key: cord-0976360-prtttq5q
authors: Wang, Ji-Xiang; Cao, Xiang; Chen, Yong-Ping
title: An air distribution optimization of hospital wards for minimizing cross-infection
date: 2020-08-11
journal: J Clean Prod
DOI: 10.1016/j.jclepro.2020.123431
sha: 92294b4fa98a15b5d9c0e24afc543fe2cb03c1f2
doc_id: 976360
cord_uid: prtttq5q

Currently, the “2019-CoV-2” has been raging across the world for months, causing massive death, huge panic, chaos, and immeasurable economic loss. Such emerging epidemic viruses come again and again over years, leading to similar destructive consequences. Air-borne transmission among humans is the main reason for the rapid spreading of the virus. Blocking the air-borne transmission should be a significant measure to suppress the spreading of the pandemic. Considering the hospital is the most “dangerous” place to occur massive cross-infection among patients as emerging virus usually comes in a disguised way, an air distribution optimization of a general three-bed hospital ward in China is carried out in this paper. Using the Eulerian-Lagrangian method, sneeze process from patients who are assumed to be the virus carrier, which is responsible for a common event to trigger cross-infection, is simulated. The trajectory of the released toxic particle and the probability of approaching others in the same ward are calculated. Two evaluation parameter, total maximum time (TMT) and overall particle concentration (OPC) to reflect the particle mobility and probability to cause cross-infection respectively, are developed to evaluate the proposed ten air distributions in this paper. A relatively optimized air distribution proposal with the lowest TMT and OPC is distinguished through a three-stage actively analysis. Results show that a bottom-in and top-out air distribution proposal is recommended to minimize the cross-infection.

Recently, a novel coronavirus named "2019-CoV-2" has caused a huge outbreak of atypical pneumonia in 2 Wuhan, Hubei, China (Zhu et al., 2019) . During months, tens of thousands of human infections have been 3 confirmed in China and even more confirmed (up to millions) cases have been reported across the world 4 rapidly. Efficient human-human transmission should be mainly responsible for such rapid infection of the 5 pandemic. Several specific approaches of the transmission of the virus such as droplet transmission (China 6 Daily, 2020), close contact , and possibly, aerosol transmission (Perlman, 2020) have been 7 identified by scientists, which means that the air-borne transmission, where viruses can be transmitted among 8 humans through aerosol or droplet particles diffused in the air way, can be confirmed to be the primary means 9 to cause human-human transmission. Similarly, air-borne transmission is also one of the main transmission 10 means for the Middle-East Respiratory Syndrome-associated coronavirus (MERS-CoV) (Kim et al., 2016) , 11 Ebola virus (Osterholm et al., 2015) , and SARS virus (2003) (Ignatius et al., 2004) , which are all deadly virus 12 causing infections of large population globally. Such emerging and re-emerging pathogens challenge public 13 health across the world over years, causing panic and economic loss. How can human actively control the 14 disease transmission from the very beginning when the initially come to host human cells without spotlight 15 should be the key to prevent global transmission of the epidemic. Blocking air-borne transmission path would 16 be the key of the key. As numerous target virus cells can be found in the patient's air way, coughs and sneezes, which was called 18 "violent respiratory events" by Dr. Bourouiba et al. (2014) , play a key role in transferring such epidemic 19 viruses that causes respiratory diseases between human and human especially in the hospital. As shown in Fig. 20 J o u r n a l P r e -p r o o f 1, considerable droplets with a certain initial velocity are generated during a human sneeze. These droplets can 1 travel as far as 7-8 m and many can suspend in the air for minutes (Bourouiba, 2020) because of the 2 entrainment effect of the sneeze-induced turbulence (Scharfman et al., 2016) . It can be inferred that sneezes or 3 coughs from a patient who is brought with certain emerging virus sneezes will increase the probability to 4 transfer this virus to others around as these ejected droplets contains considerable such virus. Such 5 public-health-threatening events may occur frequently in the hospital. It is even more dangerous when the virus 6 transmission is in its early phase as neither active safety precautions would put in place nor the public would be 7 vigilant enough against such emerging virus. What's worse, symptoms caused by these emerging virus in the 8 past twenty years such as "Covid-19" and "SARS" are similar to common cold or influenza (Huang et al. 2019) 9 where the patients with the emerging virus is more likely to be mixed with other patients. Therefore, a passive 10 precaution in the hospital for blocking the air-borne transmission of emerging epidemic viruses is critical to 11 prevent cross-infection of patients and a widespread infection. 12 A proper air distribution (AD) is classified into the above-mentioned passive precaution in this paper. 13 Although the air distribution is not a strictly passive measure as the air conditioning system consumes energy, 14 it exists everywhere to protect or harm human under the attack of air-borne virus without human conscious 15 activity once the air conditioning system was installed. As mentioned before, the AD could assist the virus to 16 host in the human cell if it is not arranged properly since the air quality largely depends on the AD ( 20 key factors to influence the air quality indoor. In addition, Verma et al. (2015) found that flow stagnant area in 21 the intensive care unit is the high-risky location which indicates that a proper AD system would minimize the 22 probability to be cross-infected. However, there has been no detailed investigation on the AD optimization for 23 minimizing the cross-infection. Considering the AD could determine the flow pattern of the tiny contaminants 24 indoor such as the virus bio-aerosols, it should be a critical factor to control the probability of cross-infection 25 among patients in a same ward which is a relatively confined space. Therefore, the AD optimization within the 26 ward is imperative to be conducted. 27 AD optimization is a topic of general interest across the world as it is highly related to the indoor air 28 quality and human health. Scientists did an extensive study on the AD in the cabin of the commercial airplane 29 which is also a confined space. As shown in Fig. 2 (a), a AD system where the fresh air flow is supplied from 30 J o u r n a l P r e -p r o o f the top and taken away from the bottom was commonly applied to the Boeing and Airbus commercial airplane 1 in the early twenty-first century (Zhang et al., 2017) . In 2013, Zhang et al. (2013) developed a novel air   2   displacement where the air flow is supplied from the bottom and taken away from the top whose schematic   3 view is shown in Fig. 2 (b) . Results demonstrates that the proposed one can eliminate the contaminants more 4 efficiently than the traditional one. A personalized AD system where the fresh air is supplied from personalized 5 inlets installed in the seats or handrails was proposed by Zhang et al. (2010) The proposed air supply inlet can 6 directly transport the conditional air to the breathing area where the CO 2 concentration can be reduced by 30% 7 compared with the traditional AD proposal. Pang et al. (2013) improved the personalized AD system where the 8 air is supplied from the under-floor and seatbacks and is absorbed from the ceiling and bottom of baggage hold. 9 Using laser-based flow visualization technology, the proposed scheme was experimentally proved to be able to 10 overcome stratification of the contaminated air above heads of passengers. From the literature review, it can be 11 concluded that a bottom-in and top-out AD pattern will be better for the passenger. Although more attention has been paid to the AD optimization of commercial aircraft cabins, such 13 investigation on a specific confined ground space especially a hospital ward, as mentioned above, is relatively 14 insufficient. A traditional AD system where the air inlet is arranged in the ceiling is rather common in the civil 15 engineering currently, while it is not recommended for the AD arrangement in an airplane passenger cabin 16 from the literature review above. Facing the severe consequences brought by the widespread epidemic diseases, 17 it is imperative for scientists and engineers to improve the AD inside a general ward to minimize the 18 probability of cross-infection in the hospital ward. 19 In order to narrow the gap of the understanding of how the AD affects the probability of cross-infection 20 among people in a hospital ward, up to ten AD proposals in a common hospital ward are displayed in this paper. 21 A Eulerian-Lagrangian scheme is adopted to simulate the sneeze process from patients with a specific which is similar to a human sneeze. Such method can also be used to track dust particle diffusion movement 4 (Chen et al., 2018) . Based on the control-volume-based computational fluid dynamics (CFD) simulation, the 5 authors provided quantitative analyses of each AD proposal to demonstrate which one is the best for 6 minimizing cross-infection. Two critical parameters, which are the total maximum time (TMT) and overall 7 particle concentration (OPC), play a critical part in the AD selection and evaluation. At last, a relatively 8 optimized AD proposal and general air distribution suggestions are offered based on the CFD investigation. 9 The largest novelty in this paper lies in the efforts towards a relatively optimized AD system for minimizing 10 cross-infection in a hospital. In addition, this paper offers these newly-developed two parameters (TMT and 11 OPC), which can give a quantitative evaluation of each AD. These two factors facilitate the selection and 12 identification of optimized AD arrangement in this paper and future investigations. 13 Reminders of this paper is organized as follows. Detailed descriptions of the focused ward and proposed 14 ten AD proposals are provided in Section 2. Section 3 describes the CFD simulation relates such as meshing, 15 governing equation, simulation cases, and boundary conditions. Simulation results and discussions are 16 provided in Section 4. Main conclusions are drawn in Section 5. As shown in Fig. 3 , a general three-bed hospital ward in China with three patients is the focus in this 2 paper. The ward's length × width × height is 7.50 × 4.00 × 2.70 m 3 . The surface index is also provided in Fig.   3 3 where the Wall and door, Wall 2, Wall 3, Wall 4, Bed 1, Man 1, Bed 2, Man 2, Bed 3, and Man 3 are clearly 4 marked. The center coordinate (x, y, z) of the mouths of man 1, man 2, and man 3 are (5.92, 0.720, 0.440), 5 (3.62, 0.720, 0.440), and (1.32, 0.720, 0.440). The internal detailed size of the bed, patient, and their relative 6 positions can be seen in Fig. 4 (a) . Fig.4 displays four first-stage AD proposals with two inlets (Inlet 1 and 7 Inlet 2) and one outlet. The size of the inlet is 0.600 × 0.600 m 2 and the size of the outlet is 0.800 × 0.800 m 2 . The two inlets of the Proposals B and C are both on the Wall 4 and their inlets on the ceiling. For Proposal B, 10 the outlet is closer to Man 2 and for Proposal C, the outlet is closer to Man 3. The two inlets are on the center 11 line of the Floor in the z direction and the outlet is on the upper part of the Wall 2. As shown in Fig. 1 , human sneeze is a complicated process as it includes highly unsteady and coupled 2 processes. Such phenomenon contains both continuous and discrete phases, the Eulerian-Lagrangian approach 3 is adopted to describe this multiphase flow. The surrounding air medium flowing pattern which is primarily 4 influenced by the AD is modelled by Eulerian method, and the movement of discrete ejected virus particles is 5 tracked by the Lagrangian formulation. 6 3.1 Continuous phase model 7 The continuous air flow is modelled by the time-averaged N-S equations. The general form of the mass, 8 momentum, and energy conservation can be modelled by Equation (1).

where ρ is the air density. φ is a universal variable which can represent different variables. u ,v , and w 10 are the velocity components in the x, y, and z direction. φ Γ and φ S are the universal transport coefficient 11 and internal source term.

φ p S is the external source term representing the two-way coupling between the 12 discrete phase and continuous phase. Detailed form of the φ , φ Γ , φ S , and φ p S are listed in the Table 1   13 where T is the temperature, μ is the dynamic viscosity of the air, p is the pressure, g is the gravitational 14 acceleration, d m Δ is the mass variance in a controlled volume, 0 , d m is the initial mass of a virus particle,

is the mass flow rate of the target particle, D C is the drag force coefficient, Re is the relative Reynold 16 number between the air and particle, d is the diameter of the particle, d m & is the mass flow rate of the 17 particle, t Δ is the time step size, d m is the average mass of the particle in a controlled volume. 18 Table 1 19

3.2 Turbulence model 1 Since a human sneeze is a turbulent process (Bourouiba, 2020), a proper turbulence model is demanded. Table 2 where ⊥ V is the flow velocity perpendicular to 9 the gravity, and t M is the turbulent Mach number which can be obtained by the Equation (5). Values and physical meanings of the coefficient in the Equation (2) and (3) 12 

Calculation formula Physical meaning J o u r n a l P r e -p r o o f

Turbulence kinetic energy produced by the average velocity gradient.

Turbulence kinetic energy produced by the buoyancy force.

Fluctuation effect on the total dissipation rate in compressible flow

Turbulent time scale divided by time-averaged strain rate of the air

time-averaged strain rate of the air

The movement of the virus particle, which is the bio-aerosol particle, is governed by the Newton's second 2 law. The trajectory of the discrete particle is solved by the differential equation of force loaded upon the ). The motion of a single particle in Cartesian coordinate system can be obtained by the Equation (6) 5 where D F is the drag force per unit particle mass per relative velocity, and x F is additional acceleration 6 force per unit mass except the drag force and gravitational force. Considering the virus particle generated by a 7 human sneeze is between 1 and 10 μm (Yang et al., 2007) , Stokes Drag force equation is adopted to calculate 8 the D F , which is expressed by Equation (7) where the c C , called Cunningham coefficient, is calculated to 9 be 1 under the atmospheric condition by the Equation (8). Also, because of the size of the bio-aerosol particle, In order to gain a better calculation accuracy, structured mesh and encryption method near the wall is 10 adopted. The generation of the mesh was done by the software ICEM. Although there are ten AD proposals, 11 the overall structure of the computational model is the same. Therefore, taking the Proposal A as an example, 12 the overall structured mesh condition and a close look of the mesh is shown in Fig. 7 . The total mesh number 13 is 748415, the network quality of which are all above 0.9, illustrating a perfect mesh quality (Chen et al., 14 2018). Results of the mesh sensitivity analysis is provided in Table 3 , in which it shows that the mesh number 15 of 748415 can attain both the accuracy and computational economy. 16 J o u r n a l P r e -p r o o f Three main assumptions are adopted in this paper: (1) Breathing effect of humans are ignored; (2) 6 Movement of people inside the ward is ignored; (3) The sneeze or cough process is simplified acoording to 7 Wong's work (Wong et al., 2015). In this paper, an ACH of 2 h -1 , where the total air mass flow rate is 1.24 8 kg/s, is adopted. The temperature of the supply air is set to be 295K, considering a typical supply air 9 temperature in a public area in winter. Other detailed information of the CFD simulation and boundary 10 conditions is listed in Table 4 . Note that all the boundary conditions subject to the "Norms for Architectural To deal with the coupling between the pressure and velocity magnitude, the pressure implicit with 1 splitting of operator is adopted to guarantee a better accuracy. Spatial discretization of the graient is selected to 2 be least squares cell based, Momentum is third-order MUSCL, and other parameters such as energy, turbulent 3 kinetic energy, turbulent dissipation rate are second order upwind. 4 The process of the simulation of each case is the same for the comparative study and the process 5 sequence is given as follows: (1) Establish the geometric model using the software Solidworks; (2) According 6 to Table 4 

Particle diameter: 8.3 μm, particle density: 1100 kg/m 3 , direction: +y direction, velocity magnitude: 50 m/s, cone angle: 15°, outer radius: 0.030 m, flow rate: 6.59×10 -9 kg/s, Discrete phase model with Brownian motion, discrete random walk model, and random Eddy lifetime. For the steady-state simulation: one-shot sneeze, particle number of streams: 8, particle number of tries: 10. For the transient simulation: particle release starts at the beginning and lasts for 100 s.

Results and discussion 1 5.1 First-stage analysis 2 Proposals A to D is the four AD proposals in the first-stage schemes. Typical simulation results of these 3 four proposals are provided in this section. Fig. 9 displays the air flow vector distributions in several focused 4 locations of Proposal A. Fig. 9 (a) shows the air flow vector distributions under the two inlets where two 5 obvious downward flows can be observed. Also, it can be seen that such downward flows will be held back 6 before touching down the floor, which causing a flow scattering just above three men. The air flow vector 7 distribution around these three men and the horizontal plane of Y=0.45 m is illustrated in Fig. 9 (b) where 8 X-direction horizontal flows are spotted which could be caused by the scattering flows in Fig. 9 (a). Note that 9 the air on both sides of Man 3 flows towards this man which would cause cross-infection with a higher 10 probability because virus particles diffused in the air could flow towards Man 3. One beneficial factor for 11 Proposal A is that air upon the man surfaces is flowing upwards, as shown in Fig. 9 (c) , which can bring the 12 particles around the man moving to higher position. It can be primarily attributed to the metabolic heat from 13 these men which bring a relatively high temperature around them which is shown in Fig. 10 . A natural 14 convection where a high-temperature air will climb high may responsible for the upward flow around these 15 three men. Fig. 11 (a) displays the 1 particle trajectories from Man 1 and Fig. 11 (b) shows the particle trajectories from Man 2. In Fig. 11 (a) , it 2 can be observed that a fair part of the particles can reach the left side of Man 2 and a small part can even 3 approach the foot area of Man 3, when Man 1 sneezes. That means a probable cross-infection may occur when 4 Man 1 bring with the epidemic virus. In contrast, When Man 2 sneezes, the virus path-lines can be fairly 5 confined within a narrow space which is beneficial to minimize the cross-infection. Such good performance 6 could be attributed to the fact that the outlet is right opposite to Man 2 which means the ejected particle can be 7 absorbed in a short period time. From Fig. 11 , the maximum particle residence time can also be obtained 8 

where the time in Fig. 11 (a) is 163 s while that in Fig. 11 (b) is only 70.8 s. These quantitative data can verify 1 the possible reasons drawn above that the released particles can be removed relatively fast when Man 2 2 sneezes. Table 5 gives the maximum particle residence times in Proposal A when each man sneezes 3 respectively. Considering the randomness in the mobility of particles, numerical experiments for each particle 4 source (Man 1, Man 2, and Man 3) were conducted three times. Therefore, Average maximum time for each 5 particle source is given as well. The total maximum time (TMT) (418.5 s for Proposal A) which is the sum of 6 the average maximum time for each particle source is given in the last column in Table 5 as an evaluation 7 parameter of Proposal A. The TMT can reflect the mobility of the released particle and a smaller TMT can be 8 supposed to have a lower probability of catching cross-infection. 9 (a) (b) Fig. 11 . Typical released particle trajectories in steady-state for Proposal A, (a) Man 1 as the virus particle source; (b) Man 2 as the virus particle source. Transient simulation revolving Proposal A is also carried out. First of all, a focused area is defined as 12 shown in Fig. 12 when taking Man 1 as the particle source. It can be concluded that when a certain man is the 13 particle source, the entire surface of other two mans and their corresponding upper surfaces of the beds are 14 highlighted as the focused area in each simulation. In order to reflect the probability of catching 15 cross-infection, the surface-averaged particle concentration upon the focused area is selected as a critical 16 evaluation parameter for each AD proposal. As shown in Fig. 13 , the transient particle concentration of the 17 focused area for each particle source is plotted. Unsurprisingly, When Man 2 sneezes, the particle 18 concentration of the focused area can be maintained to be very low, which agrees with the path-line 19 J o u r n a l P r e -p r o o f demonstration in the steady-state. When Man 1 or Man 3 sneezes, the situation could be worse, which 1 enhances the probability of cross-infection. Therefore, the hospital can place the most "dangerous" patients in 2 the position of Man 2 to minimize the cross-infection under the Proposal A. However, the doctor can hardly 3 identify the most "dangerous" patient when an emerging epidemic virus come at the very beginning time, 4 which means patients will be arranged randomly. Given that, the superposition of the particle concentration in 5 each time size of all the three particle sources, which is defined as the overall particle concentration (OPC), are 6 given. The OPC of the Proposal A is calculated to be 2.613 × 10 -6 kg/m 3 , which is a critical indicator to 7 evaluate the Proposal A. 8 Fig. 12 . Demonstration of the focused area when Man 1 is the particle source. 9 Fig. 13. Transient particle concentration of focused area for each man as the particle source in Proposal A. Table 6 summarizes the TMT and OPC of the proposed four ADs in the first-stage. Generally, a lower 10 TMT can have a lower OPC, which is beneficial to minimize the cross-infection. However, an exception is 11 J o u r n a l P r e -p r o o f spotted, where the Proposal D has the lowest OPC and the second biggest TMT. In order to explain this 1 particular case, typical air flow vector distributions and steady-steady particle trajectories for Proposal D are 2 provided in Fig. 14 and Fig. 15 respectively. Fig. 14 (a) shows the air flow conditions around these three men 3 where vertical flows and Z-direction horizontal flows are spotted. Unlike the X-direction flow in Proposal A 4 shown in Fig. 9 (b) , Such vertical flows and Z-direction flows can drive the possible virus particle away from 5 these men. The red Y-direction flow represents the relatively high-speed flow from the two inlet in the floor. 6 As the inlet flow is injected from floor to the ceiling, the upwards flow could be scattered in the ceiling which 7 would cause vertical air circulations. As marked in Fig. 14 (b) , two such vertical air circulations are existed in 8 the plane of Man 3's cross-section. Both clockwise and anticlockwise circulations would cause adverse flows, 9 shown in Fig. 14 (b) , which drives both the air and possible diffused virus particle to flow towards the Man 3. 10 Also, favorable flows are marked in Fig. 14 (b) where the air on the upper surface of Man 3 flow upwards due 11 to the relatively high temperature region.

12 Table 6 13 Summary of the TMT and OPC of the AD proposals in the first-stage. 14 Analysis of the air flow conditions in Proposal D facilitates the understanding of the virus particle 15 trajectory in this proposal, presented in Fig. 15 in which the Man 1 is the particle source. It can be spotted that 16 as the air flow pattern is from the floor to the ceiling which is correspondent with the inlet air flow, the 17 released particles is brought to the ceiling and spread in the top. Therefore, the majority of the lengthened 18 TMT in Table 6 An interesting phenomenon in the first-stage analysis is spotted that the OPC of the Proposal C can be 2 decreased by 75.6%, compared with that of the Proposal B. The only difference between these two proposals 3 is the outlet is moved from the centreline of the Man 2 (in the Proposal B) to Man 3 (in the Proposal C). Such 4 significant improvement encourages the authors to do the same alteration to the Proposal D. Therefore, the 5 outlet of the Proposal E is moved to the position opposite to the Man 3. Also, the outlets in the Proposals E, F, 6 and G are moved to the Wall 4 which are closer from the particle source (For detailed proposal structure, 7 please refer to Fig. 5 ). Table 7 gives the detailed evaluation parameters of the proposals in the second-stage. It 8 can be observed that the side-arranged outlet enlarges the OPC, which does not possess the expectant 9 improvement. It can be attributed to the from-low-to-top particle cannot be absorbed by the outlet in time, 10 which intensify the mobility of the particle. 11 closer to the particle sources. As a result, both TMT and OPC experience a significant decrease. Proposals G 15 and H can maintain the OPC around 1 × 10 -6 kg/m 3 , which is a big progress in optimizing the AD. Particle 16 trajectories of the Proposals G and H are illustrated in Fig. 16 . It can be seen that when Man 2 is the particle 17 J o u r n a l P r e -p r o o f source, both G and H can perform well where the released particle can be absorbed immediately with a low 1 probability of cross-infection, which is resulted from the upward flowing particle can reach the absorption 2 region of the outlet without any further spreading. Such superiority can be spotted in Fig. 16 (d) where the all 3 cluster of the particle can be delivered to the outlet with a maximum particle residence time of only 1.82 s, 4 which also contributes to the lowest TMT so far. However, when Man 1 is the particle source as shown in Fig.   5 16 (c), the particle can be easily transported to the area of Man 2 in that the outlet is very close to the Man 2. It 6 will enhance the probability of catching cross-infection for Man 2 when other people is firstly infected. The 7 slightly higher OPC, compared with that of the G, can verify the conclusion above. What's more, the outlet is 8 usually not recommended to be arranged too close to the man because of the noise of the returning air flow. 9 (a) (b) (c) (d) Fig. 16 . Typical released particle trajectories in the Proposals G and H, (a) Man 2 is the particle source in the Proposal G; (b) Man 3 is the particle source in the Proposal G; (c) Man 1 is the particle source in the Proposal H; (d) Man 2 is the particle source in the Proposal H. 10 Enlightened by the results in Section 5.2, extrapolated ADs from the Proposal G are continuingly 11 examined. In the final stage, each proposal has two outlets, chasing a lower TMT and OPC. Table 8 gives the 12 results which manifest that the OPC in both proposals does decrease clearly and the Proposal J has the lowest 13 TMT and OPC in this paper. In contrast, a relatively large TMT for the Proposal I is obtained. Fig. 17 may   14 shed light on the possible cause of the excellent performance of Proposal J. A massive upward air flows are 15 J o u r n a l P r e -p r o o f spotted around these three men, functioning as a protective screen to prevent the released virus particle 1 approaching humans as presented in Fig. 17 (a) . Additionally, Fig. 17 (b) shows that two tiny air circulations 2 would occur in a high position, which are different with the huge ones in Fig. 14 (b) . These two circulations 3 are too small to cause adverse flows to Man 3. Instead, large-scale favourable upward flows exist around the 4 Man 3, which would bring the low-position virus particle to a high location where these particles would be 5 exhausted by the outlet immediately, shown in Fig. 17 (a). Fig. 18 shows the simulated particle trajectories of 6 both proposes. It can be inferred that the maximum particle residence time when Man 1 is the particle source 7 makes a majority part of the TMT of the Proposal I. The released particles can form a large vortex in the 8 left-side of the Man 1, which lengthen the particle residence time and also, enhance the mobility of the particle. 9 It can be observed that some particles can be moved to the position between Man 2 and Man 3 and absorbed 10 by the Outlet 2. In comparison, the Proposal J can manage the particle more perfectly by placing the two 11 outlets to the centreline of the gap space between the men, where the Outlet 1 can be closer to the Man 1. Fig. 18 . Comparison of the Proposals I and J in terms of the particle trajectory when Man 1 is the particle source.

Through a three-stage analysis and comparisons, Proposal J is recommended to be the relatively 4 optimized AD because the two developed evaluation parameter are both the most satisfying. By actively 5 arranging positions of the inlet and outlet, the TMT can be decreased by nearly 60% and the OPC by 95%, 6 which demonstrates that an optimized AD proposal does suppress the probability of cross-infection among 7 patients in hospital wards. where the flow pattern and life span of the released particle from the patient's mouths is specially investigated. 5 Virus particle mobility and probability of catching cross-infection are evaluated and optimized quantitatively 6 with two specially-developed parameters -total maximum time (TMT) and overall particle concentration 7 (OPC). Main reasons in optimizing the air distribution are provided in the following. 8 A bottom-in and top-out air distribution proposal is recommended to minimize the cross-infection, as it 9 can bring the virus particle travelling in the ceiling and being exhausted from the ceiling. 10 Outlet closer to the men's mouths is beneficial to confine the virus mobility and lower the probability of 11 catching cross-infection significantly. 12 Generally speaking, a low OPC comes with a low TMT. 13 The TMT is an indirect parameter to reflect the probability of getting cross-infection while the OPC is the 14 direct one. Therefore, proposals with a slightly higher TMT and lower OPC is acceptable. 15 Through smartly arranging the number and place of the outlets, the TMT can be decreased by nearly 60% 16 and the OPC by 95%. 17 This paper uncovers a ward air pattern optimization method and a relatively optimized air distribution 18 proposal, which is the Proposal J. Conclusions drawn in this paper can function as a guide in the restructuring 19 the wards in hospital which treats respiratory infectious diseases specially. Note that the selected AC system 20 may only function well for a fresh air supply mode. Admittedly, there are limitations in this paper according to 21 the adopted assumption, which will be improved in our future follow-up study. 22 23 Appendix 24 The effect of air humidity on the OPC is explored in this section. In order to reflect the effect of air 25 psychrometry condition, a water-vapour species transport model is added in the governing equation as shown 26 in Eq. (A1). Simulations considering the air humidity were conducted in Proposals A and B. The boundary 27 condition subject to Table 4 except an addition item with the water-vapour mass fraction being 0.0099 28 (relative humidity: 50.6%). Such relative humidity also conforms to the GB51039-2014. 29 J o u r n a l P r e -p r o o f

where v c is the volume fraction of the water vapour in the air. v D is the diffusion coefficient of the water 1 vapour.

2 Fig. A1 shows the distribution of relative humidity upon the surface of these three men and on the plane 3 of Y=0.45 m. It shows the relative humidity under such boundary condition can conform to the thermal 4 comfort requirements in GB51039-2014. Table A1 shows the comparison of the OPCs in two simulations (dry 5 air and moist air) under Proposals of A and B. It shows that simulation results using dry air can reflect the 6 results using the moist air which is considered as a particle situation. Considering the lower computer costs, 7 the authors adopted dry air as the continuous medium in the ward in this paper. 2 Verma T.N., Sahu A.K., Sinha S.L. 2018. Numerical simulation of air pollution control in hospital. In: Sharma 3 N., Agarwal A., Eastwood P., Gupta T., Singh A. (eds) Air Pollution and Control. Energy, Environment, 4 and Sustainability. Springer, Singapore. 24 Wang, J.X., Li, Y.Z., Li, J.X., Li, C., Zhang, Y., Ning X.W. 2019. A gas-atomized spray cooling system 25 integrated with an ejector loop: Ejector modeling and thermal performance analysis. Energy Convers. 26 Manage. 180: 106-118. 

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