Analytical solutions and virtual origin corrections for forced, pure and lazy turbulent plumes based on a universal entrainment function

Ciriello, Francesco; Hunt, Gary R.

doi:10.1017/jfm.2020.225

Cited by 23 publications

(20 citation statements)

References 25 publications

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“…For typical rooms and air exchange rates, f d lies in the range of 0.0001 to 0.01. With § These expressions for v(x) and C(x) are valid in the limit of x > xv , where xv is the virtual origin of the jet, typically on the order of 10 cm (20,105). Near-field expressions well behaved at x = 0 are given by replacing x with x + xv , and normalizing such that…”

Section: Beyond the Well-mixed Roommentioning

confidence: 99%

See 1 more Smart Citation

A guideline to limit indoor airborne transmission of COVID-19

Bazant

Bush

2021

Proc. Natl. Acad. Sci. U.S.A.

377

320

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The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the “cumulative exposure time,” the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

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Section: Beyond the Well-mixed Roommentioning

confidence: 99%

“… § These expressions for

and

are valid in the limit of

, where

is the virtual origin of the jet, typically on the order of 10 cm ( 20 , 105 ). Near-field expressions well behaved at

0

are given by replacing

with

, and normalizing such that

.…”

mentioning

confidence: 99%

A guideline to limit indoor airborne transmission of COVID-19

Bazant

Bush

2021

Proc. Natl. Acad. Sci. U.S.A.

377

320

View full text Add to dashboard Cite

show abstract

“… * These expressions for v ( x ) and C ( x ) are valid in the limit of x > x v where x v is the virtual origin of the jet, typically on the order of 10cm (18, 95). Near-field expressions well behaved at x = 0 are given by replacing x with x + x v , and normalizing such that C (0) = C 0 .…”

mentioning

confidence: 99%

Beyond Six Feet: A Guideline to Limit Indoor Airborne Transmission of COVID-19

Bazant

Bush

2020

Preprint

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The revival of the global economy is being predicated on the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing droplets sufficiently small to be continuously mixed through an indoor space. The importance of indoor, airborne transmission of COVID-19 is now widely recognized; nevertheless, no quantitative measures have been proposed to protect against it. In this article, we build upon models of airborne disease transmission in order to derive a safety guideline that would impose a precise upper bound on the cumulative exposure time, the product of the number of occupants and their time in an enclosed space. We demonstrate the manner in which this bound depends on the ventilation rate and dimensions of the room; the breathing rate, respiratory activity and face-mask use of its occupants; and the infectiousness of the respiratory aerosols, a disease-specific parameter that we estimate from available data. Case studies are presented, implications for contact tracing considered, and appropriate caveats enumerated.

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“…radius to the reservoir depth; and also test the inclusion of the detailed change in the entrainment coefficient as a function of the deviation from pure plume behaviour (Ciriello & Hunt 2020).…”

Section: Discussionmentioning

confidence: 99%

“…The model equations for the plume can be summarised as where is the empirically determined entrainment coefficient. There has been a considerable amount of work carried out in which models for the variation of the entrainment coefficient in a turbulent plume have been developed as the flow evolves from being momentum dominated (jet-like) to mass flux dominated (lazy) relative to the ideal pure buoyancy-driven plume (Caulfield & Woods 1995; Hunt & Kaye 2001; Carazzo, Kaminski & Tait 2006; Craske & van Reeuwijk 2015; Ciriello & Hunt 2020). However, given the simplicity of the present model, we approximate the entrainment coefficient as a constant (Turner 1986) corresponding to the value for a pure plume; while a more detailed parametrisation is possible, we have found that the structure of the density profile in the interior of the domain is similar to that using a constant entrainment coefficient, especially for source conditions close to that of a pure plume.…”

Section: Steady-state Modelmentioning

confidence: 99%

The impact of source fluctuations in a filling box with interior diffusive mixing

Woods²

2022

J. Fluid Mech.

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We explore the interior stratification that develops in a reservoir of fluid in which there is a localised source of destabilising (positive) buoyancy and a distributed source of stabilising (negative) buoyancy at the surface of the fluid, combined with an interior turbulent diffusivity. The source of destabilising buoyancy forms a descending turbulent plume that entrains ambient fluid, and this, coupled with the interior turbulent diffusivity, leads to mixing of the interior fluid. When the ratio $Pe$ of the plume source volume flux to the diffusive flux across the whole reservoir is large, the reservoir is well mixed except for a narrow surface boundary layer, while for smaller $Pe$ , the reservoir is more stratified, consistent with the results of Hughes et al. (J. Fluid Mech., vol. 581, 2007, pp. 251–276) and Hughes & Griffiths (Annu. Rev. Fluid Mech., vol. 40, issue 1, 2008, pp. 185–208). We explore the evolution of the system when the source buoyancy flux varies in time, exploring both sudden changes and oscillatory changes in the forcing. Provided that the time scale of the change in the forcing is comparable to or smaller than the response time of the reservoir, as the source buoyancy flux decreases the plume may become trapped in the upper part of the reservoir, leading to a much shallower mixed zone. However, in the case of a source whose strength oscillates in time, as the source buoyancy flux increases, again the deeper water becomes involved in the mixing and circulation. We discuss briefly how these results may provide insight into the impact of changes in the forcing on mixing in deep ocean waters.

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Analytical solutions and virtual origin corrections for forced, pure and lazy turbulent plumes based on a universal entrainment function

Cited by 23 publications

References 25 publications

A guideline to limit indoor airborne transmission of COVID-19

A guideline to limit indoor airborne transmission of COVID-19

Beyond Six Feet: A Guideline to Limit Indoor Airborne Transmission of COVID-19

The impact of source fluctuations in a filling box with interior diffusive mixing

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