Eliminating drone with helmholtz resonators...Let's get technical
 

Hopefully someone else out there is interested in this besides me :p

So I have a custom exhaust and it drones a bit at certain RPM's. The best way to eliminate low frequency noise is using helmholtz resonators, which you can see used in some exhausts such as the HKS and Motordyne TDX2. They work by adding on chamber(s) of a calculated specific length to the existing exhaust, which will in turn bounce the desired frequency back into the original exhaust piping, cancelling it out. This is how the TDX2 is drone free.

I took some recordings of my car driving around and found (using frequency analysis) that my drone is most prominent around 129.2 Hz. I've been doing some searching around various sites, and came across others who had drone around 133 Hz, which is very close to mine. For those people, 2 side branch resonators around 24-26" in length have worked well in eliminating drone.

The formula they use is 1100 / [frequency you want to cancel out] / 4.

1100 is the speed of sound in feet per second, and the 4 is because you want a quarter wavelength.

The problem here is that 1100 should be incorrect, because it's basically assuming ambient temperature. As temp. rises, the speed of sound increases.

I wrote a small program which will take an input temperature and desired frequency to cancel out, and output the length of piping needed to cancel out the drone. I saw some estimations stating that the temp. of the air when it exits the exhaust is approx. 300 degrees F. Using this temperature, the length of the chambers must be 31.2". This is much larger than the 24-26" mentioned to work. Something doesn't make sense here...

Also, I've noticed the TDX2 and HKS use a very small resonator in length (looks like it's about 12"?), but the diameter of the piping on the resonator is larger. The larger diameter should increase the effect of the noise cancellation, however I don't understand how they can get away with such short piping in length... That should be cancelling out the range of 285-290 Hz (assuming 30 degrees C temp.)

Any ideas? :confused2:

Yes, that is because your formulas above are for a 1/4 wave resonator.

The Shockwave))) TDX2 exhaust uses a Helmholtz resonator. Its a very different kind of resonator. Helmholtz resonators have a lower Q and a much wider bandwidth of operation when compared to 1/4 wave resonators.

If you look up the principal of operation of a vented subwoofer box you will find how a helmholtz resonator works. They work the same way a empty Coke bottle can be made to resonate when you blow air across the top of the opening.

OK, thanks! That makes more sense then. I'll look into that...

But this still doesn't explain how the formula for the quarter wave resonator is incorrect when adjusting for the proper speed of sound :p

I've found the helmholtz formula (wikipedia) and am pretty sure I could design the resonators using those, but I'm probably just going to stick with the quarter-wave since there are so many success stories on other forums. Apparently you can have any number of bends and in any direction when designing them, so I can put them anywhere in the exhaust.

Should hopefully be trying this within the next few weeks :D

By the way, if anyone wants the program I made to do calculate the length, I can post it up somewhere...

Its probably because you don't have the proper speed of sound plugged into the calculation.

What are you using as the gas average molecular weight, gamma and temperature?

Post your sheet and I can possibly find out what the problem is.

As usual Tony's the man, ryan did he get technical enough for you? ;)

length isnt necessary...
i use an old tube signal generator out of a submarine (armysurplus) to tune
ported enclosures (speaker cabinetes)
i have found that not only velocity is important... too small a port or too long will
cause the wave to accelarate past the point of resonance and actually start to act
like a sealed enclosure... dont forget that the whole system must be tuned as one
entity... and since exhaust material isnt known for sound deadening.. any reshaping
of the wave must be done as soon as possible... id start with finding the free air
resonance of the system from the exhaust manifold back and experiment with
with the correct length/area port for the frequency and cfm of the gasses...
H and X pipes placed in the correct location esecentauly double the area past them
as a wave speeds down the length of the system
BTW manufactures have been Tuning the sound waves of CAI's for years... hence the
funny black boxes or bottles attached after the air filters etc..

Basically once the system reaches its resonance point... it cant flow any more or air

Perhaps switching from a simple port style to a Transmisson Line type would be much
simpler :) Esentually tuning with the lenght and diameter of the system rather than porting it
which will make noise as a port must be open to free air... or think it is lol
adding volume such as small containers like the intake system tuning might be an easier answer

I don't understand any of this :confused2:

Anyway, good luck in your research. Tony's your guy in this type of matter. Keep this convo public so we all can read :)

+ 1..my mind is definitely blown/fuked right now lol.

I was just using c = 331.3 + (0.606 * theta), where c is the speed of sound in m/s and theta is the temperature in Celsius. Is that not correct for a quarter-wave resonator?

I did some more research, and some people were saying the resonator will have no air flow into it, and that the temp. in the resonator is basically ambient temp. That would make the equation correct if that's the case.

Speed Of Sound (SOS) depends on where you are proposing to measure it or put the resonator. Where did you want to put it?

Exhaust gas temperature at the exhaust tip is at about 500'F.
The temperature in the resonator will be much higher than ambient temperature.
Probably in the 350'F to 450'F range if its near the back.


-------------------------

Below is a calculation of gasoline and air combustion properties. It shows the exhaust gas temperature as is seen in the combustion chamber.

The temperature and pressure will both decrease as the gas exits the engine but the species and average molecular weight will remain pretty much the same.


CODE WEIGHT D-H DENS COMPOSITION
44 AIR (DRY AT SEA LEVEL) 1300.000 0 0.00001 835N 224O 5AR
435 GASOLINE (LIQUID) 100.000 -794 0.02570 46H 21C

THE PROPELLANT DENSITY IS 0.00001 LB/CU-IN OR 0.0003 GM/CC
THE TOTAL PROPELLANT WEIGHT IS 1400.0000 GRAMS

NUMBER OF GRAM ATOMS OF EACH ELEMENT PRESENT IN INGREDIENTS

15.405276 H 7.032844 C 70.120926 N 18.810883 O
0.419886 AR

****************************CHAMBER RESULTS FOLLOW *****************************

T(K) T(F) P(ATM) P(PSI) ENTHALPY ENTROPY CP/CV GAS RT/V
2199. 3498. 136.05 2000.00 -76.40 2753.17 1.2540 49.799 2.732

SPECIFIC HEAT (MOLAR) OF GAS AND TOTAL= 9.769 9.729
NUMBER MOLS GAS AND CONDENSED= 49.7994 0.4200

35.05936 N2 7.04384 H2O 4.72845 CO2 2.30371 CO
0.65481 H2 0.41989 Ar* 0.00419 HO 0.00274 H
1.43E-03 NO 1.31E-04 NH3 5.45E-05 O2

THE MOLECULAR WEIGHT OF THE MIXTURE IS 27.878

****************************EXHAUST RESULTS FOLLOW *****************************

T(K) T(F) P(ATM) P(PSI) ENTHALPY ENTROPY CP/CV GAS RT/V
777. 940. 1.00 14.70 -745.72 2753.17 1.3147 49.714 0.020

SPECIFIC HEAT (MOLAR) OF GAS AND TOTAL= 8.260 8.232
NUMBER MOLS GAS AND CONDENSED= 49.7140 0.4200

35.05938 N2 6.44866 CO2 5.36922 H2O 2.25095 H2
0.54358 CO 0.41989 Ar* 0.03993 CH4 0.00152 NH3

THE MOLECULAR WEIGHT OF THE MIXTURE IS 27.925

**********PERFORMANCE: FROZEN ON FIRST LINE, SHIFTING ON SECOND LINE**********

IMPULSE IS EX T* P* C* ISP* OPT-EX D-ISP A*M EX-T
203.2 1.2822 1927. 74.69 3951.4 12.50 0.1 0.06142 746.
204.0 1.2590 1947. 75.27 4010.4 155.8 12.77 0.1 0.06234 777.

T* is the temperature of the gas exiting the heads.
C* (sos) is in feet per second.
Gamma (ratio of specific heats) is 1.3147

The above is calculated from a rocket engine propellant calculation program that I regularly use. Although it is designed for rocket engines, it is extremely helpful for combustion modeling in general and as such, it can also be used in exhaust system design.

Corrected a few minor mistakes.

Pay it forward! :5091:


On a serious note- wow.

Awesome, thanks Hydrazine :)

I didn't realize I would be using a lower gamma value for the equation. I was just using the standard 1.4.

I planned on putting them near the end most likely, since that's where the most room is. I'll have to try to reformulate these equations now and see if the results are more what I'm expecting.

One more question... Did you choose helmholtz resonators over quarter-wave just because they have a lower Q? Or other factors as well?

If you put them near the end, go with a temperature range of 450-350.

I won't use a 1/4 wave resonator because the effective bandwidth is so narrow. They will be easily thrown off by changing weather conditions.