Optimization of Cabin Virus Transmission Suppression Technology Based on Hanging Curtain Physical Isolation

Abstract

This study presents an innovative physical isolation measure for commercial scenarios, namely, hanging curtains, to prevent the spread of respiratory infections. Using computational fluid dynamics simulation techniques, the closed spaces within cruise cabins were modeled and numerically analyzed, focusing on the dispersion characteristics of droplets. Additionally, orthogonal methods were employed to investigate various arrangements of hanging curtains and their effects on droplet dispersion based on spatial positioning. The research findings indicated that hanging curtains can effectively alter the airflow within a space, realizing the innovative concept of localized pollutant containment. It was found that the spatial partitioning method based on the location of individuals contributes more to reducing droplet dispersion than other methods. Moreover, the sag height of curtains emerges as the most influential factor on individual infection risk, while the scheme for hanging curtain positions has the least impact. Finally, the optimal configuration recommendation is provided: a curtain bottom coordinate of Z = 2.3 m and a top coordinate of Z = 2.8 m when the infection source was positioned at the center of the space. This configuration has also been validated by varying the location of the infection source. The research findings provide valuable insights for formulating preventive measures for passengers on cruise ships and for pandemic control in similar scenarios.

1. Introduction

In recent years, major outbreaks of respiratory infectious diseases such as Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) and Middle East Respiratory Syndrome (MERS) have attracted widespread attention worldwide. These viruses are highly transmissible, have a short incubation period, and are difficult to prevent effectively with existing air monitoring equipment. Indoor environments have been shown to be major sites of virus transmission [1,2]. For example, SARS-CoV-2 can be transmitted through droplets, air (aerosols), and contact [3]. Cruise cabins are relatively closed environments with small spaces, and inadequate or poorly designed airflow organization makes it difficult for pollutants, such as aerosols, to be discharged in time, and they thus remain suspended in the cabin for long periods of time. These pollutants can pose a serious threat to the health of crew and passengers. Therefore, it is crucial to study the airborne mechanisms of viruses and design effective measures to curb respiratory pandemics.

Many factors, such as ventilation systems, air temperature and humidity, and social distancing, can affect the airborne transmission of respiratory infections [4]. Accordingly, in the prevention and control of respiratory infectious disease pandemics, the following main measures have been taken: improved ventilation [5], increasing personal ventilation rates [6], using devices such as ultraviolet lamps and portable air purifiers [7,8], adopting air conditioning systems with photovoltaic electrochemical oxidation filters [9], and maintaining a social distance of at least 2 m [10,11]. In addition to the above measures, physical isolation is a simple, highly independent protective measure that does not depend on specific equipment or systems, and at the same time, it is relatively inexpensive to implement and applies to a wide range of premises, including small stores and large public places. Physical isolation mainly focuses on shielding the source and altering the pathway of pathogen transmission. Masks are the main means of source shielding, playing a positive role in preventing the spread of respiratory infectious diseases. Studies have shown that wearing masks could effectively reduce the number of droplets released into the air by the infection source and decrease the socialization distance to 0.5 m [12]. However, there are differences in filter efficiency and protective ability among the various types of masks on the market [13,14]. Researchers found that the survival rate of most bacterial particles in mask filtration layers (such as filter cores) can reach 44 to 77% [15]. Ordinary masks worn by most people are less effective at stopping microorganisms, and simply wearing a mask cannot guarantee absolute safety. In the absence of the ability to change ventilation systems, except to prevent the virus at its source, intervention measures can also be implemented in the droplet transmission pathways to interrupt the spread of the virus.

Setting up screens, partitions, and other physical isolation devices to divide the space into different areas to reduce direct respiratory contact between personnel changes the transmission path of pollutants, thus achieving a reduction in infections. For example, Li et al. [16] used particle image velocimetry to monitor particle concentrations and a high-speed camera to record the effects of droplet transmission under different desktop partition placement measures and showed that using staggered configurations of desk partitions between infected and susceptible individuals can minimize droplet exposure. Mirzaie et al. [17] derived an average droplet concentration of up to 3.80 × 10⁻⁸ kg/m³ nearest to the infected person at a wind speed of 7 m/s using computational fluid dynamics (CFD) techniques, verifying that installing barriers in front of personal seats can prevent infection to some extent. Chen et al. [18] gave a barrier height of 60 cm above the desktop in a densely populated, open-plan office environment as being effective in preventing the transmission of the virus. The significance of the effect of physical barriers depends greatly on the height of the barrier. Ahmadzadeh et al. [19] modeled the risk of SARS-CoV-2 transmission in a high-speed train by taking into account a combination of temperature and humidity, ventilation rate, virus ejector source, exhaust location and capacity, and the addition of a physical barrier, proposing the use of physical barriers and high ventilation rates for personal protection. However, some studies have shown that physical barriers are somewhat limited in their ability to block droplet transmission on the path and protect surrounding susceptible individuals. Cheong et al. [20] simulated the contribution of installing partitions between beds in a hospital emergency department to reducing airborne pathogen concentrations and found that this approach was not as effective as increasing ventilation efficiency. Oksanen et al. [21] conducted an experimental study on space partitioning with dividers in a cafeteria, and the results of Phi6 virus detection as an alternative showed that spatial partitioning may adversely affect localized levels. Liu et al. [22] confirmed that desktop dividers in the canteen can cause aerosols to accumulate in the partitioned space, which poses a risk of infection to diners following the previous infected person who was seated at that seat. Nevertheless, this suggests that desktop partitions hinder the spread of particles to other surrounding individuals, so exploring the mechanism by which physical barriers impede virus transmission remains of practical significance. At present, studies on physical isolation are relatively homogenous in form, with most of them placing partitions directly on the floor or on tabletops, which, to a certain extent, affect human activities. On the other hand, although some studies have evaluated the effectiveness of physical barriers, further research is needed to investigate whether measures such as transparent barriers and screens can be effectively introduced in different locations, such as in confined spaces. Obtaining the interception effects of differently placed physical isolation on droplet transport will help assess the utility of physical masking measures and provide insights into the mechanisms by which barriers impede virus transmission.

In terms of methods for studying particle trajectories, there are two main approaches: CFD simulations and experimental measurements. Due to the high cost, long duration, and unavailability of data from experiments, CFD techniques have become the preferred choice of most researchers as they consider the complex mechanisms of airflow, heat transfer, and mass transfer to provide a three-dimensional distribution of pollutants in indoor space (concentration, velocity, pressure, etc.) [23,24,25]. In terms of methods for analyzing the probability of individual infection, the main methods are the Wells–Riley equation [26], the Dose–response model [27], and the Monte Carlo model [28]. The Wells–Riley equation calculates the average risk of infection in a population by taking into account the respiratory volume and ventilation rates as well as exposure time. Combining these two methods with CFD techniques can more accurately model the diffusion and deposition processes of airborne pollutants and provide a more comprehensive assessment of obtaining information such as the spatial distribution of pollutants and localized infections. It is also essential to note that viral activity is affected by multiple factors such as temperature and humidity as well as the duration of exercise, and the surrounding passengers may not become infected with respiratory infections despite sitting still for long periods of time during breaks. However, the research on virus activity is still immature, and the relevant mathematical model is lacking, which cannot be applied to predict virus transmission under different environmental conditions. Therefore, in this study, the probability of infection in susceptible individuals was assessed only on the basis of the mean droplet concentration in the respiratory region obtained from numerical simulations combined with the modified Wells–Riley equation.

Taking into account a combination of human behavioral habits, health protection, and the economy, this paper proposed an innovative suspended physical separation scheme considering the concept of zoning management space. The measure aimed to address the practical application of implementing physical isolation measures in small spaces, such as cruise cabins. Through numerical simulation, this paper comprehensively evaluated the effect of different hanging forms of curtains on the reduction in individual infection risk and transformed the location of the source of infection to analyze the applicability and effectiveness of the proposed program, providing a scientific basis for the development of targeted prevention and control strategies.

2. Materials and Methods

This study proposes an innovative solution for preventing the spread of respiratory infections, which is to install curtains in space to isolate pollutants. This measure requires no complex equipment and consumes no energy. Based on this idea, a physical model was created using NX, and the computational domain was meshed using ANSYS FLUENT to establish a numerical model of steady-state solutions for indoor continuous-phase airflow and discrete-phase droplet motion. The accuracy of the continuous-phase model and discrete-phase model was validated through theoretical and experimental approaches.

Furthermore, the distribution of particles emitted during continuous exhalation by a human body model was analyzed, and the curtain method was subjected to multi-parameter optimization design and comparative analysis. Finally, data post-processing was conducted using CFD-Post and Tecplot. Figure 1 depicts the design optimization process of curtains to suppress droplet diffusion.

2.1. Numerical Methods

2.1.1. Turbulence Model

To predict the flow distribution, the Re-Normalization Group (RNG) k-ε turbulence model in Reynolds-averaged Navier–Stokes (RANS) models was used. The RNG k-ε model has been extensively utilized to simulate indoor airflow fields [29]. The general governing equation is expressed as:

$$\frac{\partial (\rho \varphi )}{\partial t}+\frac{\partial (\rho \overline{u_j}\varphi )}{\partial x_j}=\frac{\partial }{\partial x_j}({\Gamma }_{\varphi ,eff}\frac{\partial \varphi }{\partial x_j})+S_{\varphi }$$

(1)

where ϕ is a universal variable that can represent the turbulent kinetic energy, dissipation rate, and other variables; ρ is the fluid density; u_j and x_j are directional velocity components and coordinates in space, respectively; Γ_ϕ,eff is the effective diffusion coefficient; and S_ϕ is the generalized source term [30].

Table 1. Representation of the dependent variable in general conservation equation.

Equation	Continuity	Momentum	Energy	Turbulence k	Turbulence ε
$\varphi$	1	$\overline{u_i}$	$c_p\overline{T}$	$k$	$\epsilon$
${\Gamma }_{\varphi ,eff}\frac{\partial \varphi }{\partial x_j}$	0	$\mu (\frac{\partial \overline{u_j}}{\partial x_i}+\frac{\partial \overline{u_i}}{\partial x_j})$	$(k_f+\frac{{\mu }_t}{{\mathrm{Pr}}_t})\frac{\partial \overline{T}}{\partial x_j}$	$(\mu +\frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\mathrm{k}}})\frac{\partial k}{\partial x_j}$	$(\mu +\frac{{\mu }_{\mathrm{t}}}{{\sigma }_{\epsilon }})\frac{\partial \epsilon }{\partial x_j}$
$S_{\varphi }$	0	$-\frac{\partial P}{\partial x_i}$	$0$	$G_{\mathrm{k}}-\rho \epsilon$	$\frac{\epsilon }{k}(C_{\epsilon 1}{p}_k-C_{\epsilon 2}\rho \frac{\epsilon }{k})$

P is the pressure; μ is the viscosity; μ_t is the eddy viscosity; σ_k and σ_ε are the Prandtl numbers for kinetic energy and dissipation, respectively; G_k is the turbulent kinetic energy generation term; C_ε1 and C_ε2 are constants.

delineates the expression of dependent variables in various conservation equations.

2.1.2. Modeling the Droplets

The trajectories of particles were tracked using the Lagrangian method based on Newton’s laws, and a discrete phase model (DPM) was used to discretize the effect of turbulent motion on particle transport, assuming that the particles did not interact with each other and that the forces were balanced on each particle. Droplets are subject to drag force, gravity force and additional forces after exhaling. The additional forces on the droplet include gravity, Saffman’s force, drag force, thermophoretic force, additional mass force, air pressure gradient force, and Brownian force. Among them, the additional mass force and air pressure gradient force are two orders of magnitude smaller than the drag force and can be ignored [31]. Meanwhile, in the cruise lounges, turbulent diffusion is dominant, and the diffusion effect of Brownian force is very small [32]. Therefore, only thermophoretic force and Saffman’s force were considered for the additional forces in this study. Taking the Cartesian coordinate system in the x-direction as an example, the equation of particle motion is as follows:

$$\frac{d{u}_p}{dt}=F_D\left(u-u_p\right)+\frac{g_x({\rho }_p-\rho )}{{\rho }_p}+F_x$$

(2)

where u and u_p are the air velocity and droplet velocity, respectively; ρ and ρ_p are the air density and droplet density, respectively; F_D (u − u_p) is the drag force per unit droplet mass; $\frac{g_x({\rho }_p-\rho )}{{\rho }_p}$ is the gravity per unit droplet mass; F_x is the additional force per unit mass. The specific contents and expressions of F_D and F_x are shown in

Table 2. The specific contents and expressions of F_D and F_x.

Force	Expression	Meaning of the Symbols
$F_D$	$\frac{18\mu }{{\rho }_p{d}_p^2}\frac{C_D\mathrm{Re}}{24}$	μ is the air viscosity; dp is the droplet diameter; CD is the drag coefficient; Re is the relative Reynolds number of particles
Saffman’s force	$\frac{2K{\nu }^{0.5}\rho d_{ij}}{{\rho }_p{d}_p{(d_{lk}{d}_{kl})}^{0.25}}(u-u_p)$	K = 2.594; dij is the deformation tensor
Thermophoretic force	$-D_{T,P}\frac{1}{T}\nabla T$	DT,P is the thermophoretic coefficient; T is the local air temperature

.

Droplets evaporate when entering cruise cabins, using the discrete phase model as the mass transfer model [33]. The rate of droplet evaporation is governed by the concentration gradient between the droplet surface and the ambient air:

$$\frac{d{m}_p}{dt}=k_c{A}_p{M}_{w,p}(C_s-C_{\infty })$$

(3)

$$k_c=\frac{D_{i,m}}{d_p}(2.0+0.6{\mathrm{R}\mathrm{e}}_d^{1/2}{Sc}^{1/3})$$

(4)

where k_c is the mass transfer coefficient; M_w,p is the molecular weight of the component; A_p is the droplet surface area; C_s and C_∞ are the water vapor mass concentrations at the droplet surface and in the air, respectively; $D_{i,m}$ is the diffusion coefficient of water vapor in the air; $Sc$ is the Schmidt number; and d_p is the droplet diameter.

In this study, the convective heat transfer between droplets and air as well as the heat transfer that occurs during mass transfer were considered. The evaporation process of water in droplets was simulated by the Species Transport model, and the heat balance equation for droplets is as follows:

$$m_p{c}_p\frac{d{T}_p}{dt}=h_p{A}_p(T-T_p)-\frac{d{m}_p}{dt}{h}_{fg}$$

(5)

where c_p is the droplet heat capacity; h_p and h_fg are the convection heat transfer coefficient and latent heat, respectively; and A_p is the droplet surface area.

2.2. The Room Model

2.2.1. The Geometry and Mesh

The examined closed cruise lounge was 6.0 m long, 3.0 m wide and 2.8 m high with air conditioning turned on. The mechanism of droplet transmission in a lounge was investigated utilizing displacement ventilation system. Air with a flow rate of 0.1141 m³/s and a temperature of 20 °C was supplied through slits located on either side of the lounge’s bottom, both of which were 0.7 m long and 0.05 m wide. Two outlets were located in the ceiling, each with an effective exhaust area of 0.04 m². The room contained six tables, each 0.3 m in diameter and 0.05 m thick. Of the nine people placed in the restroom, one with respiratory infectious diseases, called BB, was marked in red, and the other susceptible persons were marked in blue. People were separated by 2.0 m in front and behind and by 0.9 m from left to right. Assuming passengers were seated in a lounge area with a seated height of 1.291 m and their mouth center was located at a height of 1.1 m. The mouth region was simplified as a square mouth opening with an area of 4 cm², and the spherical area with a front-half radius of 0.2 m in front of the face was considered the respiratory zone [34] (refer to Figure 2).

The geometry was meshed using polyhedral cells in the ANSYS FLUENT MESHING software. The mesh refinement of the air supply, exhaust, and manikins’ parts was carried out, and a mesh independent study was performed, the results of which are given in Section 2.3.

2.2.2. Boundary Conditions and Case Description

Table 3. Boundary conditions.

Boundary	Momentum	Thermal	DPM
Door	No-slip	26 °C	Reflect [38]
Walls	No-slip	26 °C	Reflect
Table	No-slip	Adiabatic	Reflect
Bodies	No-slip	31 °C [39]	Trap
Curtain	No-slip	Adiabatic	Reflect
Outlet	Pressure outlet	/	Escape
Inlet	1.63 m/s	20 °C	Escape
Mouth (susceptible person)	−0.37 m/s	26 °C	Escape
Mouth (infected person)	0.37 m/s	33 °C [39]	Escape

describes the boundary conditions of this simulation study. It is worth noting that in this paper, the human respiratory process was simplified to a uniform exhalation airflow based on previous studies [26,35,36]. Droplets contained non-volatile solid particles (viral nuclei) that remain spherical throughout the evaporation process. Large droplets tend to deposit over shorter distances, while small droplets play a dominant role in propagating over longer distances [4]. In consideration of the spatial constraints between individuals within the model, droplets with a particle size of 1 μm were chosen in this paper. The mass fraction of the evaporable component was 91.5%, with a droplet mass flow rate of 6.35 × 10⁻¹³ kg/s (an infected person exhales 1000 particles per liter [37]). The curtain is considered to be rigid.

The direction of airflow and air distribution are among the most important parameters influencing the airborne transmission of respiratory infectious viruses in indoor environments. The addition of a curtain for spatial division changed the direction of the airflow, allowing the effectiveness and applicability of strategies to reduce the risk of infection in individuals to be comprehensively assessed. This paper involved three variables: the distribution form and vertical suspension position of the curtain, and the location of the source of the infection. A total of 27 cases were calculated. Case 1 was a simulation of droplet diffusion in a lounge without any spatial partitioning measures; cases 2 to 5 correspond sequentially to the separation scheme in Figure 3, designed to study the effect of the form of hanging curtains; cases 6 to 21 were studies of the optimal combination of curtain hanging form and vertical suspension position, with the specific orthogonal experimental design used given in Section 3.2; cases 22 to 27 were the two groups of control cases that correspond to different positions of the infected person in order to check the protocol’s validity.

2.3. Model Validation and Mesh Independence Test

In order to verify the accuracy of the present numerical model in predicting the transport process of exhaled droplets from an infected person, a two-region room with dimensions of 5 m × 2.4 m × 3 m was established with reference to the experimental conditions of Lu et al. [40]. The two regions were of the same size, and the air could be circulated inside the two regions. In the initial state, the oil particles were uniformly distributed in region 1 with a density of 865 kg/m³ and a particle size range of 1–5 μm and were influenced by fresh air (air change rate of 9.216 h⁻¹ per hour), released in region 2. Comparing the simulation results with the experimental measurements, the particle concentrations are shown in Figure 4. As the boundary conditions of the simulation cannot be completely restored to the actual boundary conditions, by comparing the experimental results with the simulation results, it can be seen that the two values cannot be exactly the same but have the same trend and a correct match.

In addition to the above verification, a ventilation test was carried out in a laboratory, in which a table was placed in the room, and the room dimensions were 3.78 m × 4.78 m × 2.86 m. Four test trees with 24 measuring points were arranged in the room to measure the indoor air temperature. The boundary conditions of the model were set according to the experimental data as much as possible. The temperature of the walls was set to 7 °C, and the heat transfer coefficient was set to 0.81 W/(m²·K), respectively. The air supply temperature was 20 °C, and the velocity was 2 m/s. Figure 5 demonstrates the test flow, laboratory model, and a comparison of the simulated data in this paper with the simulated data and experimental data regarding and temperature of the airflow. Individual points were found to be inaccurate. This may be due to the assumption that the heat transfer characteristics remain constant at any point on an isothermal wall surface, which is not realistic. Nevertheless, the overall data are in good accordance, which means that the RNG k-ε turbulence model used in this paper is appropriate.

In order to eliminate the effect of mesh size on the calculation results, the mesh was coarsened and refined by increasing all mesh sizes by a factor of 2 and 0.5, respectively. Three sets of grids (2.23 million, 4.23 million, 8.65 million) were created by selecting case 1 without a curtain to perform grid independence checking. The airflow velocities at three locations on the x = 1.5 m profile were compared. As shown in Figure 6, there is a correlation between the calculation parameters and the number of nodes, and the difference between the calculation results of 4.23 million nodes and 8.65 million nodes is relatively small. Considering the calculation accuracy and the calculation time, the number of nodes was finally selected as 4.23 million.

2.4. Analysis Methods

An assessment of the risk of infection for people in the lounge allowed for the evaluation of the suppression of respiratory infections by different measures; the probability of individual infection was obtained using the modified Wells–Riley equation proposed by Zhai [41]:

$$PI(x,y,z)=1-e^{-\frac{C\left(x,y,z\right)}{C\left(x_0,y_0,z_0\right)} \times \frac{q_s}{q_e} \times \sigma \left(x_0,y_0,z_0\right) \times t}$$

(6)

where PI represents the probability of infection (0–1); C and t are the mass concentration of the viral pathogen and exposure time, respectively; (x₀, y₀, z₀) is the spatial location of the infected; σ is the exhaled number of quanta per second, and quanta represents the minimum number of particles that can cause disease; and q_s and q_e are the inhalation rate of a susceptible person and the exhalation rate of an infected person, respectively.

3. Results and Discussion

3.1. Flow Fields and Droplet Dispersion

Figure 7 illustrates a comparison of the indoor airflow fields in the room without curtains and in the room with different curtain-hanging scenarios in the cross-section at the center point of the infected person’s mouth (Y = 3 m and Z = 1.1 m), where significant differences in the distribution of the indoor airflow fields can be observed for the different measures. These differences arose from the coupling of multiple fields. First, the specific microenvironmental field around the human body, which is due to the temperature difference of the airflow around the human body, formed an upward “thermal plume” phenomenon, and its speed range was approximately 0.3–0.4 m/s. Second, following the convergence of the airflow originating from the bilateral air supply ports, its speed falls within the range of 0.65 to 0.82 m/s, and the existence of these converging airflows reduced the interaction of respiratory airflows between AB and BB. It is worth noting that part of the air supply disrupted the flow direction of the thermal plume, resulting in an uneven distribution of velocity and pressure in the space. This uneven distribution further drove the mixing and spreading of the airflow, creating a pronounced vortex that is mainly concentrated above the head of the passenger AB. Around passengers CB and BB, the airflow ascends along their bodies, forming a kind of indented airflow shape. These airflows eventually converged with the airflows above the space and moved towards the air vents, the location of which determined the direction of the main airflows. The exhaled airflow of an infected person flows mainly in a forward direction under the influence of the three factors of air supply, respiration, body heat plume, and exhaust air. However, the fast main airflow was obstructed by the slow airflow in the region in front of the side of the infected person, thus creating a rotating vortex (Figure 7a). The mechanism of change in the indoor airflow field caused by the four designed curtain placement scenarios will be discussed in the following sections. Figure 7b shows the airflow field for hanging curtain scheme A, where the fluid above the surface of the curtain is blocked to change the flow direction, resulting in the flow field separating to form two relatively independent regions in front of and behind the curtain. The finite flow channel formed between the two passengers on the same side of the air supply stream triggered local acceleration of the flow, so the vortex collected above BB and CB. Figure 7c,d show the flow fields of scheme B and scheme C, respectively. The airflow in the intercepted XZ plane was the same principle as scheme A, which is not discussed here. The placement of vertical curtains and the increase in the number of curtains played a decisive role in the change in flow direction in the horizontal plane under different placement schemes. Scheme B made the lounge space symmetrical from front to back, so the airflow formed a more pronounced diversion in the median line. The increase in the number of curtains resulted in a more complex vortex effect as well as turbulence enhancement effects and blocked the airflow circulation between the left and right-side passengers. Depending on the length and placement of the curtains, the airflow was cut into different zones, and the flow of airflow in each zone was different. By controlling these parameters, fine control of airflow zoning could be realized, thus achieving the purpose of improving indoor air quality.

The human body’s microenvironment makes it difficult to expel virus-carrying droplets at high concentrations through the dilution effect of fresh air from the ventilation system [42]. The heat generated by the human body is transferred to the surrounding air through thermal radiation and convection, causing an increase in the temperature of the air around the body, resulting in the phenomenon of thermal plumes. The presence of thermal plumes exacerbates the turbulence level in the human body’s microenvironment, enhancing the mixing of droplets with other airflows during their ascent, thereby expanding the distribution range of droplets in space. Additionally, the suspension duration and propagation distance of droplets in the air are constrained by evaporation and settling rates, while subtle changes in temperature and humidity in the human microenvironment have a significant impact on these rates. Therefore, to reduce the risk of personnel contracting respiratory infectious diseases, it is necessary to start by changing the direction of airflow between people. Exploring the form of hanging curtains and their height to quantitatively assess their effectiveness in reducing the risk of personnel contracting respiratory infectious diseases presupposed an understanding of the diffusion mechanism of droplets in the rest lounges. In case 1, when an infected person began to exhale, the droplets were driven upward by an updraft. At the same time, most of the droplets were spread rapidly to the lateral front by the longitudinal body airflow. As the exhalation behavior proceeded, the first person to be affected was the susceptible person on the same side of the infected person’s row, and most of the droplets wrapped around that susceptible person. The height of the exhaled droplets moved up to 1.65 m. The transmission of a respiratory infection in a confined space depended on the final number of droplet nuclei transmitting the pathogen, and the results of this part are shown in the following paragraph. At the same time, the droplets were affected by the vortex, and some of them moved downward, with a very small fraction of them moving behind the infectious person. The lateral airflow made the droplets move between the two rows of passengers in the same row, but due to the intermediate partition airflow, the droplets failed to continue spreading to the opposite side of the main air supply, and the droplets were confined to the area in front of the source of infection, and the number of particles in the respiratory zone of the front passengers was much larger than that of the rear passengers. In the simulation calculation of the effect of the hanging curtains, droplets with a particle size of 1 μm were used, which are small droplets. Those droplets were virtually unaffected by gravity, could be suspended in space for long periods, and exhibited good flow characteristics, thus increasing the likelihood of infection from inhalation by susceptible people in the front. The number of droplets in front of the rear passenger increased with diffusion time until they spread throughout the lounge and were exhausted through the air vents. In an indoor environment, the trajectory and distribution of droplets were closely related to the airflow field. As demonstrated in Figure 8b–e, the droplets are driven by the airflow and transported along the airflow direction, and the droplets are fully mixed and dispersed in the turbulent flow. Specifically, the curtain separation scheme A blocked the tendency of droplets to spread forward, and the droplet particles were concentrated in the middle of the two baffles in scheme B. Due to the separating effect of the curtain, the droplets in scheme C and scheme D were concentrated in the airflow partition.

In case 1, it was demonstrated that in the absence of any physical isolation measures, the number of particles in the x = 0–1.3 m region was significantly higher than that in the x = 1.3–3 m region. The particulate concentration showed an essentially decreasing trend with increasing Y distance, and the number of particles behind the infected person was very limited. This also meant that the infected person located in the middle posed a greater risk of infection of susceptible people to their front and right, while the effect on the people to their back and left was relatively small. When a curtain was hung in front of the source of infection, the concentration of particulate matter changed significantly in the x direction, and the change in airflow direction caused more droplets to spread to the x = 1.3–3 m area. From cases 2–5 in Figure 9b, it can be observed that the number of droplets in the horizontal area where the source of infection is located after hanging the curtains is larger than the number of droplets in the front and back sides; that is, the droplets are mainly concentrated in the range of y = 2 m to 4 m. Specifically, the hanging curtains set in front of the infected person hindered the tendency of virus-carrying droplets to spread to the front, and the number of droplets increased in the range of y = 2 m to 3 m (case 2). When the space was divided equally into three areas (separation scheme B), the particulate matter in the flow field inside the lounge tended to be evenly distributed. The more detailed the division of space, the stronger the turbulence in the air and the more pronounced the movement of droplets. From the perspective of the x direction, the effect of partitioning space according to the location of tuyere to achieve partition management was not obvious (case 3). Separation scheme C (case 4) did not achieve the desired effect, and the number of particles increased overall with an increasing y distance, which is almost opposite to the conclusion drawn from case 1. In case 5, based on the scheme of dividing the space according to passenger seats, it was found that the peak value of the particulate matter concentration was about x = 0.76 m and x = 1.4 m, which is in the position of the hanging curtain and longitudinal flow of air supply. From the perspective of the y direction, separation scheme D (case 5) was able to effectively concentrate the virus-carrying droplets in the transverse region where the infected person was located, reducing the diffusion to other directions, which was the same as the result derived in the previous section. Taken together, separation schemes A and D were considered to be the better spatial division schemes.

3.2. Orthogonal Optimization

Considering that the combination of the shape and height of hanging curtains can produce different effects, this study used the four forms and heights of the suspended curtain as variables, using the orthogonal method to obtain the influence of the variables. The vertical table is defined as L_n(t ^q), with L representing the horizontal table, n the total number of experiments, q the number of factors, and t the horizontal number of each factor. There were three factors of influence in this paper, including the suspension curtain program set as variable A, the sag height of the curtain set as variable B, and the top hanging height of the curtain set as variable C. In addition, each variable had four levels; variable A had four suspended forms, as shown in Figure 3; variable B had four design parameters, Z₁ = 2.1 m, 2.2 m, 2.3 m, and 2.4 m; and variable C had four design parameters, Z₂ = 2.8 m, 2.7 m, 2.6 m, and 2.5 m. The vertical table used in this paper is L₁₆(4³) and 16 simulation calculations are based on a combination of orthogonal trials, with the average probability of infection (API) for each trial as shown in

Table 4. Average personal probability of infection for different tests.

Test Number	Scheme	Z1 (m)	Z2 (m)	API
1	A	2.1	2.8	0.1958
2	A	2.2	2.7	0.2558
3	A	2.3	2.6	0.2595
4	A	2.4	2.5	0.2230
5	B	2.1	2.7	0.2435
6	B	2.2	2.8	0.2590
7	B	2.3	2.5	0.2220
8	B	2.4	2.6	0.2530
9	C	2.1	2.6	0.2635
10	C	2.2	2.5	0.2540
11	C	2.3	2.8	0.2131
12	C	2.4	2.7	0.2330
13	D	2.1	2.5	0.2377
14	D	2.2	2.6	0.2234
15	D	2.3	2.7	0.1996
16	D	2.4	2.8	0.2633

. The average probability of infection risk value refers to the average infection risk of eight individuals, excluding the source of infection.

Figure 10 gives an extreme analysis of the average individual probability of infection under different schemes, and the slope of the line reflects the degree of influence of each influencing factor on the evaluation indicator. The higher the slope, the more significant the influence of this factor. As the diagram shows, with the location of the curtains and the top hanging height changes, the average individual infection risk increases first and then decreases, while the sag height changes show a curved trend. For the probability of infection, a smaller value represents a better program. Therefore, the optimal horizontal combination was A_DB_2.3C_2.8, which was the setting of three curtains, and the vertical coordinate position at 2.3–2.8 m was the best program. The relationship between the magnitude of the extreme difference R is R_B > R_C > R_A, so the factor that has the greatest influence on the risk of individual infection is the sag height of the curtains, and the least significant influence is the curtain hanging position scheme. When BB was the infection source, the average individual infection risk of infected people before not setting any hanging measures was 0.239, and the numerical simulation calculation yielded 0.1957 in the case of the optimal scheme A_DB_2.3C_2.8, and the average individual infection risk of infected people was reduced by 18%. In order to further investigate the inhibitory effect of the selected curtain arrangement scheme on the transmission of particles, this paper evaluated the universality of the option A_DB_2.3C_2.8 in dealing with different sources of infection.

3.3. Scheme Effectiveness Evaluation

The validity of the optimal solution A_DB_2.3C_2.8 obtained by the orthogonal method is evaluated by the change in the position of the infected person. Figure 11 and Figure 12 show the distribution of droplets and the probability of infection of an individual passenger with a sedentary time of 2 h in several typical cases after the change in the position of the infected person, respectively. As demonstrated in Figure 11, whether the source of infection is at CB or AB, the scheme A_DB_2.3C_2.8 can successfully hold droplets in the area separated by the curtain, preventing them from spreading to surrounding persons. Specifically, when the source of infection is CB, it is observed that droplets initially disperse towards the rear of the source and, subsequently, upon reaching a certain height, the droplets evaporate to form smaller particles that propagate forward. In this process, the strategic optimization of curtain layouts can effectively obstruct the dispersion of droplets into the surrounding environment, confining them within a defined area demarcated by the curtains. In the case where the source of infection is AB, the droplets are influenced by the presence of curtains, causing them to flow upwards along the curtain. This physical barrier method restricts the free dispersion of droplets, effectively reducing the range of their spread.

Figure 12a,c illustrate the individual infection risks of nine passengers when the infected individual is situated at positions CB and AB within the lounge, in the absence of any spatial separation measures, respectively. Notably, when the infected individual was positioned at CB or AB, it implied their proximity to the air supply inlet. The findings reveal that when the infected individual is located near the air supply inlet, it represents a less favorable scenario, presenting a comparatively higher threat to nearby susceptible individuals. To be more specific, when the infected individual occupied the CB position, the risk of infection for passengers in the rear row was significantly greater than for those in the front row. Among these rear-row passengers, the highest likelihood of infection was observed in the CC passenger, positioned directly behind the infected individual, rather than among passengers within the same row. This was consistent with the findings of the flow field analysis in Section 3.1. When the location of the infectious agent became AB, the overall risk of infection in the space was slightly higher relative to the source of infection CB, but passenger CC was still the individual with the highest probability of infection.

Figure 12b,d illustrate the individual infection risk of occupants in an indoor lounge under varying sources of infection, considering the optimal curtain arrangement scheme. This finding is in contrast to Figure 12a,c, Figure 12b,d clearly demonstrate how the presence of an optimal separation scheme significantly mitigates the overall infection risk within the lounge, particularly when the infection source is AB. This effect was achieved by strategically positioning curtains to alter the airflow near the exhaust outlet, causing most droplets to accumulate near the space occupied by the infected individuals, effectively preventing droplet dispersion into the surrounding area. Specifically, when CB was the infection source, the average individual infection probability without any physical isolation measures was 0.251. However, with the implementation of curtain partitioning, this probability decreased to 0.166, resulting in a 33.9% reduction in overall infection risk. Similarly, when AB was the infection source, the average individual infection probability without any physical isolation measures was 0.265. Yet, with curtain partitioning in place, this probability dropped to 0.201, leading to a 24.2% reduction in overall infection risk. These quantitative results unequivocally demonstrate that curtain partitioning is a highly effective measure for mitigating viral transmission. Consequently, the A_DB_2.3C_2.8 scheme was deemed to be an effective strategy for curtailing viral spread, applicable across scenarios involving various sources of infection.

4. Conclusions

In this study, a validated droplet evaporation and dispersion model was employed to numerically simulate the dispersion of respiratory pathogens carried within droplets in a three-dimensional cabin space defined by hanging curtains. The individual infection risks of nine passengers in a lounge were analyzed, with a particular focus on the impact of three variables: the arrangement of the hanging curtains, the sag height, and the overhang height, on the susceptibility of individuals to infection. Through our research, we found that hanging curtains as a physical isolation measure can significantly alter the airflow dynamics within a cabin space. Optimal and well-considered curtain configurations were shown to effectively inhibit the dispersion of droplets and particles. Hanging curtains between infected individuals and susceptible individuals in the front row, or partitioning the space based on passenger seating positions, were demonstrated to be preferable physical isolation strategies. The orthogonal test method showed that the optimal physical isolation strategy was achieved when the bottom coordinate of the curtain was at Z = 2.3 m and the top coordinate was at Z = 2.8 m. This configuration effectively confines and controls the dispersion of droplets. Furthermore, we verified the effectiveness of the obtained optimal arrangement. By changing the location of the infectious agent, the curtain scheme could still significantly reduce the probability of surrounding passengers being infected with respiratory infectious diseases. These results indicate that the partition management of confined spaces through rational configuration and the use of curtains is universal for reducing the risk of infection of passengers in similar scenarios, such as businesses and hospitals. During routine operations, curtains can be kept rolled up or folded to maintain the aesthetics and functionality of the cabin. However, during respiratory disease outbreaks, they can swiftly unfurl to form an effective isolation barrier. Nevertheless, this measure is not without its drawbacks, requiring regular cleaning and maintenance. Therefore, future research could explore optimizing curtain design by integrating sensors and automatic control systems to monitor air quality, crowd density, and indoor environmental parameters. This would enable automated adjustments to curtain position and operation, fully leveraging the physical isolation capabilities of hanging curtains for disease prevention. Meanwhile, it is to be noted that the applicability and effectiveness of physical isolation measures are affected by the specific environment of the place, and they cannot completely replace the role of masks. When there is a major outbreak of respiratory infections, wearing a mask is the most effective way to reduce the spread of droplets during breathing and speaking. Nevertheless, for socializing places where masks are not normally worn while eating and drinking, the proposed physical isolation method is presented as a practical means to prevent cross-infection and to alert individuals to maintain an appropriate social distance. Although this article currently focuses primarily on a single study of hanging curtains, this is just a starting point in the exploration process. We look forward to further exploring the collaborative optimization of physical isolation strategies and ventilation systems in the future to better enhance overall epidemic prevention effectiveness.