# Numerical simulation of air age in dental practices

In the article by Zhao et al.^{16} The CFD was performed using the geometry of a typical office interior space. In this study, following this approach, CFD analysis was performed using a 3D geometry of a dental office space created with CAD software (Fusion360, Autodesk) based on a 2D drawing of a typical dental practice to digitally assess air age. The width, height and depth of the dental office have been set at 9.8 m (*X* steering), 2.9m (*there* direction) and 4.0 m (*z* direction), respectively. The geometry of the three patient chairs, the three dentist chairs and the three dental cabinets was reproduced for analysis (Fig. 1). For each chair, mannequins were used to represent patients and dentists. For the air conditioning system, an open inlet, an exhaust outlet and an air conditioner have been reproduced, as shown in Figs. 1B and C. The installed chair closest to the entrance was designated Chair1; the installed chair closest to the exhaust outlet was designated Chair3; and the chair installed between the two was designated Chair2. In this study, natural ventilation from open windows was not assumed. Using this three-dimensional shape as a reference, the position of the exhaust vent and the presence of partitions were modified according to the implementation scenario. The partitions were fixed at a height of 1.7 m (2/3*H*) above floor level and were in contact with the cabinets of the chairs installed in the center of the room and on the side of the exhaust vent.

OpenFOAMv7, an open source CFD software, was used for CFD analysis. SimpleFOAM was selected as the solver, and an incompressible steady-state flow analysis was performed using a Reynolds-averaged turbulence model. An isothermal field was used and the heat transport equation was not solved. The wall conditions were set to adiabatic non-slip conditions. After the start of the influx, 300 s were observed for the calculation to stabilize in the steady-state analysis. The inlet and outlet conditions were set at one inlet/outlet, four air conditioner outlets, one air conditioner inlet, and one exhaust outlet, as shown in Fig. 1C. The exhaust outlet was defined as “exhaust far” when located near the entrance and “exhaust near” when located away from the door in Figure 1B. The details were as given in the values in Table 1. The air conditioner was set to flow only mode and the strongest wind setting, and the boundary conditions were given assuming unfiltered circulating air . The ventilation volume in the examination room was set to less than twice the volume.

Air age was used as an index to assess the ventilation efficiency of dental office geometry. Assessment of indoor air quality by air age has been reported in previous studies in hospital rooms with beds^{17.18} and offices with natural ventilation^{19}. It is possible to calculate the age distribution of air in a space using SVE3 (Ventilation Efficiency Scale 3)^{20} offered by Murakami and Kato^{21} shows the efficiency of CFD ventilation using air age. The shorter the time it takes for incoming air to reach a given point in the dental office, the lower the possibility of air contamination, and the longer the time, the greater the possibility of air contamination. big.

The air age value for the entire three-dimensional model space of the dental office outlet as a result of the calculation was undimensioned by the local average air age of the orifice d exhaust, and the space was divided into six areas, area1~6, as shown in Figure 1A. The sum of the air ages in each zone was calculated and compared. The sum of the air age for each zone was calculated using the equations. (1)–(4).

$$ cellleft( {varvec{X}} right) = mathop sum limits_{k}^{N1} cell.Vleft[ k right] $$

(1)

$$ ageleft( {varvec{X}} right) = mathop sum limits_{{i

(2)

$$ exhaust = mathop sum limits_{{i

(3)

$$ ageleft( {varvec{X}} right) = frac{{ageleft( {varvec{X}} right)}}{escape} $$

(4)

In eq. (3), where *k* is the volume of each cell and *cell.V*[*k*] is the volume of each cell, the total number of cells in each area, *cell*(** X**), is calculated. In eq. (4), for the number of cells in each area, the volume of each cell,

*cell, V*[

*i*]is divided by the total number of cells,

*cell*(

**), and the air age of each**

*X**cell*, (tau left[iright])were added and summed to calculate the total air age of the area,

*age*(

**). The average exhaust outlet air age was calculated using the exhaust and divided by the sum of the air ages to normalize the zone air age.**

*X*The cross-section used to visualize the results of the calculations is shown in Figs. 1B and C. To show the effect of the partitions, the horizontal cross section was set at the height of the center of the partition (1/2*H*). To observe the areas where the air should be particularly stagnant, the vertical section was fixed close to the installation surface of the partition and the wall (1/9* O*).

Four scenarios were proposed and simulated as shown in Table.2, depending on the location of ventilation openings and partitions. The case with a partition is denoted (+) and the case without partition is denoted (-). The case where the exhaust orifice is close to the inlet is denoted “close”, and the case where it is far from the inlet is denoted “far”.