Application of Portable Air Puriﬁers for Mitigating COVID-19 in Large Public Spaces

: This study investigated, using validated computational ﬂuid dynamics techniques, the actual performance of portable air puriﬁers for reducing the infection risks of airborne respiratory diseases such as COVID-19, by properly installing air puriﬁers in complicated large public spaces of primary concern, such as restaurants and ballrooms. The research results reveal that portable air puriﬁers with HEPA ﬁltration provide an effective solution to help mitigate virus-carrying particles/droplets in large spaces where the central air conditioning system with HEPA ﬁltration may not provide adequate dilution and/or effective ventilation. Deploying portable air puriﬁer changes the local ﬂow directions, and thus, reduces the cross-table airﬂows that may enhance the possibility of cross-infection. A ﬁeld experiment was further conducted in a restaurant and a ballroom to verify the on-site performance. This study indicates that each space is unique in furniture, occupant and system layouts and capacities, and thus, requires individualized investigation of appropriate puriﬁer number, capacities, and locations. Flexible solutions such as portable air puriﬁers are important and low-cost supplements to more elaborate solutions installed in central air systems.


Introduction
In less than two years since the coronavirus disease 2019 (COVID-19) emerged, the pandemic has changed how we live, work, study, and interact as social distancing guidelines have led to a more virtual world, both personally and professionally. This became a more severe concern when scientific data supported the possibility that the COVID-19 virus may be transmitted by aerosols (so-called airborne transmission) [1]. It was highlighted that aerosol transmission may more likely occur in particular environments, such as indoor, crowded, and inadequately ventilated spaces, where the infected person(s) spend a relatively long period of time with others (e.g., over 30 min), such as classrooms, restaurants, choir practices, fitness classes, nightclubs, offices, and places of worship. Therefore, how to reduce the infection risks of airborne respiratory diseases in a public place becomes an urgent task for epidemiologists and public health experts.
The results in the survey study of Fabisiak et al. [2] indicated that 55% of respondents will be afraid to use public spaces after the COVID-19 lockdown. Restrictions on the use of public spaces and physical distancing have been key policy measures to reduce the transmission of COVID-19 and protect public health [3]. Despite the concerns and the difficulties faced throughout the pandemic, those who were committed to investigating the new approaches to infection prevention demonstrated that they have managed to find promising solutions in their studies. Air purifiers, as traditional air pollution purification equipment, exhibit an excellent potential to reduce the infection risk of airborne

Methodologies
The actual performance of air purifiers can be determined through either a physical test or a validated numerical experiment. While providing first-hand data, a physical test in a real space is often challenging, due to many uncontrollable variables, especially for pollutant/virus-related studies. A validated numerical experiment using computational flow dynamics (CFD) techniques provides a great alternative and is applied widely in the field. This study simulated the airflow pattern and contaminant transport in the spaces using a steady-state RANS (the Reynolds-Averaged Navier-Stokes equations) method. The RNG k-ε turbulence model in the commercial CFD code ANSYS Fluent 19.2 [10,11] was used to represent turbulence characteristics. The particle simulation assumed monodispersed non-interacting spherical particles. The momentum transfer from the particles to the air turbulence has a negligible impact on the flow [12][13][14]. Equations (1) and (2) describe the governing equations of the fluid phase [12]. The buoyancy effect of air is modeled with the Boussinesq approximation.
where v j is the velocity component in three perpendicular coordinate directions (x j , j = 1, 2, 3), m/s; ρ is the air density, kg/m 3 ; p is the air pressure, Pa; µ is the kinematic viscosity coefficient of air; v i v j is the Reynolds stress tensor. When tracking the virus-carrying particles (in solid phase), the effect of the air drag force, gravity, and buoyancy were taken into account. The discrete particle model in Fluent (CFD-DPM) was used to track the individual particles [13]. The flow-governing equations of the solid phase single particle are described by Equations (3)-(6) [14]: where → F D is the air drag force acting on the particle, N, the second term on the right side of Equation (3), represents gravity and buoyancy; m p is the mass of the particle, kg; → v p is the velocity vector of the particle, m/s; ρ p is the particle density, kg/m 3 ; v is the air velocity, m/s; v p is the particle velocity, m/s; D p is the particle diameter, m; µ is dynamic viscosity, N s/m 2 ; a 1 , a 2 , and a 3 are coefficients determined by Re p .

Validation of the CFD Model
Exhaled air of an infected person is the primary source of contagious viruses. Exhaled air comes from various respiratory-related activities, such as breathing, coughing, singing, and talking. Accurate information on the release and diffusion process of exhaled airflow and particles is, thus, critical for the precise prediction of infectious disease transmission. This study focused on the talking scenario-the main concern during the dining and ballroom events when facial masks cannot be used. Studies showed that talking may release 2600 droplets per second at a speed of 1-5 m/s [15]. The range of the total airflow rate from a mouth when speaking is about 284-759 cm 3 /s [16]. Using an average of 500 cm 3 /s and assuming a mouth opening area at 1.8 cm 2 [16] leads to an average talking airflow speed of 2.77 m/s, which meets the particle image velocimetry (PIV) test result at the order of 3.1 m/s [17].
This study first conducted a test, via both physical experiment and CFD simulation, in the calm lab environment using a single table case with four occupants, including one infected person (Manikin 1) who intermittently talks, as shown in Figures 1 and 2. Table 1 lists the test case geometries. The thermal manikins of 70 Watt each have an average head/face temperature of 27 • C and an average body (with clothes) temperature of 22 • C. The space has no active air conditioning system, and the ambient room air, wall, ceiling, floor, and table surface temperatures are kept at 19 • C. mouth (with an inner size of 1.37 cm) of Manikin 1 by using stage fog (water-glycerinmixture) as the tracer gas. The exit velocity of the fog from the mouth was controlled at around 2.77 m/s, representing a scenario where people are talking loudly. The supply time of the fog from the mouth is 20-25 s in the experiment and each test runs 2-5 min. A commercially available portable air purifier with a clean air delivery rate (CADR) of 166 m 3 /h was tested for the performance, with the most effective placement location as shown in Figures 1 and 2. The sizes of the portable air purifier are listed in Table 1.    Figure 2 illustrates the created CFD model for the single table case. The virus particle details simulated in CFD are presented in Table 2. The number of the particles released from the mouth was assumed as 5000 to ensure that the deviation of the particle statistical results is less than 1% [18]. Particles larger than 10 micron tend to drop quickly, while smaller particles tend to flow with air. The mean particle size during talking was 3 micron, which was thus used in the CFD model [19]. mouth (with an inner size of 1.37 cm) of Manikin 1 by using stage fog (water-gl mixture) as the tracer gas. The exit velocity of the fog from the mouth was contro around 2.77 m/s, representing a scenario where people are talking loudly. The supp of the fog from the mouth is 20-25 s in the experiment and each test runs 2-5 commercially available portable air purifier with a clean air delivery rate (CADR m 3 /h was tested for the performance, with the most effective placement location as in Figures 1 and 2. The sizes of the portable air purifier are listed in Table 1.    Figure 2 illustrates the created CFD model for the single table case. The virus details simulated in CFD are presented in Table 2. The number of the particles r from the mouth was assumed as 5000 to ensure that the deviation of the particle sta results is less than 1% [18]. Particles larger than 10 micron tend to drop quickly smaller particles tend to flow with air. The mean particle size during talking was 3 m which was thus used in the CFD model [19].  The mock-up physical experiment simulated the virus pollutant emitted from the mouth (with an inner size of 1.37 cm) of Manikin 1 by using stage fog (water-glycerinmixture) as the tracer gas. The exit velocity of the fog from the mouth was controlled at around 2.77 m/s, representing a scenario where people are talking loudly. The supply time of the fog from the mouth is 20-25 s in the experiment and each test runs 2-5 min. A commercially available portable air purifier with a clean air delivery rate (CADR) of 166 m 3 /h was tested for the performance, with the most effective placement location as shown in Figures 1 and 2. The sizes of the portable air purifier are listed in Table 1. Figure 2 illustrates the created CFD model for the single table case. The virus particle details simulated in CFD are presented in Table 2. The number of the particles released from the mouth was assumed as 5000 to ensure that the deviation of the particle statistical results is less than 1% [18]. Particles larger than 10 micron tend to drop quickly, while smaller particles tend to flow with air. The mean particle size during talking was 3 micron, which was thus used in the CFD model [19].  [16,20].

Variable Value
Open area of the talking mouth 1.8 cm 2 Airflow rate from the talking mouth 500 cm 3 /s Average talking airflow speed 2.77 m/s Temperature of the airflow from the talking mouth 27 • C Aerodynamic diameter of the particles 3 µm Density of the particles 600 kg/m 3 Number of particles released from the talking mouth 5000 The CFD simulation first performed the grid sensitivity analysis to ensure the independence of the numerical results. Three numerical grids, 410,000, 770,000, and 1,000,000, were tested and compared using the normalized root mean square error (NRMSE) of the velocity at the pole shown in Figure 2 (30 points). The NRMSE of the velocity at the pole, respectively, between 410K and 1000K grids and between 770K and 1000K grids, are calculated as shown in Figure 3a. There is generally a great improvement in the error with the 770K grid, and the computational uncertainty is overall below 15%. By balancing the computational accuracy and cost, the 770,000 grid was, thus, chosen for the simulation. Among the 770,000 cells, fine grids were allocated around the mouths of the occupants, as shown in Figure 3b.  The CFD simulation first performed the grid sensitivity analysis to ensure the independence of the numerical results. Three numerical grids, 410,000, 770,000, and 1,000,000, were tested and compared using the normalized root mean square error (NRMSE) of the velocity at the pole shown in Figure 2 (30 points). The NRMSE of the velocity at the pole, respectively, between 410K and 1000K grids and between 770K and 1000K grids, are calculated as shown in Figure 3a. There is generally a great improvement in the error with the 770K grid, and the computational uncertainty is overall below 15%. By balancing the computational accuracy and cost, the 770,000 grid was, thus, chosen for the simulation. Among the 770,000 cells, fine grids were allocated around the mouths of the occupants, as shown in Figure 3b. The mock-up experiment exhibits clearly, in Figure 1, that the fog exhaled from Manikin 1 can easily arrive at the face of Manikin 4, who is right across the table, and Manikin 3, who is diagonally across the table, when no air purifiers are used. When air purifiers were used, most of the fog exhaled from Manikin 1 was attracted towards the air purifiers, effectively containing the turbulent spread of the contaminant.
The similar dispersion processes of the particles were observed in the CFD simulation with and without air purifiers, as shown in Figure 4. Both mock-up test and CFD modeling indicate that the particle concentration at Manikin 4 (across the table from the source person) is less than those near Manikins 2 and 3, confirming the effectiveness of the air purifier placed between Manikin 1 and 4. Most of the particles can be directly removed by the purifier or blown away by the upward air from the top exit of the purifier. The mock-up experiment exhibits clearly, in Figure 1, that the fog exhaled from Manikin 1 can easily arrive at the face of Manikin 4, who is right across the table, and Manikin 3, who is diagonally across the table, when no air purifiers are used. When air purifiers were used, most of the fog exhaled from Manikin 1 was attracted towards the air purifiers, effectively containing the turbulent spread of the contaminant.
The similar dispersion processes of the particles were observed in the CFD simulation with and without air purifiers, as shown in Figure 4. Both mock-up test and CFD modeling indicate that the particle concentration at Manikin 4 (across the table from the source person) is less than those near Manikins 2 and 3, confirming the effectiveness of the air purifier placed between Manikin 1 and 4. Most of the particles can be directly removed by the purifier or blown away by the upward air from the top exit of the purifier.
The comparison between simulation and experiment is quantitatively analyzed by calculating the reduction rate of the particle numbers (M reduction ) detected at the three locations of the sensors ( Figure 1). M reduction can be defined as follows: where M without air purifier, i is the number of particles sensed at the ith point (i = 1, 2, 3) for the case without air purifiers and M with air purifier, i is the number of particles sensed at the ith points (i = 1, 2, 3) for the case with air purifiers. Figure 5 compares the results obtained from the simulation and test.  The comparison between simulation and experiment is quantitatively analyzed by calculating the reduction rate of the particle numbers (Mreduction) detected at the three locations of the sensors ( Figure 1). Mreduction can be defined as follows: without air purifier, with air purifier, reduction, without air purifier, where Mwithout air purifier, i is the number of particles sensed at the ith point (i = 1, 2, 3) for the case without air purifiers and Mwith air purifier, i is the number of particles sensed at the ith points (i = 1, 2, 3) for the case with air purifiers. Figure 5 compares the results obtained from the simulation and test. Both the qualitative and quantitative comparisons between the mock-up experiment and the CFD simulation verify that the simulation model can project reasonable results to track the virus-carrying particles' trajectories. Therefore, a sophisticated CFD model that is made of many similar tables and occupants should be able to predict the transportation of the virus-carrying particles in a complex large built environment.

CFD Simulation and Analysis of Large Public Spaces
This study used the validated CFD model to simulate a restaurant and a ballroom as two representative public places to evaluate the effect of using portable air purifiers to mitigate COVID-19 in large spaces. Steady-state air circulation conditions were simulated to determine the best location, air exchange rate requirement, and quantity of air purifiers. The restaurant and the ballroom are conditioned with a central HVAC system, which supplies clean air from the ceiling inlets and exhausts room air from the ceiling/upper-level outlets. To assess the actual performance of the commercial purifier on mitigating COVID-19, virus-carrying particles released from one infected occupant in the restaurant and the ballroom were simulated and tracked, using the same settings as used in the validation  The comparison between simulation and experiment is quantitatively analyzed by calculating the reduction rate of the particle numbers (Mreduction) detected at the three locations of the sensors (Figure 1). Mreduction can be defined as follows: without air purifier, with air purifier, reduction, without air purifier, where Mwithout air purifier, i is the number of particles sensed at the ith point (i = 1, 2, 3) for the case without air purifiers and Mwith air purifier, i is the number of particles sensed at the ith points (i = 1, 2, 3) for the case with air purifiers. Figure 5 compares the results obtained from the simulation and test. Both the qualitative and quantitative comparisons between the mock-up experiment and the CFD simulation verify that the simulation model can project reasonable results to track the virus-carrying particles' trajectories. Therefore, a sophisticated CFD model that is made of many similar tables and occupants should be able to predict the transportation of the virus-carrying particles in a complex large built environment.

CFD Simulation and Analysis of Large Public Spaces
This study used the validated CFD model to simulate a restaurant and a ballroom as two representative public places to evaluate the effect of using portable air purifiers to mitigate COVID-19 in large spaces. Steady-state air circulation conditions were simulated to determine the best location, air exchange rate requirement, and quantity of air purifiers. The restaurant and the ballroom are conditioned with a central HVAC system, which supplies clean air from the ceiling inlets and exhausts room air from the ceiling/upper-level outlets. To assess the actual performance of the commercial purifier on mitigating COVID-19, virus-carrying particles released from one infected occupant in the restaurant and the ballroom were simulated and tracked, using the same settings as used in the validation Both the qualitative and quantitative comparisons between the mock-up experiment and the CFD simulation verify that the simulation model can project reasonable results to track the virus-carrying particles' trajectories. Therefore, a sophisticated CFD model that is made of many similar tables and occupants should be able to predict the transportation of the virus-carrying particles in a complex large built environment.

CFD Simulation and Analysis of Large Public Spaces
This study used the validated CFD model to simulate a restaurant and a ballroom as two representative public places to evaluate the effect of using portable air purifiers to mitigate COVID-19 in large spaces. Steady-state air circulation conditions were simulated to determine the best location, air exchange rate requirement, and quantity of air purifiers. The restaurant and the ballroom are conditioned with a central HVAC system, which supplies clean air from the ceiling inlets and exhausts room air from the ceiling/upperlevel outlets. To assess the actual performance of the commercial purifier on mitigating COVID-19, virus-carrying particles released from one infected occupant in the restaurant and the ballroom were simulated and tracked, using the same settings as used in the validation model. A grid sensitivity analysis was also performed to ensure the accuracy of the numerical results. The suitable total grid cells were determined to be about 650,000 and 4,470,000 for the restaurant and the ballroom, respectively.  Table 3.  Figure 6) of a restaurant (total space area 370 m 2 ) was in ICEMCFD (Integrated Computer Engineering and Manufacturing code for CFD) specifications of the restaurant are summarized in Table 3.  To evaluate the effectiveness of air purifiers on reducing the potential infection to the healthy occupants, floor-standing air purifier (FAP), and table air purifier ( were arranged in the restaurant. As listed in Table 4, two kinds of commercial pur [21,22] were employed to purify indoor air. Indoor air flows into the purifier from the of the purifier and then flows out from the top of the purifier. Eight FAPs are plac both ends of the restaurant ( Figure 6). The restaurant was operated at full capacity, 177 occupants, in which one was the virus-carrier, as shown in Figure 6c. One TAP placed at the center of the dining table occupied by the infected occupant.    To evaluate the effectiveness of air purifiers on reducing the potential infection risk to the healthy occupants, floor-standing air purifier (FAP), and table air purifier (TAP) were arranged in the restaurant. As listed in Table 4, two kinds of commercial purifiers [21,22] were employed to purify indoor air. Indoor air flows into the purifier from the side of the purifier and then flows out from the top of the purifier. Eight FAPs are placed at both ends of the restaurant ( Figure 6). The restaurant was operated at full capacity, with 177 occupants, in which one was the virus-carrier, as shown in Figure 6c. One TAP was placed at the center of the dining table occupied by the infected occupant. Particle release conditions were the same as those in the validation case (Table 2). Particle trajectories were investigated, respectively, under three ventilation conditions: (1) central air-conditioning system (CA); (2) central air-conditioning system with floor-standing air purifiers (CAF); and (3) central air-conditioning system with both floor-standing air purifiers and table air purifier (CAFT), to analyze the fate of the particles exhaled from the infected occupant.

Flow Field and Particle Trajectory Analysis
The movement of airflow is deterministic to the particle trajectory. Under the three ventilation conditions (i.e., CA, CAF, and CAFT), the velocity vector of airflow near the infected occupant (Figure 6c) at the height of the breathing zone (Z = 1.1 m) is shown in Figure 7. Installing portable air purifiers changes the local flow directions and mitigates  table airflow that may cause cross-infection. The table unit, with proper capacity, displays explicit and favorable air inflow towards the purifier. The dispersion processes of the particles under the three flow fields are shown in Figure 8. The flow paths of the viral particles exhaled from the infected occupant are different for the three ventilation conditions. The particles under the CA system can easily arrive at the breathing zone of the opposite occupant. For the CAF system, the particles move up first and are then sucked by the floor-standing air purifier placed at the back, which purifies the air with the particles. The CAFT system presents a better purification performance, because most of the particles are directly sucked into the table purifier as well as pushed upwards due to the strong upward outflow from the top air exit of the unit. air purifiers and table air purifier (CAFT), to analyze the fate of the particles exhaled from the infected occupant.

Flow Field and Particle Trajectory Analysis
The movement of airflow is deterministic to the particle trajectory. Under the three ventilation conditions (i.e., CA, CAF, and CAFT), the velocity vector of airflow near the infected occupant (Figure 6c) at the height of the breathing zone (Z = 1.1 m) is shown in Figure 7. Installing portable air purifiers changes the local flow directions and mitigates the cross-table airflow that may cause cross-infection. The table unit, with proper capacity, displays explicit and favorable air inflow towards the purifier. The dispersion processes of the particles under the three flow fields are shown in Figure 8. The flow paths of the viral particles exhaled from the infected occupant are different for the three ventilation conditions. The particles under the CA system can easily arrive at the breathing zone of the opposite occupant. For the CAF system, the particles move up first and are then sucked by the floor-standing air purifier placed at the back, which purifies the air with the particles. The CAFT system presents a better purification performance, because most of the particles are directly sucked into the table purifier as well as pushed upwards due to the strong upward outflow from the top air exit of the unit.   air purifiers and table air purifier (CAFT), to analyze the fate of the particles exhaled the infected occupant.

Flow Field and Particle Trajectory Analysis
The movement of airflow is deterministic to the particle trajectory. Under the ventilation conditions (i.e., CA, CAF, and CAFT), the velocity vector of airflow ne infected occupant (Figure 6c) at the height of the breathing zone (Z = 1.1 m) is sho Figure 7. Installing portable air purifiers changes the local flow directions and mi the cross-table airflow that may cause cross-infection. The table unit, with proper cap displays explicit and favorable air inflow towards the purifier. The dispersion pro of the particles under the three flow fields are shown in Figure 8. The flow paths viral particles exhaled from the infected occupant are different for the three vent conditions. The particles under the CA system can easily arrive at the breathing z the opposite occupant. For the CAF system, the particles move up first and ar sucked by the floor-standing air purifier placed at the back, which purifies the air w particles. The CAFT system presents a better purification performance, because m the particles are directly sucked into the table purifier as well as pushed upwards the strong upward outflow from the top air exit of the unit.    Figure 9 compares quantitively the percentage of particles that are, respectively, discharged from the central exhausts, purified by the purifiers, and deposited on different surfaces under different ventilation conditions. Particles released from the mouth of the infector are convenient to spread in the horizontal direction under the central air-conditioning system (CA), especially at the height of the breathing zone. A small fraction of the particles is discharged through the exhaust outlets under CA. Most of them are spread out in the indoor space and then deposited on the diners (33%), the table (25%), the ground (25%), and the walls (11%). The floor-standing purifiers (FAP) can purifier 28% of the particles while increasing the particle deposition on the walls (48%) due to the redirected air inflow and outflow around the purifiers. The particle concentration at the height of the breathing zone under the CAFP system is smaller than that under the CA system. With the CAFP system, most of the viral particles are purified by the table air purifier (TAP)-about 76% of particles can be purified by TAP, a remarkable performance in purifying particles.

Fate Analysis of the Virus-Carrying Particles Exhaled from the Infected Occupant
(25%), and the walls (11%). The floor-standing purifiers (FAP) can purifier 28% of ticles while increasing the particle deposition on the walls (48%) due to the redire inflow and outflow around the purifiers. The particle concentration at the heigh breathing zone under the CAFP system is smaller than that under the CA syste the CAFP system, most of the viral particles are purified by the table air purifier about 76% of particles can be purified by TAP, a remarkable performance in p particles. To assess the quantitative performance of air purifiers on reducing infectio the reduction rate of the number of particles deposited on the surrounding occupa duction) is calculated by comparing the cases with and without air purifiers. Nreduct fined as in Equation (8): without air purifiers with air purifiers reduction without air purifiers where Nwithout air purifiers is the number of particles deposited on the occupants for without air purifiers, Nwith air purifiers is the number of particles deposited on the oc for the case with air purifiers. Using Equation (8) and the data in Figure 9, Nreduc tained for the CAF and CAFT cases, respectively, compared to the CA case, as Table 5. Nreduction of CAFT is greater than that of CAF, which verifies that the tabl rifier (TAP) has a superior performance in mitigating the infection risk. The optim tion of the air purifier will be in proximity where people are seated, congregated queue. The study of Mousavi et al. [23] indicated that the best location of a single air purifier unit is inside the isolation room and near the patient's bed. The resu study is, thus, consistent with the suggestion in the literature [23]. provides an effective m help mitigate airborne transmission of pathogens in the restaurant. TAP was fu vestigated to evaluate its application for one larger event (i.e., ballroom). The CFD of the ballroom (total space area 3200 m 2 ) built in ICEMCFD is shown in Figure 10  To assess the quantitative performance of air purifiers on reducing infection risks, the reduction rate of the number of particles deposited on the surrounding occupants (N reduction ) is calculated by comparing the cases with and without air purifiers. N reduction is defined as in Equation (8): N reduction = N without air purifiers − N with air purifiers N without air purifiers × 100% (8) where N without air purifiers is the number of particles deposited on the occupants for the case without air purifiers, N with air purifiers is the number of particles deposited on the occupants for the case with air purifiers. Using Equation (8) and the data in Figure 9, N reduction is obtained for the CAF and CAFT cases, respectively, compared to the CA case, as seen in Table 5. N reduction of CAFT is greater than that of CAF, which verifies that the table air purifier (TAP) has a superior performance in mitigating the infection risk. The optimal location of the air purifier will be in proximity where people are seated, congregated or in a queue. The study of Mousavi et al. [23] indicated that the best location of a single portable air purifier unit is inside the isolation room and near the patient's bed. The result of this study is, thus, consistent with the suggestion in the literature [23]. provides an effective means to help mitigate airborne transmission of pathogens in the restaurant. TAP was further investigated to evaluate its application for one larger event (i.e., ballroom). The CFD model of the ballroom (total space area 3200 m 2 ) built in ICEMCFD is shown in Figure 10 and the specifications of the ballroom are summarized in Table 6. The ballroom is full of diners (1320 total), with one of them infected ( Figure 10). One TAP is placed at the center of the dining table occupied by the infected person. Purifier specifications and particle release conditions, respectively, are shown in Tables 2 and 4. Particle trajectories were investigated, respectively, under two ventilation conditions: (1) central air-conditioning system (CA-Ballroom) and (2) central air-conditioning system with table air purifier (CAT), to analyze the fate of the viral particles exhaled from the infected occupant in the ballroom.
specifications of the ballroom are summarized in Table 6. The ballroom is full of d (1320 total), with one of them infected ( Figure 10). One TAP is placed at the center o dining table occupied by the infected person. Purifier specifications and particle re conditions, respectively, are shown in Tables 2 and 4. Particle trajectories were inv gated, respectively, under two ventilation conditions: (1) central air-conditioning sy (CA-Ballroom) and (2) central air-conditioning system with table air purifier (CAT analyze the fate of the viral particles exhaled from the infected occupant in the ballro

Flow Field and Particle Trajectory Analysis
The velocity vector of airflow at the height of the breathing zone (Z = 1.1 m) a table with the infector is shown in Figure 11, respectively, for the cases under two v lation conditions (i.e., CA-Ballroom and CAT). The table air purifier changes the local directions, displaying explicit and favorable air inflow towards the purifier. The dis sion processes of virus particles under the two flow fields are shown in Figure 12. spread range of the viral particles for the CA-Ballroom system is much larger than tha the CAT system, even reaching the neighboring tables. These particles, however, are fined around the purifier with the CAT system due to the negative pressure effect, w avoids the viruses' large-scale spread. Although the particles are not fully attracted b table purifier, the dispersion of the virus at the horizontal plane has been reduced si icantly by using TAP.

Flow Field and Particle Trajectory Analysis
The velocity vector of airflow at the height of the breathing zone (Z = 1.1 m) at the table with the infector is shown in Figure 11, respectively, for the cases under two ventilation conditions (i.e., CA-Ballroom and CAT). The table air purifier changes the local flow directions, displaying explicit and favorable air inflow towards the purifier. The dispersion processes of virus particles under the two flow fields are shown in Figure 12. The spread range of the viral particles for the CA-Ballroom system is much larger than that for the CAT system, even reaching the neighboring tables. These particles, however, are confined around the purifier with the CAT system due to the negative pressure effect, which avoids the viruses' large-scale spread. Although the particles are not fully attracted by the table purifier, the dispersion of the virus at the horizontal plane has been reduced significantly by using TAP.     Figure 13 compares the percentage of the particles that are, respectively, exhausted from the central air outlets, purified by the purifier, and deposited on different surfaces under the two ventilation conditions. Although only 12% of particles were purified by the TAP, which is attributed to the longer distance between the unit and the infector (the larger diameter of the dining table) compared to the restaurant case, the TAP helps reduce the deposition of particles on the occupants (potential cross-infection risk) from 29% to 11%. More particles were pushed up towards the ceiling (49%) due to the upward exit flow of the TAP, rather than distributing horizontally, which is a potential cause of crossinfection.
We obtained 60.3% of Nreduction for the CAT compared to CA-Ballroom using Equation (8) and the data in Figure 13. While this number is lower than that in the restaurant, it is still promising, especially considering the small size and capacity of the purifier. The arrangement of a table air purifier can be as effective as more elaborate solutions installed in the HVAC system at a lower cost. Flexible solutions, such as portable air purifiers, can be redeployed throughout the property as needed.  Figure 13 compares the percentage of the particles that are, respectively, exhausted from the central air outlets, purified by the purifier, and deposited on different surfaces under the two ventilation conditions. Although only 12% of particles were purified by the TAP, which is attributed to the longer distance between the unit and the infector (the larger diameter of the dining table) compared to the restaurant case, the TAP helps reduce the deposition of particles on the occupants (potential cross-infection risk) from 29% to 11%. More particles were pushed up towards the ceiling (49%) due to the upward exit flow of the TAP, rather than distributing horizontally, which is a potential cause of cross-infection.

Field Experiment and Analysis of Large Public Spaces
CFD simulation indicates that the installation of portable air purifiers can be fective measure to reduce the infection risks of aerosol transmission in large public To verify the actual performance of the purifiers in the real operation condition study further conducted the field experiment in two large public spaces (restaura ballroom). A commercial purifier (Blueair-411PACF105372) of 197.7 m 3 /h was in and tested in the experiment. Stage fog (water-glycerin-mixture) was used as a tra released from the mouth of the infector. The distribution of the fog was recorded as in Figure 14, under the central air-conditioning system with and without a purifie of the fog exhaled from the infector was sucked into the table air purifier, and the d uted area of the fog with the table purifier is much more confined than that witho purifier, similar to what was found in CFD simulation.
Similar performance was observed for the test in the ballroom ( Figure 15). Alt most of the released fog was not directly sucked in by the table purifier, the spread fog to the surrounding area was slowed down due to the table purifier. It appears t negative pressure area around the table purifier cannot completely cover the infec cupant when the unit is placed at the center of a large table. A more powerful table p will be required to provide a better performance. We obtained 60.3% of N reduction for the CAT compared to CA-Ballroom using Equation (8) and the data in Figure 13. While this number is lower than that in the restaurant, it is still promising, especially considering the small size and capacity of the purifier. The arrangement of a table air purifier can be as effective as more elaborate solutions installed in the HVAC system at a lower cost. Flexible solutions, such as portable air purifiers, can be redeployed throughout the property as needed.

Field Experiment and Analysis of Large Public Spaces
CFD simulation indicates that the installation of portable air purifiers can be an effective measure to reduce the infection risks of aerosol transmission in large public spaces. To verify the actual performance of the purifiers in the real operation conditions, this study further conducted the field experiment in two large public spaces (restaurant and ballroom). A commercial purifier (Blueair-411PACF105372) of 197.7 m 3 /h was installed and tested in the experiment. Stage fog (water-glycerin-mixture) was used as a tracer gas released from the mouth of the infector. The distribution of the fog was recorded as shown in Figure 14, under the central air-conditioning system with and without a purifier. Most of the fog exhaled from the infector was sucked into the table air purifier, and the distributed area of the fog with the table purifier is much more confined than that without the purifier, similar to what was found in CFD simulation.
in Figure 14, under the central air-conditioning system with and without a purifier. Most of the fog exhaled from the infector was sucked into the table air purifier, and the distributed area of the fog with the table purifier is much more confined than that without the purifier, similar to what was found in CFD simulation.
Similar performance was observed for the test in the ballroom ( Figure 15). Although most of the released fog was not directly sucked in by the table purifier, the spread of the  fog to the surrounding area was slowed down due to the table purifier. It appears that the  negative pressure area around the table purifier cannot completely cover the infected occupant when the unit is placed at the center of a large table. A more powerful table purifier will be required to provide a better performance.   Similar performance was observed for the test in the ballroom (Figure 15). Although most of the released fog was not directly sucked in by the table purifier, the spread of the fog to the surrounding area was slowed down due to the table purifier. It appears that the negative pressure area around the table purifier cannot completely cover the infected occupant when the unit is placed at the center of a large table. A more powerful table purifier will be required to provide a better performance.
CFD simulation indicates that the installation of portable air purifiers can be an effective measure to reduce the infection risks of aerosol transmission in large public spaces. To verify the actual performance of the purifiers in the real operation conditions, this study further conducted the field experiment in two large public spaces (restaurant and ballroom). A commercial purifier (Blueair-411PACF105372) of 197.7 m 3 /h was installed and tested in the experiment. Stage fog (water-glycerin-mixture) was used as a tracer gas released from the mouth of the infector. The distribution of the fog was recorded as shown in Figure 14, under the central air-conditioning system with and without a purifier. Most of the fog exhaled from the infector was sucked into the table air purifier, and the distributed area of the fog with the table purifier is much more confined than that without the purifier, similar to what was found in CFD simulation.
Similar performance was observed for the test in the ballroom ( Figure 15). Although most of the released fog was not directly sucked in by the table purifier, the spread of the fog to the surrounding area was slowed down due to the table purifier. It appears that the negative pressure area around the table purifier cannot completely cover the infected occupant when the unit is placed at the center of a large table. A more powerful table purifier will be required to provide a better performance.

Conclusions
COVID-19 is a test like no others. Never before have the lives of so many people around the world been affected at this scale or speed. In this study, the air purifier, as a facility recommended by organizations such as the US CDC and ASHRAE, was investigated for its actual performance in reducing the infection risks of the virus. The installation of air purifiers in two typical public places (i.e., restaurant and the ballroom) was studied, as compared to the use of the existing central air-conditioning systems. Validated CFD models were created and applied to explore the qualitative and quantitative performance of the portable air purifiers, which was further verified by a qualitative field experiment in the actual restaurant and ballroom.
The research outcomes reveal that the central air condition system only exhausts a small fraction of the particles released from the mouth of the infector, and most of the particles are spread out indoors and ultimately deposited on occupants, tables, equipment, ground, and walls. Both floor-standing and table air purifiers, with proper locations and capacities, can effectively attract room air to flow towards the purifiers and, therefore, clean the "contaminated" air. Similar behavior and performance were observed in the actual restaurant and the ballroom, while the results indicate that each space is unique in geometry, layout, and system and, thus, needs to be addressed individually. Flexible solution allows the redeployments of the cleaning devices throughout the property as needed. Portable air purifiers with HEPA filtration provide an effective means to help mitigate the airborne transmission of pathogens, which can be as effective as more elaborate solutions installed in the HVAC systems at a lower cost.