CAA Benchmark Problem Category 4

Geometry	3D Annulus
Number of Blades	24
Incoming Circumferential Wave Number	16
Case	4
Tip Mach Number (Wake)	0.783
Radial Phase Shift Parameter	0
Far-field Resolution	25 x 25

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Acoustic Modes

The axial wave numbers of the acoustic modes as calculated by the three-dimensional non-reflecting boundary condition are shown below. If the imaginary component of the wave number is zero then the mode is cut-on, that is, the amplitude of the mode does not decay as it propagates in the annulus.

m	μ	Axial Wave Number		Cut On or Off	Mode Shape
		Real	Imag
-8	0	5.401	-3.04e-03	ON	[Plot]
-8	1	3.502	-2.10e-02	ON	[Plot]
-8	2	2.203	-2.859	OFF	[Plot]
-8	3	2.215	-5.062	OFF	[Plot]
16	0	2.201	-3.327	OFF	[Plot]
16	1	2.201	-5.510	OFF	[Plot]
16	2	2.197	-6.991	OFF	[Plot]
16	3	2.215	-8.120	OFF	[Plot]
-32	0	2.219	-9.506	OFF	[Plot]

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Acoustic Mode Plots

Below are plots of the acoustic mode shapes at the inlet as determined by the 3D non-reflecting boundary conditions. The real part of the pressure perturbation of the mode shape is shown on the left side and the phase of the pressure perturbation on the right side.

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