Sneeze and Cough Pathogens Migration inside Aircraft Cabins

Abstract

Transmission of respiratory infectious airborne diseases, such as influenza, H1N1, Severe Acute Respiratory Syndrome (SARS) and COVID-19 inside any closed environment like the aircraft cabins has always been a topic to be studied, because the respiratory droplets produced when a passenger with a certain infections talks coughs or sneezes have harmful effects on other occupants. They have the ability to take flight and hang in the surrounding air or land on passengers or surfaces in short time. This work presents the results of a study of airflow behavior of coughing and sneezing droplets that are produced from a moving passenger in wide-body aircraft cabin section at different velocity rates. In addition, it compared between transmission of different flow rates and velocities in order to show how can these diseases transported from a moving and standing passenger to other passengers. This numerical simulation used computational fluid dynamic (CFD) modeling simulation. The results showed that the airflow of coughing and sneezing droplets produced from the moving passengers could reach seated passengers; however, sneezed droplets had more harmful impacts than coughed droplets, also both travelled for a long distance inside the cabin. In addition, when comparing the droplets spread range resulting from the moving passenger and stand-still one, it was found that the quicker the passenger moves, the further the droplets spread.

Introduction

Influenza, H1N1, Severe Acute Respiratory Syndrome (SARS) and coronavirus disease 2019 pandemic (COVID-19) are infectious diseases that may infect humans either through droplets or airborne particles carrying these diseases [1]. The droplets or particles are produced from an infected person during coughing, sneezing or talking. Moreover, these droplets are transmitted from one person to another person through inhalation [2]. Computational Fluid Dynamics (CFD) numerical simulations as well as practical experiments are used to study the effects of transmission of the droplets inside closed environments. Table 1 summarizes the studies of the transmission of the airborne particles or droplets and their behaviors.

Table 1. A brief summary the studies of the transmission of the airborne particles or droplets and their behaviors.

Regarding respiratory infectious diseases, there are three ways to spread; direct and indirect contacts besides airborne transmission [9]. This happens inside aircraft cabins. In direct contact, the droplets that are coming from the passenger’s mouth and nose during coughing, sneezing and talking and containing viruses need only a close contact to transport [4]. Moreover, in indirect contact droplets transmitted from the surfaces like cabin’s chair or windows to the passengers [11]. There are many parameters that should be taken into consideration in order to simulate the dispersion and deposition of the expiratory droplets using computational fluid dynamics (CFD). These parameters are [8]:

·         Coughing or sneezing flow rate

·         Coughing or sneezing direction

·         Mouth area

·         Temperature of coughed or sneezed droplets

·         Size of coughed or sneezed droplets

Concerning the impacts of transmission of diseases due to the movement of passenger, Poussou et al. [12] and Mazumdar et al. [13] studied the impact of moving a passenger or cabin crew through the exhaled droplets that are generated from a seated passenger. In addition, Khalil and Kotb [14] simulated the spreading of coughed particles induced from a moving passenger inside the aircraft cabin. This investigation attempted to use computational fluid dynamic (CFD) simulation, dynamic mesh analyses technique, and Lagrangian equations model to compare between the behaviors of cough and sneeze particles induced from a passenger while moving and standing under different velocities and flow rates.

Mathematical Modeling

The Governing Equations

In this investigation, ANSYS FLUENT V18.1 CFD commercial software was used to solve mass, momentum, and energy equations that are required to simulate the case.

Continuity Equation:

                                                               (1)

Momentum Equation:

                              (2)

                               (3)

                             (4)

Energy Equation:

                                (5)

Moreover, a dynamic mesh analysis in ANSYS program was used in ANSYS FLUENT in order to present the passenger movement inside the aircrafts cabin. Due to moving of the passenger an integral form of conservation equation is used [15]:

      (6)

The model that was used during the simulation to calculate the airflow of the particles and the ventilated cabin is the realizable K − ε model, as the performance of this model is better than the standard K − ε model [16], and it is more accurate than RNG K − ε model [16]. The transport Equations for the Realizable K − ε Model are as follows [16]:

                         (7)

    (8)

Where, is the velocity vector, P is the pressure, u, v, w are flow velocity in the directions of x, y and zaxis, t is the time, V is the control volume, ϕ is a general scalar, ρ is the fluid density,  and  are flow velocity vector and mesh velocity of the moving mesh, respectively, Γ is the diffusion coefficient, Sϕ is the source term of ϕ, GK is the turbulence kinetic energy, Gb is the turbulence kinetic energy that is generated due to buoyancy, YM is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, σKand σεare the turbulent Prandtl numbers, SK and SE are terms that can be defined by the user, C1 and C2 are constants.

Calculations of Cough and Sneeze Droplets

To investigate the behaviors of the cough and sneeze droplets induced from the moving passenger, the discrete phase model was used in ANSYS FLUENT in order to predict the trajectory of the droplets; this can be done by integrating the force balance on the droplets [15].

Droplets Force Balance Equation

The forces balance of the droplet equals the droplet inertia with all forces that affect the droplet, it can be written (for the x-direction, as an example) as [15]:

                                          (9)

Where, FD (U – Ud) is the drag force per unit droplet mass, Ud is the velocity of the droplet, ρd is the density of the droplet, gX is the force of gravity on the droplet in x-direction, µis the molecular viscosity and FX is an additional force.

Model validation

In order to validate this study, ANSYS FLUENT v18.1 CFD commercial program was used. Validation process is to test the reliability and accuracy of the ANSYS Fluent CFD program that was used to simulate a numerical case. This can be done by comparing the generated CFD results with experimental data. During this investigation, the experimental data were selected from Kühn et al. [17] study that was focused on analyzing and measuring the forced and mixed convection heat transfer inside AIRBUS 380 upper-deck cross section cabin mockup. The cross section of this aircraft has a length of 6 meters, a width of 5.1 meters, and a depth of 2.2 meters. Moreover, 20 dummies were added inside the cabin to simulate the passengers. Inner heaters surrounded these manikins in order to simulate their thermal load reflection and four electrical panels were added on the top of each side of the cabin to simulate the heat input of the light. ANSYS design modeler (DM) was used to draw the cabin, as shown in Figure 1. A half of a cross-section of the cabin was created in order to speed up the CFD progress. Consequently, we used the same boundary conditions that were used during the experiment. Table 2. shows the validation boundary conditions.

Table 2. The validation boundary conditions.

ANSYS design modeler (DM) was used to create the 3D model of the cabin. The dimensions of the upper deck cross section cabin are 5.1×2.2×6 meters. Figure 1 shows the 3D model of the upper deck cabin; nevertheless, a half of the cross-section cabin was used during the simulation in order to perform the simulation in short time.

Figure 1. 3D model of the A380 upper-deck cabin.

Moreover, by using ANSYS, about 6835652 tetrahedral mesh cells and 8628058 nodes were generated. In addition, we used the realizable K – ε model.Kühn et al. [15] illustrated the results of the velocity magnitude profile of A50/50 air inlets configuration at x = 1190 mm. also used an equation to illustrate the temperature magnitude at x = 1120, as shown in Figure 2. The temperature equation is:

                                                              (10)

Where, ΔTloc, (T − Tin), (ΔT) and ΔT are the corrected and actual measured local temperature difference to the incoming air temperature.

Figure 2. A comparison between the experimental velocity and temperature magnitude and the CFD results.

From the comparison of the experimental velocity and temperature data and the CFD results in Figure 2, it was found that the argument between them is good and can be accepted.

Numerical model

Proposed model

The dimensions of the geometric model are also based on the model used by Kühn et al. [15]. Table 3 shows the simulation boundary conditions of the case study. We selected this aircraft cabin, because the probability of diseases transmission inside its cabin is higher than any other aircrafts due to including large number of passengers during long flights. Moreover, a dummy was installed in the middle of the cabin’s aisle in order to simulate the exhalation of the coughed and sneezed droplets during the movement. This dummy has a length of 1.67 m and a width of 0.45 m besides its mouth area is 4 cm², as recommended by Gupta et al. [7]. Figure 3 shows the 3D model of the moving passenger inside the cabin. Throughout our CFD simulation, the realizable K − ε model and coupled pressure-velocity coupling were used.

Table 3. The simulation boundary conditions.

Figure 3. 3D model of the cabin and moving passenger.

Design Case Setup

Economy class in the A380 aircraft cabin was selected because of the higher density of passengers inside it, which may cause a risk of pathogen diseases transmission. This study focused on transmission of coughed and sneezed droplets or particles that are produced by a passenger in case of moving with a constant speed between passengers and without any movement. To perform an accurate CFD investigation, coughed and sneezed droplets properties were used, as illustrated in Table 4.

Table 4. Properties of coughed and sneezed droplets.

 Concerning modeling turbulent dispersion of droplets, stochastic discrete- particle model that enables us to predict the behavior of the droplets through integrating the trajectory equations for the individual droplets or particles using instant fluid velocity along the droplet path during the integration [15].

Design Case Studies

Two cases were simulated during this investigation each case has two scenarios. They can be described as follows: In cases one and two, transmission behaviors of sneezed and coughed droplets or particles produced from a passenger or cabin crew member were investigated during standing without any movement and moving with a constant speed up to 0.6 m/s. In long flight that may extend up to 7 hours, too many passengers leave their seats to do different activities; therefore, these scenarios can be happened. During this investigations, different coughing and sneezing flow rates were used, moreover, different velocities, as illustrated in Table 5.

Results and their Discussions

This CFD study investigated the behavior of coughed and sneezed droplets and their transmission in the aircraft cabin during the flights using ANSYS FLUENT software.

Table 5. Coughed and sneezed droplets characteristics.

Case One

Sneezing during Standing

Figures 4 & 5 show the transmission of the sneezed droplets that were produced from the passenger mouth for one second during his/her standing. These droplets’ spread in x, y, and z positions were analyzed for 4 seconds during the CFD investigation, as shown in Figure 5 where x and y represent width and height of the cabin. From the results, after exhaling the sneezed droplets with a speed of 30 m/s and their sizes are ranged from 50 – 500 µm. Figure 5 shows that the droplets transported to more than 1.7 meters in x-direction and 1.8 meters in y-direction at the end of the simulation process. Moreover, these droplets traveled from the first to the second row.

Figure 4. Transmission of the sneezed droplets during standing still.

Figure 5. Transmission of the sneezed droplets in x- and y-directions during standing still.

Coughing during Standing

Moreover, Figures 6 – 7 show the spread of the coughed droplets that were produced from the passenger mouth for one second during his/her standing with a speed of 11.5 m/s [18]. These droplets’ transmission was simulated for 3 seconds during the CFD investigation, as shown in Figure 6 after exhaling the coughed droplets their sizes are ranged from 50 – 500 µm. Figure 7 shows that the droplets traveled to more than 1.1 meters in x- and y-direction at the end of the simulation process. Moreover, these droplets traveled from the first to the second row.

Figure 6. Transmission of the sneezed droplets during standing.

Figure 7. Transmission of the coughed droplets in x- and y-directions during standing.

Case two

Sneezing during Motion

Regarding sneeze during passenger’s movement, the moving passenger started to sneeze for 1 second with a velocity of 30 m/s during the CFD simulation as shown in Figures 8 – 9. The sneeze droplets were able to take a flight, reach the surrounding passengers directly, and still had the ability to reach other passengers as they were still in the air. Moreover, these droplets spread to 2 m in x-direction and 1.5 m in y-direction at the end of the simulation process that extended for six seconds.

Figure 8. Transmission of the sneezed droplets during motion.

Figure 9. Transmission of the sneezed droplets in x- and y-directions during moving.

Coughing during motion

The moving passenger started to cough after 3.4 seconds of moving up to 3.4 seconds, and the exhalation velocity was 11.5 m/s. Figures 10-11 shows the same droplets after 6 seconds of the passenger’s movement. Moreover, at the end of the injection period that extended for 0.3 seconds, these ranges rose to 1.75 m in x-direction and 1.4 m in y-direction.

Conclusions

Based on the present CFD simulation for the behaviors of the sneezed and coughed droplets that produced from a moving passenger inside the aircraft cabin, the relevant conclusions are as follows:

1.    The transmission of the sneezed droplets that were exhaled from the standing passenger could reach the seated passengers in the first and second rows and still have the ability to travel and reach more passengers, while the coughed droplets could travel up to 1.1 meters without any movement from the passenger.

2.    During the movement of the passenger with a constant speed, the droplets spread widely inside the aircraft cabin and managed to attacked many passengers inside it.

3.    The impacts of the sneezed droplets on the seated passengers were much stronger than the coughed droplets.

Figure 10. Transmission of the coughed droplets during motion.

Figure 11. Transmission of the coughed droplets in x- and y-directions during moving.

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