Inhalation of expiratory droplets in aircraft cabins
Jitendra K. Guptaa, Chao-Hsin Linb, Ph.D., Qingyan Chenc,a,*, Ph.D.
a National Air Transportation Center of Excellence for Research in the Intermodal Transport
Environment (RITE), School of Mechanical Engineering, Purdue University, West Lafayette, IN
b Environmental Control Systems, Boeing Commercial Airplanes, Everett, WA 98203, USA
c School of Environmental Science and Technology, Tianjin University, Tianjin 300072, China
Abstract Airliner cabins have high occupant density and long exposure time, so the risk of
airborne infection transmission could be high if one or more passengers are infected with an
airborne infectious disease. The droplets exhaled by an infected passenger may contain
infectious agents. The present study developed a method to predict the amount of expiratory
droplets inhaled by the passengers in an airliner cabin for any flight duration. The spatial and
temporal distribution of expiratory droplets for the first 3 minutes after the exhalation from the
index passenger was obtained using the computational fluid dynamics (CFD) simulations. The
perfectly mixed model was used for beyond 3 minutes after the exhalation. For multiple
exhalations, the droplet concentration in a zone can be obtained by adding the droplet
concentrations for all the exhalations until the current time with a time shift via the superposition
method. These methods were used to determine the amount of droplets inhaled by the susceptible
passengers over a 4-hour flight under three common scenarios. The method, if coupled with
information on the viability and the amount of infectious agent in the droplet, can aid in
evaluating the infection risk.
Keywords: CFD, superposition, breathing, coughing, talking
Practical Implications: The distribution of the infectious agents contained in the expiratory
droplets of an infected occupant in an indoor environment is transient and non uniform. The risk
of infection can thus vary with time and space. The investigations developed methods to predict
the spatial and temporal distribution of expiratory droplets, and the inhalation of these droplets in
an aircraft cabin. The methods can be used in other indoor environments to assess the relative
risk of infection in different zones and suitable measures to control the spread of infection can be
adopted. Appropriate treatment can be implemented for the zone identified as high risk zones.
A commercial air flight could last between 1 and 20 hours from gate to gate. During this time
period, passengers are exposed to contaminants that may exist in the cabin air. This situation
could become severe during the pandemic of a infectious disease, such as influenza, tuberculosis,
or SARS, because the droplets exhaled by an index passenger with an infectious disease carry the
Gupta, J.K., Lin, C.-H., and Chen, Q. “Inhalation of expiratory droplets in aircraft cabins,”
Accepted by Indoor Air.
infectious agents (Cole and Cook, 1998 and Duguid, 1946) that can be inhaled by fellow
passengers. However, the risk varies among the passengers. In addition to different immunities
among the passengers, the exposure of each passenger to various infectious agents/droplets is
also different because the airflow in an aircraft cabin is not perfectly mixed (Gupta et al., 2010a
and Yan et al., 2009).
Our previous study (Gupta et al. 2010a) used a CFD model to simulate the temporal
distributions of expiratory droplets for four minutes of real time from an index patient seated in
the middle of a seven-row, twin-aisle, full cabin. The simulation took four weeks of
computational time on an 8-parallel-processor computer cluster (total of two 2.33 GHz Quad-
Core Intel processors and 16 GB memory). Therefore, it is not practical or feasible to perform
the CFD simulation for a full-length cabin in 1 to 20 hours of flight time. Hence, it is necessary
to develop a feasible method that can predict the exposure risk of each passenger in an airliner
cabin due to the airborne infectious agents exhaled by an index passenger. Then possible
mitigation methods could be developed to protect the passengers in the cabin.
Research methods and validation
This section first presents a brief summary of the CFD methods. The method to extend the data
obtained from the 4 minutes of the CFD simulations (Gupta et al., 2010a) to whole flight
duration as well as a method to quantify the number of droplets inhaled by the passengers is then
This study used a seven-row, twin-aisle cabin mockup as an example for assessing the
infection risk of the passengers caused by the infected passenger seated in seat 4D as shown in
Fig. 1 (a). A tetrahedral mesh with a total of 1.5 million cells was used. A grid with 5 mm size on
mouth, nose and face of the passengers, 20 mm size on the rest of the body of the passenger and
seats, and 40 mm elsewhere was created. More than 98.5% of the cells had equi-size skew angle
of less than 0.7. The Reynolds number based on the height of the cabin or half row width and
supply inlet velocity was of the order of 4 ×105.
A commercial code, FLUENT was used to solve appropriate conservation equations for
mass, momentum, energy, humidity, turbulence variables and expiratory droplet movement. The
environmental variables solved were air velocity (all components), turbulent kinetic energy,
turbulent dissipation rate, temperature, water vapor concentration, particle velocity, particle
diameter and particle temperature. Zhang et al., 2009 and Zhang et al., 2007 found that the
renormalization group (RNG) k- model (Yakhot and Orszag, 1986) can effectively predict the
turbulent feature of the airflow in the aircraft cabins and other indoor environments. Therefore
the RNG k- turbulence model was used for the investigations. The effect of temperature on
density was considered along with the gravitational force to account for the buoyancy effects.
The expiratory droplets were tracked using the Lagrangian apporach. The Lagrangian
approach incorporated in FLUENT as discrete phase modeling was used. The Discrete Random
Walk model was used to account for turbulent dispersion of the particles (FLUENT, 2005). The
point properties for the particles, which include the droplet size, injection time period, droplet
temperature, total mass flow rate and velocities, were specified for the injections. The study used
the flow boundary conditions obtained from the experiments (Gupta et al., 2009 and Gupta et al.,
2010b) for the coughing, breathing, and talking processes. The investigations were performed
using mono-dispersed droplets for the coughing, breathing and talking cases. Therefore it was
assumed that all the droplets exhaled during a particular exhalation were of one size. The
dominating size for the droplets exhaled during the exhalation was used. For coughing, Yang et
al., 2007 found that the average mode size of droplets exhaled was 8.35 m. For breathing,
Fabian et al., 2008 reported that the most of the droplets exhaled were between 0.3-0.5 m. For
talking, Duguid, 1946 reported a wide variation in droplet size spectrum and there was no single
dominating size. The mean droplet size based on count and diameter was calculated and, was 30
m. Therefore the size of droplets simulated for the coughing, breathing and talking exhalations
was assumed to be 8.5, 0.4, and 30 m respectively, which eventually reduced to 4, 0.19 and 14
m due to evaporation ( Gupta et al., 2010a). For the transient transport of droplets a time step
size of 0.05s was used. For coughing period a time step of 0.001s was compared with 0.05s and
no significant differences in the cough jet behavior were observed, therefore a time step of 0.05s
can also be used for the exhalation period.
Droplet concentration around each passenger for any flight duration
The CFD simulations (Gupta et al. 2010a) showed that droplet distributions could be highly non-
uniform in an airliner cabin. To assess the exposure risk of fellow passengers caused by the
droplets exhaled by an index patient, it is important to know the actual number of
droplets/infectious agents inhaled by each passenger. It is also important to know the time
variation in the droplet concentration around the nose regions of the passengers. As passengers
may move their heads, a zone of volume 0.0283 m3 (1 ft3) was constructed around the nose
region of each passenger, as shown in Fig. 1 (b). The time variation of the droplet concentration
in these zones was obtained using the CFD simulations (Gupta et al., 2010a).
Figure 1. (a) Section of the seven-row, twin-aisle, fully occupied cabin used (Gupta et al., 2010a)
(b) The zone of 0.305 m × 0.305 m × 0.305 m around the nose region of a passenger for
determining the average droplet concentration
This study defined (droplet fraction-s/m3) as the average cumulative number of
expiratory droplets in the vicinity of a passenger relative to the total number of droplets exhaled
by the index passenger. The was obtained by summing up the average droplet fraction over
time and is given by equation (1).
Where, v is the zone volume around the passenger, Ni the total number of droplets in the zone
around the ith passenger at time t, and Nt the total number of droplets exhaled for the exhalation
of the index patient.
Figure 2 (a), (b) and (c) show the airflow in the cabin (Gupta et al., 2010a). The cold air
from the supply inlets moved along the top wall and exited from the outlet located on the sides
close to the base as shown in Fig. 2 (a). A part of this air moved to the center and rose up due to
the natural convection created from the passengers seated at the center. This resulted in two re-
circulation zones on both sides. The airflow around the index passenger seated on the center
column (D) was towards the back and was natural convection dominated as shown in Fig. 2 (b),
while the flow in the aisle was mixed as shown in Fig. 2 (c).
The expiratory droplet cloud from passenger 4D moved in the cabin with the bulk flow.
The local droplet concentrations in the zones where the droplet cloud reached first were high, as
the cloud was dense for the initial period. It was observed that the droplets eventually dispersed
to all seven rows, but the droplet concentrations in the row furthest from the index passenger
were relatively low. Therefore, the droplet concentration for the passengers seated only in the 3rd,
4th (index passenger), and 5th rows is discussed here.
Figure 2. Velocity fields in the cabin on (a) cross section through the index patient (b)
longitudinal section through the index patient (c) longitudinal section along the aisle (Gupta et
Figure 3 shows the average cumulative droplet fraction () for the passengers seated in A
(window), B (aisle), C (aisle), and D (center of the row) seats, respectively, for the expiratory
droplets from a single cough by index passenger 4D. The droplets exhaled from the cough first
moved to the front due to the high velocity of the cough jet. The droplets were small (8.5 m,
Yang et al., 2007) and were soon picked up by the bulk airflow. The bulk airflow around the
index passenger as shown in Figure 2 (b) moved the droplet cloud upwards and to the back. The
droplet cloud after reaching the top was picked up by the strong convective airflow as shown in
Fig. 2 (a). The droplet cloud moved along the top wall towards the window and aisle seats (5A,
5B, 4A, and 4B) in about 10s. As the droplet cloud first reached these passengers, there was
sudden increase in for these passengers at around 10s as shown in Fig. 3. The rate of increase
of was higher for 5A and 4A as the droplets first passed through these zones. The droplet cloud
then came to the lower zone in the aisle. The flow in the lower portion of the aisle was towards
the front as shown in Fig. 2 (c), which made the droplet cloud move to the forward row. The
droplet cloud then reached the passenger seated in 4C and dispersed in the 3rd, 4th and 5th rows.
The rate of increase of for the passengers seated in these rows was higher during the initial
period (<1 min).