Corresponding author: Mikhail P. Panin ( mppanin@mephi.ru ) Academic editor: Yury Korovin
© 2021 Menaouer Mehdi, Mikhail P. Panin.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Mehdi M, Panin MP (2021) Use of computational fluid dynamics tools to calculate the dispersion of gas and aerosol emissions in conditions of a complex terrain. Nuclear Energy and Technology 7(1): 2126. https://doi.org/10.3897/nucet.7.64366

ANSYS FLUENT tools were used as part of a standard turbulence kε model to simulate the air flow around a number of typical obstacles (a solid cube, a solid hemisphere, and a 2D hill) which form a potential terrain in the NPP emission dispersion area and roughly correspond to the geometry of the buildings and structures within this area. For reproducibility, a nonuniform spatial grid is plotted in the computational region which condenses near the obstacle surface and the outer boundaries. The dimensions and the positions of the obstacles were chosen such that to ensure their best possible coincidence with the conditions of the published experiments. The result of simulating the velocity and direction of the air flow as the whole shows a good agreement with the data from the wind tunnel experiments in the areas in front of and over the obstacle, as well as in its air shadow. Typical accelerated flow, vortex, and reverse flow areas are reproduced reliably. There are variances observed only in the local heavy turbulence regions in the obstacle’s air shadow near the ground surface. All this indicates that it is possible to model in full scale the dispersion of the NPP emissions taking into account the peculiarities of the plant site terrain and the major onsite structures to determine more accurately the personnel and public exposure dose.
NPP gas and aerosol emissions, turbulent diffusion modeling, ANSYS FLUENT
The dispersion of the NPP gas and aerosol emissions depends primarily on the wind direction and speed. The diffusion of emitted products, transversely with respect to the wind, is connected primarily with natural fluctuations of the wind direction, turbulent mixing of air masses caused by the state of the atmosphere (upward flows of warm air), and their own viscosity and friction on the underlying surface. The dispersion of the emission in conditions of a complex terrain (hills, ravines, etc.), as well as in the presence of buildings and structures leads to an additional source of turbulence as the result of the air flowing around such obstacles. In this case, one can hardly expect that it is possible to estimate the concentration of radioactive substances in the air based on simple Gaussian models recommended by the IAEA (
Among a variety of methods to investigate the air flow in the atmosphere, such as wind tunnel experiments and fullscale ground measurements, extensive use is made of computational fluid dynamics (CFD) (
The ANSYS FLUENT package tools (
Reynoldsaveraged NavierStokes (RANS) equations are used as the computational model in the framework of the standard kemodel of turbulence (
$\begin{array}{l}k=\frac{{\left({u}^{*}\right)}^{2}}{\sqrt{{C}_{\mu}}}\\ \epsilon =\frac{{\left({u}^{*}\right)}^{3}}{ky}\end{array}$
where C_{m} = 0.09 is the dimensionless empirical constant, and y is the vertical coordinate.
The computational region is defined by the type of the obstacle under consideration.
The obstacle in the form of a 2D hill (Fig.
$x=\frac{1}{2}\xi \left[1+\frac{{a}^{2}}{{\xi}^{2}+{m}^{2}\left({a}^{2}{\xi}^{2}\right)}\right]$ , (1)
$y=\frac{1}{2}m\sqrt{{a}^{2}{\xi}^{2}}\left[1\frac{{a}^{2}}{{\xi}^{2}+{m}^{2}\left({a}^{2}{\xi}^{2}\right)}\right]$ , (2)
where x is the coordinate along the wind direction, and y is the vertical coordinate.
The hill foot dimension is equal to 2a. The parameter x used in formulas (1) and (2) is variable in the limits of x £ a. The value m is determined through the average hill slope n = H/a as m = n + (n^{2} + 1)^{1/2}. For the calculations, the hill height H is assumed to be equal to 0.117 m, and the average slope angle is assumed to be 26°.
The problems of solid hemisphere and cubetype obstacles flown around were handled using rectangular regions the dimensions of which with the positions of the obstacles relative to the inlet plane are shown in Table
Dimensions of regions and positions of obstacles in units of the obstacle height H
Obstacle  Vertical, with respect to y  Lengthwise, with respect to x  Crosswise, with respect to z  x – distance from obstacle center to inlet 
Hill  13.7  80  –  40 
Hemisphere  7.6  26.4  7.6  4.4 
Cube  2  10  7  3.5 
For the reproducibility of the results, a nonuniform spatial mesh was given in the computational region which becomes denser near the obstacle surface and the outside boundaries. Fig.
The law of the wind inlet speed variation with the height u (y) was defined differently for different obstacles to ensure the comparability with the experimental data.
For the hemisphere, the wind speed profile was determined by the power function similar to that used in (
$\frac{u}{{U}_{0}}={\left(\frac{y}{H}\right)}^{n}$ , (3)
where n = 0.135, and U_{0} corresponds to the wind speed at the obstacle height H.
For the 2D hill, following the recommendations in (
$u\left(y\right)=\frac{{u}^{*}}{K}\left[\mathrm{ln}\left(\frac{y+{y}_{0}}{{y}_{0}}\right)\right]$ , (4)
where u^{*} is the friction velocity; y_{0} is the roughness height in m; and K is the Karman constant which was assumed to be equal to 0.41. And the free flow velocity value of U_{0} = 4 m/s was achieved on the upper plane of the region under consideration.
For the calculations of the flow around the cube, the inlet wind speed was assumed to be constant with the height, that is, u (y) = U_{0} where U_{0} = 0.6 m/s.
The actual investigation results were calculations of the wind speed values and directions near obstacles of different forms as compared with the wind tunnel experiment data (
Coordinates for determination of the flow velocity profiles in front of, over and behind the obstacle in units of the obstacle height H
Obstacle  In front of  Over  Behind 

Hill  –0.5  0  0.5 
Hemisphere  –1.17  0  1.17 
Cube  –1.5  0  1.5 
The flow distortion is minor in front of the obstacle with the distances from same being of the order of the obstacle height as such (Fig.
The profiles of the wind speed longitudinal component obtained immediately over the obstacle center are shown in Fig.
The distribution of velocities behind the obstacle and, especially, in its air shadow (Fig.
The specific properties of the flow around the cubic obstacle are clearly seen in Fig.
The cube that simulates the buildings and structures of the NPP as such is the obstacle most difficult to flow around. The downwind length of the turbulence area (see Fig.
Comparing the simulation results for the wind flow around typical irregularities of terrain against direct wind tunnels experiments makes it possible to conclude that models based on RANS equations, despite a moderate computational effort, provide for a substantially satisfactory coincidence with the experiment. The exceptions are local areas of heavy turbulence in the air shadow near the ground surface and immediately over the horizontal roofs of the buildings.
The presented comparison gives ground to believe that simulating the dispersion of the NPP gas and aerosol emissions in conditions of an irregular terrain and in the presence of buildings and structures, based on RANS equations and using the ANSYS FLUENT package, is capable to yield adequate results for calculating exposure doses for personnel and locally residing population.