Numerical Study on the Impact of Large Air Purifiers, Physical Distancing, and Mask Wearing in Classrooms

Abstract

The risk of COVID-19 infection from virulent aerosols is particularly high indoors. This is especially true for classrooms, which often do not have pre-installed ventilation and are occupied by a large number of students at the same time. It has been found that precautionary measures, such as the use of air purifiers (AP), physical distancing, and the wearing of masks, can reduce the risk of infection. To quantify the actual effect of precautions, it is not possible in experimental studies to expose subjects to virulent aerosols. Therefore, in this study, we develop a computational fluid dynamics (CFD) model to evaluate the impact of applying the aforementioned precautions in classrooms on reducing aerosol concentration and potential exposure in the presence of index or infected patients. A CFD-coupled Wells–Riley model is used to quantify the infection probability (IP) in the presence of index patients. Different cases are simulated by varying the occupancy of the room (half/full), the volumetric flow rate of the AP, two different locations of the AP, and the effect of wearing masks. The results suggest that using an AP reduces the spread of virulent aerosols and thereby reduces the risk of infection. However, the risk of the person sitting adjacent to the index patient is only marginally reduced and can be avoided with the half capacity of the class (physical distancing method) or by wearing face masks of high efficiencies.

1. Introduction

One of the technological aspects of COVID-19 mitigation measures in schools involves using heating, ventilation, and air conditioning (HVAC) systems with high-efficiency filters such as HEPA (high-efficiency particle arresting) filters [1] or low-efficiency filters such as G4 [2] or EU8 filters [3], which are effective in reducing the aerosol concentration in a classroom. The choice of air purifier (AP), however, depends on several factors, such as the size of the room, removal efficiency, noise generated while in operation and the amount of pollutants or aerosols generated [4]. A properly designed ventilation system can restrict the transmission of contaminated aerosols and can dilute the viral concentration to mitigate infection risks, whereas a poorly designed ventilation system can aggravate the viral spread [5,6]. Thus, it becomes necessary to study the airflow due to the ventilation system to control the airborne transmission of virulent aerosols. Ovando Chacon et al. [7] showed that a favorable flow pattern for adequate classroom ventilation is obtained when the ventilation outlet and the inlet are located on the same side of the classroom as the air sweep covers all areas of the classroom, and the classroom remained at the thermal comfort temperature. This suggests that installing large a AP indoors, where the inlet and the outlet are located on the device, can be a convenient option whenever a centrally pre-installed HVAC system is not available.

Duval et al. [8] conducted a review of observational studies, which reported transmission events in indoor communities and found evidence that long-distance airborne transmission of the SARS-CoV-2 virus from asymptomatic or presymptomatic people in indoor settings is prominent where either there is a lack of ventilation with clean air or a directional airflow is present. Since the transport of virulent aerosols over large distances is mostly driven by ambient flows, several computational fluid dynamics (CFD) studies have been conducted to study the highly complex flows and spread of airborne viruses in indoor settings such as buses [9,10], trains [11,12], airplanes [13], offices [14], hospitals [15], and classrooms [16,17].

These studies focused on the impact of existing ventilation systems, either mechanical or natural, on the spread of virulent aerosols. Ren et al. [18] used a CFD-coupled Wells–Riley model (WRM) to study the airflow distribution and infection risk in a naturally ventilated classroom. The authors studied the effect of using window fans to bring clean air from outside into the classroom to dilute the concentration of virulent aerosols and reduce the risks of infection. However, the method of natural ventilation might not be suitable in all weather, such as during winter weather, where keeping the window open is not a suitable option. In such cases, using AP devices would be a better option. Abuhegazy et al. [19] also conducted a numerical study on the spread of aerosols in a classroom with a ceiling diffuser and inlets and showed that the students sitting near the vortex region of the flow field close to the edge of the room have significantly higher chances of aerosol transmission compared to the rest of the classroom. The authors also showed that using sneeze guards or glass barriers can effectively reduce the transmission of aerosols between students by 92% on average.

Kumar et al. [20] experimentally showed that the location of APs in a classroom has a significant effect in removing suspended particulate matter and to obtain the maximum benefit of the AP, it should be placed at the most polluted location inside the classroom. Curtius et al. [21] experimentally showed that using four small APs placed at different locations in a classroom operating at an air exchange rate of 5.5 h⁻¹ reduced the aerosol concentration by more than 90% in less than 30 min compared to a classroom where no AP was used and the windows and doors were closed. However, small APs generates noise of a sound level higher than 40 db(A) [21], which are considered disturbing for lessons in a classroom. Parhizkar et al. [22] carried out controlled clinical trials with 11 participants placed individually in a room and asked to carry out their daily activities such as walking on a treadmill, standing, sitting silently, or attending the online conferences and recorded the viral aerosol load at different locations inside the room. The authors found that increasing the air-exchange rate from outside or using APs yielded a reduced aerosol viral load and were likely to reduce the inhalation dose and the probability of infection in indoor spaces.

Duill et al. [17] experimentally studied the effect of using three different APs equipped with HEPA filters individually in the classroom to remove aerosol particles and showed that using large APs was effective in reducing 90% of the particles from the room in less than 26 min and the noise level was well within the acceptance level of 40 db(A). The authors showed that APs with different outlet and inlet characteristics gave different results for the decay of the aerosol particles, which suggests that the airflow from the AP can have a significant impact on restricting the spread of aerosols.

The above studies suggest that using an AP or a ventilation system with filtration requires prior consideration of the design of the AP, location of the AP, and operating conditions such as volumetric flow to have a uniform flow inside the classroom and restrict the spread of virulent aerosols. In this numerical study, we will focus on the use of a large AP corresponding to AP3 from the study of Duill et al. [17]. The impact of the use of APs on the spread of virulent aerosols from a single index (i.e., infected) patient or several index patients located at different locations will be assessed by quantifying the probability of infection calculated from the modified WRM. Additionally, further mitigation measures such as physical distancing and the use of face masks with different efficiency will be compared.

2. Materials and Methods

2.1. Simulation Model

In this paper, we develop a 3D CFD model to predict the flow inside the classroom, the temperature distribution, and the spread of virulent aerosols from index patients in the presence of the APs and students [17]. In our CFD model, the flow inside the classroom is assumed to be turbulent and is solved by solving a Reynolds-averaged Navier–Stokes (RANS) equation with the closure model [23] and the density variation due to temperature is modeled using the Boussinesq approximation generally considered for ventilation cases [24]. Oksanen et al. [25] experimentally showed from the air samples collected from hospital wards of COVID-19 patients and the homes of isolated patients that approximately 85% of the viral load exhaled by an index or infected patient is typically in aerosols smaller than 5 $\mathsf{\mu }$m. Within a turbulent airflow, sub-micron particles have a Stokes number with particle relaxation timescale ${\tau }_p$ < 0.1 s and fluid timescale ${\tau }_f$ commonly being $𝒪$(1 s)–$\mathcal{O}$(100 s), which suggests that the particle moves completely with the flow field. Thus, the spread of aerosols is modeled using the Eulerian approach by solving a scalar transport equation accounting for the diffusion and convection of aerosols [10].

To calculate the infection probability, a CFD-coupled Wells–Riley model (WRM) is used [11]. The CFD-coupled WRM offers an advantage over conventional WRM [26] by accounting for non-uniform quanta distribution due to the local flow field developed in an asymmetric volume space. Quanta represent the measure of infectious dose, where the intake of one quantum leads to a 63% probability of infection [26]. Wang et al. [11] used a CFD-coupled WRM to calculate the infection probability in long-distance trains in China and stochastically validated their results with the real-world data collected from long-distance trains in China by Hu et al. [27]. A similar approach has been applied in this study to calculate the infection probability (IP) in a classroom in the presence of index patients. In the CFD-coupled WRM, the distribution of infection probability is given by

$$\begin{array}{cc}\hfill IP& =1-e^{-c\nu t}\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill c& =\frac{qY}{\nu }\hfill \end{array}$$

(2)

where $IP$ is the infection probability, c is the quanta concentration, $\nu$ is the pulmonary ventilation rate, Y is the scalar value in the target volume, q is the quanta generated by the index patient (quanta/h), and t is the exposure time (h). To account for the effect of masks worn by both the susceptibles and the index patient on the given infection probability, Equation (1) can be further modified to

$$IP=1-e^{-(1-a)(1-b)c\nu t}$$

(3)

where a is the efficiency of a face mask in preventing the aerosols from the index patient and b is the efficiency of face masks preventing the aerosols from being inhaled by the susceptibles.

2.2. Cases Simulated

To study the effect of APs in a classroom, several cases have been simulated. The air purifier chosen for this study is the TAP-L from TROX (TROX GmbH, NeukirchenVluyn, Germany), which corresponds to the AP3 in the study by Duill et al. [17]. The outlet of the AP is at a height of 2.3 m above the ground, which directs the filtered air toward the front and sides, while the inlet of the AP is at the ground level with a 360° horizontal opening. The geometry of the class is defined as in our previous work [17], having a volume of 186.4 m${}^3$ with dimensions 9.5 m × 6.5 m × 3.05 m. In most of the classrooms the desks, chairs, and blackboard are arranged in a similar way as presented in the paper, where the students are sitting facing the classroom front. This arrangement leaves the back short side and the long side of the rooms open to place the AP centrally. Thus, different cases are studied where the AP is either placed in the middle of the short side of the room or in the middle of the long side of the room, as shown in Figure 1a,b, respectively. To accommodate the AP on the long side of the room, the width of the room is slightly increased from 6.5 m to 7.2 m, changing the total volume of the room from 186.4 m${}^3$ to 208 m${}^3$. The effect of the volumetric flow rate of the AP is studied by varying the volumetric flow rate for three different values: level 1 or 800 m${}^3/\mathrm{h}$, level 2 or 1000 m${}^3/\mathrm{h}$, and level 3 or 1200 m${}^3/\mathrm{h}$, where the volume flow rate for the chosen AP can be digitally adjusted between 400 and 1600 m${}^3/\mathrm{h}$ [17]. The turbulence intensity and the turbulence length scale at the outlet of the air purifier are assumed to be 2.5% and 0.1 m, respectively.

The effect of distancing is studied by simulating the classroom with 24 students and 12 students for classrooms operating at full and half capacity, respectively, as shown in Figure 1.

In all studies, along with the number of students mentioned above, a teacher is placed in front of the students. The students are modeled sitting with their mouths at a height of 122 cm above the ground, and the teacher is modeled standing with their mouth at 175 cm above the ground. The mouths of the students and teacher are modeled as a circular section of a cylinder having an area of 0.002 m${}^2$. The index patient exhales the aerosols (scalar value Y = 1.0) at a flow rate of 0.35 m${}^3/\mathrm{h}$, which is in accordance with the study carried out by Wang et al. [11]. The scalar value is initialized as 0 everywhere. A Dirichlet boundary condition is used at the AP outlet setting the scalar value as zero for 100% efficiency of the AP; everywhere else a Neumann boundary condition is used. The turbulence intensity of 10% and the turbulence length scale of 7.5 mm are assumed to be at the mouth of the infected person. To calculate the quanta concentration, a spherical target volume of a radius double the radius of the mouth is placed at the mouth of students and the teacher for integrating the target value. The students and the teacher have a body temperature of 307 K, and the room temperature is initialized at 298 K, with adiabatic boundary conditions for the walls, AP, and desks. Due to uncertainty in the boundary conditions of windows, these are not included in the present study. A steady flow field is set up for the above test cases for 1800 s, and then the evolution of aerosols from the index patient is then calculated for 3600 s by solving the scalar equation on the steady field obtained.

Four different scenarios are simulated to assess the different mitigation measures, as shown in Figure 2. The index patient is shown by the color red. Scenario 1 concerns a scenario where one index patient is present at the further end of the AP. Scenario 2 considers an index patient situated close to the AP. In scenario 3, two index patients are chosen, one in the middle of the room and one close to the AP. In scenario 4, the teacher in the front is the index patient. The parameters varied for the analysis of the above four scenarios are summarized in

Table 1. Summary of parameters considered for analysis.

Parameters	Values
Scenarios	1, 2, 3, 4 as shown in Figure 2
Position of AP	Short side at the back of the room
	Long side of the room
Volumetric flow rate of AP	Level 0: 200 m${}^3/\mathrm{h}$ (0% efficiency)
	Level 1: 800 m${}^3/\mathrm{h}$ (100% efficiency)
	Level 2: 1000 m${}^3/\mathrm{h}$ (100% efficiency)
	Level 3: 1200 m${}^3/\mathrm{h}$ (100% efficiency)
Number of students	Half capacity: 12 students
	Full capacity: 24 students
Masks	No mask (0% efficiency)
	Cloth mask (20% efficiciency)
	Surgical mask (40% efficiency)
	N95 mask (95% efficiency)

. In scenarios 1–3, the index patients are one of the students, and are assumed to be only breathing continuously throughout the duration of a class, so a quanta generation rate of 14 quanta/h is assumed, which represents the quanta generation rate between the 95th and 99th percentiles of a person breathing at rest [11]. In scenario 4, the teacher is speaking loudly and shedding virulent aerosols, so a quanta generation rate of 30 quanta/h is used, which represents the quanta generation rate of the 75th percentile while a person speaks loudly at rest [11,28,29]. For the assessment, the infection probability values are compared for the adjacent student (shown in purple color in Figure 2), students sitting at the back of the index patient, students sitting in the same row (green), and students in the adjacent row (yellow), and the overall average is compared. Only for scenario 4, where the teacher is the index patient, the infection probability is compared for adjacent students (purple), students sitting in front benches (purple+green), and middle row (yellow) along with the overall average values.

To study the effect of face masks, it is assumed that everyone in the class either does not wear a mask or wears a mask of the same efficiency. Three different face masks are chosen for this purpose with an efficiency of 20%, 40%, and 95% for simple cloth masks, surgical masks, and N95 masks, respectively [30].

3. Results

3.1. Validation

To validate the developed simulation model, experiments with up to four aerosol spectrometers of the type AQ Guard from PALAS GmbH were used. The spectrometers cover the particle measurement range 0.178–17.780 $\mathsf{\mu }$m in 64 size classes. The specifications given by the manufacturer can be found in the appendix of our previous work [17]. For the artificial generation of aerosol particles, the aerosol generator PAG 1000 from PALAS GmbH was used, which can provide a volume flow of 0.9–4.6 L/min. The flow rate of the aerosol generator can be adjusted (high and low), each from 0–100 %. Using DEHS at the high level and 100 % (4.6 L/min) 1.2 × 109 particles/s (1.6 × 107 particles/cm${}^3$) with a size of ≥0.2 $\mathsf{\mu }$m are generated. The experimental procedure is as follows: The experiments are carried out under reproducible environmental conditions. Before the actual measurement, the particles are added to the closed room using an aerosol generator. The aerosol particles are artificially generated for 15 min and distributed evenly in the room with a fan. After the generator is switched off, the particle concentration in the room is further homogenized with a fan for 3 min. This is monitored in real time using the aerosol spectrometers so that after a total of 18 min an aerosol concentration of 5500–6000 particles/cm${}^3$ on average can be measured. This is followed by the measurement with the air purifier, with the aerosol generator and the fan switched off. At the time of the measurement, there are no people in the room and the windows and doors of the room are closed. The decay rate is measured at two locations in the classroom, as shown in Figure 3: point MP1 at the further end of the room and point MP2 at the middle of the room.

The simulation is carried out for 2400 s for a 1000 m${}^3$/h volumetric flow rate and simulated using three different mesh sizes containing 2 M, 4.5 M, and 6 M cells, respectively. Figure 4 shows the computational results for all three different mesh sizes, coarse, medium, and fine, which are in good agreement with the experimental results. Hence, for all further simulations, the coarse mesh resolution is used. The decay rates calculated from the simulation are 5.473 h${}^{-1}$ and 5.451 h${}^{-1}$ for points MP1 and MP2, respectively, whereas from experiments the mean decay rate at both points is approximately 5.4 h${}^{-1}$, so this is in excellent agreement.

3.2. Airflow Pattern

The airflow pattern developed in the cases where the AP is operated at a volumetric flow rate of 1000 m${}^3/\mathrm{h}$ and is placed on the short side of the room and the long side of the room is shown in Figure 5a,b, respectively. It can be seen in Figure 5a that the flow from the top of the AP on the short side of the room is not sufficient to cover the length of the room. Thus, a vortex is formed above the head of the students mid-way through the length of the classroom. Increasing the volumetric flow rate from 1000 m${}^3/\mathrm{h}$ to 1200 m${}^3/\mathrm{h}$ only increases the vortex length marginally. The velocity vectors show that the flow from the vortex formed mid-way through the classroom is diverted at ground level, where a part of the flow goes to the other end of the room and returns back after hitting the wall. However, this circulation is much weaker compared to the vortex formed just ahead of the AP, resulting in less dilution of the concentration of aerosols generated with filtered air in front of the room than at the back of the room.

When the AP is placed on the long side of the room, the flow is uniformly distributed, covering the width of the room and reaching the other side of the room, as shown in Figure 5b. The velocity vectors show that the flow from the AP reaches the other side of the room and returns at the ground level after hitting the wall. The difference in the flow field becomes important when the filtered air from the AP is not sufficient to reach the other side of the room and restrict the spread of virulent aerosols if an index patient is situated there, as is the case when the AP is placed on the short side of the room.

3.3. Effect of Using an Air Purifier

To study the effect of using an AP, the results for the cases with an AP working at 100% efficiency (i.e., all particles are filtered) and three different operating levels are compared with an AP working at zero cleaning efficiency (i.e., all particles are allowed to pass through) and 200 m${}^3/\mathrm{h}$ volumetric flow rate. A flow rate of 200 m${}^3/\mathrm{h}$ is randomly chosen to obtain a flow distribution inside the classroom. The results from the classroom operating at full capacity (i.e., 24 students) with none of the students or the teacher wearing a face mask and the AP placed at either the short or the long sides of the room are used. In the consecutive Figures, the filled circles are for the AP placed on the short side of the room, and crosses represent the AP placed on the long side of the room unless otherwise mentioned. The black color crosses or circles represent the AP working at zero efficiency with a volumetric flow rate of 200 m${}^3/\mathrm{h}$, whereas the circles and crosses with green, blue, and red colors are the AP working at 100% efficiency with volumetric flow rates of 800 m${}^3/\mathrm{h}$, 1000 m${}^3/\mathrm{h}$, and 1200 m${}^3/\mathrm{h}$, respectively. The Y-axis on the plots shows the infection probability in %, and the X-axis shows different positions: adjacent to the index patient, behind the index patient, in the same row as the index patient, in the row adjacent to the index patient, and the overall average in the whole class. Figure 6a shows the results for scenario 1, where the student at the further end of the AP is the index patient. The probability of infection (or the infection probility, IP) for the student seating adjacent to the index patient is reduced by 9.0% when the AP is on the short side of the room and 8.1% when the AP is on the long side of the room. For the students seated at the back and in the same row as the index patient, a maximum of 52.0% and 46.0% reductions, respectively, is seen in the infection probability when the AP is placed on the long side of the room. The reduction in the overall average probability of infection in the classroom for both cases where the AP is placed on the short side or the long side of the room is more than 30%.

Figure 6b shows the results for scenario 2, where the index patient is placed at a favorable place near the AP. The IP values for the person sitting adjacent to the index patient have reduced by more than 60% for the AP on the short side of the room and more than 80% for the AP placed on the long side of the room. For all the measured positions, it can be seen that the IP values have shown more than a 50% reduction when the AP is used at the highest volumetric flow rate and full efficiency compared to the AP operating a zero efficiency. Comparing the results of scenario 2, Figure 6b, where the index patient is sitting closer to the AP than in scenario 1, Figure 6a, we can see that overall IP values decrease when the infected student is closer to the AP. For cases when the AP is operating at the short side and long side of the room 33% and 65% reduction in overall IP values, respectively, is seen from scenario 1 to scenario 2 for different volumetric flows of AP operating at 100% efficiency.

Figure 6c shows the results for scenario 3, where two students are the index patient, one student sitting near the AP and the other one sitting in the middle of the classroom. In the case of multiple sources of virulent aerosols, the use of the AP shows that a more than 40% reduction in the IP values can be obtained for all the measured positions. Figure 6d shows the result for scenario 4, a super-spreader event when the teacher is the index patient and speaks loudly. Here, the results show that a reduction of 20% in the IP values can be achieved for students in front of the teacher and the overall average can be reduced by 30%.

The results above show that using an AP restricts the spread of virulent aerosols and consequently reduces the risk of infections by a significant amount. Increasing the volumetric flow shows a reduction in the IP values except for cases when the susceptible student is adjacent to the index patient or the index patient is situated at the further end of the AP, as in scenario 1, where only a marginal reduction in IP values is seen when the volumetric flow is increased. The reduction in IP was also seen numerically [31] when increasing the volumetric flow rate from the ventilation system in classrooms using a similar concept of CFD-coupled WRM.

3.4. Effect of Location of an Air Purifier

It can be seen from Figure 6 that in all scenarios, the IP values for the cases where the AP is placed on the long side of the room are either comparable or lower to the IP values when the AP is placed on the short side of the room. This suggests that the location of the AP impacts the overall distribution of the virulent aerosols in the classroom. To clearly show the effect of the location of the AP, scenarios 3 (Figure 7) and 4 (Figure 8) are chosen with the AP working at level 2 or 1000 m${}^3/\mathrm{h}$. Figure 7 and Figure 8 show the quanta concentration on the plane at the level of the mouths of students after 1 h in the classroom for scenarios 3 and 4, respectively. The quanta concentration is capped at 0.103 quanta$/{\mathrm{m}}^3$. It is seen that when the AP is placed on the long side of the room, the overall distribution of quanta concentration is much less compared to what can be seen in Figure 7a, where the AP is placed on the short side of the room. The quanta concentration for the AP placed on the short side of the room is much higher in the front of the room compared to the back of the room, as the filtered air from the AP reaches only the mid-point of the room and is not sufficient to reach the other end of the room, as shown in the previous Section 3.2. The filtered air from the AP placed on the long side of the room sufficiently covers the further end of the room and thus dilutes the concentration of virulent aerosols more uniformly than the AP on the short side of the room. In Figure 7b it can be seen that the student sitting in front of the index patient and right next to the AP experiences a higher quanta concentration than the student sitting adjacent to the index patient due to the suction of the AP inlet causing the contaminated air to flow towards the inlet for filtering. This effect of suction from the AP can also be seen when the AP is placed on the short side of the room, as in Figure 7a, where an increase in the quanta concentration can be seen in the empty place behind the index patient compared to the other side of the AP. The suction effect can be clearly seen by the velocity vectors of flow towards the AP. This suggests that sitting close to the AP should be avoided to avoid the virulent aerosols flowing toward the AP inlet.

The effect of the location of the AP can be further seen in scenario 4, in Figure 8, when the teacher is the index patient and speaks loudly. In Figure 8a it can be seen that when the AP is placed on the short side of the room, a very high quanta concentration due to the super-spreader event can be seen in the front of the room compared to the back of the room. When the AP is placed on the long side of the room (Figure 8b) the quanta concentration is higher at the room’s opposite corner than the room’s overall volume. It can be seen that compared to the AP on the short side of the room, the AP on the long side of the room has a lower overall quanta concentration distribution.

Thus, it can be concluded that the location of the AP has a significant impact on the virulent aerosol distribution in the classroom and that the optimum position is to place the AP in such a way that filtered air reaches uniformly throughout the classroom.

3.5. Effect of Wearing a Face Mask

Wearing a face mask restricts the spread of the virulent aerosol in two ways: by capturing the aerosols at the source and by the prevention of inhalation of the virulent aerosol. Wang et al. [13] used CFD-coupled WRM to study the risks of infection in a 12 h journey in an aircraft with a ventilation system and showed that wearing even 30% to 60 % efficiency face masks can reduce the overall average infection probability by 47% to 86% and the maximum infection probability by 32% to 73%.

In this study, Figure 9 shows the infection probability results when the AP is operating at the lowest level of 800 m${}^3/\mathrm{h}$ with the full capacity of the classroom (i.e., 24 students). It is assumed that everyone is either not wearing a mask or wearing a mask with the same efficiency. Three masks with different operating efficiencies are considered: (1) cloth masks with a 20% efficiency (shown in the color red), (2) surgical masks with a 40% efficiency (shown in the color blue), and (3) N95 masks with a 95% efficiency (shown in the color green). Further, the IP values with masks are compared to the IP values in the case where no one in the class is wearing a mask (shown in the color black). The filled circles represent the results when the AP is placed on the short side of the room and the cross represents the results when the AP is placed on the long side of the room. It can be seen, that in general, wearing a mask can significantly reduce the IP compared to the IP values when no one is wearing a mask. In all the scenarios, the IP values for the student sitting adjacent to the index patient are reduced by approximately 32% for cloth masks, more than 64% for surgical masks, and nearly 99% for N95 masks. Wearing even just the homemade cloth mask shows an overall 30% reduction in overall average IP values in the classroom and wearing a surgical mask shows more than a 60% reduction in the overall average IP values. Furthermore, if everyone wears an N95 mask in the classroom, which captures 95% of virulent aerosols from the index patient and prevents the susceptibles from inhaling 95% of aerosols, the risks of infection can be successfully averted, as shown by IP values very close to zero.

Thus, it can be concluded that wearing a face mask can significantly reduce the chances of infection and have the classroom operating at full capacity. Better results are obtained when a mask of high efficiency, such as an N95, is worn by everyone in the classroom compared to cases when a mask of lower efficiency is worn by everyone. This conforms to the experimental study carried out by Oksanen et al. [25], where the families that took respiratory protection such as surgical or FFP2 masks were able to prevent infections even when the air and surface samples from their houses tested positive for the SARS-CoV-2 virus.

3.6. Effect of Physical Distancing

Physical distancing has shown positive impacts in avoiding the risks of infection. Jonker et al. [32] stochastically found that compared to the pre-lockdown phase, a 40% reduction in the weekly SARS-CoV-2 incidence rate was seen during post-lockdown phase in 18 schools where measures such as reduced class occupancy, stricter quarantine rules, and expanded access to SARS-CoV-2 testing were implemented. Figure 10 shows the impact of physical distancing by comparing the IP values for classrooms operating at full capacity and at half capacity with the AP working at the lowest and highest volumetric flow rates. Moreover, the results of IP values of cases with a full capacity of classroom where everyone is wearing a surgical mask with 40% efficiency are also simulated and shown by triangles and squares. Black and blue color symbols represent the cases with the classroom operating at full capacity having the AP operating at 800 m${}^3/\mathrm{h}$ and 1000 m${}^3/\mathrm{h}$, respectively. The red and green symbols represent the classroom operating at half capacity where the AP operates at 800 m${}^3/\mathrm{h}$ and 1000 m${}^3/\mathrm{h}$, respectively. Circles and triangles represent the AP on the short side of the room, and crosses and squares represent the AP on the long side of the room.

Due to the obvious absence of an adjacent student when the class is operating at half capacity, the risk of infection to the adjacent student can be avoided. For other measured points, it can be seen that the IP values are either comparable to the IP values for classroom operating at full capacity or lower than those. However, it is noted that the average values for the half capacity of the class will have half the number of susceptible students compared to the full capacity of the class and hence almost half the number of infections.

In all the scenarios, it can be seen that for a classroom operating at full capacity and everyone wearing a surgical mask, shown by suffix “M” in Figure 10, the IP values are nearly halved or lower than the IP values for a classroom operating at half capacity and where none of the students are wearing a mask, shown by suffix “H” in Figure 10. This suggests that even when the classrooms are operating at full capacity, results comparable to a classroom operating at half capacity can be obtained with the use of masks.

4. Conclusions

This paper describes a computational fluid dynamics (CFD) study a using CFD-coupled Wells–Riley model (WRM) to study the impact and limitations of precautionary measures to restrict the spread of virulent aerosols in classrooms using commonly available air purifiers (APs). It is shown that using an AP has a significant impact on restricting the spread of aerosols, where a reduction of 30% to 40% in the overall average infection probability (IP) values is seen for the scenarios where the AP is operating at 100% efficiency compared to classrooms without particle filtration. Moreover, the IP values are reduced by increasing the volumetric flow rate of the AP, except for the case when the student is sitting adjacent to the index patient, where only a marginal reduction in the IP value is seen. The location of the AP also has a significant impact on the IP reduction rates, especially in the cases where there are two index patients in the class or in the super-spreader event of a loudly speaking teacher being the index patient. It is observed that placing the AP on the short side or in the back of the room allows a higher concentration of virulent aerosols in the front of the room than in the back of the room. This is due to the flow caused by the applied AP, where the filtered air from the AP could not reach the further end of the class. When the AP is placed on the long side of the room, a much lower and uniform distribution of virulent aerosols is observed as the filtered air from the AP sufficiently covers the whole classroom and dilutes the concentration of virulent aerosols. From this, it can be deduced that the flow caused by the AP has a significant impact on its cleaning effect and consequently on the probability of infection. In this paper, the effect of three different masks is also studied, which showed that if everyone uses a mask in a classroom operating at full capacity, a significant reduction in the risk of infection is seen. Masks of high efficiency, such as N95, can be used to almost completely avoid infection risks. It is observed that although physical distancing can reduce the risk of infection by half, similar results can be obtained by wearing a surgical mask in a classroom operating at full capacity. Thus, in crowded indoor places or where it is not possible to operate the facility at half capacity, masks and using APs can have a significant impact in reducing the risks of infection.