A Preliminary Numerical Investigation of Airborne Droplet Dispersion in Aircraft Cabins

The emergence of the novel coronavirus has led to a global pandemic which has led to the airline industry facing severe losses. For air travel to recover, airlines need to ensure safe air travel. In this paper, the authors have modeled droplet dispersion after a single breath from an index patient. Computational Fluid Dynamics (CFD) simulations are conducted using the k-ωSST turbulence model in ANSYS Fluent. The authors have taken into consideration several parameters such as the size of the mouth opening, the velocity of the cabin air as well as the number of droplets being exhaled by the index patient to ensure a realistic simulation. Preliminary results indicate that after a duration of 20 s, droplets from the index patient disperse within a 10 m cabin area. About 75% of the droplets are found disperse for up to 2 m axially behind the index patient. This could possess an enhanced risk to passengers sitting behind the index patient. Ultimately, this paper provides an insight into the potential of CFD to visualise droplet dispersal and give impetus to ensure that necessary mitigating measures can be taken to reduce the risk of infection through droplet dispersal.

facing a potential loss of $252 billion in 2020 [2] [3]. For the airline industry to recover, growth in air traffic is vital. However, it is necessary to forecast and moderate the risk of infection from airborne infectious diseases in aircraft cabins to enable air travel to recover to pre pandemic levels. A study of the droplet dispersion from the breath of a passenger in an aircraft cabin can provide a unique insight into mitigating measures that can be undertaken to ensure safe air travel.
Modeling of this dispersion can enable the airline industry to take the necessary measures to ensure safe travel which will instil confidence amongst passengers and lead to the growth of air travel in the near future.
The dispersion of droplets (in the case of airborne infectious diseases) greatly depends on the airflow within the aircraft cabin. The humidity of the cabin air is the prevalent factor in the aircraft cabin that can impact the transmission of airborne diseases. The distance between people seated next to each other in an airplane with full passenger loads is approximately 0.5 m or less. In the confined space of an airplane cabin, and during long flights, direct dispersion is a potential pathway for airborne transmission of infectious diseases [4]. During air travel, some of the outbreaks of tuberculosis, SARS, influenza, are alleged to have happened [5]. The direct contact, indirect contact, airborne route, or droplets could carry on the transmission of the diseases. Therefore, it is essential to quantify the potential impact of droplets exhaled from passengers within the aircraft cabin to ensure that precautions can be taken for safe air travel.
There are a limited number of studies which have investigated the generation and dispersion of particles originated from human expiratory activities in aircraft environments as compared to the built environment. Yang et al. [6] conducted an experimental investigation using a Boeing 767 aircraft cabin to study the dispersion behaviour of expiratory droplets released from a coughing person.
The investigation result shows that when the injection point was closer to the cabin wall i.e. the window section, the droplets dispersion was greatly suppressed. Similar results were obtained by Gupta et al. [7] through their numerical modeling of droplet dispersal when talking, coughing and breathing. Figure   1 shows the dispersal of droplets during a single breath by a person over a duration of 240 s. Results presented by Gupta et al. indicate that the droplet dispersal due to a single breath reduces by 52% after 1 min (shown in Figure 1). Similar results were obtained during coughing by a person and resulted in an 88% reduction in droplets after 4 minutes although the volume of droplets in coughing is much higher. While the above studies focus on the rate of droplet dispersal, the proportion of droplets dispersed through a single breath reaching other passengers is not touched upon.
In this paper, the authors will build upon existing data from literature pre-  Apart from this, the authors have considered the actual air flow velocity from the aircraft ventilation system to present a realistic and accurate picture of droplet dispersal within the cabin. This paper aims to identify the critical area of influence of droplet dispersal after a single breath from the index patient and its impact on passengers within the cabin. The quantification and visualisation of this droplet dispersal can provide an insight to airline companies to identify potential precautions to ensure safe travel in the future.

Methodology
In Section 1 it was noted that the carrier of contagious agents may be the droplets exhaled by a passenger who might be the carrier of an infectious disease.
Aircraft cabins being an indoor environment, may be highly susceptible to airborne contagious agents. The transmission of droplets exhaled by the index patient has been computed in the present investigation for a passenger who is seated in the middle of a seven-row, twin-aisle, fully occupied cabin using the This section is divided into two main subsections. Subsection 2.1 deals with the geometry for the model whereas Subsection 2.2 deals with the simulation setup as well as the details of the mesh.

Geometry of the Model
The geometry for the model involves the use of life-size human model with accurate geometrical dimensions of a real person. The mannequin/index patient was designed to have a height of 1.75 m and was placed in a seated position as shown in Figure 2. The mannequin was designed using the blender software and imported into ANSYS for mesh generation.
The mannequin was designed with two circular nostrils with a diameter of 11 mm. The mouth opening was modeled to have an area of 120 mm 2 . To make the design as realistic as possible, the respiratory frequency of breathing was assumed to be 15.5 min −1 . To ensure rapid and accurate results, the geometry was simplified once it was imported into ANSYS and several surfaces were combined for ease of mesh generation. The seat was also deleted from the simulation, mainly because the simulation focused on tracking the droplet dispersal and the seat would result in use of additional computer resources without influencing the results. Figure 3 shows the insertion of the mannequin into the actual fluid domain.

Simulation Setup
To ensure rapid and accurate results and to simplify the preliminary study, the authors considered a portion of the cabin that covers an area of 10 m 2 around the passenger. An assumption was made on the size of the cabin taking into consideration the distance travelled by the droplets during a normal exhalation [9].
Due to the complex geometry of the mannequin, the authors decided to use an  unstructured mesh with a total mesh size of 1.9 × 10 5 elements with a minimum element size of 0.3 mm (shown in Figure 4). The mesh size was determined by following the standard procedure for performing a mesh independence study in order to ensure a good balance between accuracy and computational processing capabilities [10].

Results and Discussions
In   Figure 1) after 20 s [7] highlighting the accuracy of the simulation setup as well as the results. From the pathlines, it can also be observed that the majority of the risk exists to passengers sitting immediately behind the index patient. Approximately 75% of droplets from the index patient disperse to the area behind the patient. As this forms a majority of the droplets that an average human breathes out in a single breath, the chances of droplet transfer from the index patient to the passengers sitting behind the patient increase dramatically. These droplets also tend to have a high concentration around the facial region of the passenger sitting 2 m behind the index patient potentially increasing the chance of droplet inhalation. The impact to passengers sitting in front of the index patient appears to be minimal beyond a distance of 0.47 m from the index patient.
It is also interesting to note that most of the droplets disperse axially behind the mannequin and only disperse transversally at the very back of the cabin area in question (shown in Figure 6). From the pathlines, it can be concluded that  Modern aircraft ventilation systems are designed to use 50% outside air, and 50% recirculated air to maintain a more acceptable relative humidity level, and to increase the fuel efficiency [8]. Mitigating actions are necessary to reduce the potential risk of airborne infections in an aircraft cabin. Face mask protection has been found to be 45% in a pseudo-steady environment [18]. Thus, in the present study, the use of a face mask could potentially reduce droplet dispersal by 45%. For air travel to return to normal in the future, several mitigating actions are required by airline companies which are beyond the purview of this paper.

Conclusions
In this paper, the authors performed a numerical simulation of droplet dispersal within an aircraft cabin. An index patient/mannequin of average human height was modeled and placed inside a designated cabin area. Droplet dispersal due to a single breath was simulated.
Preliminary results in this paper indicate that within 20 s, droplets exhaled to cross flow dispersal in the transverse direction is minimal.
As the bulk air within the aircraft is recycled every 2 -3 min, a dispersal time of 20 s can be potentially infectious. As this paper is a purely academic exercise to track droplet dispersal, further study is required to understand impact of droplet dispersal within the cabin and the probability of infectious droplets being inhaled by passengers.

Disclaimer
The authors have presented this study as a purely academic exercise to track droplet dispersal. Results presented herein should not be taken as evidence of any pathogenic spread within an aircraft cabin. The impact and the possibility of pathogenic spread are beyond the purview of the authors' technical expertise.