Investigation on the cross-infection control performance of interactive cascade ventilation in multi-scenario of winter

Abstract

With the wide spread of COVID-19, numerous cases demonstrate that proper ventilation method can reduce the cross-infection risk obviously. Interactive cascade ventilation (ICV) as a recently proposed ventilation method, the advantage of indoor environment construction has been proven. However, few studies are conducted to investigate the virus prevention and control characteristics of ICV, which is particularly important under epidemic normalizing. Hence, this study explored and compared the cross-infection control performance of three ventilation strategies, namely mixing ventilation (MV), stratum ventilation (SV), and interactive cascade ventilation (ICV), with a validated CFD model. A typical office was selected as the background scene, where an infected person coughs, sneezes with standing or sitting at different positions. Exposure doses, health infection risk, and disease burden (DB) were employed as the evaluation indicators under different ventilation methods of multi-scenario. The research results indicated that the average aerosol exposure dose among the human respiratory region under ICV was 0.29 g/day, which was reduced by 67 % and 50 % compared with MV and SV. In addition, only in ICV can the health infection risk meets the EPA standard. The average disease health burden for exposed persons under ICV was 0.93 $\times$ 10⁻⁶ DALYs pppy, which was 37 % and 70 % lower than SV and MV. The findings obtained from this study confirm that ICV performs excellently in reducing the cross-infection risk, providing the theoretical basis for future epidemic prevention and control.

Nomenclature

COVID-19

Coronavirus disease

MV

Mixing ventilation

SV

Stratum ventilation

ICV

Interactive cascade ventilation

DB

Disease health burden

WHO

World Health Organization

DV

Displacement ventilation

HVAC

Heating Ventilation Air Conditioning

$\stackrel{\rightharpoonup }{U}$

velocity vector

${\Gamma }_{\phi }$

effective diffusion coefficient

${\stackrel{\rightharpoonup }{S}}_{\phi }$

source term (kg/m·s)

${\stackrel{\rightharpoonup }{U}}_P$

particle velocity (m/s)

$R_i$

net rate of production

${\stackrel{\rightharpoonup }{\nu }}_S$

gravitational settling velocity of the particle (m/s)

$D_p$

Brownian diffusion coefficient

$C_D$

drag coefficient

${\rho }_P$

density of the particle (kg/m³)

Re

Reynolds number

$S_{pp}$

per person of minimum required ventilation (m³/s)

$S_{PA}$

ventilation required per unit of floor area (m/s)

$Q_i$

energy generated by interior loads (w)

$Q_s$

energy of supply air (Cooling load) (w)

EC

exposure aerosol concentration (kg/m³)

BR

breathing rate (m³/day)

AG

aerosol ingestion rate (%)

d

daily dose(kg/day)

$P_y\left(d\right)$

infection per person

UFAD

Under-floor air distribution

RANS

Reynolds Average Navier-Stokes

QMRA

quantitative microbial risk assessment

P(y) d

Annual probability of infection

U.S. EPA

U.S. Environmental Protection Agency

CFD

computational fluid dynamics

RNG

Re-Normalization Group

φ

solving variables (i.e., velocity, temperature and concentration)

t

flow time (s)

ρ

Density (kg/m³)

$Y_i$

local mass fraction of particles (%)

$S_{Yi}$

rate of the source (m²/s³)

${\mu }_{eff}$

Effective viscosity (kg/m·s)

ε_p

particle turbulent diffusion coefficient

$d_p$

diameter of particles (m)

${\rho }_a$

density of the ambient air (kg/m³)

${\left(S_a\right)}_{\mathit{min}}$

minimum required ventilation (m³/s)

O

number of cooling load with different actual occupancy at different cooling loads

A

floor area (m²)

Q_e

energy generated by exterior loads (W)

OA%

share of the total room load of outdoor air

pppy

per-person-per-year

T

daily exposure duration (hour)

P_i(d)

risk of infection per daily exposure (DALYs pppy)

k

model parameter

n

frequency of exposure

1. Introduction

The widespread outbreak of coronavirus disease (COVID-19) shows an unprecedented impact on global society and human health. To quickly stop the spread, countries adopt various measures such as social distancing and restrictions on access to entertainment venues.etc. With outdoor activities being greatly limited, the time people spend indoors is obviously increased [1]. According to the research results [2], the novel coronavirus can be transmitted by direct contact and airborne transmission. In an enclosed space, the virus particles are first released by coughing and sneezing of an infected people. Then these virus particles polymerize into aerosols and droplets and begin to spread in the air [3]. Hence, the indoor ventilation patterns strongly impact the airborne transmission of pathogens. Proper ventilation method can effectively prevent virus transmission and reduce the cross-infection risk. While the aerosol transmission can be even intensified under an unreasonable ventilation method, leading to a large number of virus-positive samples circulating in the air [4]. Numerous cases during the pandemic are still caused by the poor indoor environment due to the unreasonable ventilation methods. As reported by the WHO in 2022 [5], large outbreaks of the epidemic usually occur in a crowded indoor settings, such as restaurants, choir practices, fitness classes, nightclubs, offices and places of worship. Talking, shouting, breathing heavily or singing loudly can facilitate the spread of the virus. Based on the WHO Statista [6], at least 17 million people in the European Region have experienced long COVID-19 in the first two years of the pandemic, and millions may have to live with it for years to come. Fortunately, physical measures such as wearing masks [7], increasing social distancing [8] and adding protective barriers [9] can effectively reduce the transmission risk of aerosol particles. However, these physical measures cannot be last for all the day in an enclosed space with people taking different behaviors. Therefore, it is urgent to seek for a proper ventilation method to block the spread of the virus and reduce the cross-infection risk in an effective way.

Many studies have researched the aerosol diffusion characteristic under different ventilation methods. Ren et al. [10] studied three airflow organization strategies of mixing ventilation in novel coronavirus pneumonia prefabricated wards. It proposed that the pollutant particle size was a key factor on the removal efficiency of different ventilation methods. The configuration with inlets and outlets installed on the opposite sidewalls showed the highest removal efficiency for small particle pollutants. He et al. [11] compared the exhaled droplet transmission for different diameters of 0.8 μm, 5 μm and 16 μm between occupants under different ventilation strategies in a typical office room. The research results indicated that displacement ventilation performed best concern protecting the exposed manikin from the pollutants exhaled by the polluting manikin without personalized ventilation. Lu et al. [12] contrastively investigated the pollutant distribution and exposure risk in a ward served by stratum ventilation, mixing ventilation, under-floor air distribution, and displacement ventilation, respectively. The research results demonstrated that stratum ventilation can obviously reduce the exposure risk of the healthcare workers. Research conducted by Kong et al. [13] also showed that stratum ventilation can minimize airborne viral contamination. Lin et al. [14] compared the particle diffusion of three representative scenarios in a classroom under displacement ventilation and stratum ventilation through numerical simulations, and pointed out that stratum ventilation showed best on the anti-airborne infection performance. It follows that COVID-19 poses new challenges to the current air conditioning systems. In addition to the current thermal comfort and energy-saving, the ability of virus prevention and control has also become the important indicator of HVAC system under the normal epidemic situation. Recently, Li et al. [15] proposed a novel ventilation method named interactive cascade ventilation (ICV) and indicated ICV showed good performance on indoor comfort and energy-saving. ICV as a novel ventilation method innovatively introduces different grade energy to obtain air jets with various temperatures. The air supply inlets of ICV are installed at different heights of the same wall. The upper supply air inlets provide lower temperature airflow while the lower supply air inlets provide higher temperature airflow. The thermal buoyancy force generated by the temperature difference between jets of the ICV can prevent the upper layer of fresh air from floating up fast. Hence, more clean air stay in the respiratory layer under ICV due to its special air flow characteristics, which is supposed to reduce the risk of cross-infection in the room. However, current studies on the HVAC system are mainly focused on the performance and thermal comfort. Few studies are conducted to investigate the virus prevention and control characteristics of ICV, which is particularly important under epidemic normalizing. Therefore, this paper conducted an in-depth comparative study on the cross-infection control performance in a typical office served by mixing ventilation (MV), stratum ventilation (SV) and ICV, respectively.

In this study, a typical office served by MV, SV and ICV was selected as the background environment. Reynolds Average Navier-Stokes (RANS) method was adopted to conduct the numerical calculation for investigating the cross-infection control performance of different ventilation methods by considering an infected person coughed, sneezed with standing or sitting at different positions. Quantitative microbial risk assessment (QMRA) was introduced to explore the health risk and disease burden (DB) associated with exposure to aerosol environments [16]. The findings obtained from this study can provide guide and new ideas for the further HVAC system design by considering the cross-infection control ability for a healthy indoor environment.

2. Methodology

2.1. Ventilation method

In this study, three ventilation methods, namely mixing ventilation (MV), stratum ventilation (SV) and interactive cascade ventilation (ICV) were selected as the research objects. Usually, MV is used to provide a uniform indoor environment by diluting to reduce air pollutant concentrations [17]. SV is proposed to realize a non-uniform environment, which delivers fresh air directly to the breathing region to make the air pollutant concentration much lower. ICV as a novel ventilation method is also employed to build a non-uniform indoor environment. Two air jets with different temperatures of ICV are sent from the inlets at various heights at the same sidewall. And different grades of energy are introduced into the ICV to obtain the two air jets, as shown in Fig. 1 . The thermal buoyancy force caused by the temperature gradient between jets can slow the warm air coming up. The upper warm air with a lower temperature (24 °C) can produce a downward settling force on the lower warm air with a higher temperature (26 °C). Conversely, the lower jet also exerts a lifting force on the upper jet. Therefore, ICV can make more fresh air delivered from the upper jet stay in the breathing region, reducing the cross-infection risk. As shown in Fig. 1 (b), the two jets locate in the superimposed region will change their original jet trajectories due to the interaction between jets. During the outbreak, ICV can adopt the mode of upper fresh air coupled with lower return air to realize a clean breathing layer with less energy consumption. The studies conducted by Li et al. [15] and Kong et al. [18] have demonstrated that ICV can overcome the defect of warm air floating on to a certain extent, which also enhance the effective fresh air volume meanwhile. However, the virus prevention and control ability of ICV is still a gap.

Fig. 1.

The airflow distribution of interactive cascade ventilation.

2.2. Model description

The physical models of three ventilation modes are presented in Fig. 2 . The size of the office room is set as 9.8 (length) × 12.4 (width) × 2.6 m (height). The volume of the office room is about 316 m³, referring to the research model conducted by Ren et al. (2021) [17]. The office is equipped with 43 workstations, including one staff member and one table. The staff member is simulated with a size of 0.4 (length) × 0.3 (width) × 1.1 m (height). And the ahead (including neck) size is 0.2 (length) × 0.2 (width) × 0.2 m (height). The mouth size is 3 cm × 2 cm. The heat dissipation of the staff members is also considered in the models. A constant temperature of 37 °C is used as the thermal boundary condition to simulate the human body temperature. Five row desks with the size of 1.2 (length) × 0.7 (width) × 0.8 m (height) are located in the office room. Air supply parameters are determined in accordance with GB50736-2012 [19] and indoor heat requirements. For MV, six air supply inlets (M1-M6) and one return outlet (E1) are located in the ceiling (c.f. Fig. 2b). For SV, four air supply inlets (S1-S4) with a diameter of 0.3 m are installed at 1.2 m of the side wall (c.f. Fig. 2c). For ICV, the sidewall air inlets are circular diffuser with a diameter of 0.2 m. The upper air inlets (ICV 1, 3, 5, 7) are located at the height of 1.2 m and the lower air inlets (ICV 2, 4, 6, 8) are located at 0.7 m. The exhaust louvres (E2-E5) of ICV are 1.2 m above the floor on the opposite wall (c.f. Fig. 2d). More detailed information has been presented in Table 1 [17,20].

Fig. 2.

(a) Layout of open office (b) Mixing ventilation (c) Stratum ventilation (d) Interactive cascade ventilation.

Table 1.

Numerical Boundary condition settings.

Ventilation methods	Supply air temperate (°C)	Supply air velocity (m/s)	Turbulence Intensity (%)	ACH (h−1)	Supply volume (m3/s)	size (m)
MV	25	0.3	5	5.12	0.45	0.5 × 0.5
SV	25	2		5.12	0.45	φ = 0. 3
ICV	Upper inlet:24	1.5	5	5.12	0.45	φ = 0.2
	Lower inlet:26	1.5
Mouth	37	Cough:13	4	–	–	0.02 × 0.03
		Sneeze:50
Outlet	Outflow					MV
						0.2 × 0.2
						ICV/SV
						0.2 × 0.3

An infected person is set to produce virus-containing droplets or aerosols by coughing with a speed of 13 m/s [21] or sneezing of 50 m/s [22], along with the behaviors of sitting or standing meanwhile. The airflow temperature during coughing and sneezing is 37 °C [23]. The initial droplet aerosols are assumed as spherical with the density of 998 kg/m³[24]. The size of droplet nuclei produced by human coughing and sneezing is 1 μm, whose evaporation can be neglected according to the previous studies [25]. The turbulence intensity is calculated based on equation (1):

$$I=\frac{0.16}{\mathrm{R}{{\mathrm{e}}_{DH}}^{0.125}}$$ (1)

where Re_DH is the Reynolds number derived from the hydraulic diameter as the characteristic length. The material emission component Re_DH is calculated as:

$${\mathrm{R}\mathrm{e}}_{DH}=\frac{\rho uDH}{\mu }$$ (2)

where ρ is the density, considering air density as 1.29 kg/m³ in this study; u is the flow velocity, m/s; DH is the hydraulic diameter, m; μ is the kinematic viscosity, kg/m·s. The kinematic viscosity of air and droplet nuclei is $1.7894\times {10}^{-5}$ kg/m·s and 0.0011 kg/m·s, respectively. Hence, the turbulence intensity at the supply air terminal and infector mouth is 4.86 % and 3.92 %.

For the three ventilation methods, the external wall surface temperature is −15 °C. The air supply volume is designed as 0.45 m³/s. And the ventilation flow rate is calculated as 5.12 h⁻¹ considering the room volume as 315.95 m³. Considering the heat transfer through the building envelops, internal load, and cold air penetration load, the total heating load is 1.94 kW. The heat input through the ventilation system is 2.08 KW. The detailed information of the related parameters has been list in Table 2 . It can be seen that it is heat balanced for all three systems.

Table 2.

Detailed information of load calculation.

Surface	Materials	Heat transfer coefficient (W/m2∙K)	Size	Tn(oC)	Tw (oC)
West/East wall	Concrete hollow blocks	0.83	12.4 × 2.6 (m)	22	−15
North/South wall		0.85	9.8 × 2.6 (m)
floor		0.3	9.8 × 12.4 (m)
ceiling		0.45	9.8 × 12.4 (m)
staff	80W heat source		43 (per)

This study conducts the stable numerical analysis of coughing or sneezing for further research. Actually, they are transient. This method may overestimate the airborne transmission/infection risk to some extent. On average, a healthy person sneezes four times per day and coughs two times per day [26]. However, if a patient is infected with the respiratory infectious disease, such as COVID-19 or SARS, the coughing and sneezing will occur more frequently. A reasonable ventilation method can minimize the infection risk to surrounding people in cases where the exposure is high. The worst environment caused by infected people should be considered to maximize the protection of the uninfected. Hence, this study replaces transient simulation with steady-state simulation for further research. In addition, the relevant research also points out that the analytical velocity of saliva droplets produced by coughing is overestimated [27].

2.3. Governing equations

The analysis of particle diffusion and deposition is performed by computational fluid dynamics (CFD) simulations with software tool ANSYS Airpak 3.0.16 [28]. In this study, incompressible flow and steady-state condition are considered and solved by Reynolds-averaged Navier-Stokes (RANS) turbulence model, which is better for calculating the indoor airflow environment [29]. Standard wall functions are introduced to deal with near-wall condition. A discrete coordinate radiation model is used to simulate the radiative heat exchange between human body surfaces, luminaires and other interior surfaces. The convergence criterion is set as 10⁻⁴ for the momentum residuals and 10⁻⁶ for the mass residuals, turbulent kinetic energy residuals, turbulent dissipation residuals, energy residuals and radiation intensity residuals.

The conservation equation of mass, momentum, energy, K and ε is shown as follows:

$$\frac{\partial \left(\rho \phi \right)}{\partial t}+\mathrm{div}\left(\rho \stackrel{\rightharpoonup }{U}\phi \right)=\mathrm{div}\left({\Gamma }_{\phi }\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\phi \right)+{\stackrel{\rightharpoonup }{S}}_{\phi }$$ (3)

where $\phi$ is the solving variables (i.e. velocity, temperature and concentration); $t$ is the flow time; $\rho$ is the density; $\stackrel{\rightharpoonup }{U}$ is the velocity vector; ${\Gamma }_{\phi }$ represents the effective diffusion coefficient; ${\stackrel{\rightharpoonup }{S}}_{\phi }$ is the source term [30]. More detailed information about the governing equation is shown in Table 3 .

Table 3.

Diffusion terms and source terms in the governing equation.

Item	Variable	${\Gamma }_{\phi }$	${\stackrel{\rightharpoonup }{S}}_{\phi }$
Continuity	1	0	0
Velocity	${\mu }_i$	${\mu }_{eff}=\mu +{\mu }_t$	$-\frac{\partial \mathrm{p}}{\partial x_i}+s_{ui}$
Temperature	T	$\frac{\mu }{\mathit{Pr}}+\frac{{\mu }_t}{{\sigma }_T}$	$s_T$
Kinetic energy	k	${\alpha }_K{\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}$	$G_K+G_B-\rho \epsilon$
Dissipation rate	$\epsilon$	${\alpha }_{\epsilon }{\mu }_{\mathrm{e}\mathrm{f}\mathrm{f}}$	$C_{1\epsilon }\frac{\epsilon }{k}\left(G_K+C_{3\epsilon }{G}_B\right)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}-R_{\epsilon }$
Concentration	C	$\frac{\mu }{S_c}+\frac{{\mu }_t}{{\sigma }_c}$	$s_c$

${\mu }_i$ is the component in the i direction of velocity; $\mathit{Pr}$ and ${\sigma }_T$ are laminar and turbulent Prandtl numbers; ${\sigma }_T$ is taken as 0.85; ${\alpha }_K$ = ${\alpha }_{\epsilon }$ = 1.393 is the inverse turbulent Prandtl number; $P$ is the static pressure; $S_{ui}$ is the external and gravitational body forces in the i direction; $S_T$ is the volumetric heat source; $G_K$ and $G_B$ represent the turbulent kinetic energy caused by the mean velocity gradient and buoyancy, respectively; $R\epsilon$ is the source term of the reformulation; $C_{1\epsilon }$ = 1.42, $C_{2\epsilon }$ = 1.68, $C_{3\epsilon }$ = $\tanh \left|\frac{{\mu }_i}{{\mu }_k}\right|$; and ${\sigma }_c$ = 0.7.

Euler and Lagrangian methods are two basic theoretical methods to solve particle dispersion. Both of them can well predict particle dispersion under steady-state condition [31]. The drift-flux model based on Eulerian-Eulerian method has been validated for simulating particles in indoor flow fields, which takes into account Brownian diffusion, turbulent diffusion, and gravitational settling. The controlling equation for particle concentration is similar to the Navier-Stokes equation, combining the particle gravitational settling effect into convective term [32]. For solving the dispersion of particles, the species transport model is used:

$$\frac{\partial \left(\rho Y_i\right)}{\partial t}+\Delta \left(\rho \left({\stackrel{\rightharpoonup }{U}}_P+{\stackrel{\rightharpoonup }{\nu }}_S\right)Y_i\right)=\Delta \left(\frac{{\mu }_{eff}}{{\sigma }_c}\Delta Y_i\right)+S_{Y_i}$$ (4)

where $Y_i$ is the local mass fraction of particles; $\left({\stackrel{\rightharpoonup }{U}}_P\right)$ is the particle velocity; ${\stackrel{\rightharpoonup }{\nu }}_S$ is the gravitational settling velocity of the particle; ${\mu }_{eff}$ is the effective viscosity, the total of molecular and turbulent viscosity; ${\sigma }_c$ is the Prantl number, usually set as 1; $S_{Y_i}$ is the rate of the source [33]. The above equations are discretized directly into algebraic equations by the finite volume method with second order accuracy. Buoyancy effects are considered by the Boussinesq model. The methods for analyzing the performance of different ventilation methods used in this study have been confirmed and verified in other similar studies[[33], [34], [35]].

The key assumptions in the simulations are as follows:

• 1.Without considering the effect of particles on the turbulent flow, the interaction between the carrier air and particles can be treated as a unidirectional coupling.
• 2.The diameter of exhaled aerosols ranges from 1 μm to 1000 μm, with most droplet nuclei falling in the 1–10 μm size range [36]. Droplets smaller than 10 μm can reach the alveolar region more efficiently, thus causing a greater infection risk to susceptible individuals [37]. Therefore, droplet nuclei of 1 μm are chosen to be simulated. The evaporation process can be neglected due to its transient occurrence time [38].
• 3.Aerosol condensation does not change particle size due to low particle loading.
• 4.The rebound and resuspend of droplets are ignored.
• 5.For particles 1.0 μm in size, the Brownian diffusion coefficient $D_p$ is much weaker than kinetic viscosity and the turbulent diffusion coefficient. Therefore, $\rho \left(D_p+{\epsilon }_p\right)$ is replaced by ${\mu }_{eff}$ in Eq (4).

Eq (5) can be obtained as follows:

$$\left|v_s\right|={\left[\frac{4}{3}\bullet \frac{g{d}_p}{C_D}\bullet \frac{\left({\rho }_P-{\rho }_a\right)}{{\rho }_a}\right]}^{1/2}$$ (5)

where $C_D$ is the drag coefficient, $d_p$ is the diameter of particles, ${\rho }_P$ and ${\rho }_a$ are the density of the particle and ambient air. The directions of settling velocity and gravity are the same.

The drag coefficient $C_D$ is derived from the Stokes equation (Re < 1) or the modified equation (1<Re < 1000):

$$\begin{array}{cc}{C}_D=\frac{24}{Re}& \mathrm{R}\mathrm{e}＜1\end{array}$$

$$\begin{array}{cc}{C}_D=\frac{24}{Re}\left(1+0.15R{e}^{2/3}\right)& 1＜\mathrm{R}\mathrm{e}＜1000\end{array}$$ (6)

where Re is the Reynolds number according to the relative velocity of particle and air.

2.4. Grid-independent tests

To exclude the influence of the grid number on the calculation results, three groups of the coarse, medium, and fine grids are set up for the grid independence analysis. The coordinate points for test are defined as (x, y)=(4.55 m, 1.55 m) with the alternative heights of 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2 and 2.4 m. The validation data for the measurement points are obtained from experiments. The mesh grid number for the three simulation cases is 2,934,123, 4,212,373, and 8,913,257, respectively.

Fig. 3 presents the comparison results of different grid numbers. The results demonstrate that the simulation results employing 4,212,373 and 8,913,257 meshes are in good agreement. The deviation is less than 6 %. Considering the long computation time due to high grid number, this study selects the grid number of 4,212,373 for further calculations.

Fig. 3.

Grid independence analysis for different grid numbers.

2.5. Evaluation index

Quantitative microbial risk assessment (QMRA) [39] is conducted in accordance with the National Academy of Sciences Risk Assessment framework, including hazard identification, exposure assessment, dose response assessment, and risk characterization [40]. This study investigated the airborne transmission characteristic of virus-containing aerosols exhaled by coughing or sneezing of the infector under different ventilation methods. Risk characterization is based on the dose response model. The health risk levels recommended by the U.S. Environmental Protection Agency (2005) for infections and the criteria for disability-adjusted life years (DALYs) recommended by the World Health Organization (2008) are introduced to assess health risk in this study. The U.S. EPA benchmark is ≦ 10⁻⁴ infection cases per-person-per-year (pppy), and the WHO benchmark is ≦ 10⁻⁶ DALYS pppy [41].

2.5.1. Hazard identification

The following aspects should be considered when assessing the cross-infection risk in exposed aerosols: (a) different stages of the COVID-19 outbreak; (b) percentage of people infected; and (c) different ventilation methods.

2.5.2. Exposure assessment

The daily dose (kg/day) of SARS-CoV-2 aerosols inhaled by the staffs in an office is given by [42].

$$d=EC\times BR\times T\times AG$$ (7)

where EC is the exposure aerosol concentration, kg/m³; BR is breathing rate, m³/day. Usually, the breathing rate of one adult man is 18.65 m³/day [43]. T is the daily exposure duration, h. This study considers 8 h for the occupational exposure. AG is the aerosol ingestion rate, %.

2.5.3. Dose response assessment

The risk or probability of getting infected through intake of pathogens is estimated with dose–response model. The exponential dose response model for human coronavirus suggested by Watanabe et al. (2010) is as follows [44]:

$$P_i\left(d\right)=1-e^{-k_{ill}d}$$ (8)

where $P_i\left(d\right)$ is the infection risk per daily exposure of staff to aerosols/droplets of SARS-CoV-2, DALYs pppy; d is the daily dose, kg/day; and k _ill is the model parameter, which is considered as the disease response endpoint value of Equation (8), 5.39 × 10⁻² is employed in this study [44].

The annual infection risk of SARS-CoV-2 per person $P_y\left(d\right)$ is estimated by Equation (9) [45].

$$P_y\left(d\right)=1-{\left[1-P_i\left(d\right)\right]}^n$$ (9)

where n is the exposure frequency. In this research, it is defined as 365.

The disease burden (DB) can be obtained by Equation (10) [43].

$$DB=P_y\times HB$$ (10)

where HB values for 0.00427 according to the previous research results [46].

3. Study cases

To investigate the cross-infection control performance of different ventilation methods, various scenarios with an infected person coughing or sneezing with the behaviors of standing or sitting (c.f. Fig. 4 b) at different locations of the room are considered in this study. Three typical locations, namely closing to the air supply inlets, closing to the air return outlets, and the center of the room, are considered (c.f. Fig. 4a). Based on this, a total of 36 working conditions are analyzed subsequently. Detailed information of the study cases are provided in Table 4 .

Fig. 4.

Scenario settings (a) XY plan; (b) YZ pan.

Table 4.

Detailed information of the study cases.

case	Air distribution	scenario	Source location	case	Air distribution	scenario	Source location
Case1	MV	Sit cough	Source 1	Case13	MV	Sit cough	Source 2
Case2		Sit sneeze		Case14		Sit sneeze
Case3		Stand cough		Case15		Stand cough
Case4		Stand sneeze		Case16		Stand sneeze
Case5	SV	Sit cough		Case17	SV	Sit cough
Case6		Sit sneeze		Case18		Sit sneeze
Case7		Stand cough		Case19		Stand cough
Case8		Stand sneeze		Case20		Stand sneeze
Case9	ICV	Sit cough		Case21	ICV	Sit cough
Case10		Sit sneeze		Case22		Sit sneeze
Case11		Stand cough		Case23		Stand cough
Case12		Stand sneeze		Case24		Stand sneeze
Case25	MV	Sit cough	Source 3	Case29	SV	Sit cough	Source 3
Case26		Sit sneeze		Case30		Sit sneeze
Case27		Stand cough		Case31		Stand cough
Case28		Stand sneeze		Case32		Stand sneeze
Case33	ICV	Sit cough		Case35	ICV	Stand cough
Case34		Sit sneeze		Case36		Stand sneeze

4. Results and discussion

4.1. Model validation

Hang et al. [47] and Duguid et al. [48] point out that the particles with diameters between 0.5 and 10 μm can remain in the air for longer time and their transport pattern is similar to gases. The droplet nuclei containing pathogens exhaled by infectors are particulate matter. Bivolarov et al. [49] confirmed that tracer gas can be reliably used to simulate small particles in airborne measurements by comparing the human exposure at the concentrations of tracer gas and monodisperse particle (0.07, 0.7 and 3.5 μm), respectively. Hence, tracer gas CO₂ is introduced to simulate the virus-bearing droplet nuclei exhaled by an infector in this study. And the species models are validated by the experimental data. It is noted that the research method can be accepted even though the particle diffusion and deposition models are not been verified. The experiment is carried out in an environmental chamber with the size of 4.9 $\times$ 4.8$\times$ 2.17 m. The size of air inlets and outlets of MV is 0.5$\times$ 0.5 m. The air supply inlet diameter of SV and ICV is 0.3 m, and the air outlet is 0.5$\times$ 0.5 m. The air supply parameters used in the simulations are the same as experiments. Specific parameter settings of supply air are presented in Table 5 . Cardboard boxes with dimensions of 0.54 × 0.29 × 1.2 m are used to simulate manikins. The Cardboard boxes are fitted with electric heat tape to realize a surface temperate of 37 °C to consider the heat dissipation of the people, and ensuring to heat the CO₂ gas pipe meanwhile. Hence, the temperature of CO₂ is similar to that of the air exhaled by the infector. The experimental method has been proven to be an effective alternative for investigating the interaction between occupants and indoor environment [50]. Two 42 W LED lamps are installed on the ceiling. Detailed information of the building envelops has been listed in Table 2.

Table 5.

Detailed air supply parameters.

Ventilation method	ACH (h−1)	Supply air volume (m3/h)	Supply air temperature (oC)	Supply air velocity (m/s)
MV	5.2	540	25	0.3
SV	5.2	540	25	1.2
ICV	5.2	540	24/26	1.2

To avoid oversupply or undersupply of conditioned air, the method of Anand [51] et al. is introduced to determine the minimum required supply air flow rate based on occupancy and load information. The fresh air flow rate for the target area can be calculated as follows:

$${\left(S_a\right)}_{\min }=S_{pp}\times O+S_{IL}$$ (11)

where (S _a)_min is the minimum required ventilation rate, (m³/s); S _pp is the minimum required ventilation (0.0025 m³/s) per person; O is the number of occupants. The material emission component S _IL is calculated as:

$$S_{IL}=S_{PA}\times A$$ (12)

where S _PA is the required ventilation per floor area, m³/s per m²; A is floor area, m².

The simplified heat balance model is shown as follow:

$$Q_i+Q_e=Q_s$$ (13)

where Q _i is the energy generated by interior loads, W; Q _e is the energy generated by exterior loads, W; Q _s is the energy of supply air, W.

$$\left(S_a\right)=\frac{{\left(S_a\right)}_{\min }}{OA}\%$$ (14)

where OA % is the exterior load percentage of the total load.

By calculating, S _a is 0.16 m³/s, which is met the minimum requirements of 0.15 m³/s.

In the experiments, temperature, velocity, and CO₂ concentration of different heights are recorded at measurement points (c.f. Fig. 5 b). The accuracy of T-type thermocouple is ±0.1 °C in the range of −200^∼260 °C, and hot wire anemometer measurement (TESTO440 MODE TYPE 06280152 SERIAL No. 61183753) is ±0.07 m/s in the range of 0.02–3.0 m/s. The CO₂ concentration is measured by Telaie 7001 with an accuracy of ±50 ppm in the range of 0–10000 ppm. CO₂ tanks and flowmeters are employed to release gas through a hole at 1.1 m of the rectangular thermal manikin to simulate the respiration. The locations of the measurement points are presented in Fig. 5 (a). The experimental results at test point are compared with the corresponding simulation data, which are shown in Fig. 6 .

Fig. 5.

The location of the measurement point (a) Schematic of the vertical view; (b) Real image.

Fig. 6.

Comparisons of simulated and experimental at the measuring points (a) Velocity; (b) temperature; (c) CO₂ concentration.

It can be seen that most of the numerical values are in good agreement with the experimental data. The maximum relative error of velocity, temperature and CO₂ concentration is 9.2 %, 4.3 % and 5.4 %, respectively. It is mainly caused by the instrument error, measurement error and slight fluctuation of the outdoor conditions. The comparison results indicate that the accuracy of the model is reliable and can be used for further research.

4.2. Exposure dose of different pollution sources

Fig. 7, Fig. 8 present the velocity distributions with infected people sitting to cough at pollution source 1. Under MV, uniform environment can be obtained. However, most of the clean warm air is concentrated at the ceiling due to the thermal buoyancy. Under SV, the air supply inlets can directly deliver fresh air to the breathing zone. Nevertheless, the air velocity and temperature are also decayed with distance increasing. It can be concluded that the people far away from the inlets cannot get enough fresh air. Aiming at the problems exposed in the stratum ventilation, ICV introduces two jets with different temperature. Depending on the interaction between the jets, ICV can realize the direction change of thermal buoyancy, thus to alleviate the warm air rising. It can be seen that a more comfortable indoor environment with “sandwich” characteristic remaining more clean warm air in the breathing zone is provided under ICV.

Fig. 7.

Velocity distributions (Y = 6.1 m) with infector sitting to cough at pollution sources 1 under different ventilation methods.

Fig. 8.

Velocity distributions (Z = 1.1 m) with infector sitting to cough at pollution sources 1 under different ventilation methods (a) MV (b) SV (c) ICV.

The effect of the pollution source location on the ventilation performance is extremely obvious. As shown in Fig. 9 , significant variations exist among the exposure bioaerosol concentrations with one infector sitting to cough at source 1, source 2, and source 3 served by different ventilation methods. It can be seen that the dispersion of the pollutants changes with the pollutant source locations.

Fig. 9.

Exposure aerosol concentration distributions at source 1, source 2 and source 3 under different ventilation methods.

Under MV (c.f. Fig. 8(a–c)), the pollutant concentration range becomes more widely when the infector is located at source 2. With the concentration of 0.012 kg/m³ as the center of the pollution source 2, the diffusion radius can reach at least 9 m. It is due to that the contamination source is located at the room corner, which is far from the return air outlets. And the supply air carries the pollutants throughout the room. Source 1 also presents the wide diffusion range. The pollutant transmission radius is around 7 m with a concentration limit of 0.012 kg/m³. Source 3 is located near the return air outlet. Hence, the exhaled aerosol with virus can be quickly sucked and cleared out. Fig. 9a demonstrates that the diffusion radius is only 3 m with the concentration boundary of 0.012 kg/m³. Fig. 9(d–f) presents the exposure bioaerosol concentration distribution under SV. It demonstrates that the pollutant source location shows a minor effect on the concentration distribution under SV. The pollutant diffusion radius is all about 3 m with the exhaled aerosol concentration of 0.012 kg/m³ as the boundary. However, when the infector is closed to the supply air inlets, it is easier to cause the aerosol with virus to be delivered to the human respiratory region, leading to a relatively high exposure of the staff across from and in the same row as the infector. Under ICV, Fig. 9(g–i) indicate that the variation of the source location has no significant effect on the aerosol dispersion compared to MV and SV. And the pollutant diffusion radius can be reduced to 2–3 m under ICV.

The average contaminant exposure dose at the nose of a healthy staff, who sits across from the infector, is contrastively presented in Fig. 10 . The results reveal that the contaminant exposure dose is the highest under MV while lowest under ICV. In addition, the infector located at source 2 can lead to the highest exposure dose under MV. Due to the similar airflow organization of SV and ICV, the exposure dose to virus-containing aerosols caused by sneezing was both higher when the infector locates at source 3 under the two ventilation methods.

Fig. 10.

Comparison of exposure doses under different ventilation methods.

4.3. Annual infection probability

Considering the infector coughing/sneezing with sitting/standing at various locations, the annual infection probability P_y(d) for bioaerosol health risk under different ventilation methods is shown in Fig. 11 . The U.S. EPA benchmark is ≦ 10⁻⁴ infection cases per-person-per-year (pppy). According to the previous research [52], the calculation results and criteria can be expanded by a multiple of 10³ to make the expression clearer, which has no impact on the judging of the indicators. Hence, 0.1 presented in Fig. 11 is the healthy infection risk benchmark after index unitization. It can be seen that the health infection risk under ICV is the lowest among the three ventilation methods. Ventilation methods show noteworthy effect on the indoor health risk. Also, the location and behavior of infected individuals can further influence ventilation performance and lead to the differentiation of human health risks.

Fig. 11.

Heat map of annual infection probability under various ventilation scenarios. (a) Locations of pollutant source; (b) Source 1; (c) Source 2; (d) Source 3.

Under ICV, the aerosols exhaled by the infector coughing at sources 1 and 2 can be effectively diluted by the clean air, which makes the infection risk lower and meet the baseline. Due to the source 3 is closed to the supply air inlets of SV and ICV, the infection risk is higher than the U.S. EPA standard in all scenarios. Compared with SV, there are two heights of the ICV air supply inlets to form a particular airflow distribution with “sandwich” characteristic. Although the aerosol containing virus is quickly diffused to the breathing region under ICV, clever airflow pattern can effectively control the spread of the virus, realizing a much lower health infection risk for exposed individuals compared with SV and MV.

As for MV and SV, the health infection risk for the exposed person is always above the benchmark. It can be concluded that the indoor health infection risk hardly meet U.S. EPA standards served by MV and SV. Even so, the overall health infection risk under SV is still less than MV. It shows the superiority of non-uniform environment construction technology in epidemic prevention and control. The research results of the annual infection probability demonstrate that the indoor health infection risk varies greatly under different ventilation methods. Hence, reasonable ventilation methods should be introduced as the appropriate control strategy for reducing the cross-infection risk to an acceptable level, which is especially important when the epidemic is normalized.

4.4. Disease burden

Fig. 12 presents the assessment results of disease burden (DB) in various scenarios. It can be seen that the estimations of $P_y\left(d\right)$ and DB are nearly identical. WHO benchmark of DB is ≦ 10⁻⁶ DALYS pppy. Similar to the annual infection probability, the calculation results and criteria of DB are expanded by a multiple of 10⁵ to make the expression clearer, which has no impact on the judging of the indicators. 0.1 employed in Fig. 12 is the DB benchmark after index unitization. The disease health burden can be acceptable if the value is less than 0.1. Hence, the red numbers shown in Fig. 12 represent that the DB exceeds the allowed value under the corresponding scenario (ventilation methods, infector behavior, and infector location).

Fig. 12.

Heat map of disease burden under various ventilation scenarios (a) Locations of pollutant source; (b) Source 1; (c) Source 2; (d) Source 3.

Under ICV, the lowest disease health burden can be realized in all the discussed scenarios. It can be concluded that ICV is more effectivity on reducing aerosol concentrations in the breathing region of exposed individuals. When an infected person is sitting or standing, the aerosols exhaled through coughing can be effectively diluted by the clean air. However, the exhaled airflow is much larger when the infector sneezes. Hence, the position of the infector obviously affects the burden of disease borne of the exposed person when the infector sneezes. With the infector locating in the center of the room (source 1) and near the supply air inlets (source 3), the burden of the exposed person increases significantly. Due to the source 2 is located near the exhaust vents, the aerosol concentration in the breathing zone can be quickly reduced owe to the peculiar flow patter of ICV. Therefore, the health burden of disease for exposed individuals can all be within allowed values for both standing and seated aerosol exhalation when the infector is at source 2.

As for SV, the calculation results of the disease burden of exposed individuals indicate that ventilation performance of SV is slightly less effective than ICV. Compared with MV, SV can better deal with aerosol pollutants in the respiratory region when the infector coughs. In addition, the position of the infector has a significant effect on DB under SV. When an infected person sneezes with a large velocity of exhaled air, SV is less effective in removing aerosols than ICV, while stronger than MV. It is also noted that the health burden of disease on the exposed person is unbearable with the infector near the air inlets (source 3) under SV. It can be known that the infector should be avoided near the air inlets as far as possible, so as not to cause a wide range of infection under SV. However, no such limit exists under ICV.

Unfortunately, it is difficult to ensure the disease health burden on exposed individuals within tolerable limits in almost all scenarios under MV. The value is still over the benchmark under a conservative estimate. At source 3, the high velocity aerosols generated by the infector sneezing are directly sent into the exhaust vent, thus to realize an acceptable burden of the exposed people.

In general, ICV shows excellent advantages in reducing aerosols concentration in the respiratory region of exposed people. The indoor exposed population burden mostly meets the WHO baseline requirements under ICV from the perspective of human health. However, this research only studied the potential impact of the health risks in some specific scenarios. Deeper research on the real-life and more scenarios of public health protection are still need to be investigated in the future.

5. Conclusions

This study introduced a typical office as the background scene, where an infected person coughs, sneezes with standing or sitting at different positions. The cross-infection control performance of three ventilation strategies, namely mixing ventilation (MV), stratum ventilation (SV), and interactive cascade ventilation (ICV), was explored and compared with a validated CFD model. The related conclusions can provide a basis for designing and selecting the reasonable ventilation systems under the normal situation of the epidemic. The main conclusions of this study are as follows:

• (1)Compared with SV and ICV, the cross-infection control performance of MV is the weakest. The location and behavior of the infector show a significant impact on the exposed person at other locations under MV. The diffusion range of pollutants under MV is even increased three-fold over ICV. When the pollution source was near the air supply inlets, the pollutant diffusion range becomes more expansive, increasing the exposure doses by 52 % under discussed ventilation methods. The exposure does under ICV is 0.29 g/day, which can be reduced by 67 % and 50 % compared with MV and SV, respectively.
• (2)The health risk of the exposed person under ICV is 0.21 × 10⁻³ DALYs pppy, which is consistently lower than SV by 32 % and MV by 69 %. The health risk is greatest under MV while minimum under ICV for all exposed people in all discussed scenarios.
• (3)The average disease health burden for exposed persons under ICV is 0.93 $\times$ 10⁻⁶ DALYs pppy, which is consistently 37 % and 70 % lower than SV and MV, respectively. Compared to coughing, aerosols produced by sneezing of the infector under MV hardly meet the disease burden criterion. However, the percentages of the scenarios that meet the criterion under SV and ICV are 33 %and 75 %, respectively.

It can be concluded that ICV is a feasible ventilation strategy for the crowded indoor environment, which can effectively reduce the cross-infection risk and improve virus prevention and control. However, it is noted that the concentrated low velocity air supply inlets are employed in the MV model in this study, which may weaken the evaluation effect of virus control of MV. Hence, it is also worth studying on the effect of different air inlet arrangement and supply air velocity on virus prevention and control under different ventilation methods. Moreover, this study is focused on the virus prevention and control performance of the ventilations in winter scenario, which is the high outbreak season. Nevertheless, the load distribution, airflow distribution, and thermal buoyancy direction are different and more complex in summer scenario. The related conclusions based on the heating conditions cannot be applied directly under cooling condition. Therefore, future work will be comprehensively conducted under the summer conditions to improve the main conclusions obtained at this stage.

Author statement

Han Li: Conceptualization, Methodology, Formal analysis, Investigation, Data Curation, Writing - Original Draft.

Yuer Lan: Conceptualization, Methodology, Formal analysis, Investigation, Writing - Review & Editing.

Xiuqin Ma: Investigation, Resources.

Xiangfei Kong: Conceptualization, Methodology, Funding acquisition, Writing-Review & Editing.

Man Fan: Investigation, Resources, Review & Editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Data availability

Data will be made available on request.