Troels Dyhr Pedersen.indd - Solid Mechanics

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11.9 COMSOL calculations of cylinder acoustic resonance
The simulation software COMSOL is capable of calculating resonance frequencies in any
given cavity. This allows the resonance frequencies of irregular combustion chambers to
be determined. To perform this calculation for a given chamber, the only information
necessary is the temperature and the gas composition. Using air as gas at a temperature of
approx. 1800 K will provide a good approximation for HCCI combustion.
Figure 20: The first four resonance modes in a disc shaped geometry
In figure 20, the four resonance modes with the lowest frequencies are shown. From left,
he first circumferential mode (1,0), the second circumferential mode (2,0), the first radial
mode and the third circumferential mode.
Figure 21 shows an example of calculated resonance frequencies in the ring shaped
geometry, with the piston in the TDC position. This calculation was used to verify that
the frequencies measured with this particular geometry were in fact caused by resonance,
as well as identifying the modes.
Figure 21: The first four circumferential resonance modes in a ring shaped geometry.
The frequencies of the modes in fig. 21 are (from left to right): 3.9 kHz, 7.8 kHz, 11.7
kHz and 15.5 kHz. The higher frequencies are overtones (multiples) of the first mode, as
a consequence of the similarity with resonance in a tube. The first four circumferential
resonance modes were all found to be present in the measurements, and higher predicted
modes with frequencies of approx. 20 kHz and 24 kHz were also present at detectable
amplitudes. The first radial and axial modes should have frequencies of approx. 28 kHz,
but this frequency was hardly distinguishable from the noise level in the FFT analysis.