Trying to attenuate resonance in my exhaust using a quarter wave tube

[panek]

Hi,

I am interested in attenuating some resonance at 2500 to 3000 rpm in my custom exhaust system and would like to get some input from the experts.

First, some background information: The car is a Toyota mr2 spyder with a 1.8L 4 cylinder engine with a garret GT28 turbo charger. My exhaust set up (see pictures below) is 3” throughout with a high flow cat and straight through borla muffler. As stated above the resonance occurs between 2500 and 3000 rpm or 83 to 100 Hz. The resonance only occurs after the exhaust track has warmed up to normal operating temperatures and temporarily goes away if I’m really pushing the car. The lengths of the system are listed in the following table:

Section length (inches)
Total system 94.5
Turbo to cat 28.5
Cat to muffler 20.5
Cat 10.75
Turbo to muffler 60
Muffler plus tailpipe 34.5
Tailpipe 21.5


If I assume the temperature of the exhaust gas is 200 C during normal driving the length of a standing wave at 3000 rpm or 100 Hz is = (453.4/100)/4 or 1.13 meters. The equation I used is standing wave in a tube with one open end and one closed end = (speed of sound/frequency)/4. So at 200 C and 3000 rpm I have a standing wave of 1.13 meters or 44.65 inches. The double of this is 89.3 inches or close to the length of my exhaust track. At 2500 rpm the standing wave would be 53.8 inches, which doubled would give 107.6 inches. If I wanted to use a quarter wave tube to remove the resonance it should be between 11.2 and 26.9 inches.

Now for the Questions:

1) Are the equations used above correct for my system?
2) Is 200 C a reasonable temp for the exhaust gas?
3) Where should I place the quarter wave tube in the system?
just after the cat at approximately 40 inches
just before the muffler at approximately 56 to 58 inches
just after the muffler at approximately 73 inches
4) Does a quarter wave tube need to be a straight pipe at 90 degrees to be effective or would something similar to the schematic diagram work?

Thanks in advance,

Mark Panek

 

[MikeHalloran]

1) Search for "naca-report-1192.pdf".

2) 200C seems low for a gas temp, credible for a pipe surface temp. Marine Diesels run egt of 450..600C at the turbo exit flange at max power. I think gasoline engines run a bit hotter at WOT. On the other, other hand, you're working on a part- load resonance, so the egt will be down a bit.

3,4) Read the NACA report.



Mike Halloran
Pembroke Pines, FL, USA

 

[TurboXS]

We tried this and it does work. However we measured the resonance frequency directly and did not use the RPM point. Basically use a microphone and frequency analysis software. This gives the frequency. The speed of sound is guessed, but 200 deg C sounds quite low for your exhaust gas temperature. We used a much higher number based on thermocouple measurements.

The exhaust we tested had no rear muffler so we attached the quarter wave pipe near this point.

The main issue is that the frequency is not stable, probably due to pressure and temperature, so you need a low Q which is not possible with a closed pipe. Look into Helmholtz resonantor.

Also a quarter wave length pipe can be relatively long.