# Prevention and Control of the Spread of Pathogens in a University of Naples Engineering Classroom through CFD Simulations

^{*}

## Abstract

**:**

_{2}contour zones at fifteen-minute intervals for a total duration of two hours, the probability of infection was calculated using the Wells–Riley equation.

## 1. Introduction

_{2}O) and particles (0.07, 0.7 and 3.5 μm) in a room [7]. The gas and particle concentrations were measured in the main part of the room and in the breathing zone of the dummy. The results showed that the use of tracer gas in the breathing zone of the seated dummy allows reliable prediction of the characteristic dispersion pathways for all three particle types investigated, regardless of the variation in ventilation rate and the presence of objects in the room [7].

_{2}O) and particulate matter (3–5 μm) were released from a heated cylinder simulating a bedridden patient. The results showed that both the N

_{2}O tracer gas and the particles well simulated the behavior of bioaerosols [9].

_{2}as the tracer gas were examined. Results show that the spatial distribution of particles no larger than 2.5 μm is very close to that of the tracer gas [11]. A study by Beato-Arribas et al. (2015) concluded that the distributions of CO

_{2}tracer gas and aerosolized Bacillus bacterium detected within an isolated hospital room in which 12 hourly changes are performed show comparable results [12].

- The ventilation system is on and operating according to current guidelines; the mask is not worn by the infected student.
- The ventilation system was turned off; the mask was not worn by the infected student.
- The ventilation system is on and functioning according to current guidelines; the mask is worn by infected students.
- The ventilation system is on (flow rate tripled); the mask is not worn by the infected student.
- The ventilation system is on (flow rate tripled); the mask is worn by the infected student.

- 6.
- The exposed students and/or teachers are not wearing PPE.
- 7.
- The exposed students and/or teachers are wearing surgical masks.
- 8.
- The exposed students and/or teachers are wearing FFP2 masks.

## 2. Methodology

#### 2.1. CFD Model: Geometrical Domain

^{3}. Next, the model was spatially constructed using Autodesk AutoCAD 2021 software. As reported in Figure 1, there are different air supply elements that are better visible and described in Figure 2. The ventilation system is characterized, as shown in Figure 2a, by ten square air supply elements with dimensions of 0.6 m × 0.6 m and two rectangular elements with dimensions of 6.67 m × 0.15 m. The return air characteristic elements, as highlighted in Figure 2b, are six and rectangular in size, equal to 0.96 m × 0.36 m. The guaranteed hourly changes, as shown in the circular issued by the university, are five, and per the current COVID-19 standard, 100% fresh air is provided. Then, the indoor air, once directed to the supply air duct, is expelled to the outside [23]. Noting the geometry and relevant characteristics of the ventilation system, it was possible to calculate the velocity of airflow from the single supply element with a value of 0.3 m/s.

#### 2.2. CFD Model: Mesh Building

#### 2.3. CFD Model: Equations and Boundary Conditions

_{2}is an excellent biomarker of exhaled breath for risk assessment since it has a density similar to the air-particle cloud of suspended viruses. It is naturally released through exhaled breath along with the virus, and it was already used in previous works [12]. The transient flow of the continuous phase treated as an ideal gas and consisting of two components (air and CO

_{2}), was simulated by means of the Ansys Fluent software (version 2021 R2) using the time-averaged Navier–Stokes equations (URANS), the Eulerian approach and implementing the k-ε model as a turbulent sub-model.

^{−3}) is the fluid density, $\mathit{u}$ (m s

^{−1}) is the fluid velocity vector, $p$ (Pa) is the static pressure, $\mathit{\tau}$ (Pa) is the stress tensor, and $\mathit{g}$ (m s

^{−2}) is the gravity vector. With regards to the species transport, Ansys predicts the local mass fraction of the species through the solution of a convection–diffusion equation for the species. The conservation equation takes the following general form:

_{2}, ${\mathit{J}}_{C{O}_{2}}$ (kg m

^{−2}s

^{−1}) is the diffusion flux of CO

_{2}which arises due to gradients of concentration and temperature, ${D}_{C{O}_{2},m}$ (m

^{2}s

^{−1}) is the mass diffusion coefficient for CO

_{2}, ${\mu}_{T}$ (Pa s) is the turbulent viscosity, $S{c}_{T}$ (−) is the turbulent Schmidt number, ${D}_{C{O}_{2},T}$ (m

^{2}s

^{−1}) is the thermal (Soret) diffusion coefficient, $T$ (K) is the absolute temperature.

_{2}, and temperature equal to 310.15 K. The velocity can take a value of 0.5 m/s if the infected individual wears the FFP2 mask, while it is equal to 1 m/s in its absence [24]. The student’s body was set as a wall, generating a heat flux value equal to 70 W/m

^{2}. Twelve velocity inlet type boundary conditions were set at the twelve supply elements of the ventilation system with the following characteristics: zero CO

_{2}mass fraction (100% fresh air from outside, no internal recycling), temperature set at 293.15 K, variable airflow velocity (0 m/s with the system off, 0.3 m/s normal operation, 0.9 m/s with tripled outside airflow rate). The six return elements were set as pressure outlets with the null value of gauge pressure. The floor, roof, and perimeter wall of the classroom were set as walls with null heat flow (adiabatic system). In the initialization of the solution (standard initialization), the room temperature was set to 293.15 K and the CO

_{2}mass fraction to zero. In Table 2, we briefly summarize the main boundary conditions for the five case studies; as you can see, the differences between the various scenarios reside solely in the different values of the velocity of the supply elements (inlet air velocity) and in the velocity of the CO

_{2}flow coming from the infected individual (inlet mouth velocity), it is the latter in fact that determine different ventilation conditions and presence or absence of the FFP2 mask. In particular, in Case 1 and Case 3, the air velocity was set at 0.3 m/s, a value corresponding to the actual level of ventilation existing in Classroom C, while in Case 4 and Case 5, the ventilation rate was triplicated in order to investigate its effect on the infected cloud dispersion. In Case 2, the ventilation rate was 0 m/s; thus, the ventilation was off (worst-case scenario). Regarding the inlet mouth velocity, in Case 1, Case 2 and Case 4, it is equal to 1 m/s and represents the case in which the infected student did not wear PPE, while in Case 4 and Case 5, the student wore a FFP2 mask, and the velocity of the infected cloud is set at a reduced value. A pressure outlet boundary condition at atmospheric pressure was set for all the outlets.

#### 2.4. Calculations of Infection Probability

_{0}is the concentration at which 100% probability of infection corresponds, and it is set to 60,000 ppm [27], E is the variable concentration of CO

_{2}as a function of time and space. In the case where the individual exposed to SARS-CoV-2 is wearing a face mask, it is necessary to introduce the efficiency ${\eta}_{s}$ of the mask:

## 3. Results

#### 3.1. Results Case 1

_{2}concentration at intervals of 15 min, starting at time 0 (beginning of the lesson) up to 120 min (end of the lesson) on the sectional plane at a height of 1.65 m above the floor. The CO

_{2}concentration, which is representative of the virus concentration, varies from 0 ppm (blue color) to 1000 ppm (red color), the minimum value. The highest levels of carbon dioxide concentrations are measured near the infected person and at the back of the classroom.

#### 3.2. Results Case 2

_{2}concentration at regular intervals of 15 min. A wave of CO

_{2}concentration can be observed spreading through the classroom and reaching an almost uniform concentration after 2 h. As can be seen, high CO

_{2}levels of up to 1000 ppm can be seen, particularly at the back of the classroom. It should be noted that the ventilation systems are all located on the ceiling, while the outlet areas are mainly located at the back of the classroom, so the cloud is preferentially located at the back due to the resulting flow field.

#### 3.3. Results Case 3

_{2}concentration at regular intervals of 15 min. The concentration map is similar to that of Case 1, but the areas of high concentration are more limited due to the infected person’s face mask.

#### 3.4. Results Case 4

_{2}concentration at regular intervals of 15 min, starting at time 0 (beginning of the hour) up to a maximum of 120 min (end of the hour). In comparison to Case 1, although the infected person is not wearing a mask, the high concentration zone is only maintained in the areas immediately next to the person due to the optimized ventilation.

#### 3.5. Results Case 5

_{2}concentration at regular intervals of 15 min. Compared to Case 4, the presence of PPE in the infected person leads to a significant reduction in the extent of the high CO

_{2}concentration zone, reaching an average concentration of less than 100 ppm in the classroom. In addition, the zone of high CO

_{2}concentration is practically limited to the position of the infected student, which is an indication that a lower escape velocity combined with the presence of PPE and optimized ventilation can reduce the impact zone and, thus, the risk of infection.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Characteristic measurements of Classroom C at the University of Naples Federico II. The top view shows maximum width and length (

**a**), the side view shows average and maximum wall height (

**b**) and was drawn with Autodesk Autocad 2021 software.

**Figure 2.**The twelve characteristic elements of the supply (

**a**) and return elements of the ventilation system (

**b**) were drawn with Autodesk Autocad 2021 software.

**Figure 3.**Contour maps in terms of carbon dioxide concentration were obtained every 15 min in Case 1.

**Figure 9.**Trends of the infection probability in the classroom as a function of the presence of DPI and kind in all the five analyzed cases for different positions: 1 m away from the infected student (

**a**), typical professor position (7 m, (

**b**)), and 3 m away from the infected student (

**c**,

**d**).

**Table 1.**Comparison of the number of nodes, elements and average orthogonal quality among the used meshes.

Information about Mesh | Sparser Mesh | Sparse Mesh | Dense Mesh | Denser Mesh |
---|---|---|---|---|

Nodes number | 180,502 | 461,301 | 660,654 | 774,116 |

Elements number | 972,754 | 2,467,544 | 3,539,133 | 4,149,493 |

Average orthogonal quality | 0.751 | 0.753 | 0.754 | 0.747 |

Case | Description | Inlet Air Velocity | Inlet Mouth Velocity | Outlet Air Gauge Pressure |
---|---|---|---|---|

Case 1 | Ventilation on Mask off | 0.3 m/s | 1 m/s | 0 Pa |

Case 2 | Ventilation off Mask off | 0 m/s | 1 m/s | 0 Pa |

Case 3 | Ventilation on Mask on | 0.3 m/s | 0.5 m/s | 0 Pa |

Case 4 | Hyperventilation on Mask off | 0.9 m/s | 1 m/s | 0 Pa |

Case 5 | Hyperventilation on Mask on | 0.9 m/s | 0.5 m/s | 0 Pa |

**Table 3.**Probability calculations were performed for Case 1 after 15 min, considering students and the teacher without DPI, with surgical and FFP2 masks.

Position | E (ppm) | DR | Probability without DPI | Probability with Surgical Mask | Probability with FFP2 Mask |
---|---|---|---|---|---|

a | 600 | 100 | 7.2% | 5.1% | 1.9% |

b | 750 | 80 | 8.9% | 6.4% | 2.3% |

c | 950 | 63 | 11.2% | 8.0% | 2.9% |

d | 300 | 200 | 3.7% | 2.6% | 0.9% |

e | 50 | 1200 | 0.6% | 0.4% | 0.2% |

f | 300 | 200 | 3.7% | 2.6% | 0.9% |

g | 600 | 100 | 7.2% | 5.1% | 1.9% |

h | 200 | 300 | 2.5% | 1.7% | 0.6% |

i | 600 | 100 | 7.2% | 5.1% | 1.9% |

**Table 4.**Probability calculations were performed for Case 2 after 15 min, considering students and the teacher without DPI, with surgical masks and with FFP2 masks.

Position | E (ppm) | DR | Probability without DPI | Probability with Surgical Mask | Probability with FFP2 Mask |
---|---|---|---|---|---|

a | 1000 | 60 | 11.8% | 8.4% | 3.1% |

b | 1000 | 60 | 11.8% | 8.4% | 3.1% |

c | 1000 | 60 | 11.8% | 8.4% | 3.1% |

d | 800 | 75 | 9.5% | 6.8% | 2.5% |

e | 800 | 75 | 9.5% | 6.8% | 2.5% |

f | 800 | 75 | 9.5% | 6.8% | 2.5% |

g | 850 | 71 | 10.1% | 7.2% | 2.6% |

h | 800 | 75 | 9.5% | 6.8% | 2.5% |

i | 850 | 71 | 10.1% | 7.2% | 2.6% |

**Table 5.**Probability calculations were performed for Case 3 after 15 min, considering students and the teacher without DPI, with surgical masks and with FFP2 masks.

Position | E (ppm) | DR | Probability without DPI | Probability with Surgical Mask | Probability with FFP2 Mask |
---|---|---|---|---|---|

a | 950 | 63 | 11.2% | 8.0% | 2.9% |

b | 950 | 63 | 11.2% | 8.0% | 2.9% |

c | 950 | 63 | 11.2% | 8.0% | 2.9% |

d | 400 | 150 | 4.9% | 3.4% | 1.2% |

e | 50 | 1200 | 0.6% | 0.4% | 0.2% |

f | 600 | 100 | 7.2% | 5.1% | 1.9% |

g | 400 | 150 | 4.9% | 3.4% | 1.2% |

h | 50 | 1200 | 0.6% | 0.4% | 0.2% |

i | 50 | 1200 | 0.6% | 0.4% | 0.2% |

**Table 6.**Probability calculations performed for Case 4 after 15 min, considering students and the teacher without DPI, with surgical masks and with FFP2 masks.

Position | E (ppm) | DR | Probability without DPI | Probability with Surgical Mask | Probability with FFP2 Mask |
---|---|---|---|---|---|

a | 950 | 63 | 11.2% | 8.0% | 2.9% |

b | 950 | 63 | 11.2% | 8.0% | 2.9% |

c | 950 | 63 | 11.2% | 8.0% | 2.9% |

d | 300 | 200 | 3.7% | 2.6% | 0.9% |

e | 50 | 1200 | 0.6% | 0.4% | 0.2% |

f | 150 | 400 | 1.9% | 1.3% | 0.5% |

g | 150 | 400 | 1.9% | 1.3% | 0.5% |

h | 50 | 1200 | 0.6% | 0.4% | 0.2% |

i | 50 | 1200 | 0.6% | 0.4% | 0.2% |

**Table 7.**Probability calculations performed for Case 5 after 15 min, considering students and the teacher without DPI, with surgical masks and with FFP2 masks.

Position | E (ppm) | DR | Probability without DPI | Probability with Surgical Mask | Probability with FFP2 Mask |
---|---|---|---|---|---|

a | 950 | 63 | 11.2% | 8.0% | 2.9% |

b | 950 | 63 | 11.2% | 8.0% | 2.9% |

c | 350 | 171 | 4.3% | 3.0% | 1.1% |

d | 50 | 1200 | 0.6% | 0.4% | 0.2% |

e | 50 | 1200 | 0.6% | 0.4% | 0.2% |

f | 150 | 400 | 1.9% | 1.3% | 0.5% |

g | 50 | 1200 | 0.6% | 0.4% | 0.2% |

h | 50 | 1200 | 0.6% | 0.4% | 0.2% |

i | 50 | 1200 | 0.6% | 0.4% | 0.2% |

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**MDPI and ACS Style**

Portarapillo, M.; Simioli, S.; Di Benedetto, A.
Prevention and Control of the Spread of Pathogens in a University of Naples Engineering Classroom through CFD Simulations. *ChemEngineering* **2024**, *8*, 37.
https://doi.org/10.3390/chemengineering8020037

**AMA Style**

Portarapillo M, Simioli S, Di Benedetto A.
Prevention and Control of the Spread of Pathogens in a University of Naples Engineering Classroom through CFD Simulations. *ChemEngineering*. 2024; 8(2):37.
https://doi.org/10.3390/chemengineering8020037

**Chicago/Turabian Style**

Portarapillo, Maria, Salvatore Simioli, and Almerinda Di Benedetto.
2024. "Prevention and Control of the Spread of Pathogens in a University of Naples Engineering Classroom through CFD Simulations" *ChemEngineering* 8, no. 2: 37.
https://doi.org/10.3390/chemengineering8020037