Initial Pressure Pulse
The sonic compression wave resulting from this abrupt release of cylinder pressure travels down the exhaust pipe until it reaches the beginning of the divergent cone, or diffuser, of the expansion chamber. From the perspective of the sound waves reaching this junction, the diffuser appears almost like an open-ended tube in that part of the energy of the pulse is reflected back up the pipe, except with an inverted sign (a rarefaction, or vacuum pulse is returned). The angle of the walls of the cone determine the magnitude of the returned negative pressure, and the length of the cone defines the duration of the returning waves:
Returned Negative Pressure
The negative pressure assists the mixture coming up through the transfer ports, and actually draws some of the mixture out into the exhaust header. Meanwhile, the original pressure pulse is still making its way down the expansion chamber, although a considerable portion of its energy was given up in creating the negative pressure waves. The convergent section of the chamber appears like a closed-end tube to the pressure pulse, and as such causes another series of waves to be reflected back up the pipe, except these waves are the same sign as the original (a compression, or pressure wave is returned). Notice that this cone has a sharper angle than the diffuser, so that a larger proportion of energy is extracted from the already weak pressure pulse:
Mixture Extraction
This pulse is timed to reach the exhaust port after the transfer ports close, but before the exhaust port closes. The returning compression wave pushes the mixture drawn into the header by the negative pressure wave back into the cylinder, thus supercharging (a bigger charge than normal) the engine. The straight section of pipe between the two cones exists to ensure that the positive waves reaches the exhaust port at the correct time:
Supercharging
Since this device uses sonic energy to achieve supercharging, it is regulated by the speed of sound in the hot exhaust gas, the dimensions of the different sections of the exhaust system, and the port durations of the engine. Because of this, it is only effective for a very narrow RPM range. This explains why two-stroke motorcycles equipped with expansion chambers have such vicious powerbands (especially in the old days before variable exhaust port timing existed). With the design illustrated here (i.e. a single divergent stage and a single convergent stage), the powerband of the engine will be akin to a 'light switch' - once the expansion chamber goes into resonance, there will be a HUGE, almost instantaneous increase in power. The powerband can be softened somewhat by reducing the angles on the cones, but this is simply due to a lower degree of supercharging. In order to get the best of both worlds (a large power increase and a wide powerband), the cones should consist of several sections, with a different angle for each section. Proper design of even a simple expansion chamber is somewhat of a black art, even though formulae exist that will get you in the ballpark (there is quite a bit more to this than simply choosing the appropriate angles and lengths based on sonic velocity - everything about the pipe comes into play, including the headpipe diameter and length, and the tailpipe ('stinger') diameter and length). Design of a multi-stage expansion chamber becomes incredibly difficult - it basically comes down to the old 'cut and try' approach in the end. This of course is not even considering whether or not the exhaust and transfer port timings and outlet areas have been optimized for expansion chamber use.
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