International audienceResearchers from Inria and the French Aerospace Lab ONERA are collaborating on a joint project. The goal is to assess the variability in the advice for social distancing precautions that can be drawn from numerical simulations of airborne dispersion. This variability depends on a number of factors, including: physical variables (e.g. droplet size, ejection velocity), modelling methods used (e.g. turbulence model) and numerical aspects (mesh). We use sensitivity analysis tools to quantify and order the role these factors play in influencing the numerical results

Bossy, Mireille

Guillard, Hervé

Henry, Christophe

Martinez-Rodriguez, Kerlyns

Murrone, Angelo

Rutard, Nicolas

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HAL Id: hal-03041624https://hal.inria.fr/hal-03041624Submitted on 5 Dec 2020HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Social Distancing: The Sensitivity of NumericalSimulationsChristophe Henry, Kerlyns Martinez-Rodriguez, Mireille Bossy, HervéGuillard, Nicolas Rutard, Angelo MurroneTo cite this version:Christophe Henry, Kerlyns Martinez-Rodriguez, Mireille Bossy, Hervé Guillard, Nicolas Rutard, et al..Social Distancing: The Sensitivity of Numerical Simulations. ERCIM News, ERCIM, 2021, Specialtheme: Pandemic Modelling and Simulation, 2021 (124). ￿hal-03041624￿Social Distancing: The Sensitivity of Numerical Simulationsby Christophe Henry, Kerlyns Martinez-Rodriguez, Mireille Bossy (Université Côte d’Azur, Inria,  CNRS, Cemef, France), Hervé Guillard (Université Côte D’Azur, Inria, CNRS, LJAD, France), Nicolas Rutard and Angelo Murrone (DMPE, ONERA, France)Researchers from Inria and the French Aerospace Lab ONERA are collaborating on a jointproject. The goal is to assess the variability in the advice for social distancing precautions thatcan be drawn from numerical simulations of airborne dispersion. This variability depends on anumber of factors, including: physical variables (e.g. droplet size, ejection velocity), modellingmethods used (e.g. turbulence model) and numerical aspects (mesh). We use sensitivity analysistools to quantify and order the role these factors play in influencing the numerical results.Airborne transmission of respiratory diseases involves a number of disciplines such as virology, orfluid mechanics. The outbreak of COVID-19 has triggered a number of numerical studies to betterunderstand the fate and transport of respiratory droplets in the air. This research aims at developing amethodology  to  evaluate  the  variability  in  numerical  simulations  of  airborne  dispersion  that  canprovide astimations of social distancing precautions. For that purpose, we rely on standard techniquesavailable in computational fluid dynamics (CFD) software to run numerical simulations of airbornedispersion. We then used variance-based methods [2], such as the “Sobol indices” or “variance-basedsensitivity indices”, to analyse the variability of a number of parameters that were demonstrated toaffect droplet dispersion.  For illustrative purposes, this paper details the results from the simple scenario of droplet emission inquiescent air.  In this scenario, two observables are considered: the number of particles remainingabove a given height after a period of time (here 1.5 m after 20 s) and the mean distance from thesource after a given time period (here 20 s).We performed numerical simulations with the Lagrangian tracking module of Code_Saturne  CFDsoftware [L1]. Prior to injection, the fluid was at rest and at a temperature of 25 °C. Droplets wereinjected into a box with dimensions of 4 x 3 x 2 m. Droplets are injected in the domain at a givenlocation,  with  a  height  representative  of  an  average  adult’s  height  (here  1  x  2  x  1.7  m)  andapproximating the shape of a mouth (an ellipsoid with a width of 0.03 m and height of 0.015 m). Inaccordance with previous studies [1,2], we assumed droplets to be expelled from the mouth within afixed cone, i.e. with a vertical injection angle in the range of 15 to 40° and with a horizontal injectionangle in the range of –5 to 5°. Droplets were all injected with the same size and velocity. Simulationswere run for a physical time of 20 s (with a time step of 0.01 s). To complete the simulation set-up,five additional input parameters were used as uncertainty sources modelled with the help of standardrandom distributions. A simulation is realised with a random trial of the input parameters according tothe following distributions:   The droplet diameter (uniform distribution between 1 and 10 µm); The number of injected droplets (uniform distribution between 700 and 1,300); The cough velocity (Gaussian distribution, mean of 10 m/s and variance of 2 m/s); The cough duration (Gaussian distribution, mean of 75 ms and variance of 6 ms); The head angle in relation to the vertical direction (uniform distribution from –15 to 50°).ResultsFigure 1 shows a typical set of results from our simulations: the droplets are dispersed in the flow atrest. Once injected in the simulation, these droplets undergo only Brownian motion and settling due togravity. Due to their size and the fact that no evaporation is accounted for, gravity is the predominantforce, which leads to their sedimentation on the ground within a finite time.Using OpenTurns scientific library and API [2, L2], 6.000 simulations were performed with variousvalues of the five uncertainty sources (i.e. droplet diameter, number of droplets, head angle, coughvelocity and cough duration). The results obtained with the first order Sobol index are summarised inTable 1.Observable Number ofdropletsDropletdiameterCoughvelocityCoughdurationHead angleNp (z>1.5 m) 0,252435  -0,0593705  0,0942603 -0,0427005 0,434486<Xp-X0> 0,0838429 0,084791 0,346216 0,123051 0,765763Table 1. First-order Sobol indices obtained from 6,000 simulations, with a column for eachuncertainty source and two lines corresponding to the two observables (number of droplets remainingabove a height of 1.5 m and the mean distance from the point source along the x-direction) .As expected, it appears that the number of droplets remaining above a certain height (here 1.5 m)varies mostly with the angle at which the head is tilted. The second parameter that affects the results isactually the number of droplets emitted during coughing, while the injection velocity is only the thirdmost influential parameter (with a much lower importance). Yet,  if the observable of interest is taken to be the mean distance travelled by droplets along thehorizontal direction, then the analysis changes. The results are again mostly affected by the angle atwhich the head is tilted, but the second input affecting the results is the velocity of injection of thedroplets. The cough duration, the number of particles and the diameter of particles are less influentialon the result.This study illustrates the application of sensitivity analysis techniques to investigate the variability ofnumerical simulations of airborne dispersion. The first results show the robustness of such techniquesas well as their limitations. In particular, in the simple case considered, the head angle during thecough is  the  key parameter  driving  the  particles  towards  the  ground.  However,  these  results  areexpected to change significantly if another observable is used. Moreover, this study shows that, asprerequisite of the sensitivity analysis, a clear definition of an observable is needed. Simulations in more complex cases are still underway due to the high numerical costs and size of datagenerated by such numerical experiments. In the near future, our analysis will move towards morerealistic descriptions, including models for droplet evaporation/condensation as well as new modelsrelated to  viral  and biological  properties  (lifetime,  contagiousness,  etc.)  that  appear  to  be key indesigning more efficient public health recommendations [1].Links: [L1]: https://www.code-saturne.org/[L2]: http://openturns.github.io/openturns/master/contents.html References: [1] L. Bourouiba, E. Dehandschoewercker, J. W. Bush: “Fluid Mech.”, 745, 537-563, 2020[2] J. K Gupta,. C. H. Lin, Q. Chen: “Indoor air”, 19(6), 517-525, 2009.[3] M. Baudin,et al., in Handbook of Uncertainty Quantification, Springer International Publishing, 2016.Please contact: Christophe HenryUniversité Côte d’Azur, Inria, CNRS, Cemef, Francechristophe.henry@inria.frFigure 1. 3D plot of droplet dispersion generated from two simulations: 997 droplets of 7.6 μm injected during a time of 705 ms and at a velocity of 12.4 m/s (red dots); 997 droplets of 5.7 μm injected during a time of 743 ms and at a velocity of 11.4 m/s (blue dots).Note: the person’s drawing was added for visualisation purposes only.

Social Distancing: The Sensitivity of Numerical Simulations

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Social Distancing: The Sensitivity of Numerical Simulations

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