Teardrop shape for muffler? Any equations for this?

[ScooterGuy]

Hi, all.

I have an idea I want to try out for a muffler design on a single-cylinder engine (174.5 cc liquid cooled fuel injected scooter engine).

My idea is to create as free-flowing a muffler as possible (lowest backpressure) while still making it as quiet as possible using the concept of destructive interference of the pressure pulses to smooth out the exhaust note. Other design priorities are that it be as small and light as possible, and have room for exhaust heat recovery that will be used to increase engine efficiency.

Anyway, it would appear to me that creating a passage that is teardrop shaped, (essentially two teardrop shapes, one inside the other), and forcing exhaust gasses to follow the curve of those teardrop shapes from the pointed end to the blunt end would allow for maximum destructive interference (and hence attenuation) of the sound pulses.

Imagine one teardrop shape inside another larger teardrop shape. The exhaust gasses are routed between the walls of these two teardrop shapes from the pointed to the blunt end, where the exhaust pulses meet head-on in a 360 degree collision to self-attenuate before the gasses go out the exhaust pipe at the blunt end of the outer teardrop shape.

Sort of like a 3-D version of what muffler manufacturers do when they split then rejoin the exhaust stream to cause destructive interference sound cancellation using baffles, as seen in the "Sound Canceling" image here:
http://cdn.exhaustvideos.com/wp-content/uploads/2010/12/muffler-design-types.jpg

Would this provide for maximum destructive attenuation of the exhaust gas pulses, or am I off on a completely wrong tangent? Is there any math that would show how effective (or ineffective) such a shape would be at destructive interference sound cancellation of exhaust pulses?

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[ScooterGuy]

Not sure what information you want. The OEM muffler is 15.25" circumference and 13.5" length, the maximum allowed dB (by law) is 80, the engine is 174.5 cc 4 stroke with a redline RPM of 8000 and rev limiter of 9200 RPM.

The reason I want to build a different muffler is so I can recapture some of the heat of the exhaust (the bike is so small there's nowhere else to put exhaust heat recovery except inside the muffler, and putting it in the muffler will make the bike look more stock than hanging it elsewhere). So, to save as much space inside the muffler as possible, I looked for what would seem to be the best shape for destructive interference of the exhaust pulses. The teardrop shape seems to allow three distinct advantages:

1) the constrained expansion of gases (as opposed to unconstrained, like when it goes out the end of the exhaust pipe) from the sharp end of the teardrop shape to the blunt end would mean gas expansion dilates the negative pulse traveling back up the exhaust pipe, meaning it should have a pretty wide RPM range for the enhanced scavenging effect of that negative pulse (ie: no 'power band').

2) the 360 degree destructive attenuation of sound at the blunt end of the teardrop shape (right before the exhaust gases move out to the exhaust pipe tip, which will have a spiral linear occlusion (ie: an auger shaped insert) to further dampen noise) should make for a quiet exhaust with very little backpressure.

3) There's room *inside* the inner teardrop shape to put some of the heat recovery equipment, where it'll be protected from exhaust gasses, but still absorb a good deal of heat. The rest of the equipment will go either before or after the teardrop shaped passage.

But that's all just seat-of-the-pants guesstimation... so I'm looking for some math geniuses who could show me some equations that'll let me figure out how large the teardrop shape would be, what kind of sound attenuation I can expect from it, etc.

 

[jack action]

I'm no expert on the subject and I don't want to rain on your parade, but I think that your idea would fall into the «If it was working, it would already have been done» category.

If I understand well, you want to replicate the active noise control concept, but by using the exhaust gas itself instead of microphones.

The problem I anticipate is that at the blunt end of your muffler where the gases shall collide with itself to attenuate the sound, you will still need an opening to exit the gases. That opening creates a source for expansion of the gases and therefore the gases will prefer that route instead of the collision and that will completely defy the purpose you had in mind. The solution would be to increase the restriction of the tailpipe, which would lead to increase of back pressure; another unwanted result.

Just my 2¢.

 

[ScooterGuy]

Yes, the gasses will prefer the opening to the exhaust tip, but the sound pulse carried along with those gasses, not so much. When I build it, I plan on including in the center of the blunt end of the teardrop a spherical cavity such that when the sound pulses reach that spherical cavity, they'll self destruct. Around the perimeter of that spherical cavity on the outside of the outer teardrop shape will be holes that lead to the exhaust pipe tip.

See the attached .png file. It's a 2-D representation of what I want to do in 3-D. If it's still too loud without the "Simple pipe loop" in the image, I'll include it, otherwise the spiral linear occlusion will be the last sound dampening measure in the muffler.

But I still need the mathematics to determine how effective (or ineffective) it'll be, and to fine-tune the size for best attenuation.

 

[AlephZero]

I don't see how this will work at all. Sound pressure is a scalar quantity, not a vector. It doesn't have a "direction" associated with it. The sound pressure in the flows that "meet in a 360 degree collision" (did you really mean 180 degrees?) after traveling equal distances around your teardrop shape will just add up, not cancel out.

If you want the sound pressure to cancel out at certain frequencies, you need to make two or more different path lengths, so the sound waves arrive out of phase with each other when they are mixed together. For example like this:

http://store.uucmotorwerks.com/technology-reflective-sound-cancellationrsc-c536.aspx

 

[ScooterGuy]

Hmmm... it appears you're right. So back to the drawing board for me.

Yeah, the gasses would meet 180 degrees out. The '360 degrees' was my attempt to explain that rather than it happening in just one plane as current mufflers do, it'd be in a complete circle.

Why do the muffler manufacturers put those V-shaped baffles in their mufflers? It splits then rejoins the exhaust stream, but since the sound waves constructively recombine, the net effect of those baffles would be zero, right? All it appears those baffles are doing is cancelling the velocity of the air stream, but the sound waves recombine and aren't dampened... exactly the opposite of what one wants from a muffler.

 

[AlephZero]

An "empty" cavity would give a strong resonance at particular frequencies. Apart from the noise, the pressure build-up at the resonant frequency could shorten the life of the muffler before a mechanical failure, or produce a high back pressure for the engine. With nothing to damp the resonance, the peak pressures at the resonant frequency could easily be 10 times the average exhaust pressure, or even higher. This might produce "dead spots" in the engine power curve when the RPM hit the resonant frequency.

Inserting angled baffles will tend to lower the resonant frequencies by making the sound waves travel a longer path through the chamber, and also absorb more of the sound because it is reflected more times from the baffles and walls of the chamber.