased rapidly.
• The value of NEV* approached the advection air velocity as the percentage of return air increased. NEV*/U gradually decreased and approached 1.0 as the percentage of return air increased because the transport of pollutants is largely dominated by the convection effect as the ratio of return air increases.
• When the proportion of return air increased, the L-PFR ap-