# Reducing Virus Transmission from Heating, Ventilation, and Air Conditioning Systems of Urban Subways

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## Abstract

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## 1. Introduction

## 2. Numerical Method and Simulation Setup

#### 2.1. Formulation of the Subway HVAC Air Flows in the Cabin

_{0}, p, u, C, T, k, and ${D}_{eff}$ are the density, reference density, dynamic pressure, velocity, aerosol concentration, temperature, thermal conductivity, and diffusivity of the fluid, respectively. In Equation (3), the Boussinesq approximation is used for the momentum equation. In addition, in Equation (4), ${D}_{eff}$ = $\frac{{\nu}_{t}}{S{c}_{t}}+\frac{\nu}{Sc}$, where Sc

_{t}and Sc are the turbulent and laminar Schmidt numbers, respectively, and Sc

_{t}= Sc = 1 [36]. In this study, a filter-based approach is used, which combines parts from both large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equations (RANS) and compares the length of the characteristic with the mesh size-spatial filter to re-establish the turbulent viscosity as follows:

_{3ε}= 1 in the present case. To ensure that the numerically resolvable scale is compatible with the filtering process, the lower bound of the filter is set as ${\Delta}_{grid}$, where ${\Delta}_{grid}={(\Delta x\Delta y\Delta z)}^{\frac{1}{3}}$. The standard k–ε turbulence model is used in the following equations:

_{ij}is the convection term; D

_{T,ij}is the turbulent diffusion term; D

_{L,ij}is the molecular diffusion term; P

_{ij}is the stress production term; G

_{ij}is the buoyancy production term; φ

_{ij}is the pressure strain term; ε

_{ij}is the dissipation term; and F

_{ij}is the production by the system rotation.

#### 2.2. Numerical Technique and Boundary Conditions

^{−5}, 10

^{−8}, 10

^{−7}, and 10

^{−8}, respectively. To simulate aerosol movement within the urban subway, we ignored (i) the generation and (ii) interaction (collision) of particles due to the cloudy behavior of breath aerosols. The aerosol concentration is sensitive to the HVAC-induced airflow pattern, temperature, and ambient pressure. Among these environmental factors, relative humidity is a determinant parameter that strongly influences respiratory particle size during breathing. Various studies, such as those by Zhang et al. [36] and Liu et al. [29], demonstrated the traveling distance of respiratory particles based on their weight and size. The smallest particles were neutrally buoyant at a relative humidity of 20% and moved passively with the carrier fluid. Therefore, we ignored the Brownian motion of the particles and used a buoyant solver in OpenFOAM. In this method, gravity effects are considered instead of using the Lagrangian particle transport equation with Brownian motion. Zhang et al. [36] applied the buoyancy method to demonstrate respiratory particle transmission. However, both approaches are suitable.

^{2}; for category B, this value was lower or equal to 4 passengers/m

^{2}. The DIN EN-14750-1:2006 standard notes that the minimum fresh air rate for categories A and B are 14 and 10 hr

^{−1}, respectively. Furthermore, the Ashrae standard [64] determined that the air quality inside urban subway should be kept within the ranges of 10 to 13 hr

^{−1}to provide adequate protection for public health. In this paper, category B satisfied our passengers’ configurations. In this study, the air change rate (ACR) of the urban cabin was 10 hr

^{−1}. The temperature values of the supply air, human breath, ambiance, and other cabin interior surfaces (such as mannequins, seats, and walls) were set at 20 °C, 30 °C, 25 °C, and 27 °C, respectively. The supply temperature was selected based on the standard ambient temperature for summer season. The temperature of a healthy human being is approximately 37 °C, while the exhaled breath temperature varies between 30 °C to 34 °C [65]; we set the human breath temperature to the lower temperature (30 °C) of this range to consider a lower evaporation of aerosols. The ambiance was set to the standard temperature and pressure (STP) conditions, and the thermally active surface temperature was set at 27 °C [66]. We defined thermally active surfaces in various HVAC systems as surfaces that are in direct contact with people or their respiratory flows. Figure 3 shows different views of the mesh configuration. Figure 4 shows mannequin meshing, which uses the snappyHexMesh utility in OpenFOAM. Figure 5 shows the schematic of the six cases. Red, yellow, and green mannequins represent infected individuals standing or sitting at the center (under combined exhaust and fresh air ducts), under the fresh air ducts, and under the recirculated ducts of the subway, respectively. The cell sizes of the mouth domain and ventilation ducts were 2 × 10

^{−3}m and 5 × 10

^{−2}m, respectively. The main input characteristics of the evaluated case studies are demonstrated in Table 1.

^{2}/W [67,68]. In other words, we supposed that mannequins’ clothing level is trousers with a long-sleeve shirt. In this simulation, we used the fixed temperature boundary condition over the mannequins selected from Angelova’s work [69].

#### 2.3. Numerical Technique and Boundary Conditions

^{−5}; $v$ is the air velocity; and $\Delta n$ represents the thickness of the supply panel. To obtain accurate results, a porous boundary condition was applied to the supply air ducts. The values of ${C}_{2}$ and $\frac{1}{\alpha}$ were set at 150,000 m

^{−1}and 1.5 × 10

^{6}m

^{−2}, respectively. The calculated points were positioned at the two ends and in the middle of the subway cabin and averaged in the z-direction. We calculated the average velocity and temperature in the passenger compartment of the subway at three horizontal measurement points and compared the findings with those from the experimental work of Tao et al. (v

_{a}and T

_{a}) [56]. Additionally, the maximum differences in the horizontal (v

_{x}and T

_{x}) and vertical (v

_{z}and T

_{z}) velocities and temperatures were calculated and compared. The maximum relative deviations of the velocity and temperature for the two cases in Table 2 were approximately 1.2% and 1.79%, respectively. The maximum temperature and velocity differences were used as evaluation metrics for the air distribution performance. These values were calculated using specific points along the x- and z-directions of the subway cabin. The European norm DIN EN-14750-1:2006 standard was applied to calculate the temperature and velocity differences and define specific points [63]. In addition, a new index, namely, the aerosol encounter probability inside an urban subway was defined to quantitatively evaluate the degree of the suppression effect of the HVAC system on airborne transmission. A grid independence test was performed to compute the required number of numerical cells to obtain convergent results. To obtain grid-independent results, simulations were performed on three different mesh topologies. A numerical grid with 900,000 cells for one core of the parallel solution was selected which had a convergent solution with an optimized computational cost (Figure 6). The maximum skewness of the grid was 0.3, which was suitable for obtaining accurate results. The number of grid points over the mannequin in the fine mesh was 8000. The Y

^{+}values were well below 1.0 over most regions of the mannequin surface and were limited to a maximum of 3.0, and the maximum value of x

^{+}and z

^{+}on any part of the mannequin was 2.0. The mesh quality influences the detailed flow in the vicinity of the complex geometry. However, as shown in our mesh independent test, selection of a suitable wall function near the wall limits the influence of mesh conditions on aerosol behavior. In addition, we selected a time step of 10

^{−6}s to obtain an appropriate and convergent solution. The time-step size was set based on a maximum Courant number of 10. The results show that both the standard k–ε and RNG k–ε models can accurately simulate the fluid flow and temperature inside an urban subway HVAC system. The RSM turbulent approach had similar results to k-ε for the velocity parameter, but for temperature fields, the RSM results were significantly closer to Tao et al.’s study [56]. The results of the k-ε model were closer to the experimental data. A comparison of the four turbulence models is presented in Table 2. In addition, the standard wall function was applied to predict the near-wall turbulence. A no-slip boundary condition was applied to all solid surfaces (except the vents). The maximum velocity rate at the supply duct inlet was 4.2 m·s

^{−1}, and recirculated air and exhaust ducts circulated 75% of aerosols exiting through the HVAC system. A ZeroGradient boundary condition was applied at the exhaust ducts.

#### 2.4. Modelling of Aerosol

_{1}is the time in which all aerosols reach a dynamic balance in the simulation, and t

_{2}is selected based on the traveling time of the urban subway between stations. The diffusion of aerosols from the infected person’s mouth to the subway domain occurs close to equilibrium conditions only if the environmental concentration is minimal. Nonequilibrium diffusion occurs in environmental flows with high concentrations. A healthy individual inside an urban subway may create such environmental flows. We used a suitable initial condition to simulate aerosol transport to determine if all aerosols reached a dynamic balance. The equation $DR=\frac{C}{{C}_{0}}$, which is used in the probability of an aerosol encounter, is the ratio of continuous breathing source concentration to initial concentration in the subway cabin. The initial concentration cannot be equal to zero. The minimal concentration (equilibrium flow) value should be used to start the simulation. If we solved it with a higher concentration, the problem would not be related to the present work; it would be related to the science of aerosol interaction (nonequilibrium flow). Some researchers have used appropriate initial conditions in their simulations to ensure an equilibrium flow field and obtained satisfactory results [70,71]. Based on the typical temperature and ventilation velocity in an urban subway, the Wells–Riley equation,$P=1-{e}^{\frac{-qt}{DR}}$, may be used for aerosol encounter probability, where q is the quantum generation rate for an infected person (quanta·s

^{−1}) [49]. A higher DR value in a certain zone indicates a higher risk of transmission [28]. The number of ejected particles is defined [36] as

^{3}·s

^{−1}, respectively [36]. In this study, we assumed continuous flow at the breathing sources inside the cabin. Besides, we assumed that the air at the individuals’ mouths is constantly outward at a breathing frequency of 0.2 breaths/s (respiratory period of ~5 s and 12 breathing per minute). The simulation time is sufficiently long; such periodic effects can be neglected because our focus is on airborne transmission far from the emission source. The continuous breathing model is suitable for analyzing virus movement inside an urban subway cabin over exposure time. Therefore, the pulsatile nature of breathing was neglected. Instead, we used a steady flow velocity that was equivalent to the average velocity of the entire respiratory period. This length of time is mandatory for an exhalation-based viral load and essential for simulating aerosol dispersion in a specific confined space. Some researchers used this assumption (continuous flow at the breathing sources) to simulate aerosol extraction by breathing and achieved satisfactory results under flow settings similar to our current configuration [72,73]. The modeled breathing source had a hydraulic diameter of 0.04 m.

## 3. Results and Discussion

#### 3.1. Infected Individual Breathing near the Supply and Exhaust Ducts (Cases 1 and 2)

_{10}(DR) when the infected individual was standing and sitting, respectively (Cases 1 and 2). The left column (a) shows the proposed HVAC system, and the right column (b) shows the conventional HVAC system of the urban subway. As shown in Figure 9, when the infected individual was standing and breathing near the exhaust and fresh-air ducts at the center of the cabin, the viral load was maintained than that of the proposed HVAC system over time. In the proposed HVAC system, the aerosol concentration near the floor of the subway cabin was, at times, higher than that of the conventional system.

_{10}(DR) along the sampling surfaces is shown in Figure 9 and Figure 10. Logarithmic scales were used to delineate concentration figures. As shown in Figure 9, the average aerosol concentration along the standing sampling surface of the proposed HVAC system was lower than that of the conventional HVAC system. In addition, the average aerosol concentration along the sitting sampling surface for the proposed HVAC system was much lower than that of the conventional HVAC system. The main difference between the proposed HVAC system and conventional HVAC system was the flow pattern inside the urban subway. The longitudinal ventilation flows of the conventional HVAC system dispersed the aerosols more than those of the proposed HVAC system. The probability of aerosol encounters over the sampling surfaces for Case 1 is shown in Figure 9. The highest value of the aerosol encounter probability corresponding to the sitting sampling surface of the conventional HVAC system was 32.1%. This rate was 83.8% higher than that for the same surface in the proposed HVAC system.

_{10}(DR) for case 2, in which the infected individual was sitting near the exhaust and fresh-air ducts. The left column shows that in the case of the proposed system, a higher proportion of the aerosol cloud moved toward the cabin floor. The remaining part was dispersed in the surrounding spaces following the ventilation flows. However, in the case of the conventional HVAC system, aerosol clouds dispersed upward and affected a more extensive zone. The right side of the cabin, where the infected passenger was seated, contained a higher concentration of aerosols in both the HVAC systems. The aerosol concentrations in the standing/sitting surfaces of the conventional HVAC system were higher than those on the same surfaces in the proposed model. The probability of aerosol encounters at each sampling surface in Case 2 is shown in Figure 4. In the conventional model, the maximum aerosol encounter probability was 39.2% for the sitting sampling surface. This rate was 6.125 times higher than that of the proposed model. The lowest rates were on the surface in both models, and the rate for the proposed HVAC system was significantly lower, i.e., 4.2%. Impeding aerosols from rising inside a subway cabin is crucial to reduce the probability of aerosol encounters. By locating exhaust ducts near the floor of the subway, the overall aerosol concentration can be reduced through the suppression effect, which is defined as the rapid removal of indoor air pollutants by ventilation in a short pathway. This concept was considered in the development of the proposed model. However, some amount of aerosol continues to rise within the proposed HVAC system owing to the velocity distribution irregularities and position of the recirculated air ducts along the ceiling.

#### 3.2. Infected Individual Breathing near the Fresh-Air Ducts (Cases 3 and 4)

_{10}(DR) values than the proposed HVAC system. The distribution patterns of breath aerosols demonstrate that when an infected individual breathes under the fresh-air ducts of the cabin, the conventional HVAC system airflow carries these particles to the exhaust ducts. In this case, the traveling aerosol pathways are near the standing sampling surface and traverse a long distance toward the exhaust ducts, thus increasing the aerosol encounter probability.

#### 3.3. Infected Individual Breathes near the Recirculated Ducts (Cases 5 and 6)

_{10}(DR) counters of cases 5 and 6, we can conclude that a uniform air distribution reduces the suspension of aerosols under the recirculated and return ducts inside the subway cabin. The horizontal spreading of aerosols was minimal in the proposed model. The proposed HVAC system results in a lower aerosol concentration than that of the conventional model if the infected individual is in a standing position. The highest probability of aerosol encounters in the proposed HVAC system was 8.2% for the sitting sampling surface, which was 68.09% lower than that of the conventional HVAC system (Figure 13). Based on Figure 13, the highest aerosol encounter probabilities for the seated case near the recirculated ducts in the proposed and conventional HVAC systems were 8.2% and 25.7%, respectively. Our study shows that conventional HVAC systems can propagate airborne virus-bearing aerosols near recirculated ducts on the top side of the cabin, which can increase the transmission risk. In other words, the infected person may stand under the exhaust ducts, and the flow pattern expels particles in the conventional HVAC system. The log

_{10}(DR) variations over the sampling surfaces for Cases 5 and 6 are shown in Figure 13 and Figure 14, respectively.

#### 3.4. General Comparison of Cases 1 to 6

#### 3.5. Effect of Supply Temperature of HVAC for Case 3

#### 3.6. Effect of Supply Air change Rate (ACR) of HVAC for Case 3

^{−1}. Based on Figure 11, an ACR of 10 hr

^{−1}with an induced temperature of 20 °C represents the worst-case scenario. In this case, aerosol propagation on both sampling surfaces was higher than that on the same surfaces in the conventional HVAC system. An essential method to reduce aerosol encounter is to increase the fresh air velocity, which can be achieved by increasing the ACR. The HVAC system consumes higher energy with an increase in the ACR value. The calculated probabilities of the standing sampling surface aerosol encounters for 10, 11, 12, and 13 hr

^{−1}were 51.2%, 42.3%, 35.2%, and 30.1%, respectively; the corresponding values for sitting sampling surface were 48.3%, 40.9%, 30.5%, and 25.4%, respectively. The aerosol concentrations over the sampling surfaces for the various ACRs are shown in Figure 17.

^{−1}with an induced temperature of 20 °C on the breathing aerosol spreading inside the cabin. In a poorly ventilated ACR, the weak shear flow cannot overcome the aerosol cloud to change its path and direct it toward the exhaust ducts. The zone with high concentrations of aerosol encounter levels were created in the poorly ventilated scenario, which corresponded to the locations where virus transmission was greater than that in other places. These zones were spread in the longitudinal direction of the cabin, allowing the breathing aerosols to move in any desired direction. The calculated probabilities of the standing sampling surface aerosol encounters for 4, 5, 6, and 7 hr

^{−1}were 76.1%, 74.4%, 68 %, and 65.1%, respectively; the corresponding values for sitting sampling surface were 71%, 70.2%, 62.2%, and 60.3%, respectively.

#### 3.7. Effect of Imperfect Filtration of HVAC for Case 3

## 4. Conclusions

#### 4.1. Concluding Remarks

#### 4.2. Practical Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic of a conventional urban subway car having supply air ducts, exhaust ducts, recirculated air ducts, and seats.

**Figure 2.**Schematic of a breathing source within the urban subway cabin, showing two mannequins (one standing and one seated) representing infected passengers.

**Figure 3.**Schematic of mesh configuration for the present work. (

**a**,

**b**) are side views of urban subway fine mesh, (

**c**) is the back view of fine mesh, and (

**d**) is the front view of fine mesh.

**Figure 4.**Schematic of mesh configuration for the present work, showing two mannequins. (

**a**) the front view of the meshed mannequins, (

**b**) the back view of meshed mannequins.

**Figure 6.**Log

_{10}(DR) at 20 cm in front of mouth vs position along the height of urban subway obtained using coarse mesh 500,000, fine mesh 900,000, and finest mesh 1,300,000 (the structures of these meshes are shown in Figure 3). DR is the ratio of the continuous breathing source concentration to the initial concentration in the subway cabin.

**Figure 7.**Comparison between a conventional (

**left side**) and the proposed (

**right side**) HVAC systems for an urban subway cabin.

**Figure 8.**Comparison between the streamlines of a conventional (

**a**) and the proposed (

**b**) urban subway HVAC systems. The velocity contours shown are in the mid-planes.

**Figure 9.**Time evolution of the counters of log

_{10}(DR) when the infected individual was standing near the supply and recirculated air ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 1).

**Figure 10.**Time evolution of the counters of log

_{10}(DR) when the infected individual was sitting near the supply air and recirculated ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 2).

**Figure 11.**Time evolution of the counters of log

_{10}(DR) when the infected individual is standing near the supply air ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 3).

**Figure 12.**Time evolution of the counters of log

_{10}(DR) when the infected individual is sitting near the supply air ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 4).

**Figure 13.**Time evolution of the counters of log

_{10}(DR) when the infected individual is standing near the recirculated ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 5).

**Figure 14.**Time evolution of the counters of log

_{10}(DR) when the infected individual is sitting near the recirculated ducts of the proposed (

**a**) and conventional (

**b**) HVAC systems (Case 6).

**Figure 16.**Evolution of the counters of log

_{10}(DR) when the infected individual is standing near the supply air ducts of the conventional HVAC systems (Case 3) at the time of 180 s for various temperatures (summer and winter season).

**Figure 17.**Evolution of the counters of log

_{10}(DR) when the infected individual was standing near the supply air ducts of the conventional HVAC systems (Case 3) at the time of 180 s for various well-ventilated air change rates.

**Figure 18.**Evolution of the counters of log

_{10}(DR) when the infected individual was standing near the supply air ducts of the conventional HVAC systems (Case 3) at the time of 180 s for various poorly ventilated air change rates.

**Figure 19.**Evolution of the counters of log

_{10}(DR) when the infected individual was standing near the supply air ducts of the conventional HVAC systems (Case 3) with imperfect filtration at the time of 180 s for various removed particle present (RPP).

No. Case Study | Different Inputs | Common Inputs |
---|---|---|

The conventional HVAC system (Case studies 1, 2, 3, 4, 5 and 6) | The length and width of exhaust ducts are 2.5 m and 1.6 m, respectively. The number of exhaust ducts is 6, | Air change rate is 10 hr^{−1}. The temperature values of the supply air, human breath, ambiance, and other cabin interior surfaces (such as mannequins, seats, and walls) are set at 20 °C, 30 °C, 25 °C, and 27 °C, respectively. |

The proposed HVAC system (Case studies 1, 2, 3, 4, 5 and 6) | The length and width of exhaust ducts are 4 m and 0.6 m, respectively. The number of ducts is 12. | ν = 1.5 × 10^{−5} m^{2}/s, T0 = 20 °C, β = 3 × 10^{−3} K^{−1}, Pr = 0.71, Prt = 0.9, g = 9.81 m/s^{2}, Sc = 1, Sct = 1, clothing insulation of mannequins is 0.60 clo. |

**Table 2.**Comparison of the velocity and temperature with the results of the study by Tao et al. [56].

Values | Experimental Data | Present Work (RSM) | Present Work (k–ε) | Present Work (k-ε RNG) | Present Work (k–ω) | Present Work (k–ω SST) |
---|---|---|---|---|---|---|

v_{a} (average velocity) | 0.170 | 0.168 | 0.168 | 0.168 | 0.160 | 0.161 |

v_{x} (horizontal velocity) | 0.250 | 0.248 | 0.248 | 0.247 | 0.240 | 0.242 |

v_{z} (vertical velocity) | 0.590 | 0.578 | 0.578 | 0.578 | 0.562 | 0.560 |

T_{a} (average temperature) | 26.90 | 26.85 | 27.00 | 27.00 | 24.00 | 24.00 |

T_{x} (horizontal temperature) | 06.68 | 06.65 | 06.80 | 06.80 | 05.71 | 05.81 |

T_{z} (vertical temperature) | 06.94 | 06.94 | 07.02 | 07.02 | 06.07 | 06.20 |

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**MDPI and ACS Style**

Nazari, A.; Hong, J.; Taghizadeh-Hesary, F.; Taghizadeh-Hesary, F.
Reducing Virus Transmission from Heating, Ventilation, and Air Conditioning Systems of Urban Subways. *Toxics* **2022**, *10*, 796.
https://doi.org/10.3390/toxics10120796

**AMA Style**

Nazari A, Hong J, Taghizadeh-Hesary F, Taghizadeh-Hesary F.
Reducing Virus Transmission from Heating, Ventilation, and Air Conditioning Systems of Urban Subways. *Toxics*. 2022; 10(12):796.
https://doi.org/10.3390/toxics10120796

**Chicago/Turabian Style**

Nazari, Ata, Jiarong Hong, Farzad Taghizadeh-Hesary, and Farhad Taghizadeh-Hesary.
2022. "Reducing Virus Transmission from Heating, Ventilation, and Air Conditioning Systems of Urban Subways" *Toxics* 10, no. 12: 796.
https://doi.org/10.3390/toxics10120796