What do radioactive particles and viruses have in common? The answer is they’re both spread by aerosols and have a parameter (the neutron multiplication factor for radiation and the reproduction number, R0, for pathogens) to indicate whether the population of neutrons/ infected people is growing or shrinking. So technologies developed in the nuclear industry, such as Jacobs’ ANSWERS software, can be used to improve our understanding of the spread of COVID-19. Paul Smith, ANSWERS Technical Director, explains how in the current issue of Nuclear Future magazine.

1. The professional journal of the Nuclear Institute Vol. 18 #2 u March/April 2022 u ISSN 1745 2058
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The modelling techniques used in
nuclear science and engineering
can be highly relevant to many high
hazard situations. Over a period of
time when various industries have
been supporting the response to
the coronavirus pandemic, nuclear
modelling experts have been involved
in helping to better understand
airborne transmission of the virus.
During the early stages of the
pandemic, the Royal Society
established the Rapid Assistance in
Modelling the Pandemic (RAMP)
initiative. This consisted of a
number of task groups focused on
addressing different aspects of the
pandemic. Task group 7 was concerned
with investigating environmental
transmission of the virus, with an
important mechanism being via
airborne particulate material (aerosols).
It has been known for some time that
airborne particles are responsible for
dispersing radioactive material resulting
from a severe accident in a nuclear power
plant. As a result, several decades of
effort have been devoted in the nuclear
industry to better understand the
formation and dispersion of particulate
material in the event of a severe accident.
This work includes Sher and
Hobbins on ‘Transport and Removal
of Aerosols in Nuclear Power Plants
following Severe Accidents’ (American
Nuclear Society, 2011), and Williams
and Loyalka on ‘Aerosol Science
Theory and Practice with special
applications to the nuclear industry’
(Pergamon, 1991). These review the
phenomenology of accident conditions
and provide details on the modelling of
aerosol behaviour and dispersion.
The property of prime importance
when considering a system involving
the distribution of fissile material is the
neutron multiplication factor. This is
known as ‘Keff’ to reactor physicists
and nuclear engineers and is the ratio
of the number of fission neutrons in
the current generation to the number
in the previous generation.
This parameter, which indicates
the transient decay or growth of the
neutron population, is analogous to
the now well recognised reproduction
number, R0, in epidemiology – the
average number of secondary infections
produced by an infected person. With
this connection made, it is immediately
clear that the knowledge gained from
decades of research into nuclear
particle spreading could be immensely
valuable to understanding the spread of
the COVID-19 virus.
AEROSOL
TRANSMISSION OF
COVID-19
A key area of concern in the aerial
transmission of coronavirus is
the manner in which it becomes
attached to particles and the size and
distribution of the droplets or aerosols
to which it attaches.
Whenever a person breathes, coughs
or sneezes, droplets are formed through
the hydrodynamic breakup and
entrainment of saliva due to instabilities
in the surface of the saliva created by the
high-speed breath in the mouth. If the
entrained saliva is contaminated with
the virus, airborne droplets containing
the virus are ejected into the air.
This is similar to what occurs in a
High Pressure Melt Ejection (HPME)
accident scenario in a Pressurised
Water Reactor (PWR). In this case,
the Reactor Pressure Vessel (RPV)
is breached and molten corium is
discharged into the reactor cavity,
followed by the blowing down of the
gas remaining in the vessel. When
the gas blows over the surface of
the molten corium, it breaks up and
entrains drops from the liquid surface.
In a 1989 report by Morris and
Roberts, models were described for
the breakup and entrainment of
molten core material (including size
distribution) during HPME from the
RPV, based on linear stability theory.
These models are inherently valuable
to exploring the similar traits of droplet
formation related to the virus.
In terms of dispersion, when droplets
leave the warm, moist mouth, they will
contract or expand depending on the
relative temperature and humidity of the
surrounding atmosphere. Again, this is
analogous to a potential nuclear situation
where aerosols leave the primary circuit
of a reactor and enter the relatively
humid containment atmosphere.
In the aforementioned Sher book,
models are presented to estimate the
growth of the particles as they enter
the reactor containment building due
to condensation, dependent upon the
chemical composition of the particles.
Again, a similar approach could be
applied to estimate the change in the
size of particles exiting the mouth.
TRANSPORTATION
OF PARTICLES IN THE
ATMOSPHERE
Back in 1969, a paper by Briggs
outlined models for the dispersal
of radioactive aerosols on plumes
emanating from a nuclear reactor in a
severe accident. Similarly, the particles
ejected from the mouth will be
transported on gas jets and/or plumes
emanating from coughing, sneezing or
just breathing. The larger particles will
fall from the breath under gravity and
be deposited on surfaces in the vicinity
of the person, but the smaller particles
will be transported further away on the
breath emanating from the mouth.
A more sophisticated approach to
evaluate this effect is to use detailed
Computational Fluid Dynamics
How nuclear modelling can help in understanding
and mitigating COVID-19 transmission
Methodologies and techniques used in nuclear science and engineering are being
re-applied to further support the response to the pandemic
By Paul Smith,
Christopher Pain
and Ali Tehrani –
Applied Modelling
and Computation
Group, Imperial
College

3. March/April 2022 | 20 |
(CFD) simulation to capture the
underlying flow patterns in a building,
with superimposed buoyant plumes.
This was explored in a 2021 study by
C. Ihebenachi ‘Solving advection-
diffusion equations based on Gaussian
plume modelling applied to airborne
transmission of COVID-19’.
In this approach, the concentration
field (representing the breath of
individuals) is advected with the
mean velocity taken from the CFD
and is also diffused with a turbulent
diffusion coefficient calculated from the
fluctuating velocities of the Large Eddy
Simulation (LES) turbulent flow model.
The resulting iso-surfaces (which
are shown in the image in this article)
represent a concentration of one
thousandth of that in the exhaled
breath from four people in a ventilated
room. This is an alternative approach to
running numerous CFD calculations,
which can be computationally expensive,
and builds on the work on Gaussian
plume models used to model radioactive
plumes in the nuclear industry.
CFD simulations provide important
insights into aiborne transmission. One
example is a recent study indicating that
in an indoor environment that is not
well-mixed, there can be situations in
which a person’s exposure to the virus
can result mainly from infected people
that are more than two metres away.
EFFECTIVENESS OF
MITIGATIVE ACTIONS
To contend with the spread of the
virus, mitigative actions have ranged
from full lockdowns and working from
home to two-metre social distancing
and the use of face coverings.
Understanding the effectiveness of
different measures is key to achieving
an effective way of coping with the
continued presence of the virus.
Engineering models of filtration
systems, including fibrous filters,
have been reviewed for application to
filtered containment venting systems
designed to mitigate containment
overpressure scenarios. Such models
could be used to estimate the filtration
efficiency for breath passing through
the fibrous material of a face mask.
The deposition of aerosol particles
due to impaction and interception, when
the carrier gas flow is forced to change
direction in a pipe bend, was studied
extensively for modelling severe accidents
in the aforementioned books by Sher and
Williams. The same mechanisms pertain
to breath forced to change direction and
escape through the side of an imperfectly
fitting face mask. Similarly, if someone
coughs or sneezes into the crook of
their arm, the change of flow direction
will result in the deposition of particles,
especially larger ones.
In a room, the convection caused by
a person’s body temperature heating
the surrounding air produces buoyant
flows and the associated air tends to
accumulate near the ceiling. The air
mixture from the breath of people with
elevated temperature, CO2
content and
water vapour after turbulent mixing
(due to breathing) tends to be denser
than the air heated by the body. This
can result in a layer of fluid, known
as the ‘lockup layer’, just under the
stratified layer created by the heated air
from people, as outlined in a report by
Qian in 2018, preventing virus-laden
breath from rising to the ceiling and
out of harms way.
As a result, having a ventilation
system that can remove the lockup
layer just below the layer where the
temperature from the body effects
the stratification may be an effective
mitigation strategy.
The impact of using natural
building ventilation or opening of
windows has been the subject of recent
studies by Mottet 2020, and the effect
of forced (mechanical ventilation) may
be seen as one of the most important
mitigation mechanisms.
Ultraviolet light is known to
inactivate the virus and this may be
also used within indoor environments
to reduce infection risk. For example,
a filter may be constructed containing
the source of ultraviolet light and
the air passed through that filter, or
as in a 2021 paper by Buchan et al,
the whole room is exposed to high
frequency ultraviolet light, which
is considered harmless to biological
tissue. Radiation modelling used
within that paper is born from the
methodologies developed within the
nuclear modelling community.
EXPLORING
EPIDEMIOLOGY
There is a strong analogy between
neutron multiplication in a nuclear
reactor, which is modelled by the
Boltzmann transport equation, and
infection dynamics, governed by the
Airborne dispersion from four people in a room obtained from a Gaussian plume model but with the
mean flows determined from the time averaged LES CFD model Fluidity.

4. www.nuclearinst.com March/April 2022
| 21 |
SEIRS equation (Susceptible - Exposed
- Infectious - Recovered – Susceptible).
Within a nuclear reactor, neutrons
with different energies behave
differently and so deterministic models
of their behaviour divide the energy
range into a number of subgroups.
The neutrons belonging to different
subgroups behave differently and
interact with each other. Similarly, in
SEIRS models, people are divided into
different groups, which can include
different ages, mobilities, infection
statuses etc. These groups behave
differently and interact with each other.
A neutronics code can be used as
a SEIRs model by using the energy
groups as surrogates for people
categories or compartments and
modifying the nuclear interaction
terms to represent human interactions
and the behaviour of the virus – e.g.
people moving from being exposed
to being infected. This can create a
schematic diagram, for example of a
small town (shown in an image in this
article), presenting the total number of
people that are infected in the town by
certain strains (e.g. an Omicron variant
and a Delta variant). This was explored
in Cheung’s MSc thesis (2021).
A nuclear code has been modified to
model the transmission of two strains of
a virus around the town, accounting for
the daily and weekly cycle of people’s
movements and two vaccination
categories (non-vaccinated and
vaccinated). The results have provided
valuable insights into the rise, peaking
and decline of the different strains. These
are also shown in an image in this article.
Nuclear models have an inherent
spatial distribution within them that
can be used to model the spread of
the virus within various situations
(e.g. a large 3D building, groups of
large buildings, towns, a country or
the world) by dividing the domain
into a large number of cells. This
allows people or groups which are
represented by compartments to move
through these cells. This is shown in
the Small Town Transmission model
outputs, where the spatial variation
within the small town on different
days can be shown.
Nuclear models find the eigenvalue
of the system of equations, which
turns out to be the neutron
multiplication factor, Keff. When a
nuclear code is modified to simulate
virus transmission it can provide
an estimate of the eigenvalue of the
equations, which in this case is the
reproduction number, R0.
The authors will present some of the
key outcomes from this activity during
the Annual Modelling in Nuclear
Science and Engineering Seminar at
Imperial College London on 7-8 April.
Acknowledgments
We would like to acknowledge and thank a large number of
individuals from different organisations that supported or have
contributed to this work. Much of this work is drawn from Task
7 (Environmental and Aerosol Transmission) of the RAMP
working group set up by the oyal Society in . We would
like to thank Paul F. inden, who co-led ask with Christopher
C. Pain, and the many members who contributed to this task
the Nuclear nstitute Special nterest Group formed after the
annual odelling in Nuclear Engineering and Science Seminar
in November and various consortia that have continued
research into different aspects of modelling the pandemic
ACK EP E AN EP C A EP
C ACE EP W P EC SE-funded
C D- National Core Study and P E E E EP .
Schematic diagram of a small town and the total number of people that are infected by two variants
of the virus.
The Small Town Transmission model, where the top line shows temporal
variation of exposure on day 8 and the bottom shows spatial variation of
exposure on day 8.