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Simulation of COVID-19 Ultraviolet Disinfection Using Coupled Ray Tracing
and CFD
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Accepted for publication and presentation at Building Simulation 2021, Bruges, Belgium, September 1-3, 2021
https://bs2021.org/
Simulation of COVID-19 Ultraviolet Disinfection Using Coupled Ray Tracing and CFD
Nathaniel L Jones1, Paul Lynch2, Joseph Hewlings3, Justin Boyd4, Ryan Seffinger3, Dan Lister4,
and Renee Thomas3
1
Arup, Boston, USA
2
Arup, Manchester, UK
3
Arup, San Francisco, USA
4
Arup, Sheffield, UK
Abstract
Ultraviolet Germicidal Irradiance (UVGI) is the effective
technique of inactivating disease-causing bacteria, mould
spores, fungi, and viruses using ultraviolet radiation. In
this study, we seek to quantify the efficacy and COVID19 infection risk reduction achieved by UVGI in the upper
unoccupied zone of a room so that we may specify the
type and placement of UVGI emitters optimally. We
present a computational fluid dynamics (CFD) based
approach to model disinfection of aerosolized pathogens
in a non-uniform ultraviolet field with mixing driven by
air exchange and temperature gradients. We validate our
CFD against simple calculation methods for UVGI
effectiveness in well mixed spaces, and we integrate it
with the Wells-Riley model of airborne infection risk to
assess the relative benefit of UVGI with and against other
measures. We demonstrate an order of magnitude
reduction in infection risk as a result of applying UVGI,
as well as the ability to quantify infection risk in non-wellmixed settings where simplified calculations methods do
not apply.
hope for the pandemic’s resolution, new variants will be
an issue for years to come, and trends in urban
densification and global travel virtually guarantee the
spread of future novel viruses and multi-drug-resistant
strains. Building designers must plan accordingly.
One promising technology in the fight against COVID-19
is upper-room ultraviolet germicidal irradiation (UVGI).
Radiation in the UV-C band (100 – 280 nm) is particularly
effective in altering chemical bonds in viral RNA
molecules, thereby preventing the virus from reproducing
(Ariza-Mateos, et al., 2012). The inactivation of a given
pathogen is proportional to UV-C intensity and exposure
time. Used in the upper part of a room, above head height,
air containing viruses in respiratory droplets can be
irradiated soon after it is breathed out by an infected
person (Figure 1).
Key Innovations
•
•
•
Simulation of 3D ultraviolet radiative field
Pathogen concentration, inactivation, and
infection risk modelling in CFD
Application to complex room geometries
Practical Implications
Our simulation workflow quantifies COVID-19
disinfection efficacy and infection risk in indoor spaces
where size, partitions, or obstructions limit air mixing.
Using our workflow, we can design UVGI systems for
offices, schools, entertainment venues, transportation
hubs — anywhere large groups of people transit or gather.
We can combine CFD with less resource-intensive tools
to tailor the level of analysis as appropriate — from rapid
screening of infection control measures to fine-tuning of
UVGI system designs.
Introduction
The COVID-19 pandemic has sparked renewed interest in
architectural solutions to minimize airborne pathogen
transmission. To date, the virus has claimed 3,501,002
lives, a number rising so quickly as to make its reporting
here moot (Johns Hopkins, 2020). Although the recent
development and emergency approval of vaccines offers
Figure 1: Upper room air volume utilizing UV-C
irradiance, courtesy of the Illuminating Engineering
Society of North America
For upper-room UVGI, today’s marketplace is broadly
lacking in accurate software-based dosing calculation
tools that can model the ultraviolet irradiance required to
disinfect air volumes and surfaces while simultaneously
protecting building occupants from inadvertent incidental
exposure or excessive cumulative exposure to ultraviolet
radiation over time. In this paper, we present a workflow
that allows users to quantify exposure and rate the
efficacy of ultraviolet disinfection systems. Our process
includes three main contributions. First, we show novel
methods for assessing UV-C irradiance in a volume based
on the selection and spatial arrangement of ultraviolet
emitters. Second, we apply the derived radiative field in
computational fluid dynamics (CFD) simulation to get
steady-state or transient pathogen concentrations. Third,
we calculate the expected reduction in infection risk due
to combination of airflow and UVGI. We validate the
derived concentrations against zonal models from
previous literature for a simple case study, and we
demonstrate that our method may be applied in larger
settings where zonal approximations do not apply.
Background
The COVID-19 pandemic has shifted the focus of
communicable disease research from contaminated
surfaces (Garcia, 2019) and drug-resistant organisms
(Chen, et al., 2018) to airborne transmission. SARS-CoV2, the virus that causes COVID-19, spreads primarily in
respiratory droplets and aerosols (Morawska & Cao,
2020), while the risk of infection from surface contact is
low (Harvey, et al., 2021; Pitol & Julian, 2021). Airborne
spread of coronaviruses has likewise been observed in the
previous SARS (severe acute respiratory syndrome) and
MERS (Middle East respiratory syndrome) outbreaks of
2003 and 2012 (Yu, 2004; Fears, et al., 2020).
Superspreader events in poorly ventilated spaces strongly
suggest the role of airborne transmission of SARS-CoV2, including at distances greater than 2 meters (6 feet). In
a restaurant in Guangzhou, nine patrons became infected
as a result of their proximity to a recirculating fan coil unit
that spread the pathogen up to 5 meters (16 feet) from an
infected customer (Lu, et al., 2020). Shen, et al. (2020)
document two more events in China, the infection of 23
bus passengers and of 15 conference attendees, in which
many of those who contracted COVID-19 were seated
more than 2 meters from the carrier. An outbreak in a
Korean call centre led to testing of all 1145 building
occupants, which found a cluster of 94 cases among
individuals who worked on the same floor (Park, et al.,
2020). In Washington, 53 of 61 attendees to a 2.5-hour
choral rehearsal were infected by one symptomatic
individual (Miller, et al., 2020). Monitoring in hospitals
in Wuhan, Nebraska, and Oregon has detected airborne
and deposited SARS-CoV-2 at distances greater than 2
meters from infected patients (Liu, et al., 2020; Santarpia,
et al., 2020), including in air ducts (Horve, et al., 2020).
Recent studies claim to have detected infectious virus in
the air 3 hours (van Doremalen, et al., 2020) or 12 hours
(Fears, et al., 2020) after emission.
Use of UVGI
The use of ultraviolet light as a disinfectant stretches back
more than a century. In 1892, Ward showed UV-A and
UV-B radiation in sunlight to be effective in destroying
Bacillus anthracis (Ward, 1893). Wells (1934) proposed
that pathogens might reside in airborne respiratory
droplets and pioneered the use of upper air-volume UVGI
disinfection systems in hospitals. Wells subsequently
used this technology to treat a 1937 – 1941 measles
epidemic among suburban Philadelphia schoolchildren,
reducing the infection rate from 53.6% to 13.3% (Wells,
et al., 1942). Riley, Permutt, and Kaufman demonstrated
the effect of convection and air mixing on UVGI efficacy
(1971a) and quantified the disinfection rate from UVGI
for a specific pathogen as equivalent to 33 – 83 room air
changes per hour (ACH), depending on temperature
gradient (1971b). Upper-room UVGI is today recognized
as an effective means of controlling airborne pathogens
such as tuberculosis (CDC, 2009).
The dosage required to achieve a certain reduction in
pathogen concentration, typically expressed in J/m 2 or
mJ/cm2, is the ultraviolet fluence, or integral of irradiance
with respect to time. UV-C fluence dosages have been
catalogued for SARS-CoV-2 (Arguelles, 2020; Lim,
2020) and other pathogens (Malayeri, et al., 2016). The
low reflectivity of most building materials in the UV-C
band may protect occupants from harmful long-term
exposure to ultraviolet radiation (First, et al., 2005).
Zone Calculation Methods
Simple calculation methods for UVGI efficacy and
infection risk assume a well-mixed space divided into an
occupied lower zone and an irradiated upper zone.
Rudnick and First (2007) propose a method for
quantifying the survival rate of a pathogen under steady
state conditions:
𝐶𝑈𝑉
=
𝐶𝑛𝑜𝑈𝑉 1 +
1
1
(1)
𝑉𝑘𝑣
2𝐻𝑘𝑣
+
𝑉𝑢𝑣 𝑘𝑢𝑣
𝑆̅
where CUV and CnoUV are the steady-state pathogen
concentrations with and without UVGI, V is the room
volume and H its height, S is the mean vertical airspeed
between the occupied and irradiated zones, and kv is the
outdoor air exchange rate. The UVGI inactivation rate is
kuv = zE, where z is the pathogen susceptibility to UVGI
(Beggs & Avital, 2020), and E is the mean UV-C
irradiance in the irradiated zone with volume Vuv.
Beggs and Sleigh (2002) provide a formulation for nonsteady-state conditions:
𝐶𝑡 =
𝑞
𝑞
+ (𝐶0 −
) 𝑒 −𝑘𝑒𝑞𝑣 𝑡
𝑉𝑘𝑒𝑞𝑣 𝜀
𝑉𝑘𝑒𝑞𝑣 𝜀
(2)
𝐻𝑢𝑣
(3)
𝐻
where C0 and Ct are pathogen concentrations at the start
and at time t, and q is the rate of pathogen introduction.
The decay rate keqv is the sum of the outdoor air exchange
rate, natural decay rate kd, surface deposition rate ki, and
UVGI inactivation rate in the irradiated zone with height
Huv. Equation 2 contains an incomplete mixing term ε,
which Beggs and Sleigh assume near 1 for full mixing.
The probability of infection P is described by the WellsRiley equation:
𝑘𝑒𝑞𝑣 = 𝑘𝑣 + 𝑘𝑑 + 𝑘𝑖 + 𝑘𝑢𝑣
−𝐼𝑝𝑞𝑡
(4)
𝑃 = 1 − 𝑒 𝑉𝑘𝑒𝑞𝑣
where I is the number of infectors in the space, and p is
the average breathing rate (Sze To & Chao, 2010). Riley,
et al. (1978) developed this equation to study a measles
outbreak and based it on Wells’ (1955) “quantum of
infection,” the number of airborne particles required to
infect a susceptible individual. Though highly influential,
the Wells-Riley equation has been criticized for assuming
a
b
c
Figure 2: An arrangement of UV-C emitters with (a) directional intensity indicated by colour produces (b) low
UVGI intensities in the occupied zone and (c) high UVGI intensities in the upper zone
a uniform quanta generation rate and instantaneous
mixing, which could underestimate infection risk by 15%
or more (Noakes & Sleigh, 2009).
Integration with CFD
Analysis of incomplete mixing cases requires CFD.
Respiratory droplets produced by talking (Asadi, et al.,
2019) and coughing (Yang, et al., 2007; Lindsley, et al.,
2012) typically measure less than 10 microns in diameter.
Droplets at this scale fall with a lower velocity than the
typical vertical air speed in a room, so they will be
transported by the air movement. They tend to initially
rise toward ceiling level due to the warmth of the exhaled
air and the thermal plume rising from the infectious
person. These droplets may be modelled in CFD either as
particles, which react to gravity, or more simply as a
neutrally buoyant passive scalar concentration.
Several studies have examined pathogen spread with
CFD. Qian, et al. (2009) modelled a 2003 SARS outbreak
in a hospital by implementing the Wells-Riley equation in
a steady-state RNG k-ε CFD model to accurately predict
the number of infections in various wards. It is unclear
whether this study modelled particles or passive scalar
concentrations. The efficacy of UVGI has been tested
using both passive scalar concentrations in a Reynoldsaveraged Navier–Stokes model (Noakes, et al., 2004) and
particles in a Lagrangian transport model (Alani, et al.,
2001), although the latter study revealed that airborne
pathogens may reside in the space longer than indicated
by the ventilation rate. Compared to factors such as grid
resolution, CFD simulations of UVGI are highly sensitive
to UV-C distribution (Gilkeson & Noakes, 2013).
Method
Our aim is to determine UVGI efficacy and infection risk
in spaces of arbitrary complexity. We do so in two steps.
First, we simulate the UV-C radiance field to determine
the pathogen inactivation rate at each point in space.
Depending on the complexity of the space, we propose
two irradiance calculation methods. In simple spaces, we
perform interactive raytracing using the visual
programming language Grasshopper within the
Rhinoceros 3D environment (Robert McNeel &
Associates, 2019). For spaces with large numbers of
UVGI emitters, reflective surfaces, or extensive
occluding geometry, we calculate spherical irradiance
using RADIANCE software (Ward Larson & Shakespeare,
1998). Second, we calculate the concentration of
pathogens that remain in the space using CFD. The decay
rates we determine allow us to predict infection rates via
the Wells-Riley equation.
Low Complexity: Interactive Raytracing
For simple geometric cases with few occluding surfaces,
we calculate direct UV-C irradiance in a Grasshopper
script. Our Grasshopper tool allows the user to specify
room geometry and UV-C emitter locations, and to assign
radiance distributions (from IES files or other sources) to
each emitter. For convenience, geometry prepared for
CFD simulation can be used directly in the radiometric
calculation (Figure 2). The user may specify calculation
points as a 3D grid (for air volume irradiance) or 2D grid
(for surface irradiance).
The Grasshopper tool uses the inverse square law to
determine the UV-C irradiance at each point on the grid.
For surfaces, the irradiance is cosine-weighted, whereas
for volumetric grids, it is the unweighted sum of the
contributions from each emitter. Our script automatically
discretizes emitters into patches to account for angle
variation of large or nearby radiant surfaces. For example,
a UV-C tube converts to a string of points with the output
wattage of the tube evenly distributed among the points.
The same UV-C radiometry is applied to each point.
This tool offers two major advantages: the ability to
handle moderately complex geometry and results that
update in response to live geometric manipulation, thanks
to the Grasshopper environment. Additionally, the tool
automatically formats the results for input to CFD.
However, calculation time is non-negligible and becomes
prohibitive for cases with many emitters, many grid
points, or many occluding surfaces. The practical
raytracing capabilities of Grasshopper also do not allow
for reflection, requiring an assumed 0% reflectivity for all
surfaces.
High Complexity: Spherical Irradiance
For large spaces with reflective or occluding surfaces, we
calculate UV-C irradiance with the RADIANCE software
platform. RADIANCE employs a sophisticated, scalable,
and validated raytracing algorithm to accurately model
light propagation and material interaction in threedimensional space (Ward Larson & Shakespeare, 1998).
Our RADIANCE workflow is entirely self-contained within
a Grasshopper script and uses the same geometry,
radiometry, and grid inputs as the interactive raytracing
method. This allows seamless transition between the two
methods (although the inputs could also be provided to
RADIANCE by other means). Similarly, the results for both
3D and 2D grids can be displayed and exported to CFD
using the framework previously described.
The core RADIANCE programs use light-backward ray
tracing to calculate the irradiance reaching a virtual sensor
from both direct and indirect pathways. Though used
mainly for visible light, the RADIANCE algorithms are
equally valid for non-visible wavelengths (Ahmed, et al.,
2018), so long as the wavelength is much smaller than the
scale of objects in the scene. For use with UV-C
wavelengths, the only alteration necessary is the use of
material albedos for UV-C wavelengths, which are
generally much lower than visible reflectance values.
Where UV-C albedos are unknown, a low default value
may be used. The calculation may use zero ambient
bounces for a conservative approach where occupant
exposure is not a concern, or one ambient bounce for
increased accuracy. Based on an assumed 6% albedo in
UV-C bands, including a second reflection would
increase irradiance by only 0.36%, which is below the
sensitivity of most measurement devices.
While 2D grid calculations proceed in the same way as
typical RADIANCE irradiance calculations, 3D grids
require a different approach because the sensors have no
associated normal direction. When two UV-C sources
irradiate a point in space at a 90° angle to one another,
both contribute fully, with no cosine weighting. We could
calculate irradiance from each source separately with
different normal vectors and add the irradiances together,
but this is infeasible for large numbers of sources and
difficult to justify mathematically. Instead, we count
incident radiation from all directions equally in a single
calculation by generating a set of planar irradiance
sensors evenly distributed about the surface of an
infinitesimal virtual sphere at each grid point. The number
of directions sampled at each point determines the
accuracy of the simulation and affects simulation time.
We provide several accuracy settings in Grasshopper
(Table 1).
Table 1: Spherical irradiance accuracy settings
Accuracy
Setting
Low
Medium
High
Ultra
Accuracy
Value (n)
5
8
20
100
Directions Sampled
(2n2)
50
128
800
20,000
Using RADIANCE scripting, sample points are arranged
over two disks representing upper and lower hemispheres.
Given an accuracy value n, the script uses Shirley-Chiu
sampling (Shirley & Chiu, 1997) to evenly place n2
samples over each disk, producing 2n2 directional
samples. It then converts the 2D points (xd, yd) that are
evenly spaced on each disk to 3D points (xs, ys, zs) evenly
spaced on each hemisphere as follows:
𝑟𝑑 = √𝑥𝑑2 + 𝑦𝑑2
(5)
𝑧𝑠 = 1 − 𝑟𝑑2
(6)
(7)
𝑟𝑠 = √1 − 𝑧𝑠2
𝑟𝑠
𝑥𝑠 = 𝑥𝑑
(8)
𝑟𝑑
𝑟𝑠
𝑦𝑠 = 𝑦𝑑
(9)
𝑟𝑑
Given many evenly distributed samples, the mathematical
solution is to sum radiance rather than irradiance. The
total irradiance on the infinitesimal spherical surface is 4π
times the mean radiance in W/m2/sr for a uniformly
distributed set of directions. This can be calculated by
Monte Carlo sampling at the expense of requiring many
rays to reach all the sources.
We observe that by calculating irradiance in each
direction instead of radiance, all directions are still
sampled equally, and thus the cosine weighting is
removed by the mean function (leaving a factor of π).
Therefore, the spherical irradiance is four times the mean
irradiance in W/m2. The advantage is that RADIANCE
optimizes the calculation of irradiance from light sources.
This significantly reduces the number of sample
directions needed at each point.
CFD Analysis
Heating, ventilation, and air conditioning (HVAC)
systems and movement of infected individuals influence
how airborne droplets disperse. In spaces with low
ventilation rates, aerosols may circulate for extended
periods, creating a risk of a cumulative viral load that can
result in infection. We use CFD to simulate the dynamic
behaviour of moving air within three-dimensional
architectural space in order to translate the UV-C
radiative field into steady-state or transient pathogen
concentrations.
From Equation 2, microorganisms exposed to UVGI
decrease in population approximately according to an
exponential decay function:
𝐶𝑡
= 𝑒 −𝑧𝐸𝑡
(10)
𝐶0
We represent this in a CFD model as a sink term with
spatially varying strength:
𝑑𝐶(𝑥, 𝑦, 𝑧, 𝑡)
(11)
= −𝑧 𝐸(𝑥, 𝑦, 𝑧) 𝐶(𝑥, 𝑦, 𝑧, 𝑡)
𝑑𝑡
The irradiance E in each cell of the CFD mesh is
interpolated from the point data calculated by
Grasshopper or RADIANCE, which we import into the CFX
(ANSYS, 2019) environment for CFD simulation.
We model the pathogen as a passive scalar, an appropriate
simplification for the transport of droplets under 10 μm in
diameter whose settling velocity is much lower than the
typical indoor air speed. These are the droplets for which
upper-room UVGI is expected to be most effective, as
they are likely to circulate on air currents rather than
deposit on surfaces. To generate accurate air movement,
we include all air vents and returns for forced air mixing
and use representative occupancy and equipment thermal
loads to generate convective currents. The output of the
CFD simulation yields steady-state or transient pathogen
concentrations that account for both ventilation and UVGI
with spatial granularity that cannot be achieved by the
zonal approximation in Equation 2.
Results
We carried out ray tracing and CFD simulations of a
typical meeting room with 3 occupants (Figure 2). The
room has dimensions 7.2 m × 5.1 m × 2.7 m high. A
ceiling mounted fan-coil unit supplies cooling through
four ceiling diffusers, and five slot diffusers supply fresh
air (Figure 3). Three UVGI emitters below the slot
diffusers on the long wall irradiate the upper 0.7 m of the
room’s height with 8.5 W each in the UV-C band. We
tested a range of ventilation rates (1, 2, 4, and 8 ACH)
spanning from an under-ventilated space that would most
benefit from UVGI to a well-ventilated space where we
expect minimal impact from UVGI. For each ventilation
rate, we applied three ultraviolet intensities: full, half, and
no UVGI.
FCU return
Balancing vent
Steady-State UVGI Efficacy
Our interactive raytracing method shows an average
UVGI intensity in the upper air volume of 0.29 W/m2 for
full intensity, and 0.145 W/m2 for half intensity. The
intensity is distributed unevenly with its highest levels
near the emitters (Figure 5). Air in the room is generally
well mixed, although plumes arising from the occupants
contain more heat and, in the case of an infected occupant,
a higher concentration of pathogens than the surrounding
air (Figure 6).
FCU diffuser
Figure 5: Volumetric UV-C irradiance is highest next to
the UVGI emitters
Ventilation
supply
Figure 3: Diffuser and return locations in the small
conference room
Irradiance Calculation Accuracy
In a test with 1296 gridded sample points and three UVC sources, the RADIANCE calculation takes approximately
2 ms per point (Figure 4). In this model, 99.9% accuracy
is achieved with at least 100 samples per grid point, which
requires 3 – 4 seconds for the entire simulation.
Figure 4: The simulation error decreases (left axis dots)
and computation time increases (right axis line) with the
number of irradiance samples per sensor point
Figure 6: Plumes of exhaled pathogens rise from each
occupant
We emit a pathogen as a scalar concentration with unitary
concentration from the mouth each simulated occupant in
the room at a rate of 7.5 L/min. For our purposes, we are
concerned only with relative concentrations, and thus the
precise units of the input are unimportant. At the lowest
ventilation rate, application of full UVGI in our CFD
study reduces the steady state concentration of the
pathogen by an order of magnitude, and even at the
highest ventilation rate with half the UVGI dose, a 45%
reduction in concentration is achieved (Figure 7). Figure
8 shows examples of pathogen distribution in the space at
the lowest ventilation setting.
80%
No UVGI
Half UVGI
Full UVGI
Survival Rate
Concentration (m-3)
0.01
0.001
0.0001
0
2
4
6
60%
40%
20%
0%
8
0
ACH
2
4
6
8
ACH
Figure 7: Steady state CFD pathogen concentration as a
result of ventilation and UVGI
CFD - Full UVGI
CFD - Half UVGI
Rudnick - Full UVGI
Rudnick - Half UVGI
Beggs - Full UVGI
Beggs - Half UVGI
Figure 9: Survival rate of pathogen as a result of UVGI
Dissipation of Pathogen under UVGI
We use transient CFD to model the change in pathogen
concentration after the occupants leave. For the 1 ACH
and 4 ACH cases, we monitor the rate of pathogen
removal from the air in the small conference room with
and without UVGI. The concentration drops more quickly
with higher air change rates, and more intense UV-C
produces faster decay (Figure 10).
Relative Concentration
100%
80%
60%
40%
20%
0%
0
Figure 8: Pathogen concentration distribution at 1 ACH
without UVGI (top) and with full UVGI (bottom)
We calculate the UVGI survival rate as the ratio of the
pathogen concentration with and without ultraviolet
application (Figure 9). Lower survival rates indicate
greater amounts of the pathogen inactivated by UVGI,
and thus increased utility of the UVGI installation. We
compare the survival rates calculated with CFD to those
predicted by Rudnick and First (2007) in Equation 1 and
by Beggs and Sleigh (2002) in Equation 2. Rudnick and
First’s algorithm yields this ratio directly. For Beggs and
Sleigh, we treat C0 as the steady-state concentration
without UVGI and Ct as the steady-state concentration
with UVGI, and we set the elapsed time t very large.
100
200
CFD - 1 ACH - Full UVGI
CFD - 1 ACH - Half UVGI
CFD - 1 ACH - No UVGI
CFD - 4 ACH - Full UVGI
CFD - 4 ACH - Half UVGI
CFD - 4 ACH - No UVGI
300
400
Time (s)
500
600
Beggs - 1 ACH - Full UVGI
Beggs - 1 ACH - Half UVGI
Beggs - 1 ACH - No UVGI
Beggs - 4 ACH - Full UVGI
Beggs - 4 ACH - Half UVGI
Beggs - 4 ACH - No UVGI
Figure 10: Decay in pathogen concentration after exit of
infected individual from room
We compare the decay rates observed in our CFD model
to those predicted by Beggs and Sleigh (2002) in Equation
2. In general, the analytical method predicts faster decay
(i.e. larger keqv) in the presence of UVGI and slower decay
(smaller keqv) otherwise. The overprediction with UVGI is
likely the result of incomplete mixing between the room’s
upper and lower zones, while the underprediction without
UVGI may indicate that the room was not fully mixed to
begin with. Excluding the first two minutes, in which
pathogen concentration remains higher in areas
previously occupied by infected individuals, we calculate
10%
1 ACH
4 ACH
Error in k_eqv
5%
0%
-5%
-10%
-15%
Full UVGI
Half UVGI
No UVGI
Figure 11: Difference in analytical prediction of decay
rate compared to CFD, with positive values indicating
faster decay in CFD
Effect of UVGI on Infection Risk
The Wells-Riley model describes the probability of
infection among susceptible individuals exposed to an
infectious person (Equation 4). For the small conference
room, we consider the case in which one occupant is
infectious with various durations of exposure. Figure 12
expresses the probability of infection given a quanta
generation rate of 55 per hour. For a one-hour meeting,
each susceptible individual has a more than 20% chance
of becoming infected if the room is poorly ventilated
without UVGI. A well-ventilated room with 4 ACH
reduces the probability to 6%. However, even without
increasing ventilation, UVGI at half intensity reduces the
probability to 3%. With a combination of increased
ventilation and full ultraviolet intensity, 1% probability is
achieved.
Probability of Infection
100%
80%
60%
40%
20%
0%
0
2
4
Time (hr)
6
8
CFD - 1 ACH - Full UVGI
Beggs - 1 ACH - Full UVGI
CFD - 1 ACH - Half UVGI
Beggs - 1 ACH - Half UVGI
CFD - 1 ACH - No UVGI
Beggs - 1 ACH - No UVGI
CFD - 4 ACH - Full UVGI
Beggs - 4 ACH - Full UVGI
CFD - 4 ACH - Half UVGI
Beggs - 4 ACH - Half UVGI
CFD - 4 ACH - No UVGI
Beggs - 4 ACH - No UVGI
Figure 12: Probability of infection calculated via the
Wells-Riley model
We may also express this as a reduction in the number of
infections if the scenario is repeated often, as might be the
case in a large office building. Figure 13 shows the
number of infections prevented as a result of adding
UVGI without adjusting airflow. The addition of UVGI at
full intensity prevents infection in 75% of occupants who
are exposed to infectors for the full day in poorly
ventilated spaces like this one.
Infections Prevented per 100 Occupants
the average decay rate in CFD and compare it to the
analytical prediction in Figure 11.
100
80
60
40
20
0
0
2
4
Time (hr)
6
8
CFD - 1 ACH - Full UVGI
Beggs - 1 ACH - Full UVGI
CFD - 1 ACH - Half UVGI
Beggs - 1 ACH - Half UVGI
CFD - 4 ACH - Full UVGI
Beggs - 4 ACH - Full UVGI
CFD - 4 ACH - Half UVGI
Beggs - 4 ACH - Half UVGI
Figure 13: Number of infections prevented by the
addition of UVGI
Discussion
In rooms where HVAC systems promote vertical mixing
(e.g. ceiling-level fan-coil units, low-level warm air
supplies, ceiling fans, or jet nozzles), we expect the air
volume to be well-mixed. Analytical calculations using
simplified zonal models provide effective predictions of
pathogen concentration, UVGI efficacy, and infection
risk in these situations. In our case study, the analytical
methods by Rudnick and First (2007) and by Beggs and
Sleigh (2002) predict UVGI effectiveness within 1% and
5% of CFD, respectively, on the basis of pathogen
survival rate with ventilation at or below 4 ACH. Higher
error occurs at 8 ACH, possibly due to reduced mixing. In
transient simulation, we observe up to an 11% difference
in the decay rate between CFD and the analytical
approach by Beggs and Sleigh. However, this translates
to only a 3% difference in infection risk.
In large enclosed spaces (e.g. open-plan offices), or where
vertical mixing is not promoted by the HVAC system, or
where UVGI emitters provide uneven coverage, we
cannot depend on analytical approaches with well-mixed
assumptions. In these cases, CFD is necessary to
determine system performance in reducing pathogen
levels. Figure 14 shows the range of pathogen
concentrations in an open-plan office with several
infected individuals calculated via CFD. Our CFD
method can determine UVGI efficacy and infection risk
in specific areas of the model, while analytical methods
based on zonal averages would fail in this case.
Figure 14: Locations of occupants (top) and associated
pathogen concentrations (in shades of pink, bottom) for
an open-plan office calculated in CFD reveal that wellmixed assumptions will not apply
Recommendations
Our simulations demonstrate that upper air volume UVGI
is effective for reducing infection risk in well-mixed
spaces. Furthermore, we suggest that CFD in unmixed
spaces may be used to identify locations of high pathogen
concentration for targeted UVGI application. In small
spaces that are reliably well-mixed, we recommend the
algorithm by Beggs and Sleigh to quickly determine the
effectiveness of UVGI emitters based on simple ray
tracing calculations of kuv in the upper air volume. The
approach by Rudnick and First, though reliable, is more
unwieldy because it requires a measure of vertical air
speed, which is difficult to obtain without CFD.
We recommend the use of CFD modelling in large spaces,
spaces with unpredictable ventilation, and spaces with
moving occupants. In these cases, we cannot depend on
well-mixed assumptions. The close fit between our CFD
simulations and analytical predictions suggests CFD to be
a reliable tool for studying airborne infection risk.
Limitations
Several limitations to our method might be solved with
more detailed CFD studies. We did not consider natural
inactivation or deposition rates, leading us to more
conservative estimates of infection rate. Experiments
have demonstrated a limited lifespan for pathogens
suspended in aerosols (Stadnytski, et al., 2020; de
Oliveira, et al., 2021). Modelling pathogens as droplets
rather than passive scalar concentrations would allow
consideration of gravitational effects on pathogen
transport (Alani, et al., 2001).
Additionally, we are forced to make assumptions about
UV-C reflectance of materials due to lack of available
data and difficulty of measurement. By ignoring
reflections, we produce conservative predictions of viral
inactivation, but not of human exposure to ultraviolet
radiation (First, et al., 2005). Future studies might benefit
from potentially safer far UV-C (207 nm – 222 nm)
radiation (Buonanno, 2017; Welch, 2018).
The lack of readily available radiometry is a hurdle in
modelling UV-C fluence. In some cases, radiometry is
supplied in IES, EULUMDAT, or TM14 files, which
specify luminous intensity in candela. As no standard file
format exists for UV-C radiant intensity, manufacturers
must reinterpret these data formats for UV-C emitters.
Often, such data is simply not available to modelers. UVC radiometry is harder to measure than visual photometry,
although new approaches may increase its availability
(Rudnick & Nardell, 2016; Bolton & Santelli, 2017).
Alternatively, we can create approximate radiometry by
using a Grasshopper script to apply occlusion effects of
the emitter housing to an idealized lamp.
Even when information is available, the lack of adopted
standards or governance for measuring UVGI system
performance means that data is not always consistent in
quality or format. We identified three ways of reporting
system efficacy, which yield contradictory impressions:
1. Reporting UVGI survival or kill rate emphasizes the
value of adding UVGI to an existing space. It shows
the highest value when ventilation or other means of
viral inactivation are not available.
2. Reporting pathogen concentration favors systems that
combine to yield the greatest reduction. Spaces that
combine UVGI with high ventilation rate appear
most successful by this scale.
3. Reporting infection rate encourages UVGI
application mainly in spaces with long term
occupancy by large groups.
Additionally, the reported efficacy of any system depends
on whether a production source term is included in the
calculation. Practitioners must recognize the means used
to report the efficacy of UVGI and other disinfection
systems. We support the adoption of uniform standards to
rate disinfection efficacy.
Conclusion
Upper air volume UVGI is an effective tool for
combatting airborne infectious pathogens such as SARSCoV-2. We developed workflows that allow us to
quantify UVGI efficacy and infection risk in a variety of
space types, including spaces that are not well-mixed. Our
workflows include radiometric dosing calculations, which
we can perform in real-time using Grasshopper or in
RADIANCE for larger and more complex geometries. We
can apply this radiometric field to a CFD model to
determine pathogen concentrations and risk of infection.
We validated the CFD results against the Rudnick & First,
Beggs & Sleigh, and Wells-Riley equations for simple
geometries, but CFD also allows analysis of spaces in
which size, partitions, or architectural obstructions limit
air mixing.
Comparing our CFD calculations to analytical methods,
we predicted pathogen concentrations within 5% and
infection risk within 3%. In our case study, UVGI reduced
infection risk during a 1-hour interaction with a COVID19-infected person from 20% to 3% even in poorly
ventilated conditions. This evidences the usefulness of
UVGI in battling the spread of pandemics.
Today, lighting, electrical, and mechanical engineers face
a fundamental challenge to design effective applications
of UVGI technology with available data and analysis
tools. Despite major lighting manufacturers rushing to
create new UVGI products, assessment tools that use UVC radiometry and CFD to calculate risk reduction and
enhance infection control are largely absent from the
marketplace. Our methodology can provide designers
with confidence in selecting UVGI technology to protect
the health of building occupants and keep economic
enterprises open and viable. It will aid our industry in
making facilities safer and slowing the spread of COVID19 as well as future respiratory virus outbreaks.
Acknowledgement
This project was funded by Invest in Arup 27091 with the
support of Brian Stacy. Connor Black performed
additional Grasshopper development, and Arup’s UK and
San Francisco CFD teams provided support and review.
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