Modeling of the Distribution of Radon and Its Decay in a Traditional Hammam: Dose to Adult Members of the Public

Radon and its descendants are the main causes of lung cancer in non-smokers. Therefore, the study of the behavior of radon and its descendants in indoor air is of the highest importance, in ordre to limit the risk of radiation dose due to inhalation of indoor air by members of the public. This article focuses to study the effect of meteorological parameters on the concentration and distribution of radon and its descendants inside a traditional Hammam by using CFD simulation. The results of modeling are qualitative and show that the concentration and distribution of radon and its descendants decrease when the ventilation rate increases, as well as, as the temperature increases; however, it increases with the increase relative humidity. Moreover, the committed equivalent doses due to 218Po and 214Po radon short-lived progeny were evaluated in different tissues of the respiratory tract of the members of the public from the inhalation of air inside the traditional Hammam. The influence of the activity of 218Po and 214Po and mass of the tissue on the committed equivalent doses per hour of exposure was investigated. The annual effective dose due to radon short-lived progeny from the inhalation of air inside the traditional Hammam by the members of the public was investigated.


Introduction
Radon is emitted by radium in soil, groundwater, and building materials. It can penetrate into the interior air where it accumulates. It is well known that inhalation of radon and its decay products contribute a significant share (over 50%) of the natural radiation dose to humans. [1]. Therefore, the estimation of the behavior of radon and its decay into the interior air is very important to evaluate the radiation dose received from inhalation of radon and its decay by members of the public.
More recently, CFD (Computational Fluid Dynamics) simulation has taken on a distinct place in the study of the behavior of radon in indoor air. Many researchers have predicted the behavior and distribution of radon in buildings, apartments, offices, and schools, using CFD simulations [2][3][4][5][6][7][8][9]. Despite the importance of these studies, the evaluation of the influence of meteorological parameters on the behavior of radon and its descendants in indoor air has not been fully investigated using CFDs.
In this article, we analyze the influence of meteorological parameters on the behavior of radon inside a traditional Hammam Moroccan. The study will focus essentially on the effects of ventilation, temperature, and relative humidity on the concentration and distribution of radon and its descendants inside a traditional Hammam. Finally, we evaluate the annual effective dose due to the inhalation of 218 Po and 214 Po inside the traditional Hammam by members of the public.

The Hammam Plan Geometry
A traditional Hammam Moroccan is a place of relaxation and care generally consists of three rooms whose temperature varies; so that we find a coldroom when entering, another warmroom in the middle, then the hotroom (Figure 1). These rooms summarize the three main steps of the bath process.

Governing Equations Used
In this study we applied the Navier-Stokes equations in the laminar regime, written as follows [7]: The conservation of mass equation: The momentum equation: The energy conservation equation: The equation of dispersion for radon and its descendants: where: u, v and w are the velocity components, x, y and z are the Cartesian coordinates used, T is the temperature, p is the pressure, α is the thermal diffusivity, C is the concentration of radon decay (j= 0, 1, 2, 3 and 4 for 222 Rn,

Resolution Method
The Navier-Stockes equations described above have been discretized by the Finite Volumes Method. The mesh employed is structured quadratic. The advection terms are discretized using the QUICK scheme. Diffusion terms are processed using the second-order scheme. The SIMPLER algorithm was used for the pressure-velocity coupling.

Boundary Conditions and Input Data
The floor in the hotroom is considered a source of heat and vapor, and all walls and ceilings are modeled adiabatic. The heat is produced by water vapor which gives a very humid environment (with a humidity rate of up to 100%), whose temperature varies between 20°C and 50°C. The details of the boundary conditions are presented in the Table 1. The boundary condition of radon decay on the walls is simplified by (∂C j )/∂n= 0, where n is the direction normal to the wall [6].

The Equilibrium Factor
The equilibrium factor between radon and its descendants is a dimensionless parameter and is defined as follows [10]: where C is the concentrations of radon decay in the house (Bq m -3 ), respectively (j= 0, 1, 2 and 3 for 222 Rn, 218 Po, 214 Pb and 214 Bi).

Determination of Annual Committed Equivalent Doses
According to the ICRP Publication 66 [12] (Figure 2), the human respiratory tract is divided into two major regions: 1) The thoracic region: is divided into four sub-regions (alveolar interstitium AI, bronchioles bb, bronchi BB and lymphatics LN TH ). 2) The extrathoracic region: contains four compartments named ET 2 , ET seq , LN ET and ET 1 . The alpha-activity of radon decay in compartment i of the respiratory tract am given by the following. [12]: ./ 0 . = F . i I " j + ∑ λ 5,7 5 A 9 5 j − ∑ λ 7,5 + λ 5 A 9 where F . i is the fractional deposition in the compartment i of the respiratory tract (ICRP), I " j is the average breathing rate. C j is the concentration of the radon decay product inside the Hammam, λ 5,7 is the clearance rate from region n to region i due to particle transport (ICRP). The alpha-equivalent dose rate (Sv s -1 ) in a tissue T of the respiratory tract of an individual due to the inhalation of the radon decay given by: where A j t Bq is the alpha-activity of radon decay product in the tissue T of the respiratory tract, Q is the quality factor, which is equal to 20 for F-particles [12]. m is the mass of the target tissue T, K is the branching ratio, R is the range of the F-particle emitted by radon decay product, S is the stopping power of the tissue T for the emitted F-particle and k (1.6 × 10 -10 ) is a conversion factor. R j and S j were calculated by using the SRIM program [12].
The equivalent dose in the tissue T of the respiratory tract for radon decay is given by the following: where t P ′ is the exposure time of the tissue T and H ; j is the alpha-equivalent dose rate (Sv s -1 ) in a tissue T.
Regional doses, weighted with factors assigned for the partition of radiation detriment, are summed to give a value of committed equivalent dose for the thoracic H Q j and extrathoracic H R j regions. According to the ICRP 66 [12], we have the following equations: and where H SS j , H TT j and H /U j are the equivalent doses in the BB, bb and AI tissues of the thoracic region, respectively; H R $ j and H R V j are the equivalent doses in the ET 1 and ET 2 tissues of the extrathoracic region, respectively; A BB = 0.333, A TT = 0.333 and A AI = 0.333 are the weighting factors for the partition of radiation detriment for the BB, bb and AI tissues of the thoracic region, respectively, and A R $ = 0.001 and A R V = 1 are the weighting factors for the partition of radiation detriment for the ET 1 and ET 2 extrathoracic regions [12]. The annual effective dose (mSv y -1 h -1 exposure) due to radon decay products inside the Hammam was evaluated by using the following equation: The annual effective dose (mSv y -1 h -1 of exposure) due to the radon decay to the members of the public was also estimated according to the following formula [1]: where Ac( 222 Rn) is the radon concentration inside the Hammam (Bq m -3 ), F is the equilibrium factor between radon and its decay inside the Hammam, t= 1 h y -1 and D= 9.0 × 10 -6 mSv (Bq m -3 h) -1 is the dose conversion factor.

Effect of Mesh on the Numerical Solution
The sensitivity of the results compared to the mesh was checked before proceeding to the calculations. To do this, we took into account three different meshes (2,026,990, 2,902,409 and 3,777,828 cells). The results obtained after the convergence for each mesh are shown in Table 2. It is clear that the variation in the average radon concentration between mesh sizes 2,026,990 and 3,777,828 is negligible.

Effect of Ventilation
In order to study the effect of ventilation on the concentration and distribution of radon and its descendants inside the Hammam, we considered two cases: In the first, we considered  Figures 3 and 4 show the iso-concentrations of radon in the Hammam for the two cases studied respectively, plotted in the horizontal median plane (Y = 1.5 m). We observe that the radon concentration decreases by increasing ventilation. This decrease is caused by the introduction of fresh air.
In Tables 3 and 4, we present the average concentrations of radon and its descendants as well as the equilibrium factor for different cases of ventilation. We note that the ventilation sufficiently dilutes the concentration of radon and its descendants inside the Hammam. We also note that the hotroom is more polluted than the other rooms (coldroom, warmroom). This is due to the fact that the ventilation rate decreases when as we move away from the entrance to the Hammam.    218 Po and the distribution of the equilibrium factor, plotted on the horizontal median plane (Y = 1.5 m). We notice that the 218 Po has a distribution similar to that of radon, similar results have been found by other authors [13,14]. We also find that the equilibrium factor is more important in the hotroom. This is because the humidity level is too high in this room (Figure 7).

Effect of Temperature
The influence of temperature on the concentration and distribution of radon and its descendants inside the Hammam studied. We have considered five temperatures the values are 15, 17, 20, 22, and 25°C, with a relative humidity is around 40% and the interior doors are left open. Table 5 represent the average values of the concentration of radon and its descendants inside the hotroom as a function of temperature. We observe that the concentration of radon and its descendants decreases considerably with temperature.  To have a clear idea of the effect of temperatures on the distribution of radon inside the Hammam, we present the isoconcentrations of radon for two temperatures 35°C and 45°C respectively (Figures 8 and 9). By comparing these figures, we see that the increase in temperature has a slight influence on the radon distribution.

Effect of Relative Humidity
In order to study the effect of relative humidity on the concentration and distribution of radon and its descendants inside the Hammam, we considered different values: 30%, 40%, 50%, 60%, 70%, and 80%, with a temperature is around 30°C and the interior doors are left open.  Figure 10. Average equilibrium factor in hotroom for 40%≤RH≤80%. Table 6 represent the average values of the concentration of radon and its descendants inside the hotroom as a function of relative humidity. We observe that the concentration of radon and its descendants gradually increases with increasing relative humidity. Indeed, when humidity increases inside the Hammam, the diffusion coefficient decreases, which reduces the diffusion length of radon and consequently reduces its transfer to areas of low concentration. Figure 10 shows the evolution of the average equilibrium factor as a function of relative humidity, we see that the equilibrium factor increases as relative humidity increases. This can be interpreted by the attachment of radon descendants to tiny drops of water suspended in the air [7].
In order to have an idea of the effect of relative humidity on the distribution of radon, we present the isoconcentrations of radon at different relative humidity levels (60% and 80%) which are illustrated in Figures 11 and 12. By comparing these figures, we see that the radon concentration increases slightly with relative humidity.

Committed Equivalent Doses Due to Radon and Its Decay Products in the Respiratory Tract Inside the Hammam
The annual committed equivalent doses due to the 218 Po and 214 Po have been evaluated in the respiratory tract of different age groups inside the Hammam. Data obtained for the adult males, females, Child 10 y and Child 5 y are shown in Tables 7, 8 and 9. It is found that the annual committed equivalent doses due to the 214 Po are smaller than those due to 218 Po in the extrathoracic ET and thoracic TH regions, this is due to the fact that 214 Po has a very short half-life (1.64×10 -4 s) compared with the exposure time of the tissues.
We remark that the adult male is more exposed than the adult female. This is due to the physiological nature of these adults (breathing rate).
Annual effective doses due to radon progeny from the inhalation of radon decay inside the Hammam by the members of public were evaluated by using the model given here (Equation 11) and the UNSCEAR formula (Equation 12) (Table 10). Data obtained for the average effective dose obtained by using the model given here for different age groups of individuals were found in good agreement with those obtained by using the UNSCEAR model for the general public.

Conclusion
We have studied numerically using CFD simulation the effects of ventilation, temperature, and relative humidity on the concentration and distribution of radon and its descendants inside a traditional hammam. The results showed that the concentration of radon decreases while increasing the rate of ventilation, as well as, when the temperature increases, however, it increases with increasing relative humidity. As well as, the Annual committed equivalent doses due to 218 Po and 214 Po were determined in the respiratory tract of adult members of the public from the inhalation of air inside the hammam. From this, we see that the CFD simulation a good tool to assess the doses of radon to individuals from inhaling radon offspring in indoor air.