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5th-6th Thermal and Fluids Engineering Conference (TFEC)
May 2628, 2021
Virtual Conference
Reid Prichard1, Wayne Strasser1, Scott Leonard2, Brian Walsh1
1Liberty University, Lynchburg, VA 24502, USA
2Vapotherm, Inc., Exeter NH 03833, USA
In this paper, we used a computational fluid dynamics model to evaluate the effects of a novel medical apparatus
(“Felix-1”) on the spread of contagion in a hospital room. We found that Felix-1, consisting of nasal cannula and
an oxygen mask, captured 96% of the mass of exhaled particles ranging from 0.1µm to 100µm. This is more
effective than a surgical mask. It was less effective at capturing small particles, but their mass is insubstantial.
The caregivers inhaled only 24 parts per billion of particle mass exhaled by the patients. Our model included a
full hospital room with two patients and four caregivers, each represented using medical imagery and realistic
nonuniform breathing rate curves. Room ventilation was also modeled, and we allowed over a minute of flow
time for the room to reach quasi-steady-state, which we evaluated using flow statistics and particle tracking
The “Felix-1” apparatus was proposed by Felix Khusid (RRT, NY Presbyterian Hospital) and implemented by
Vapotherm, Inc. The purpose of the apparatus is to administer mild ventilation while capturing exhaled particles
which might spread contagion. Its first component is a high-velocity nasal insufflation (HVNI) cannula, a form
of ventilation that injects high-velocity oxygen into a patient’s nostrils. The second component is a face-tent
oxygen mask; instead of supplying oxygen, it is connected to a suction line to evacuate exhaled matter.
While it is not meant to be an alternative to cloth mask, Felix-1 has several potential advantages over a surgical
mask. First, its components can be reused, reducing waste and cost to the hospital. Additionally, cloth masks can
cause discomfort due to the physical contact of the mask and the increased humidity on a patient’s face. Felix-1
sits away from the patient’s face and constantly circulates fresh air to avoid buildup of moisture and heat. Lastly,
its active evacuation of particles is less susceptible to mask leakage, which could result in higher effectiveness.
Fig. 1 Study domain, featuring two patients (P1, P2) and four caregivers (CG1A, CG2A, CG1B, CG2B). The
patients are wearing Felix-1, while the caregivers have no respiratory protection.
2.1 Domain We modeled a full hospital room containing six people: two patients and four caregivers. The
model included a ventilation system, with eight wall vents blowing air into the room and four ceiling vents
removing air. The patients were denoted “P1” and “P2” and the caregivers “CG1A”, “CG1B”, “CG2A”, and
“CG2B” as illustrated in Fig. 1. The patients were fitted with Felix-1, while caregivers did not wear masks.
One unique aspect of our model was the accurate representation of airways using medical imagery. As shown in
Fig. 2, we modeled the airway from the trachea’s midpoint upward. Except for the oral cavity, the entire airway
was modeled with medical imagery. In addition to their effect on particle emission, lifelike airway models were
important so that the effects of the HVNI cannula could be accurately resolved. The airway models also ensured
that the mouth/nose flow proportion and turbulent properties of the flow would be correct.
Fig. 2 Cutaway view of the realistic airway model. The patient, mask, and cannula have been halved, while the
full airway is depicted in pink.
2.2 Boundary Conditions The room’s ventilation was set to a representative hospital value of 6 room air
changes per hour. The nasal cannulae injected air at 40 L/min, and the masks evacuated air at 30 L/min. The
breathing boundary conditions for our subjects were highly sophisticated, featuring anatomically accurate,
asymmetric inhalation and exhalation; four unique breathing rates; and varying breath amplitude. These features
are shown in Fig. 3. These breathing curves were developed based on experimental data from the Liberty
University respiratory therapy program.
Fig. 3 Illustration of breathing curves. Only three of six curves shown. Noteworthy features are the randomly-
varying amplitude from breath to breath as well as diverse breathing rates.
Unique breathing rates
oral cavity
HVNI cannula
Mask suction
Fig. 4 Mesh blocking showing distribution of element types along one cross-section.
We injected into the patients’ airways particles with diameter 0.1µm to 100µm, listed in Table 1.
Table 1 Distribution of injection diameters. This distribution obtained from [1].
Mass fraction
Mass fraction
2.3 Mesh Our domain was both physically large and intricately detailed, so careful meshing was crucial.
Tetrahedral elements are inefficient [2], so a purely tetrahedral mesh likely would have been either prohibitively
large or unusably coarse. Selectively decomposing the geometry into simple shapes (“blocking”) allowed the use
of efficient hexahedral elements in much of the volume, and elsewhere we used polyhedra. Our final mesh
featured elements of volume on the order of 10-14 m3 in the airways and 10-6 m3 in the main volume of the room.
2.4 Numerics We conducted this study using Ansys Fluent 2020R2 in single precision. We modeled turbulence
with the SST K-omega unsteady RANS method, and we used steady-state, Lagrangian, one-way coupled particle
tracking. We paid particular attention to the effects of the particle tracking model’s settings on our particle
capture results and adjusted them for maximum conservativeness. This optimization process is outside the scope
of this paper, but we optimized step count, step length factor, and loop factor. We also tested the high-resolution
tracking setting, which subdivides mesh elements for more precise particle tracking. We found high-resolution
tracking profoundly influenced results, so we enabled it despite its additional cost.
Viruses can survive in droplets for a substantial amount of time; over 3 hours for COVID-19 [3]. However, the
lifetime of the droplet itself is limited by evaporation, whose rate depends on parameters such as humidity and
temperature. We found 10 minutes to be a reasonable estimate for typical hospital conditions [4], so we ceased
tracking of particles at 10 minutes.
Because our mesh was so large, it was important to carefully choose the number of CPUs we use to avoid
unnecessary cost. It is commonly known that CFD codes such as ANSYS Fluent do not scale perfectly.
Doubling the number of cores may only increase computation speed by 50%. It would not be practical to run on
a single core, so a balance must be struck between computation time and cost. Furthermore, real-world hardware
limitations mean certain core counts may be outperform or underperform the trend. Due to these factors, we
conducted a scaling analysis to find an optimum number of cores. For this analysis, we created a cost efficiency
𝐶 = number of machines ×cost per machine per second
mesh element count ×seconds per iteration =cost per iteration per element (1)
This normalization allows direct cost comparison between alternatives, although numbers created using this
metric cannot be expected to extrapolate to other hardware or other models. If the metric were twice as large, our
model would cost twice as much, regardless of how many machines are used or how long the solution took.
We used a cluster of Microsoft Azure’s HBv2 machines, which each have 120 cores, and we tested from 1 to 36
machines (120 to 4320 cores). As expected, we saw the general trend that higher core counts were less cost-
efficient. Running a single machine was most efficient, followed by three machines. Unexplainedly, using two
machines was substantially less efficient than three. The third most efficient scaling tested was 18 machines,
skipping over 6, 9, 10, 12, and 15. Efficiency declined substantially at cluster sizes greater than 18 machines.
However, efficiency is only part of the picture. It was also important that we obtain results in a reasonable
timeframe, so we had to balance solution speed with our cost metric. We deemed 1 machine or 3 machines to be
infeasibly slow, which left 18 as the clear choice. For only 20% higher overall cost than 3 machines, we obtained
5x the solution speed.
Fig. 5 Scaling analysis results showing 18x120 cores to be the optimum.
010 20 30 40
Cost metric
Machine Count
Fig. 6 Convergence of particles captured by CG2A's airway (left) and P1’s mask (right). Blue dots represent the
particles captured by the indicated region, and the dashed lines show the patients’ breath rates. Notice the
synchronization between particle capture and exhalation.
We monitored a broad range of flow statistics to assess convergence. Some of these, such as mass flow through
the subjects’ mouths, settled into quasi-steady-state (QSS) behavior relatively quickly. Others, such as the
turbulent kinetic energy at a point in front of the subjects’ mouths, took over 60s of flow time to reach QSS. Yet
others, such as the mean velocity in the domain, continued to directionally trend until the end of our study. We
primarily relied on particle capture data to assess convergence, as that is the focus of our study. These data are
too vast to portray here, but Fig. 6 is shows two examples. Though the particle capture on CG2A’s airway had
not completely settled, any error would underrepresent Felix-1’s effectiveness, which we deemed acceptable. In
contrast, the particle capture by the mask had leveled off.
Because we used steady-state particle tracking, it was necessary to average particle capture data over a range of
flow conditions. After reaching steady state, we continued to gather data for about 7 seconds. This represents 2-4
breaths depending on breathing rate.
Steady-state particle tracking is less realistic at low mass flow rates, and computational limitations prevented us
from fully resolving particles’ paths at low velocities. Consequently, we only considered data where P1 and P2
were exhaling at a mass flow rate greater than a certain threshold. To calibrate this, we performed a sensitivity
analysis, the results of which are displayed in Fig. 7. Interpretation of these results is subjective, but we chose a
threshold of rate of 1.5 × 10−4 kg/s, which is about 15% of the peak inhalation/exhalation rate. The incomplete
particle count dropped negligibly at larger thresholds. It is important to note that this threshold affects the
calculated mask effectiveness.
Commented [RP1]: Ditch the mass flow curves?
Fig. 7 Mass flow threshold sensitivity analysis results. “Incomplete” particles are those whose full path could
not be resolved. The black line indicates the number of incomplete particles considered at a certain threshold;
this quantity should be minimized. The orange and blue lines show the computed effectiveness of each patient’s
mask at a given threshold. This value decreases at lower thresholds because incomplete particles skew the
Felix-1 captured 95.8% of particle mass from 0.1 to 100µm. Fig. 8 shows that it is most effective at large particle
sizes, while effectiveness drops markedly below 10µm. These smaller droplets represent an insubstantial portion
of total mass, and recent research indicates that droplets smaller than 4.7µm cannot carry COVID-19 [5].
While a surgical mask theoretically captures nearly 100% of particles over 1µm, leakage around the mask
reduces this number in practice. A previous numerical study showed that a surgical mask, in combination with
HVNI, captured 88.8% [1] 7% less than Felix-1.
Fig. 8 Felix-1 particle capture curves based on diameter and volume. Higher capture is better.
Fig. 9 This image shows a cross-section of P1. Large particles are captured by the mask, whereas those escaping
are much smaller and practically invisible in this image. The pressure created by the cannula prevents particles
from entering the sinuses. Contours of air velocity are shown on the cross-section.
With Felix-1 in place, very little particle mass was inhaled by the four caregivers. Inhalation was measured as a
particle landing on the airway wall or traveling through the airway boundary at the base of the throat. As shown
in Fig. 10, the caregivers did not inhale any particles larger than 5µm. The caregivers inhaled just 24 parts per
billion of the particle mass exhaled by the patients.
Fig. 10 Proportion of overall particle mass inhaled by caregivers.
We have many ambitions for continuation of this work. Even the data we already have is vast, and there is much
room for additional analysis. We also hope to consider other flow scenarios involving factors such as changes to
room ventilation or modeling a cough or sneeze. Additionally, we would like to improve the accuracy of our
particle modeling by using transient particle tracking and by modeling evaporation and particle breakup.
We have observed that the flow does not aim down the tube of the mask. Instead, part of the flow turns and
travels up out of the mask. To correct this, we hope to adjust the design of the mask to align the suction with the
patient’s breath.
To our knowledge, this work represents the first computational study on the airborne spread of contagion using
realistic airway models and breathing curves. The results indicate that Felix-1 is more effective than a cloth
surgical mask at preventing the spread of contagion when HVNI is used, allowing only half as much particle
mass to escape. By utilizing active suction, Felix-1 is less affected by leakage than a surgical mask. In total, only
24 parts per billion of exhaled particle matter were inhaled by the caregivers standing adjacent to the patients. In
addition to our conclusions about the effectiveness of Felix-1, we demonstrated a method to optimize
computational core count based on a metric that correlates to total project cost.
We would like to thank Microsoft Azure for supporting this work via their Microsoft AI for Health COVID-19
grant program, and we also extend our gratitude to Ansys, Inc. for granting us licenses and technical support for
our work.
[1] Leonard, S., Strasser, W., Whittle, J., Volakis, L., DeBellis, R., Prichard, R., Atwood, C., “Reducing
aerosol dispersion by High Flow Therapy in COVID‐19: High Resolution Computational Fluid
Dynamics Simulations of Particle Behavior during High Velocity Nasal Insufflation with a Simple
Surgical Mask,” Journal of the American College of Emergency Physicians Open, 1(4), pp. 578-591
(2020). Journal Paper
[2] Strasser, W., “CFD Investigation of Gear Pump Mixing Using Deforming/Agglomerating Mesh,”
Journal of Fluids Engineering, 129(4), pp. 476-484 (2007). Journal Paper
[3] van Doremalen, N., Morris, D., Holbrook, M., Gamble, A., Williamson, B., Tamin, A., Harcourt, J.,
Thornburg, N., Gerber, S., Lloyd-Smith, J., de Wit, E., Munster, J., Aerosol and Surface Stability of
SARS-CoV-2 as Compared with SARS-CoV-1,” The New England Journal of Medicine, 382, pp. 1564-
1567 (2020). Letter
[4] Stadnytskyi, V., Bax, C., Bax, A., Anfinrud, P., “The airborne lifetime of small speech droplets and their
potential importance in SARS-CoV-2 transmission,Proc Natl Acad Sci USA, 117(22), pp. 11875-
11877 (2020). Journal Paper
[5] Lee, B., “Minimum Sizes of Respiratory Particles Carrying SARS-CoV-2 and the Possibility of Aerosol
Generation,” International Journal of Environmental Research and Public Health, 17(19), p. 6960
(2020). Journal Paper
ResearchGate has not been able to resolve any citations for this publication.
Full-text available
This study calculates and elucidates the minimum size of respiratory particles that are potential carriers of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); furthermore, it evaluates the aerosol generation potential of SARS-CoV-2. The calculations are based on experimental results and theoretical models. In the case of maximum viral-loading derived from experimental data of COVID-19 patients, 7.18 × 10-4% of a respiratory fluid particle from a COVID-19 patient is occupied by SARS-CoV-2. Hence, the minimum size of a respiratory particle that can contain SARS-CoV-2 is calculated to be approximately 4.7 μm. The minimum size of the particles can decrease due to the evaporation of water on the particle surfaces. There are limitations to this analysis: (a) assumption that the viruses are homogeneously distributed in respiratory fluid particles and (b) considering a gene copy as a single virion in unit conversions. However, the study shows that high viral loads can decrease the minimum size of respiratory particles containing SARS-CoV-2, thereby increasing the probability of aerosol generation of the viruses. The aerosol generation theory created in this study for COVID-19 has the potential to be applied to other contagious diseases that are caused by respiratory infectious microorganisms.
Full-text available
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Speech droplets generated by asymptomatic carriers of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) are increasingly considered to be a likely mode of disease transmission. Highly sensitive laser light scattering observations have revealed that loud speech can emit thousands of oral fluid droplets per second. In a closed, stagnant air environment, they disappear from the window of view with time constants in the range of 8 to 14 min, which corresponds to droplet nuclei of ca. 4 μm diameter, or 12- to 21-μm droplets prior to dehydration. These observations confirm that there is a substantial probability that normal speaking causes airborne virus transmission in confined environments.
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