## 2 Materials and Methods
### Particle Tracking  
The discrete phase model (DPM) in the FLUENT software was used to calculate the particle concentration variation by tracking particles [40; 41; 42]. After solving the velocity, temperature, and air age distributions in the room under steady state conditions, using this solution, the concentration variation and particle movements were calculated under a transient regime [43]. Randomly distributed, injected particles in the room were tracked through the air separately using the Lagrangian approach. The diameter of exhaled particles varies between 0.01 \(\upmu\)m and 1000 \(\upmu\)m, contingent upon the origin and mode of formation [44]. It should be noted that the temperature and humidity of the surrounding air, in addition to the makeup of the particles, affect the size of water droplets. For small droplets, equilibration happens quickly (less than a second), but it can be complicated if a surfactant layer covers the droplet's surface, delaying condensation or evaporation [44; 45]. However, [PERSON] et al. [46] reported that even droplets as large as 30 \(\upmu\)m can remain suspended in the air for extended periods. Exhaled air is an aerosol made up of droplets that are produced internally. Despite being liquid droplets, these contain nonvolatile substances and water; therefore, the physical term for them is \"particles\". Since the present study considers the performance of an ACD, the respiratory particles, alongside other pollutants present in the indoor air, were simulated virtually by using water properties. Considering the fact that the inhaled particulate matter responsible for the airborne transmission of viruses consists of water droplets, all the particles were treated as liquid water spheres, and the heat and mass transfer between particles and fluid were ignored so that there would be no evaporation from the droplets. The thermodynamic properties of the particles were as follows: the density of a particle was 998.2 kg/m\({}^{3}\), the thermal conductivity of a particle was 0.6 W/mK, and the specific heat of a particle was 4182 J/kgK. Measured numbers of human expired particles during different respiratory activities vary between subjects, with the numbers roughly varying between 1000 and 10,000 for vocalizing, coughing, and breathing, although the numbers could rise up to 350,000 for sneezing [45]. [PERSON] et al. [47] reported that the size distribution that was measured was substantially greater than that of aerosol in the respiratory system. It is plausible that homogeneous nucleation took place, leading to a significant rise in the quantity of droplets. The reported amounts were significantly higher than those seen in previous research [47]. [PERSON] et al. [44] stated that low aerosol concentration in experimental works may necessitate measurements of extended duration and many repeats. This is also true for numerical simulation studies. Therefore, a large number of particles results in a better evaluation of particle concentration change in the room. Once the concentration change function isobtained, this can be used with any number of particles present in the room. In light of these, in the present simulation study, about 30,000 particles, either with a diameter of 1 \(\upmu\)m or 10 \(\upmu\)m, were instantly (0.002 s time interval) injected from 1500 randomly distributed points at average room air temperature. After that, the movement of randomly distributed particles in the room was tracked with 0.1 s time intervals by solving the force balance on the particles. A particle may be affected by a number of forces when it travels in an environment with fluids. The balance equation considering the forces acting on the particles is given in Equation (6) [42]. \[m_{p}\frac{du_{p}}{d_{t}}=F_{d}+F_{g}+F_{s}+F_{b}+F_{th}+F_{pg}+F_{vm} \tag{6}\]  
In Equation (6), the particle velocity is represented by \(\upmu\)p (m/s), the particle mass is represented by \(\upmu\)p (kg), and the force to which the particle is subject is represented by F (N).