Second Computational Aeroacoustics (CAA) Workshop on ...

2. Find the pressure envelope inside the duct along the four radial lines r = 0, 0.34, 0.55,
0.79. The pressure envelope, P(x), is given by
P(x)= max p(r,¢,x,t).
over time
Give P(x) from x = -6 to x = 0 at Ax = 0.1.
For both parts of the problem, consider only n = 0, m = 2 and the two cases
(a) co = 7.2
(b) = 10.3
Note: #o2 = 7.0156. You are to solve the linearized Euler equations.
Category 3 m Turbomachinery Noise
The purpose of these problems is to study the computational requirements for modeling
the aeroacoustic response of typical rotor-stator interactions that generates tonal noise in
turbomachinery. You may solve either the full Euler or Ilne_(zedEuier equations. Be sure
to specify the grid size, the total CPU time required, the CPU t:[me per period, and the
type of computer used for each problem.
and
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This problem ........ is designed to test the ability of a numerical scheme to model the acoustic
response ofacascade to an incident "frozen gust_,',_
ConslaeT_h_-c_scaae of flat-plate airfoils Shown in figure41 The mean flow is uniform
and axial wi{h inflow velocity Uoo and s{atiC density po_. The inflow Mach number M_:{S
0.5. The length (chord) of each plate is c, and {he gap-ico-chord ratio g/c is i.0.
: We will use non-dimensional variables with U_ as velodty scale, c as length scale,
c/U_ as time scale, poo as density scale and pooU_ as pressure scale.
The incident:vortical gust, which is carried along by the mean flow; has z and y
velocities givefi by ......
. L
: : : : :: : Z72 L ::
v = cos( x + av (2)
respectiveiy;::where vG = 0.01. Consider two cases. For CaSe 1, the Wavenumber/3 is
g_r[2 Correspond{ng:{o an "interblade phase angle!' a of 5rr/2. The frequency w (same
as the reduced frequency based on chord, k)_is equal to 5rr/2 (_ 7'864). For Case 2,
a = k = 13_r/2 (_ 20.42). The gust is convected by the mean flow. Therefore, the
x-wavenumber _ for both cases is equal to co.:
7;
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