Helmholtz blues
"A Helmholtz resonator consists of a volume connected to a duct". That is what Wikipedia tries to tell you.
But that is a Helmholtz resonator in its simplest form; one that you won't find anywhere in an engine.
What you
do find in an engine is an intake tract with a variable cross-sectional area. This tract is from time to time connected to a variable volume (the crankcase) through a very variable window (the intake port / reed valve / rotary inlet).
The crankcase is connected to a number of transfer ducts with variable cross-sectional areas, which are from time to time connected to a very variable volume (the cylinder) through a number of very variable windows (the transfer ports).
The cylinder is from time to time, through a very variable window (the exhaust port), connected to an exhaust pipe with a very variable cross-sectional area who at the same time doubles as a volume. This pipe volume is constantly connected to a big volume (the outside world) through a tailpipe with a constant cross-sectional area and constant entry and exit windows (thank God, finally someting that's not variable).
We call this a compound Helmholtz resonator .
The various papers also tell us how to calculate the resonator's frequency:
" frequency = speed of sound / (2*pi)* Sqr ( cross-sectional area of the neck / ( volume of the resonator * effective neck length ) ) ".
O yes, the speed of sound... It is dependent on temperature, which is not really constant in the intake tract and the crankcase, rather variable in the transfer ducts and very variable in the cylinder and the exhaust pipe.
Now the above frequency formula is not exact; it is an approximation that is usable as long as the volume of 'the' tract is very small compared to the resonator's volume.
So when engines are concerned, that formula goes very far out the window.
Who said gas dynamics is
simple dull?
PS:
It's a similar story with acoustics. That is a sub-branch of gas dynamics, simplified with a lot of assumptions that are acceptable as long as the sound pressure does not exceed a certain limit. The wave pressures in a two-stoke exhaust exceed that limit by a factor of thousand. Bye bye, acoustics...
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