High-resolution large-eddy simulation of indoor turbulence and its effect on airborne transmission of respiratory pathogens-Model validation and infection probability analysis

Abstract

High-resolution large-eddy simulation (LES) is exploited to study indoor air turbulence and its effect on the dispersion of respiratory virus-laden aerosols and subsequent transmission risks. The LES modeling is carried out with unprecedented accuracy and subsequent analysis with novel mathematical robustness. To substantiate the physical relevance of the LES model under realistic ventilation conditions, a set of experimental aerosol concentration measurements are carried out, and their results are used to successfully validate the LES model results. The obtained LES dispersion results are subjected to pathogen exposure and infection probability analysis in accordance with the Wells-Riley model, which is here mathematically extended to rely on LES-based space- and time-dependent concentration fields. The methodology is applied to assess two dissimilar approaches to reduce transmission risks: a strategy to augment the indoor ventilation capacity with portable air purifiers and a strategy to utilize partitioning by exploiting portable space dividers. The LES results show that use of air purifiers leads to greater reduction in absolute risks compared to the analytical Wells-Riley model, which fails to predict the original risk level. However, the two models do agree on the relative risk reduction. The spatial partitioning strategy is demonstrated to have an undesirable effect when employed without other measures, but may yield desirable outcomes with targeted air purifier units. The study highlights the importance of employing accurate indoor turbulence modeling when evaluating different risk-reduction strategies.

FIG. 1.

Visualization of the restaurant room facilitating the study. Four windows on the rear wall are colored with cyan and the entrance opening with yellow. The entrance is sealed shut for the experiments. The wavy-shaped chain-like overhanging structure is a sculpture. A grid with $0.5\hspace{0.17em}\mathrm{m}$ spacing is shown on the floor for visual assistance.

FIG. 2.

Schematic illustration of the ultrasonic nebulizer filled with potassium phosphate solution. Ultrasonic vibration is transmitted through water into the solution. Due to vibration, aerosol particles are released and carried out from the chamber by air flow. The wet size of the produced particles was 6–8 μm.

FIG. 3.

Overview of the sensor arrangement and their naming convention. The sensor coordinates are labeled such that W, C, and D indicate the location in the x-direction as shown, numbers 1, 2, or 3 specify the location in the y-direction (1 being closest to the aerosol source) and vertical positioning is given by LO, MID, and HI in accordance with the sensor height. The aerosol source is situated to coincide with the mouth of the imaginary infected individual who is shown in red at the end of the table closest to the W1 sensor mast.

FIG. 4.

A real-life picture of the study environment. The wavy-shaped chain-like overhanging structure is a sculpture. The three masts with the three sensor nodes attached to each of them are shown in panel (a). An individual sensor node is shown in more detail in panels (b) and (c). The sensor node comprised of a black 3d-printed frame (the rectangle-like part) and a mast mounting arm. The frame was used to house the Sensirion PM- and T/RH-sensors and a micro-controller, which controlled the sensors and output data to a central PC.

FIG. 5.

Front (a) and rear (b) view of the complete LES domain with inlet and outlet ducts highlighted in blue and red, respectively. The inlet boundary conditions for momentum are set by imposing fixed velocity value on each inlet plane. The desired volume flow rate $Q_{in}^{(i)}$ is thus obtained by sizing the cross-sectional area $A^{(i)}$ of each inlet duct.

FIG. 6.

Overview of the LES model featuring all solid objects within the restaurant. Generic (GEN) seating configuration is displayed in (a) while an alternative configuration with $1.5\hspace{0.17em}\mathrm{m}$ tall space dividers (DIV) is shown in (b). A grid with $0.5\hspace{0.17em}\mathrm{m}$ spacing is drawn on the floor for spatial reference.

FIG. 7.

Cropped 3D visualization of the model specifying representative winter month surface temperatures for the room. The windows were assigned temperature distributions that were measured during the aerosol experiment. Human head and torso temperatures were estimated from infrared images. All other surfaces (some not shown) were set at room temperature 21 °C ( $294\hspace{0.17em}\mathrm{K}$).

FIG. 8.

Comparison of measured (left) and modeled (middle) normalized concentration time series in the window-side mast row without the air purifiers (GEN) and tabulated evaluation metrics (right) with color coding. The color coding and the acceptance criteria are tabulated on the lower right corner.

FIG. 9.

The same as in Fig. 8 but with the air purifiers (GEN+FLT).

FIG. 10.

Bar plot comparison between the experiment and LES simulation of elapsed time $\Delta t_0$ to reach $0.05\hspace{0.17em}{c}_{t\to \infty }^{+}$ at each measurement sensor. Subfigure (a) features for the generic ventilation configuration and (b) the configuration with air purifiers.

FIG. 11.

Volume rendering of instantaneous $\left|\mathbf{u}\right|$ field within the domain using two different view angles. Subfigure (a) depicts the GEN configuration and (b) the GEN+FLT configuration with added air purifiers. Note that regions where $\left|\mathbf{u}\right|<0.04\hspace{0.17em}\mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}$ are shown transparent revealing how the air purifiers intensify the flow system. The discharge jets of the air purifiers are visible in (b) as they become incident with the side walls.

FIG. 12.

Visualization of mean and instantaneous temperature distributions for (a) GEN and (b) GEN+FLT configurations. The volume-averaged mean temperatures are $⟨\overline{\theta }⟩=294.35\hspace{0.17em}\mathrm{K}$ and $294.46\hspace{0.17em}\mathrm{K}$ for GEN and GEN+FLT configurations, respectively. The most notable temperature gradients are introduced by the radiators within 1 and 3 inlet ducts and the cool windows.

FIG. 13.

Probability density distributions ${\rho }^{*}$ of (a) mean turbulent kinetic energy speed ${\overline{u\hspace{0.17em}}}_{\mathrm{tke}}(\mathbf{x})$ and (b) mean flow speed $\left|\overline{\mathbf{u}}\right|(\mathbf{x})$ for all x within the indoor LES domain. The shown speed range is focused on the characteristic indoor ventilation flow range outside the immediate vicinity of inlet and outlet ducts.

FIG. 14.

Distributions for (a) the number of occurrence n and (b) the normalized scalar content $m^{*}$ for relevant concentrations at time instance $t=120\hspace{0.17em}\mathrm{s}$. At this instance, the differences in distributions are not due to filtration but solely due to air purifiers' influence on indoor turbulence level. The improved dilution rate arising from higher turbulence level in GEN+FLT reduces high concentration levels and shifts the scalar content distribution toward low concentrations faster.

FIG. 15.

Temporal evolution of normalized spatially averaged concentrations according to LES without (GEN) and with (GEN+FLT) air purifiers, and with space dividers (DIV) and with both space dividers and air purifiers (DIV+FLT) compared with the analytical solution (13) without and with air purifiers. All results are normalized by the asymptote of the analytical solution $c_A{|}_{t\to \infty }=G_q/Q_{\text{eff}}$ without air purifiers.

FIG. 16.

Infection probability as a function of time (s) since the arrival of the infecting person in the reference case. Left: comparison of Eq. (17) using the spatially averaged concentrations from LES with the fully analytic solutions (16) using concentration from Eq. (15). Middle: spatially varying probabilities according to Eq. (17) for the GEN case as percentiles: 5th, 25th, 50th, 75^th, and 95th and also the mean. Right: the same as in the middle, but for the GEN+FLT case.

FIG. 17.

Effects of the risk-reduction strategies in infection-probability distributions over the room at $t=1\hspace{0.17em}\mathrm{h}$ for $G_q=100\hspace{0.17em}{\mathrm{h}}^{-1}$. On the left (GEN) is the infection-probability distribution for the GEN case, and the other plots show the differences $\Delta {⟨P⟩}_z$ due to the risk-reduction strategies for the cases GEN+FLT, DIV, and DIV+FLT in percentage units such that negative (blue) means reduction. The probabilities are vertically averaged over the living zone, i.e., the range $0.1\hspace{0.17em}\mathrm{m}\le z\le 2.0\hspace{0.17em}\mathrm{m}$. The $2\hspace{0.17em}\mathrm{m}$-radius cylinder around the source denoting the near-source area, which is not of primary interest in this study, is shown as opaque gray disk in each plot.

FIG. 18.

Comparison of measured (left) and modeled (middle) normalized concentration time series in the center mast row without the air purifiers (GEN) and tabulated evaluation metrics (right) with color coding. The color coding and the acceptance criteria are tabulated on the lower right corner.

FIG. 19.

The same as in Fig. 18 but for the door-side mast row.

FIG. 20.

The same as in Fig. 18 (center mast row) but with the air purifiers (GEN+FLT).

FIG. 21.

The same as in Fig. 18 but for the door-side mast row and with the air purifiers (GEN+FLT).