Troels Dyhr Pedersen.indd - Solid Mechanics

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The way explosions and detonations may result in pressure osciallations is described in
the following sections.
12.2 Explosions
12.2.1 Uniform explosion
An explosion is defined as a fast, uniformly progressing chemical reaction in a perfectly
stirred volume of reactants. The rate of reaction is thus governed solely by chemical
kinetics. An explosion in a confined space with no volume change is referred to as a
constant volume explosion, whereas an explosion in unconfined space which do not lead
to a pressure increase is called a constant pressure explosion. In HCCI combustion, only
constant volume reactions are relevant since the volume change is very limited during
combustion.
An ideal constant volume explosion creates a spatially uniform pressure increase without
gradients in pressure or temperature. Real explosions however are rarely ideal, so some
spatial and temporal variation usually occurs in the reacting volume, but the overall
picture is still that the volume has exploded.
12.2.2 Non uniform explosions and pressure wave amplification
Under some circumstances, such a locally elevated temperature or higher fuel
concentration, the explosion will develop faster and thus become a local event in the
reacting volume some time before the remaining volume reaches the same rate of
reaction. This will result in the exploding volume expanding, and the partly reacted
volume being compressed adiabatically. The subsequent reaction in the compressed
volume will then be progressing faster, but not necessarily fast enough to complete while
the pressure is high.
If the remaining charge explodes while pressure is high it will result in a compression
wave with a higher peak pressure than that created in a uniform explosion. This could be
an explanation to some situations with large pressure oscillations [24].
It should be noted that the lowest frequency of a standing wave is approximately 5 kHz in
a chamber 85 mm across, as given by acoustic theory in the previous chapter. Hence the
major part of the heat release must occur within less than 0.2 ms in order to amplify the
incoming wave, and ideally peak during the stagnation of the pressure wave. This is a
very short time span given the circumstances. Therefore, increasing the time where the
pressure is high will also increase the chances of the heat release amplifying the pressure
wave properly.
During the tests with piston crowns it was found that the piston crown with 4 chambers
formed between piston and cylinder liner gave very large pressure oscillations. This
chamber has a resonance frequency of 3.5 -4 kHz due to its Helmholz resonance
characteristic. It is plausible that the lower resonance frequency with this piston crown