Environmental Engineering Reference
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shorter time than LES. It may also be considered to use time averaged LES results
in order to improve the turbulence closures used in RANS models.
4.4 An Example
In the following we will briefly describe an example of how CFD-RANS models
can be used to derive spatially averaged information. The example is taken from
Santiago et al. (2007) and Martilli and Santiago (2007). Only the points relevant
for the scope of this article are presented here. For more details we refer to the
publications.
The CFD-RANS model used in this study is FLUENT (Fluent Inc., 2005), with
the
standard turbulence closure. It has been run over an aligned array of cubes,
with the distance between the cubes equal to the cube's side. This is the same con-
figuration used in a wind tunnel study at Los Alamos National Laboratory (Brown
et al., 2001). The first step of the study, then, is to validate model results against
wind tunnel measurements. This has been done using a hit rate methodology pro-
posed by Schlünzen et al. (2004)
.
κ
-
ε
1
if
≤
P
i
−
O
i
O
i
i
=
1
n
RD
or
|
P
i
−
O
i
| ≤
AD
N
n
1
n
q
=
=
N
i
with
N
i
=
0
else
where,
q
is the hit rate,
n
is the total number of points compared,
O
i
and
P
i
are
wind tunnel data and model results, respectively.
RD
and
AD
represent a relative
deviation and an absolute deviation of model results from reference data, respec-
tively. Results are satisfactory and fulfil the criteria proposed by Schlünzen et al.
(2004) which fix the limit for validation at
q
> 66% in the case of the refer-
ence data are wind tunnel measurements. This step gives, then the confidence that
the model is able to capture the most important features of the urban boundary
layer.
The second step consists of performing horizontal spatial averaging over hori-
zontal slabs, with an extension equal to the cube's unit (Fig. 4.1).
This spatial average has been done for the six cubes' units and for the whole
array. The values obtained are, then, spatial averages that can be considered similar
to mesoscale models variables (e.g. variables of a non-building resolving model).
With this methodology it is possible, for example, to evaluate the importance
of the dispersive stress (vertical flux of momentum due to mean motions smaller
than the cube's unit), and compare it against the spatially averaged Reynolds stress
(momentum flux due to the turbulent motions), as can be seen in Fig. 4.2.
Such results show that the dispersive stress may play a significant role in the ver-
tical transfer of momentum within the urban canopy. Other important information
is derived also for the formulations of the drag term in the momentum equation, and
the value of the drag coefficients. We refer to the publications for more details on
this topic.
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