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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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