THESE de DOCTORAT - cerfacs

5.3 Combustion noise Analysis 77
‘coarse’ mesh ‘refined’ mesh
Nodes 706 854 1’887 891
Cells 3’824 053 10’ 518 559
Maximum grid size
in flame region ∼ 1 mm ∼ 0.5 mm
Table 5.3: The two computational grids under study
is evaluated through Pope’s criterion [75]. The Smagorinsky filter and the grid resolution for
both cases should be sufficient to resolve at least 80 % of the energy remote from the wall. Introducing
the resolved (k f ) and the modeled (k sgs ) turbulent kinetic energy , the resolved to
total kinetic energy reads:
Q LES =
k f
k f + k sgs
(5.3)
where k f = 1 2ũiũ i and k sgs = 2ũiu 1 i − 1 2ũiũ i = 3 2 (u′ sgs) 2 and ˜() stands for the LES filter. The
subgrid scale velocity is computed from
u ′ sgs =
ν t
C∆x
(5.4)
where ν t is the turbulent viscosity, ∆ is the filter width and C is a constant estimated as C ≈ 0.12
in case of isotropic homogeneous turbulence (IHT) or as C ≈ 0.06 in the case of a turbulent
channel. For this case the value of C ≈ 0.12 was used. Figure 5.4 demonstrates that, for both
LES cases, Q LES is greater than 0.8 for almost the entire computational domain excepting regions
near walls. The premixer turbulence is however better captured by the ‘refined’ mesh. It
is well known that extremely high computational costs arise when a proper LES of boundary
layers is sought. Nevertheless, boundary layers are assumed to contribute little to noise radiation/scattering
of turbulent flames. A high resolution in regions near walls is therefore not
considered.
Both meshes are found to reproduce the mean PIV very well. This can be observed in Fig. 5.5.
Both LES succeed in predicting the central recirculation zone satisfactorily. The LES on the ‘refined’
mesh is however more accurate for the outer region, particularly for the radial velocity.
The fluctuating velocity field is characterized by rms profiles. Figure 5.6 shows that on the
‘coarse’ mesh a high overprediction of velocity fluctuations is obtained in both axial and radial
components. On the fine grid however the LES clearly recovers the experimental velocity
fluctuating field.
Acoustics and flame dynamics of the system represented by the heat release are, on the contrary,
more difficult to evaluate than the mean and fluctuating velocity fields. The mean value
of heat release is similar in both LES and is close to the 40kW experimental thermal power, as