
 
2 MATERIAL AND METHODS 
In what follows will be detailed the mathematical 
modelling and the numerical resolution using a 
commercial software, FLUENT
®
 for the odours 
atmospheric dispersion only. The same methodology 
is adopted for the two other case of study, namely 
the gas liquid mass transfer in the case of the surface 
aerators and the hydrodynamic study of an airlift 
algal pond used for a real scale municipal 
wastewater treatment plant. 
2.1 Mathematical Modelling 
Atmospheric dispersion consists of two processes: 
transport and diffusion. Equations governing this 
problem are obtained using the Favre decomposition 
and are given in the following table. 
The introduction of fluctuating terms makes this 
equation system open. Its closure requires the use of 
a turbulence model that allows getting an equal 
equation’s number to the unknown number. For this 
survey, a first order closing model was adopted. 
With the use of the latter, transport equations for the 
turbulent kinetic energy (k) and its dissipation rate 
(), are given in the table below, where R is the 
dissipation rate production term, C
1
 , C
2
 , C
3
 are 
empiric coefficients having the values of 1.42, 1.68 
and 1, respectively (Fluent User Guide, 2006). 
 
Mass balance 
0
   
  
 
j
j
u
x
 
Momentum 
balance 
()
ji
ij
ij
jij
uu
p
uu
xxx
  
 
Concentration 
balance 
'' ''
()
m
m
j
m
j
jjj
uC
C
DuC
xxx
 
Energy balance 
Pr
j
      
T
       
   x x
j
pt
jjt
uT
C
x
 
 
(k) 
Pr
t
i
ijkj
k
ku P G
xx x
 
 
 
 
() 
132
²
Pr
t
i
ij j
uCPCGCR
xx xk k
 
  
 
 
 
(k): Turbulent kinetic energy balance 
(): Dissipation rate balance 
 
In the present work, all simulations are carried 
out using a finite volume method FLUENT to model 
3D steady turbulent atmospheric dispersion of 
odorous compounds. In the present finite volume 
method, the solution domain is subdivided into a 
finite number of continuous control volumes. 
2.2 Numerical Solver 
The FLUENT software offers several CFD models: 
the Reynolds Average Navier–Stokes (RANS) 
models which include the standard renormalisation 
group (RNG) and real (RSM) model. After testing 
each of these, respectively, the RNG k– model was 
selected because odour emission velocity at the 
source outlet is feeble, besides RNG k– model 
generated the least cells number, compared to other 
models. Its calculating time per iteration was 
obviously small compared to the calculating time per 
iteration of the RSM model. 
The RNG k– model is based on two transport 
equations for the turbulent kinetic energy k and its 
dissipation rate  which uses a cross-diffusion term 
in the  equation to ensure the appropriate equations 
model behaviour in both the near-wall and far-field 
zones (Fluent user guide, 2006). 
The FLUENT 6.2 steady three-dimensional 
segregated solver was used to solve the RNG k– 
model using the implicit scheme. The upwind 
second and first orders of discretisation schemes 
were used to convert the governing equations into 
algebraic equations for their numerical solution. The 
Standard scheme was used to solve for pressure 
while the upwind first and second orders were used 
to solve for odorous compounds dispersion, 
momentum, turbulent dissipation rate, turbulent 
kinetic energy and energy. The SIMPLE method 
was used to calculate for pressure-velocity coupling. 
Several wind speeds were used to study the 
influence of aerodynamic aspects on odorous 
compounds dispersion in the vicinity of the WWTP 
of Monastir and to estimate the distribution of the 
contaminants concentrations released by that source 
in the atmosphere, and consequently characterizing 
the propagation of their odours in the neighbouring 
buildings. 
2.3 Meshing 
Previous runs proved that the contribution of drying 
beds is by far great compared to the odours intensity 
released by the other devices in the WWTP of 
Monastir, and this is due to their important size. In 
fact the pollutant plume emitted by the drying beds 
was by far great compared to the plume emitted by 
the other devices. Therefore, the study was limited 
to odorous compounds emitted by the drying beds, 
in order to reduce the calculation time and the 
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