2.2. 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 in-door flow field could be expressed by continuity and conservation of momentum equations as follows, respectively [8, 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; and ρ is the density (kg m− 3). 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 equation [8, 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 = 1.2m × 0.8m), respectively. Normally, 1 ACH is adequate to meet ventilation requirements and the corresponding air velocity at the inlet that was applied in this study 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 2,000 when ACH = 1 h-1 and higher (turbulent regimes), the standard k-ε model, which has been used by many scholars [8, 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., 2021 [17]. Furthermore, Porestendorfer (1994) 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-1 [19]. 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:
$$G=\frac{\sum _{i=1}^{3}{E}_{i}\times {A}_{i}}{{V}_{room}}$$
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.
By selecting the species transport model in ANSYS Fluent, all volumetric species, including radon, air and water vapor, were defined. 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 and the mass fraction of radon was predicted before being converted into an activity concentration (Bq m− 3).