## Introduction

A number of techniques have been used to measure the radon concentrations and their decay products in the environment including Active and Passive methods. The devices and methods may vary over a wide range of grab sampling, time-integrated sampling (short-term and long-term) and continuums sampling (known as real-time radon monitoring). However, radon measure devices are also classified differently based on their used method of radon monitoring in addition to other classification, i.e., electrostatic collection of decay products (RAD7, Tesla TSR2, EQF3220), ionizing chamber device (AlphaGUARD), photo-multiplier counter and scintillation (Liquid scintillation or scintillation cell), radon absorption (active charcoal), etched track detectors (CR-39, LR115). We have to decide what technique to use on the basic of the feasibility and cost of the measurement as well as accuracy and applicability of the technique.

In case of standard problems for measuring of indoor radon concentrations, indeed, radon measurements in homes are easy to perform, but need to be based on standardized (e.g., national) protocols to ensure accurate and consistent measurements. They do not address all technical aspects of measurement device technology, quality assurance or techniques to specifically identify radon sources such as radon in water supplies, building materials or relative to the possession and handling of radioactive materials. In addition, high variation of indoor radon makes short-term measurements unreliable for most applications. Another problem is related to the type of detector which should be carefully selected since it influences the cost of measurement per dwelling and therefore the cost of a radon program on a national level.

In confined areas, a vital factor with regard to human health, indoor air quality and energy efficiency is the ventilation rate since the degree of exposure can be significant, especially in buildings with poor ventilation systems where radon gas, which is heavier than air, can easily accumulate and reach lethal activity concentrations in terms of human health. It is worth mentioning that ventilation does not directly affect occupant health, but the rate of ventilation affects indoor air pollutant concentrations that, in turn, modify the occupants’ health. Previous studies have reported that indoor radon and thoron concentrations are related to environmental meteorological parameters and building ventilation conditions by applying numerical and experimental methods as well as different pieces of computational fluid dynamics (CFD) software as analytical and powerful tools8,9,10,11,12,13,14. For instance, Zhou et al. applied the finite difference method to derive discrete equations before linking them to the commercial FU-JITSU/a-FLOW code to study the concentrations and their distributions of 222Rn and 220Rn as well as their progenies in a model room8. Rabi et al. implemented a 222Rn distribution inside a typical Moroccan room using Fortran software12. Chauhan et al. and Agarwal et al. in this regard also used the software Fluidyn MP based on the Finite Volume Method (FVM)11,14. As a result, appropriate ventilation could reduce indoor pollution due to radon exhalation from the ground or from contaminated building materials.

## Models and computational methods

### Geometric model

The geometric model considered in this study was based on the typical size of a room at the Institute of Radiochemistry and Radioecology at the University of Pannonia in Hungary (Fig. 1). The overall computational dimensions of the room geometric model were 3.0 m (W) × 4.0 m (L) × 2.8 m (H) along the X, Y and Z-axes, respectively, including one window (1.2 m × 0.8 m) in the middle of the wall on the right-hand side, which faces the outdoor environment, and a door (2.2 × 1.0 m) on the left-hand side of the front wall. Furthermore, unstructured triangular meshes were used for ANSYS meshing due to their simplicity and degree of accuracy which is accessible for our simple geometry. In addition, the unstructured mesh has a high-efficiency mesh distribution, which permits creation of fewer cells than a structured one19. The convergence study has been performed for the model and the average area velocity at the outlet has been considered as a basis. In this study, the close-door configuration with Ach 4.3 (Air changes per hour) (h−1) simulated for four different types of the meshing. The convergence of the model is shown in Fig. 2; consequently, the total number 1,267,543 cells with minimum volume of 2.3 × 10–9 m3 has been used for the analysis.

### Numerical modelling approach, boundary conditions and Parameters

CFD computer codes solve the set of conservation of mass, energy and momentum equations to specify the fluid flow and related phenomena. By discretizing and linearizing equations as well as under the relevant boundary conditions, the computational domain is defined. In this study, some assumptions are considered: (A) air enters the room from the outer environment through the window (inlet) and leaves the room through the door (outlet); (B) continuous and incompressible air flow inside the room; and (C) homogeneous indoor temperature distribution. Therefore, the steady-state indoor flow field could be expressed by continuity and conservation of momentum equations as follows, respectively8,11:

$$\rho \left( {\nabla .U_{i} } \right) = 0$$
(1)
$$\rho \left( {\frac{{\partial U_{i} }}{\partial t} + \nabla .\left( {U_{j} U_{i} } \right)} \right) = - \nabla .P + \nabla .\left( {\mu_{e} \nabla U_{i} } \right) + S$$
(2)

In the above equations, Ui and Uj denote the velocity vectors (m s−1) (i, j are the indices representing the velocity components); P represents the pressure (N m−2); μe = (μ + μt) stands for the effective viscosity (N s m−2), where μ and μt refer to the dynamic and turbulent viscosities, respectively; ρ is the density (kg m−3) and S is radon source term (Bq m−3 s−1). Moreover, in order to simulate the dispersion of radon inside the room, the advection–diffusion equation is also applied:

$$\frac{\partial C}{{\partial t}} = S + \nabla .\left( {D\nabla C} \right) - \nabla .\left( {UC} \right) - \lambda C$$
(3)

where C represents the radon concentration in the room (Bq m−3), S stands for the radon source term (Bq m−3 s−1), D denotes the radon diffusion coefficient in air (1.2 × 10–5 m2 s−1), U refers to the mean air flow velocity (m s-1) and λ is the decay constant of radon (2.1 × 10–6 s−1).

On the other hand, since creating an appropriate model and characterizing suitable boundary conditions both play a key role in employing CFD techniques, some major boundary conditions and parameters are applied in this study:

• The inlet air velocity was calculated by taking into account the ACH value. The air velocity in terms of the inlet boundary condition (window) corresponding to the different ventilation rates and the ventilation area was calculated by the following equation8,11:

$$V = \frac{{Ach \times V_{room} }}{{A_{vent} }}$$
(4)

where Vroom and Avent denote the volume of the room, which was assumed to be 33.6 m3, and the ventilation area (window area = 1.2 m × 0.8 m), respectively. Normally, 1 ACH is adequate to meet ventilation requirements. In this study the inlet air velocity was calculated to be approximately 0.01 m s−1 to validate the CFD simulation results by following passive and active methods.

• For the room parameters and inlet velocities, since the calculated Reynolds numbers were found to be greater than the 2000 when ACH = 1 h−1 and higher (turbulent regimes), the standard k-ε model, which has been used by many scholars8,10,11, was used to incorporate the effect of turbulence on the flow field given that it is capable of describing the investigated phenomenon.

• Another major input parameter is surface radon exhalation rates. Average surface radon exhalation rates for cement samples were measured to be 3.1 ± 0.1 (Bq m−2 h−1) according to a closed accumulation chamber technique using a professional AlphaGUARD PQ2000 PRO, which has been outlined in detail by Kocsis et al.17. Furthermore, Porestendorfer has summed up the others surveys and reported the typical range of surface radon exhalation rates for building materials used in different countries which fall within the range of 0.36–10.8 Bq m−2 h−120. The values reported in this study are also in line with these ranges. Consequently, the rate of radon generation (Bq m−3 h−1), as an input parameter in the CFD code, can be calculated from Eq. 5:

$$G = \frac{{\mathop \sum \nolimits_{i = 1}^{3} E_{i} \times A_{i} }}{{V_{room} }}$$
(5)

where i = 1, 2 and 3 denote the wall, floor and ceiling of the room, respectively, while Ei (Bq m-2 h-1) and Ai (m2) represent the radon exhalation rate and surface area, respectively.

• In this study, the average outdoor radon concentration was also measured to be approximately 10 Bq m−3 before being converted and used as an input in the CFD code.

• In this simulation, the convergence criteria is defined as the maximum relative difference between two consecutive iteration must be less than 10–6.

In Table 1, a list of all boundary conditions for each surface of the model is presented. By selecting the species transport model in ANSYS Fluent, all volumetric species, including radon, air and water vapor, were defined. For modelling humidity, water vapor content would be defined in the model as a species. The other materials considered in the model are lightweight concrete for floors, dense concrete for walls, window materials and basic door materials. Subsequently, simulations were run until convergent results were obtained at different ventilation rates. Finally, software solved all the relevant equations by the coupled scheme with second order of discretization, and the mass fraction of radon was predicted before being converted into an activity concentration (Bq m−3).

### Analytical calculation

In a ventilated room, the radon diffusion coefficient is disregarded and the radon transport equation or radon concentration in a building or room with volume V is described 21 as the following:

$$C_{i} \left( t \right) = C_{0} e^{ - \lambda t} + \frac{EA}{{V\lambda }} \left( {1 - e^{ - \lambda t} } \right)$$
(6)

where Ci is the indoor radon concentration (Bq m−3) at time t (h), C0 is either the initial radon content at t = 0 (h) or the outdoor radon concentration, λ is the total radon decay rate and ventilation rate (λ = λRn + λV) in h-1, E (Bq m−2 h−1) is the radon flux or radon exhalation rate from the soil or building material, A is the exhalation surface area (m2) and V is volume (m3) of the house.

### Annual radon effective dose rate

In order to estimate the annual radon effective dose rate (AED) originating from the inhalation of indoor radon, the following equation is used1:

$$AED = C_{Rn} \times F \times t \times K$$
(7)

where AED stands for the annual radon effective dose rate from exposure to radon (mSv yr−1), CRn denotes for the average radon concentrations in the room (Bq m−3), F represents the indoor equilibrium factor for radon of 0.4 which was provided by United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) in 2000, and t refers to the number of hours spent inside annually (2000 h based on the spent time by the staff). Furthermore, K denotes the radon dose conversion factor recommended by the International Commission on Radiological Protection (ICRP) Publication 115 of 12 nSv per unit of integrated radon concentration (Bq h m−3)22.

## Results and discussion

The CFD technique based on the finite volume method was used to predict, visualize and calculate the radon distribution and concentration inside the room as well as the mixture of indoor radon-air flow. Moreover, by using the obtained average indoor radon concentrations, the effective dose rate the staff are exposed to was also estimated.

### CFD simulations results

By setting up the input parameters in the CFD code, the contours of the radon distribution at different air flow velocities in both aforementioned scenarios were simulated and are illustrated in Figs. 3 and 4. From the CFD results, it can be seen that as a result of the air flow velocity through the door and window, the radon gas concentration led towards the center of the room. Accordingly, the radon accumulated nearer to the surface of the left-hand corner of the room when the ACH was increased to 4.3 h−1. The ventilation profiles revealed that the indoor radon distribution was not uniform. By assuming that ACH = 1 h−1 in order to comply with ventilation requirements of buildings, the radon concentration in the middle of the room (in both scenarios) was low, moreover, the average radon concentration according to the CFD simulation was found to be 70.21 and 66.25 (Bq m−3) for the closed- and open-door scenarios, respectively.

Based on Figs. 3 and 4, the highest concentrations of radon were recorded close to the floor and upper wall around the inlet which are reduced by increasing the air exchange rate, while the lowest values were observed near to the inlet and front wall. These results are due to the air velocity profile (m s-1) in the room shown in Figs. 5 and 6, which was simulated in both scenarios at two different air exchange rates of ACH = 1 and 4.3 h−1 to comply with ventilation requirements and to compare with others studies, respectively. Increase in flow-rate generates higher turbulent kinetic energy in the higher velocity gradient region, thus increasing the turbulent intensity at some places. Spread of higher turbulent intensities increases with enhancing flow rates, and affects the mixing patterns and concentration inside the room. Moreover, moving up from the floor enhances the flow mixing, and affects the source contribution simultaneously. In order to compare the CFD results with other studies, Visnuprasad et al.23 and Zhuo et al.8 assumed ACH = 4.3 h−1 in the open-door scenario and the average indoor radon concentrations in their studies were reported to be 29 and 15 Bq m-3, respectively, while in this study it was simulated to be 20 Bq m−3, the results of which are given in Table 1. The average indoor radon concentration reported by Rabi et al.12 was 49 Bq m−3 which assumed that ACH = 1 h−1, in the closed-door scenario, while in this study the corresponding value was around 70 Bq m−3.

In this survey, the average indoor radon concentration according to CFD calculations represents the annual average radon concentration. Finally, according to the simulation results, the corresponding annual effective dose from the inhalation of radon when ACH = 1 h−1 was calculated as 0.68 and 0.64 mSv yr−1 in the closed and open-door scenarios, respectively. These annual effective doses are less than the limit recommended by ICRP of 3–10 mSv yr-124. However, as simulated and shown in Figs. 2 and 3, it could be inferred that due to the poor ventilation and air velocity profile at some locations in the test room, e.g. close to the floor in the inlet, radon gas can accumulate more so the risk of exposure the staff are subjected to would be higher. Therefore, at this location, the corresponding dose received by the staff 1 m above the floor and when ACH = 1 h−1 could be approximately 1.63 and 1.48 mSv yr−1 in the closed and open-door scenarios, respectively, which are also less than the range recommended by the ICRP of 3–10 mSv yr-1.

In Table 2, the results of the analytical calculation and CFD simulation are compared. By computing the percentage difference between the estimated results according to ANSYS-Fluent and the analytical calculations at each ventilation rate, the maximum difference was found to be 19% when ACH = 4.3 h−1 in the open-door scenario. At the desired air exchange rate of 1 h−1, the difference was also found to be approximately 11% and 5% in the open- and closed-door scenarios, respectively. As is evident from Table 1, the different ventilation rates have distinct effects on the indoor radon concentration in the test room, which is also illustrated in Fig. 7. The simulation results indicate that the air flow pattern within the room is an important function with regard to the distribution of the indoor radon concentration. Moreover, it is noteworthy that the indoor radon concentration varies depending on the size of the room, radon exhalation from building materials and the air exchange rate.

### Effect of relative humidity on indoor radon concentration

Factors that affect the radon concentration in the room include building materials, ventilation rate, wind effect, temperature difference between inside and outside the room as well as the indoor air humidity. Regarding indoor air humidity, a negative correlation is observed between this parameter and the ventilation rate25. In this study, different values of the relative humidity (30%, 40%, 50%, 60%, 70% and 80%) are considered in the CFD code to explore the influence of the relative humidity on the indoor radon concentration. The temperature and air exchange rate were set at 24 °C and 0.5 to 1 h−1, respectively. By applying these assumptions and running the code, the results of the CFD model as well as the relationship between the relative humidity and average indoor radon concentrations (Bq m−3) in the room were plotted in Fig. 8A, B. This was simulated at two different air exchange rates to present the effect of the relative humidity on the indoor radon concentration. Accordingly, it can be seen that by increasing the relative humidity from 30 to 50%, the average indoor radon concentration was reduced by approximately 5% and then started to rise by increasing the relative humidity. Therefore, this clearly indicates that the relative humidity influences both the radon concentration and distribution.

### Validation of the simulations results with Passive and Active indoor radon measurements

The measured values of the radon concentration according to active and passive methods were compared with CFD predictions at the same points. The comparisons are presented in Tables 3 and 4 in the open- and closed-door scenarios, respectively. Accordingly, the average indoor radon concentrations measured by the AlphaGUARD and RAD7 detectors, for instance, at a height of 1.0 m above the ground in the open-door scenario (regarded as the breathing zone for a standing adult) were 77 Bqm−3 and 81 Bqm−3, respectively, which exhibit a relative deviation of approximately 7% and 2% (Relative deviation = $$(\left(\left|\mathrm{Measurement}-\mathrm{CFD prediction}\right|\right)$$/CFD prediction). Regarding the passive measurements according to the Raduet and NRPB detectors, the corresponding average indoor radon concentrations were measured as 68 and 64 Bqm−3, respectively with corresponding relative deviations of approximately 17% and 23%. However, in the closed-door scenario, the corresponding relative deviation was higher. Furthermore, the highest relative deviation of 39% was measured by the NRPB detectors from 20 cm above the ground in the closed-door scenario. As a result, it can be observed that both experimental results and simulations somehow yielded a similar trend, that is, the radon concentration reduced as the distance from the ground increased. Furthermore, based on the deviations, the average indoor radon concentrations predicted from the CFD code were seen to be closer to the experimental values with the exception of point A in both scenarios due to the poor air circulation resulting in the accumulation of radon at that point. Correspondingly, the results of the CFD simulations are in good agreement with the experimental measurements.

## Conclusion

The minimum standard ventilation rate for dwellings is important not only to ensure the health and comfort of dwellers but also to eliminate and dilute the dominant pollutants. Recently, the CFD method has drawn attention to the prediction and visualization of the distribution pattern of radon and thoron concentrations in confined areas. The purpose of this survey is to estimate the radon concentration at different ventilation rates for a typical room by using the CFD technique before comparing and validating the CFD results with analytical calculations and experimental measurements. This study applied both an experimental and CFD model (using the commercially available CFD software ANSYS Fluent 2020 R1 based on the FVM method) to investigate the radon dispersion under typical indoor ventilation (natural ventilation) as well as open- and closed-door scenarios. The calculations were validated by comparing the CFD results with active measurements taken by the AlphaGUARD and RAD7 radon monitors as well as passive measurements recorded by NRPB and RADUET detectors based on CR-39. These results would be useful for the organizations and authorities to have a picture of critical point of higher indoor radon concentration which should take into consideration for dose assessment.

By assuming an air exchange rate of 1 h−1 to comply with ventilation requirements, the radon concentrations in the middle of the room (in both scenarios) were low and the average radon concentrations from the CFD simulations were 70.21 and 66.25 Bq m−3 in the closed- and open-door scenarios, respectively. The difference between the results of the analytical calculations and CFD simulations were found to be approximately 11% and 5% in the open- and closed-door scenarios, respectively. The measured radon concentrations recorded by the active measurements were also in good agreement with the CFD results, e.g., with a relative deviation of approximately 7% and 2% according to the AlphaGUARD and RAD7 radon monitors at a height of 1.0 m above the ground in the open-door scenario. Moreover, the maximum relative deviation of 39% was recorded by the NRPB detectors at a height of 20 cm above the ground in the closed-door scenario. The highest radon concentrations were detected in close proximity to the floor and upper wall around the inlet which was reduced by increasing the air exchange rate, while the lowest values were observed close to the inlet and front wall. On the basis of these results, it can be concluded that these trends are due to the air velocity profile. The simulation results revealed that the air velocity distribution inside the room plays a major role with regard to the distribution of the indoor radon concentration. The results also demonstrate that CFD modelling is capable of predicting the indoor distribution of radon gas. Finally, regarding mitigation of radon, the best ways are26,27,28: (1) as shown in the simulation, increase air flow in the confined area by opening windows and using fans and vents to circulate air; (2) Sealing the cracks in floors and walls with plaster, caulk, or other materials designed for this purpose.