Environmental Engineering Reference
In-Depth Information
Figure 16: Comparison of two-dimensional NACA 0012 data to predictions for
a
=
7.8
o
at several Mach numbers (after [26]).
review of the computational methods for aeroacoustic predictions is given in
[27]. Direct solution of the acoustic fi eld by solving the compressible Navier-
Stokes equations being computationally too expensive for practical applica-
tions, the most promising approaches for aeroacoustic computations are the
hybrid
methods. The hybrid methods are based on the observation that for low
Mach numbers the amplitude of the acoustic fl uctuations is several orders of
magnitude smaller than the hydrodynamic fl uctuations. Based on this scale
separation the governing equations can be divided into a set of fl ow equations
and a set of acoustic equations having sources determined by the fl ow vari-
ables. Such hybrid approaches have several advantages as compared to direct
computations. First, the acoustic fi eld can be computed on a larger domain
than the fl ow fi eld, fl ow computations are needed only in regions where sig-
nifi cant noise is generated. Second, the solution methods for incompressible/
semi-compressible fl ows are faster than for compressible fl ows. Additional
gain in computational effort is due to the possibility of having larger mesh
spaces in the acoustic solver and the fact that for the acoustics commonly only
one equation has to be solved.
Lighthill's analogy (presented earlier in this section) was the fi rst method to
separate the acoustics from the fl ow computations. Recently, a more systematic
approach has been presented by Slimon
et al.
[28]. Their method is based on the
expansion about incompressible fl ow. The compressible fl ow variables are
expanded in a power series in
e
2
=
g M
2
:
2
4
6
( 32 )
pp
=+
e
p
+
e
p
+
e
p
+
0
1
2
3
2
4
6
(33 )
rr er er er
=+
+
+
+
0
1
2
3
2
4
6
uu
=+
e
u
+
e
u
+
e
u
+
(34 )
i
i
0
i
1
i
2
i
3
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