Troels Dyhr Pedersen.indd - Solid Mechanics

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11.7 Theory of cylinder acoustics
Cylinder pressure oscillations are initiated by the strong pressure gradients formed when
the combustion proceeds unevenly in the chamber. The pressure gradient may be created
by a confined explosion in the charge due to spatial variation in fuel or temperature
distribution, or a developing detonation, which are discussed in the next chapter.
Once a pressure difference is introduced, the pressure will drive the gas towards the low
pressure area. The momentum of the gas means that the gas will continue into the low
pressure region even after pressure equalization, thereby increasing the pressure to that of
the former high pressure region. The pressure distribution is now reversed and the gas
will be forced back to its origin. This behavior is known as resonance.
Established resonance modes in the cylindrical geometry fall in to three categories:
circumferential modes, radial modes and axial modes. These are explained in the
following subsections. The modes may appear simultaneously by the principle of
superposition as shown in table 5.
11.7.1 Circumferential modes
If the charge is pushed from one side of the cylinder wall it will oscillate across the
chamber in a transverse motion. This situation is equivalent to pushing a glass of water,
which forces the water into moving from side to side. The first mode has one node which
runs through the diameter of the cylinder. All of the fluid moves from the low pressure to
the high pressure zone across the chamber. This mode is therefore the most powerful in
terms of momentum transport.
The second mode has two nodes that are orthogonal and hence two high pressure zones
that must be opposite. The gas does not move across the two symmetry lines. The gas
movement takes places from the sides of the high pressure zones to the sides of the low
pressure zones. In this case the gas movement is split into four directions. This means that
less energy is transported across the chamber and hence less energy is transferred to the
walls by momentum and heat transfer. So, despite being measurable in the chamber, this
mode is less important in terms of energy losses and transmitted sound.
11.7.2 Radial modes
If the pressure rises in the center (or throughout the entire perimeter simultaneously) it
will create a radial wave moving from the center towards the cylinder liner. This
corresponds to the familiar rings that form when a drop of water hits the surface of a
water pool. Like in a glass of water, the wave is reflected back towards the center.
The first mode of vibration has a high and low pressure zone and a circular node. The
higher nodes that may be formed have more pressure zones in the same ring pattern. As
with the transverse waves, only the lowest mode carries enough momentum to be
important.