key: cord-0946656-zq74b6ca authors: Luo, Qiqi; Ou, Cuiyun; Hang, Jian; Luo, Zhiwen; Yang, Hongyu; Yang, Xia; Zhang, Xuelin; Li, Yuguo; Fan, Xiaodan title: Role of pathogen-laden expiratory droplet dispersion and natural ventilation explaining a COVID-19 outbreak in a coach bus date: 2022-05-21 journal: Build Environ DOI: 10.1016/j.buildenv.2022.109160 sha: 7a00129ea61d7e762d2a10f372ac0d31036e35bc doc_id: 946656 cord_uid: zq74b6ca The influencing mechanism of droplet transmissions inside crowded and poorly ventilated buses on infection risks of respiratory diseases is still unclear. Based on experiments of one-infecting-seven COVID-19 outbreak with an index patient at bus rear, we conducted CFD simulations to investigate integrated effects of initial droplet diameters(tracer gas, 5μm, 50μm and 100μm), natural air change rates per hour(ACH = 0.62, 2.27 and 5.66h(−1) related to bus speeds) and relative humidity(RH = 35% and 95%) on pathogen-laden droplet dispersion and infection risks. Outdoor pressure difference around bus surfaces introduces natural ventilation airflow entering from bus-rear skylight and leaving from the front one. When ACH = 0.62h(−1)(idling state), the 30-minute-exposure infection risk(TIR) of tracer gas is 15.3%(bus rear) - 11.1%(bus front), and decreases to 3.1%(bus rear)-1.3%(bus front) under ACH = 5.66h(−1)(high bus speed).The TIR of large droplets(i.e., 100μm/50μm) is almost independent of ACH, with a peak value(∼3.1%) near the index patient, because over 99.5%/97.0% of droplets deposit locally due to gravity. Moreover, 5μm droplets can disperse further with the increasing ventilation. However, TIR for 5μm droplets at ACH = 5.66h(−1) stays relatively small for rear passengers(maximum 0.4%), and is even smaller in the bus middle and front(<0.1%). This study verifies that differing from general rooms, most 5μm droplets deposit on the route through the long-and-narrow bus space with large-area surfaces(L∼11.4m). Therefore, tracer gas can only simulate fine droplet with little deposition but cannot replace 5–100μm droplet dispersion in coach buses. infecting seven of the passengers. These infected passengers (in pink) were respectively 127 located at seats 1D, 5C, 6A, 6D, 9C, 9D and 13D. Among them, the passenger at seat 128 1D is farthest away from the index patient, at a distance of 9.46 m. 129 All the windows could not be opened with the skylights (as shown in Fig. 1a) for 130 natural ventilation. Fresh air entered the bus through the skylight inlet at the rear ceiling, 131 and contaminated air escaped from the skylight outlet at the front ceiling (Fig. 1a) . The 132 measured ACH could change with the various air pressure difference between the 133 indoor and outdoor of the bus due to the various running speeds. More detailed 134 information about the experimental setup can be found in our previous study [11] . We utilized Gambit to build the bus cabin and manikin models (Fig. 1) . We created 140 a refined grid with 0.005 m size on mouth and nose, which is smaller than the grid of 141 0.03 m size around the human body, 0.01 m mesh size on the skylight inlet/outlet and 142 heat radiator, and 0.05 m for the bus body (Fig. 1c) . A total number of 5,379,993 143 unstructured meshes were generated, which was verified to ensure grid-independent 144 requirements. 145 Twenty-one cases were considered as shown in Table 1 To simulate the airflow field, we assumed that the variables were unchanging 164 (steady) in the bus. CFD simulations were run until residuals became constant, for all 165 cases the iterations were over 100,000 times. Convergence was achieved after non-166 dimensional residuals for continuity equation, velocity components, energy, k and ε 167 were below 10 -3 , 10 -4 , 10 -6 , 10 -4 and 10 -4 , respectively and the monitored variables at 168 specific surfaces were stable. We also checked energy balance and mass balance to help 169 determine the convergence. 170 After the steady airflow field calculation was solved, we started the simulation of 172 tracer gas dispersion and particle tracking, separately. The second-order upwind scheme 173 was adopted in the tracer gas simulation. The mass fraction of C2H6 in the index 174 patient's exhalation flows was 0.32 in CFD simulations according to Ou et al. [11] . 175 Lagrangian method with the Discrete Phase Modeling (DPM) was adopted to simulate 176 the droplet dispersion with initial diameters of 5 µm, 50 µm and 100 µm [28, 43] . 177 Lagrangian equations of the droplets for i direction are as follows: 178 (2) 180 where xp,i and up,i are the droplet displacement (m) and velocity (m/s) in i direction, 183 respectively; Fdrag,i is the drag force (Eq. (3)), Fg,i is the gravitational force (Eq. (4)). In 184 addition, Fa,i is the additional forces (Eq. (2)) for which we only considered Brownian 185 force and Saffman's lift force [28, 44] . ρp and ρ are the density of droplets and air, 186 respectively. fD is the Stoke's drag modification function of Reynolds number for large 187 aerosol (Rep) [45] . 188 In Eq. (3), τ p is the aerosol characteristic response time, which is defined as: 190 where μ t is the turbulent viscosity (kg m −1 ·s −1 ) and d p is the droplet diameter. Cc is 192 the Cunningham slip correction factor, which is defined as [46]: 193 where λ is the molecular mean free path of air. 195 In CFD simulations, the mass ratio of liquid (water) and solid element (sodium 196 chloride) in droplets is assumed as 9 [47] . The densities of water liquid and sodium 197 chloride are respectively 998.2 kg/m 3 and 2170 kg/m 3 . The evaporation process will 198 continue until the droplets' volatile composition (i.e., water) is completely consumed. 199 The vaporization rate is governed by the gradient of the vapor concentrations between 200 the droplet surface and the bulk gas. The molar flux of vapor is defined as: 201 where k c is the mass transfer coefficient (m/s) which can be obtained by Sherwood 203 relationship [48] . The vapor concentrations at both droplet surface C i,s (kg·mol·m -3 ) 204 and bulk air C i,sr (kg·mol·m -3 ) are calculated by the assumption of the ideal gas. 205 After the steady airflow field with water vapor was solved, the single-diameter 218 droplets were uniformly released from the mouth of the index patient at a rate of 20 219 droplets per time step (t = 0.1s, 18,000 iterations in total). The initial velocity of exhaled 220 droplets was 1.5 m/s and the initial temperature was 32 ℃. After 30 min continuous 221 releasing, we got a fully-developed droplet distribution with a total droplet number of 222 360, 000. When a droplet encountered a surface, it would have three different fates: trap, 223 reflect and escape. As shown in Table 3 , different droplet sizes, surface roughness and 224 other factors would lead to different boundary conditions of droplets on the surfaces 225 [28, 49] . The trap condition was utilized for the floor, human surfaces and seats, which 226 means droplets were trapped once they touched the objects and the trajectory 227 calculations were terminated. While for the glass, roof, luggage racks and vertical walls, 228 the reflect condition was applied due to smooth surfaces or gravity, which means 229 droplets rebound off the surface and continue dispersion [28, 44, 50] . Escape condition 230 was adopted to the skylight outlet and passengers' noses (except the index patient). 231 Some of the CFD simulations in this study were completed on the Tianhe II 232 supercomputer with the support of the National Supercomputer Center in Guangzhou. 233 where P is the probability of infection risk; Cinfected is the number of infected cases; 241 Ssusceptible is the number of susceptible people; I is the number of people in the infectious 242 stage or infectors; q is the quanta of PLD produced per infector per second (quanta/s); 243 p is the pulmonary ventilation rate of each susceptible (m 3 /s); Q is the room ventilation 244 rate with virus-free air (m 3 /s); t is the exposure time (s); is the number of PLD 245 inhaled by susceptible person, which was calculated for droplets and tracer gas by using 246 different equations. 247 For droplets, N S is defined as [54]: 248 where Cg,q is the airborne quanta concentration at the target position (quanta/m 3 concentrations at the measuring location, ventilation supply inlet and ventilation 306 exhausts, respectively). Particles with a diameter of 1 μm are released from the patient's 307 mouth. In order to quantify the reliability of the validation, we calculated the 308 normalized mean square error (NMSE) and fractional bias (FB), whose ranges were 309 respectively 0.3 to 1.3 and 0.01 to 0.27, which satisfied the recommended criteria 310 In order to describe the flow pattern and tracer gas dispersion more clearly, seat 320 locations are shown in Fig. 4a : 13 rows (Row 1-13) and 5 columns (Column A, B, C, 321 D, E) of seats in the passenger cabin. We regard the 1st to 4th rows as the bus front, the 322 5th and 8th rows as the bus middle and the 9th to 13th rows as the bus rear. The index 323 patient is located at seat 12D (Row 12, Column D, scarlet). 324 Fig. 4a indicates that when the bus speed is high (ACH = 5.66 h -1 ), the fresh air 325 enters the skylight inlet at the rear roof, then mixes with the dirty air and moves from 326 the rear to the front. Finally, the mixed air leaves through the outlet at the front roof of 327 the bus. There are body thermal plumes which lead to significant upward airflow near 328 and above human bodies (Fig. 4b) . The upward airflow will intertwine with the main 329 flow field and subsequently affect the droplet dispersion. Fig. 4c displays that the 330 airflow exhaled by the index patient first moves forward, then rises up and finally 331 deflects backward to the bus rear. As depicted in Fig. 4d , the body thermal plumes are 332 most obvious under idling condition (ACH = 0.62 h -1 ). The ventilation flow from bus 333 rear to bus front enhances significantly as ACH rises with the increasing bus speed (Fig. 334 4e) . We have investigated the impacts of ventilation rates on the dispersion of droplets 363 in different initial diameters (5 μm, 50 μm and 100 μm), and find that the dispersion 364 mechanism is more affected by the gravity force and less influenced by the ventilation 365 airflow for larger droplets. Thus, to better reveal the influence of ventilation rates, we 366 only select 5 μm droplets to display their distribution under RH = 35% at t=5s, 30 s, 60 367 s and 300 s with three ACH, as shown in Fig. 7 . 368 As verified in Fig. 7a1-b1 , after being exhaled by the index patient, droplets first 369 move forward due to the initial exhalation flow, then rise up following the upward flow 370 near the index patient, and spread with the main airflow routes (Fig. 7a2-b2 ). Due to 371 the variation in ventilation rates, the spatial distribution of droplets also differs 372 significantly (Fig. 7a3-a4 ). When ACH = 5.66 h -1 with larger supply airflow blowing to 373 the bus front, more droplets move forward and escape from the skylight outlet, leaving 374 relatively fewer droplets in the bus rear ( Fig. 7a4-b4) . The results show that increasing 375 the ventilation rate is beneficial to droplet dilution and excretion, and significantly 376 reduces the droplet concentration near the index patient (i.e., seats 11D, 12C and 13D). into nuclei, so they are more significantly affected by the airflow field, and spread wider 382 in the whole bus ( Fig. 8a1-a3) . Due to the combined action of airflow pattern and 383 gravity force, 50 μm droplets mainly concentrate at the bus rear ( Fig. 8b1-b3) . With the 384 dominance of gravity force, 100 μm droplets rapidly settle down from the exhalation 385 jet after being exhaled from the index patient's mouth (Fig. 8c1-c3) . Basically, the 386 larger the initial diameter is, the quicker the droplets deposit, and hence the smaller 387 range they propagate and the more they remain in the bus. 8 . Droplets distribution in low bus speed with RH = 35%: (a)dp = 5 µm, (b) dp = 50 µm, (c) dp = 100 µm. Fig. 9 depicts the 30-minute-exposure intake fraction (TIF) of each passenger 391 which is defined as dividing the number of droplets a passenger inhaled by the total 392 number of droplets released from the index patient (360,000). Fig. 10 depicts the 30-393 minute-exposure infection risk (TIR) of each passenger which is calculated by Wells-394 Riley equation (Eq. (9) ). The X-axes represent the row of each passenger, where 12D is 395 the location of the index patient and 8C is unoccupied. Passengers without data indicate 396 that they did not inhale PLD released by the index patient. 397 For 5 μm droplets, the ventilation rates influence the TIF and the subsequent TIR, 398 with a higher ventilation rate leading to more passengers at TIR. When ACH = 0.62 h -399 1 , only few 5 μm droplets are inhaled by passengers in the bus front (Fig. 9a) , leading 400 to most front passengers at no droplet TIR (Fig. 10a) . When ACH increases to 5.66 h -1 , 401 even more front passengers are at TIR, and both TIF and TIR of passengers decrease 402 with the distance between the passenger and index patient (Fig. 9c) . Although 5 μm 403 droplets disperse more widely with the increasing ventilation, the TIR is quite low 404 (<0.01%) for front passengers. Regardless of ventilation rate, more than 97% of 50 µm 405 droplets deposit near the index patient due to gravity (Table. S1), so only the middle 406 and rear passengers are at TIR with the highest infection risk for passenger 12C (3.13% 407 under ACH = 5.66 h -1 ) (Fig. 10b) . While for 100 μm droplets, over 99.5% of them 408 deposit locally due to gravity (Table. S1), making nobody at TIF, so we don't display 409 the infection risk. 410 For the tracer gas, a higher ventilation rate leading to lower TIR. The TIR is 11.10-411 15.29% under ACH = 0.62 h -1 , and decreases to 1.27-3.09% when ACH = 5.66 h -1 (Fig. 412 10c) . The TIR of tracer gas for each passenger is more uniform and distinctly higher 413 under the same condition, compared with that of droplets. The total duration of the bus journey is 200 min, and the passenger seating 418 arrangement and driving route are depicted in Fig. 11a . We adopted the calculated 30-419 minute simulation results to infer the quanta of virus-laden droplets or tracer gas inhaled 420 by each passenger throughout the whole journey. Fig. 11b-11d 12D). Note that the logarithmic coordinate system is employed in Fig. 11c-11d . 423 Under all conditions, the highest WIR of the tracer gas, 5 μm and 50 μm droplets 424 occurs at seat 12C with 33.85%, 16.99% and 17.40%, and followed by seat 13D with 425 24.97%, 4.28% and 1.57%, respectively. It can be seen from Fig. 11 that the WIR of 426 front-seat passengers significantly decreases with the increasing initial droplet diameter. 427 However, passengers near the index patient (i.e., seats of 11D, 12C and 13D) are always 428 at comparatively high WIR. 429 For the tracer gas (Fig. 11b) , the WIR of front passengers is relatively even at 430 ~14.00%. For 5 μm droplets (Fig. 11c) , the WIR is quite discrepant for passengers at 431 different locations, and is less than 0.15% for the front passengers (Rows 1-4) , while 432 up to 16.99% for the passenger at 12C. For 50 μm droplets (Fig. 11d) Tracer gas, (c) dp = 5 μm, RH = 35%, (d) dp =50 μm, RH = 35%. (Note: infection risk is calculated based on this epidemic case.) open up for fresh air, but no windows are openable. Fig. 12 depicts the external surface 440 wind pressure coefficient around the running bus. It shows that the pressure on the rear 441 half is higher than the front half of the bus, which leads the air enter the bus from the 442 rear skylight and exit from the front, i.e., the indoor main airflow is moving from the 443 rear to front. This unique rear-to-front airflow pattern makes the pathogen-laden 444 expiratory droplets propagate the entire bus when the index patient is seated at the bus 445 rear (12D) and hence results in large-scale transmission in this outbreak, as was also 446 found in Mesgarpour et al. [58] . If the index patient was in the middle or front of the 447 bus, the rear of the bus will be a low-risk area [59] . Redrow et al. [38] demonstrated that 10 μm droplets could evaporate completely 462 in 0.25 s at RH = 20% and 0.55 s at RH = 80%, and RH influenced 0.4-10 µm droplet 463 transport in a simulated room where the mean air velocity was almost zero. Liu et al. 464 [17] revealed that 100 μm droplets took more than 100 s to evaporate at RH = 95% and 465 <2 s at RH = 35%, which made 100 µm droplet dispersion totally distinct under different 466 RH in an empty room. However, our study achieved a completely different finding: RH 467 rarely influences the droplet (5-100 µm) dispersion in the coach bus. The possible 468 reason may lie in the complex indoor environment of the coach bus which is different 469 from those in the above literature. In our study, we found that the interaction of the main 470 airflow and body thermal plumes made the airflow much more complex, which 471 significantly influenced the droplet/tracer gas dispersion. Moreover, Chen and Zhao [62] 472 and Xie et al. [33] indicated that regardless of the RH, small droplets evaporated 473 completely quickly, and big droplets deposited downward immediately before fully 474 evaporating due to gravity dominance. Therefore, there was a tiny difference of droplet 475 ultimate fates and infection risk between different RH (Table. S1, Fig. S2 ), which agreed 476 well with the study on coach bus conducted by Yang et al. [28] . 477 The droplet diameter is the fundamental property that determines its transport 478 characteristics. The transport behavior of a droplet depends on its interaction with the 479 surrounding gas molecules, as well as the force acting on it [63] . When the droplet 480 diameter increases, its dominant influencing mechanism changes into gravity force or 481 drag force [64, 65]. Zhu et al. [66] indicated that the droplets of 30 µm or smaller were 482 mostly influenced by indoor airflow, but those of 50 -200 µm were significantly 483 affected by the gravity force. Our study found that small droplets (i.e., tracer gas and 5 484 µm droplets) can follow the airflow and spread throughout the cabin, while large 485 droplets (i.e., 50 µm and 100 µm) deposited near the index patient due to the dominant 486 gravity force. Namely, small droplets can travel farther than large droplets, leading to a 487 larger range of inhalation transmission. 488 When the droplet is small enough, the behavior of the droplets and the surrounding 489 gas requires the kinetic theory of gases. Therefore, tracer gas was adopted as a surrogate 490 for droplets and droplet nuclei smaller than 5 µm in general room environments, which 491 had been verified by existing studies [36, 44, 67] . However, unlike general rooms, buses 492 are longer and narrower in shape (11.4 m long and 2.5 m wide in our study) with more 493 obstacles (i.e., human bodies and seats), which provides much more surface for droplets 494 to deposit. Our study verifies that most droplets deposit on the route through the long-495 and-narrow bus so that only a small fraction can spread to the bus front. Therefore, 496 passengers in the bus front can expose to few droplets and lead to a quite low infection 497 risk. However, tracer gas does not deposit and can disperse in the whole cabin, resulting 498 in distinctly higher infection risk under the same condition. Hence, tracer gas cannot be 499 utilized to mimic the dispersion processes of droplets which can be deposited on the 500 surfaces. Meanwhile, Zhao et al. [68] indicated that the deposition of 0.7 µm particles 501 was insignificant in an aircraft cabin. Lai and Nazaroff [69] reported that droplets in the 502 range of 0.1-0.2 µm has the lowest deposition rate in indoor environments. Hence, we 503 conclude that tracer gas can only be adopted to simulate the dispersion of fine droplets 504 (e.g., 0.1-0.7 µm) with little deposition in coach buses. 505 van Doremalen et al. [6] have found that the SARS-CoV-2 virus can remain 507 infectious in aerosols for hours and up to days on surfaces, leading to probable 508 transmission. Among the three main transmission routes, the aerosol inhalation route is 509 predominant and can occur over a long distance when the ventilation is insufficient [64, 510 70]. Therefore, this study aims to investigate the mechanism of factors affecting the 511 aerosol inhalation transmission and infection risk in a crowded coach bus. 512 Enhancing the indoor ventilation rates can promote dilution and removal of 513 pathogen-laden expiratory droplets or droplet nuclei, and hence reduce the infection 514 risk [10, 67, 71] . Our study also confirms that the infection risk is closely related to 515 ventilation rates. When the ventilation rate is small, droplets can only disperse in the 516 bus rear and middle. Larger ventilation airflow drives droplets to disperse more widely 517 in the bus, but the infection risk is relatively low in the bus front (lower than 0.1% when 518 ACH = 5.66 h -1 for 5 µm droplets). While for tracer gas, the inhalation infection risk can 519 be reduced by an order of magnitude as ACH increases from 0.62 h -1 to 5.66 h -1 . Thus, 520 for the large range of initial diameters of respiratory droplets, the infection risk 521 decreases with the increasing ventilation rates. 522 The Another merit of this study lies in that we utilized the real outbreak data to back-534 calculate the infection risk of each passenger according to the bus speeds and the 535 corresponding exposure time in this COVID-19 outbreak inside the coach bus. Based 536 on the numerical calculation results, we explained the following three characteristics 537 for the spatial distribution of infected passengers in this realistic epidemic: (1) more 538 infected passengers in the middle and rear of the cabin (six in Row 5-13) than in the 539 front (only one in Row 1-4); (2) more infected passengers on the index patient side (six 540 in Column C-D) than on the opposite side (only one in Column A-B). 541 The trajectory of droplets is determined by the airflow pattern, gravity force, and 542 the process of evaporation in terms of their diameter. 50 µm droplets can transmit a 543 short distance and then gradually deposit due to the gravity force, so only part of them 544 can be inhaled by passengers in the rear and middle, which leads to short-range aerosol 545 inhalation transmission [7] . Meanwhile, smaller droplets ( ≤ 5 µm) can continue 546 spreading to the bus front, leading to both short and long-range aerosol inhalation 547 transmissions. Thus, the infection risk is higher near the index patient and decreases 548 with distance, namely, more passengers in the middle and rear were infected than those 549 in the front. the index patient's breathing activity, because the epidemiological survey suggests that 578 the index patient did not cough or talk to anyone during the whole trip. In the future, 579 we will further consider more respiratory activities and more influencing parameters 580 (e.g., natural ventilation modes by opening windows, source location, ambient 581 temperature, different total heat flux for occupant etc). Meanwhile, it deserves further 582 investigation on how the droplet final fates change with various ventilation rates and 583 initial diameters under the combined effect of ambient airflow, gravity and body thermal 584 plumes. Due to the positive pressure at the bus rear and the negative pressure at the bus 585 front, opening the windows at the bus rear is beneficial to increase the ventilation rates, 586 but the specific method needs further evaluation. Additionally, during the epidemic of 587 infectious disease, public vehicles are required to be less than half occupancy in order 588 to reduce the infection risk, which has not only caused great economic losses to the 589 transportation operation companies, but also caused inconvenience to people's travel. 590 Therefore, it is worth further investigating the infection risk under different seat 591 arrangements to give a more specific suggestion for arranging the occupancy in 592 different coach buses. 593 594 Based on experiments of one-infecting-seven COVID-19 outbreak with an index 596 patient at bus rear, this paper performed CFD simulations to explore the PLD dispersion 597 and infection risk in a crowded coach bus, which is important but still scarce. The 598 integrated effects of initial droplet diameters, natural air change rates per hour and 599 relative humidity are considered. (2) The pressure difference between the bus rear and front makes the air enter the 605 bus from the rear ceiling-level skylight (inlet), and leave through the bus front 606 ceiling-level skylight (outlet), carrying droplets/tracer gas disperse from the 607 rear to the front. Higher bus speed leads to more ventilation rates. 608 (3) Tracer gas can only be adopted to simulate fine droplet (e.g., 0.1-0.7 µm) 609 dispersion in coach buses. The gaseous inhalation transmission can occur in 610 the entire cabin, and its infection risk is greatly reduced with the increasig 611 ventilation rates. When ACH increases from 0.62 h -1 to 2.27 h -1 and 5.66 h -1 , 612 TIF of tracer gas for each passenger decreases from 11.10-15.29% to 3.20-613 13.08% and 1.27-3.09%. 614 (4) Over 99.5%/97.0% of large droplets (i.e., 100µm/50µm) deposit locally due to 615 gravity. Thus, the TIF of 100µm/50µm droplets is almost independent of ACH, 616 with a peak TIF (~3.1%) near the index patient. Because gravity is less 617 significant for 5 μm droplets which can spread more widely with the 618 ventilation airflow from bus rear to front and disperse even further with the 619 increasing ventilation. 620 (5) Unlike ordinary rooms, most droplets will deposit on objects when spread in 621 the long-and-narrow bus, but tracer gas will not deposit. therefore, the 622 infection risk of tracer gas is obviously higher than that of 5-100µm droplets. 623 (6) Relative humidity (RH=35% and 95%) affects the droplet evaporation process, 624 but insignificantly influences the dispersion and infection risk. 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