TECHNICAL FEATURE Modeling Virus Propagation Through an Air-Handling System FIGURE 2 Diagram of the virus-laden aerosol travel through air-handling system. Uninfected Person Exhaust Air Figure 2 shows a typical air-handling system. The Infected Person air-handling unit delivOutdoor Air Heating Coil D O C ers conditioned air to the Return Air B spaces through ceiling difCooling Coil Supply Air fusers and returns the air to the unit through ceilingAir Filter mounted return air grilles. Ceiling Plenum Outdoor Air Damper To provide space ventilaD A D E tion, the unit adds outdoor Supply and Return Air Fans Source Space Recipient Spaces air to the supply airstream. S Airflow R Breathing Yellow arrows show the air Zone Virus-Laden Aerosol pathway between the unit and spaces. (CS ) are different and relate as follows: Ez = (CA − CD )/ The infected person(s) emits the viral contamination (CS − CD ).8 The variable Ez is the zone air distribution with a consistent over time rate into the breathing zone of one of the spaces. This space becomes a source of con- efficiency. The concentration gradient in the recipient spaces is substantially lower than in the source space tamination for the other spaces. In this paper, the space and was neglected: CR = CE. with the infected person will be referred to as "source The return airflow at Point B mixes the contamination space," and the other spaces as "recipient spaces." from the source space with the one from the recipient The return airflow in the source space entrains the contamination and distributes it with a reduced concen- spaces with the ratio: CB = FA CA + (1 - FA)CR, where varitration to the recipient spaces. The contamination path- able FA is the ratio of the source space's floor area to the total floor area served by the system. The ceiling height way is shown by red arrows. and air change rate of all spaces is assumed to be the Typical space occupancy (exposure to contamination) varies from 4 hours to 24 hours. Typical hourly air same. The unit adds the outdoor air with a concentration of change rates of 8 to 20 mean that the time required for CO = 0 to the airstream and reduces the concentration the contamination to travel from the source to recipifrom CB to CC based on the following the equation: CC = ent spaces is 8 minutes to 3 minutes, respectively. The (1 - OA)CB. The variable OA is the percent of outdoor air potential travel time is incomparably lower than the in the total airflow rate provided by the system's controls exposure period. The comparison allows us to assume when the system operates in the minimum ventilation that after a number of cycles, the virus concentramode. tion in the source space (Points S and A) and recipient The air filter further reduces the virus concentraspaces (Points E and R) and in the air-handling unit tion in the airstream as per the following equation: (Points O, C and D) in Figure 2 have achieved a steady CC(1 − EF ) = CD. Coefficient EF is the air filter's efficiency state. The assumption was made to exclude time from to capture selected contamination. the model. The equations have been solved to determine the relaA suite of steady-state mass balance equations has been constructed at critical points in the contamination tionship between the virus concentration in the recipient spaces (CR ) and the breathing zone of the source pathway using the following rationale and assumpspace (CS ): tions. The air density difference at the points has been neglected. CR = (1 - CCE)CS (1) In the source space, the contamination concentration at the return air grille (CA) and in the breathing zone J U LY 2 0 2 0 ashrae.org ASHRAE JOURNAL 19http://ashrae.org