How do you avoid COVID-19 Transmission by social distancing ?

By

Dr. Sharad N. Pachpute

 

1. Scope of CFD Modelling for COVID-19 Transmission

• The severe acute respiratory syndrome (SARS) pandemic has been a topic of interest for last decades as these viruses have endangered many lives
• After taking precautions of corona virus transmission, its control is a cumbersome process for many governments. Hence, many scientists, medical professionals, and engineers have been working to understand the behavior of the corona virus (COVID-19) transmission using various analysis techniques
• There are three major reasons behind spreading of viruses which are person-to-person contact, droplets transmission to air and surface, and its airborne transmission
• Therefore, social distancing and wearing mask are used to control transmission. Effect of face mask on flow physical is studied in the previous article
• Other parameters like room size and ventilation are also important to understand the social distancing between people

• To control spreading of corona virus, social distancing has been implemented in may countries
• This one of best way to avoid or reduce the effect of droplet transmission from infected person

• To study corona virus transmission by person-person spreading is difficult. Hence, CFD modelling allows to study effect of various parameters like exhalation and inhalation flow pattern by mouth or nose, temperature, and distribution of viral particle in air
• CFD analysis helps also determine the rate infection to exposed person and effective social distance

2. COVID-19 Transmission by Person-to-person Spreading

• The transmission of SARS like COVID-19 disease is more significant when a SARS infected patient comes closely with other people
• This article presents a CFD analysis of the human respiration process, the effect of transport of exhaled air on the adjacent person considering breathing, coughing, and sneezing
• CFD analysis of coronavirus spreading by person-to-person seating carried out by Gao et al. (2006) and research group is presented here.
• Three different cases for the COVID-person have been analysed for normal respiration through the nose or mouth, and sneezing or coughing process

2.1 Typical Domain for CFD Analysis

• Computational domain for a ventilated room (2.6m X 2.5mX2.2m) considered by Gao et al. (2006) is shown below to study the effect of person-to-person spreading on indoor room air quality by considering the computational thermal manikin (CTM)
• Air inlet is specified at the bottom of wall and outlet of air is at the top of side walls
• Computational thermal manikin (CTM) models placed in the centre of room. One person is coronavirus (SARS-2) infected and other one is an exposed person

2.2 Typical Mesh Model

• Hexa-hedral cells in rooms and tetrahedral elements considered around the manikin
• The total number of cells is around 2.5 million
• The mesh around the manikin body was refined such a way that y+ as taken less than 1

2.3 Models and Boundary conditions

Details of CFD models and boundary conditions for above case are given below

• Transient state with full buoyancy effect
• Turbulence model: RNG k-ε model including low-Reynolds number effect, enhanced wall treatment
• Numerical scheme: Upwind second-order difference
• Room air inlet: V = 0.2 m/s, T= 22 ° C, Turbulent intensity = 20%, hydraulic diameter = 0.35 m
• Room air outlet: pressure outlet
• Room walls: adiabatic wall
• Human body wall temperature at 31°C
• Nose or mouth specified with velocity or flow rate of respiration as a function of time. The flow rate of breathing is presented as a sinusoidal function of respiratory frequency (RF) and tidal volume (TV).

 

 

2.3 Modelling of Respiration from COVID-19 person

• For normal breathing process, number of droplets in the exhalation is negligible. Hence, tracer-gas diffusion analysis is considered for CFD modelling
• For the COVID person (CTM), the real respiration process is modeled by a sinusoidal curve
• In the above CFD model by Gao et al. (2006), the frequency of respiration for light physical work is around 17 times per minute with a time-mean rate of 8.4 L/min
• Tracer gas of concentration (Cex = 1000 ppm) added into the exhaled air. The transient spreading of tracer gas is calculated in the room space based on the species (φ) transport equation

Here, φ is tracer gas concentration. ρ is air density. U is velocity vector, D_φ is diffusion coefficient, and S_φ is the source term of tracer gas.

• After solving the tracer gas concentration, the mass fraction ( f )of the exhaled air calculated as, f = φ/ Cex
• For sneezing or coughing process, the effect of shear stress, gravitational and electrostatic forces are not considered for simulating droplets by conservation equation of species
• However, initially for several seconds after sneezing or coughing, the use of tracer-gas method is applicable because of the same high velocity for droplets and the exhaled air. We can neglect the momentum, heat, and mass exchanges between droplets and room air
• After this initial period, the evaporation and cohesion phenomenon are significant and effect of aerodynamic on droplets or particles are necessary
• In this simulation by Gao et al. (2006), the tracer gas movement represent fine droplets which have an aerodynamic diameter less than 2.5μm
• To model the motion of larger-size particles, we need to use the trajectory model (Langrage approach)
• The transient inhalation process of the exposed person (CTM) simplified to a steady state with an inhaled air flow rate of 0.14 L/s
• For normal breathing, cough and sneezing, the opening areas are 1.5 and 2.5 cm² for nose and mouth, respectively
• The angle of the exhaled airflow is taken to be 30° downward and 0° (horizontal) from nose and mouth, respectively
• The exhalation air is considered at 34°C and density of 1.15 kg/m³
• The assumed time of sneezing is around 1 second with the volume flow rate of air at 250 L/min
• For the sake of simplicity, only one sneezing process modelled, even though people can sneeze more than one in a typical cycle of sneezing or coughing

2.4 Modelling of COVID-19 Infection to Exposed Person

• The infection to exposed person is modelled using the infection index, η

where

V = inhalation rate (m³ /s),

ρ = inhaled air density (kg/m³),

C = mass fraction of the sneezed air in the inhaled air

• In the CFD analysis of Gao et al. (2006), the value of η for the exposed person was taken to be 800 mg

2.5 Modelling of Droplets

• To model droplets (particles) exhaled from the infected or COVID person, discrete phase model (DPM) is used to predict the concentration of particles if particle effect on air flow is significant
• For multi-phase model, Eulerian and Lagrangian model is used if particle concentration in air flow is less than 10%
• The Newton’s second law of motion is applied to find particle location

3. CFD Results

Some CFD results of Gao et al. (2006) and other research groups have been presented below for flow pattern of exhalation and inhalation from mouth or nose, infection and sneezing

3.1 Respiration processes

• The vectors of airflow around the facial region when the person breathes through the nose and mouth is shown below
• The inhaling and exhaling processes have negligible influence on the room airflow pattern because of relatively small airflow rate of respiration

3.2 Inhalation and exhalation from nose of COVID person

• To understand the flow pattern, path lines of inhaled and exhaled air through the nose and mouth of the COVID-person are presented
• Based on CFD results, the exhaled air through the nose of the COVID person is affected in the upward direction by the thermal plume

 

3.3 Inhalation and exhalation from mouth of COVID person

• The exhaled air through the mouth of person can get away from the enclosure of the warm rising airflow around the human body (CTM) since the exhaled airflow is highly directional in horizonal direction at a high momentum level

3.4 Sneezing of Air without droplets

• Variations of the mass fraction of sneezed air during and after sneezing have been analysed based on CFD analysis by Gao et al. (2006)
• High velocity jet of air containing viruses are exhaled from the mouth of COVID person and exposed person receives that virus particles by breathing

 

• Sneezed air mass fraction in the inhaled air of the exposed person is presented below during the sneezing process of COVID person
• COVID transmission created by sneezing can affect the purity of clean air entered in the room
• Other factors like masks of exposed person and social distance between two persons can influence the percentage of infection

• It is important to note that the exposure to sneezing or cough is highly directional. It can be well understood using CFD modelling
• Due to the ventilation of air, the large part of COVID transmission can be exhausted by the ventilation air

3.5 Sneezing with droplets

• Mehran Salehi (2020) carried out a CFD analysis of two persons standing in a room which are separated by 6 feet
• Transient simulations were carried out using discrete phase model (DPM) for droplets exhaled by the COVID-person
• The size of droplets considered in the range of 1 -100 μm in diameter
• The COVID person has the coughing speed of 50 m/s
• The CFD results show that axial momentum of particles decreases within 6 feet
• Larger particles start falling to ground faster due to inertia of heavier particles which is than lighter particles

 

• The engineers of ANSYS FLUENT also carried a numerical simulation of droplet from the infected person standing close to the exposed person by considering multi-phase flows of air and droplets, and wall film model for particles
• It is observed that the number of particles reached to exposed person is very high for a small social distancing (3feet)
• This situation is pretty common when two person talk each other without wearing masks

 

• ANSYS FLUENT carried out numerical simulations of three person standing close to each other
• A longer social distancing can help to reduce the effect of corona particles

3.6 Effect of face shield

• Dassault engineers analysed the effect of 3D printed masks (face shields ) on droplet transmission from COVID person using their CFD solver SIMULIA and PowerFLOW software
• Their CFD results suggest that medical staff should use both masks and face shields to protect against coronavirus transmission

• Watch the video of results CFD simulation carried out Dassult engineers

 

4.Summary

• CFD simulations have carried out by many research groups to understand the flow physics of sneezing , coughing and their effect to exposed persons
• The flow pattern of sneezing or coughing is affected by social distancing between two persons, facemasks, ventilation, and surrounding environments
• Most of CFD results show that droplets exhaled by COVID-19 or infected person start falling after 6 feet. After it, the effect of particles is less. However airborne transmission cannot be neglected which is difficult to model numerically.
• Using both facemask and shields, the effect of corona particles is very less

References

1. N. Gao, J. Niu, Transient CFD simulation of the respiration process and inter-person exposure assessment, Building and Environment 41 (2006) 1214–1222
2. V. Vuorinen et al, Modelling aerosol transport and virus exposure with numerical simulations in relation to SARS-CoV-2 transmission by inhalation indoors, Safety Science (2020)0104866