Second Computational Aeroacoustics (CAA) Workshop on ...

Duct wall
M=0.5___ \
--_" D/2
S
1
r
Source x
Figure 2
The length L and the diameter D of the shell are equal (L = D). The flow variables and
the geometrical quantities are nondimensionalized using D as the length scale, the ambient
speed of sound a_ as the velocity scale, the ambient density p_ as the density scale, and
2
p_a_ as the pressure scale. Time is made dimensionless by the time scale D/a_. The
problem is axisymmetric and should be solved using the linearized Euler equations given,
in dimensionless form, as
0 0
0-7
where the source S' is given by
P
" Moop + u
M_u + p
Mc_ v
M_p + u
S=0.1exp -48(gn2) _ (x 2+r 2) cos(kDt), withkD=167r.
An equivalent set of equations could also be used. Calculate the intensity of sound, _-,
along the circular arc x 2 + r 2 = (5/2) _ at A0 = 1 °, 0 measured from the x-axis. There is
no requirement to use a specific domain or number of grid points. However, for algorithm
assessment purposes the investigator is asked to report the computer used, the total CPU
time, time step size, total number of time steps, total number of grid points, and the size
of the physical domain.
Problem 2
Consider the radiation of sound from a thin wall duct as shown in figure 3. The param-
eters of this problem have been so chosen that unless some fundamental understanding of
duct acoustics such as duct modes, cutoff frequencies are incorporated in the design of the
computational algorithm, the computed results would, invariably, be quite poor.
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