Quarter Wave Resonator vs Drone

[Dust Buster]

Your assistance is requested in best determining length of my Quarter Wave Resonator to add to my free-flow exhaust system.

Where drone is the sympathetic resonant frequencies in the cabin, also called cabin resonance / harmonics / room gains / room modes / corner loading.

Quarter Wave Resonator is also called side branch resonator / back pressure tubes / resonant frequency / “J” shaped pipe / advanced resonance tuning (Motordyne Engineering) / narrow band acoustic attenuator / standing wave dynamics (physics): which is a “T” off the exhaust pipe with the same diameter pipe, a cap end, no acoustic material, any bends are optional (with 90 degrees being a “J” pipe) and pipe length where longer lengths are required for lower Hz.
Examples: http://www.regimage.org/no-drone-resonator/

The following formula is from several sites including: http://www.enoisecontrol.com/related_ar ... r_wall.pdf

Resonator length = 0.25 * Speed at Temp / Drone frequency (Hz)

The 0.25 is for a quarter of the wave length of sound causing the drone. The purpose being to reflect a sound wave back at the exhaust pipe between cycles (at least three quarters of the wave, but probably augmenting the main pulse a quarter of the time). The side pipe is closed and is not supposed to impede the flow.

The speed of sound increases with higher temperatures, but most people use the wrong exhaust gas temperature for diesels, which burn hotter than petrol engines.
Speed at Temp =331.3+(0.606*Temp) m / s where 331.3 is the speed of sound at zero degrees and the temp inside a diesel tailpipe was measured to be 213.4 degrees C.
https://www.fs.fed.us/eng/pubs/pdf/08511816.pdf· PDF file
Speed at 213.4 C Temp =331.3+(0.606*213.4) = 460.6 m/s

Drone frequency – herein lies my problem. There seems to be two ways of calculating the drone frequency.

Method One:
Drone frequency = (2 x rpm where drone is heard) / 60 (to convert the revs / minute to revs per second to align with Hz which is the measurement of cycles per second)

The “2”
In a four-stroke motor, the cylinders fire every second stroke or once every two rotations. In a four cylinder engine, that would be twice per revolution (2 = 4 / 2)

My cabin drones between 1750 and 2000 rpm.
58.33 = (2 x 1750) / 60

66.67 = (2 x 2000) / 60

Resonator length = 0.25 (¼ wave) * Speed at Temp / Drone frequency (Hz)
= 0.25 * 460.6 / 58.33
= 1.97 m at 1750 rpm

= 0.25 * 460.6 / 66.67
= 1.73 m at 2000 rpm

Method Two:
However, I measured 170 Hz at 1750 rpm on my smartphone app and 176 Hz at 2000 rpm. Some record the drone and then run the file through a spectrum analyser app.
Resonator length = 0.25 (¼ wave) * Speed at Temp / Drone frequency (Hz)
= 0.25 * 460.6 / 170
= 0.68 m at 170 Hz

= 0.25 * 460.6 / 176
= 0.65 m at 176 Hz

So, what length should I make my quarter wave resonator (1.97m, 1.73m, 0.68m or 0.65m)?

I don't know how to make a variable length tube to test for optimal suppression of the drone.

Bell_shaped_Tee.PNG

The other thing I don't know how to do is to make a bell-shaped "T" joint. I was thinking that cutting a 57mm pipe (my exhaust size) three times at 45 degrees and then wrapping the two cut pieces around a normal "T" joint for marking, cutting and welding might work. The reason I wanted a bell-shaped "T" joint is that it supposedly reduces the sound volume by 25 to 29 dB due to catching more of the sound wave as it passes at 90 degrees.
http://data.mecheng.adelaide.edu.au/avc ... h_geom.pdf

Bell_shaped_Tee_2.PNG

Thanks in advance

[Dust Buster]

I guess I could hedge my bets and try to combine the two. I'd need to figure the size of larger pipe to fit over the 57mm side branch to allow the donut to bounce back something near equivalent to the 57mm feeder pipe. I also don't know the distance I should allow between the end cap and the end of the open 57mm feeder pipe.

Variable_length_side_branch.PNG

Any thoughts?

[ptuomov]

Diesel exhaust is usually cooler than gasoline engine exhaust. That’s reflected in the turbocharger temperature ratings.

Instead of fabricating complicated J-resonators immediately, I’d consider simply picking the longest pipe section in the existing exhaust and placing a small, regular straight thru muffler/resonator at 2/5ths length of that such that it divides the pipe section to about 2/5ths and 3/5ths sections. If the drone comes from the exhaust, that may cure the drone. If it’s some other source plus cabin resonance, then the drone will likely remain. Just a thought.

[ptuomov]

What’s the engine type and what’s the current exhaust configuration?

[dannobee]

Aren't there various Helmholtz calculators available free online to do the math on this?

The quick and easy way is to weld a J pipe into the exhaust pipe at 90 degrees to the flow, then on the end of the J pipe, find another straight pipe with one end welded up, that fits over the outside of the other pipe, and attach with a muffler clamp. Test drive and vary the length until you're satisfied with the sound, then weld it in place.

[chevyfreak]

Can try some bolt on rubber dampers or hollow capped tube sections. Can move it around on the pipe and or various sizes of dampers.

Chevyfreak.

[pcnsd]

Drone Freq Hz=(Drone rpm/60)*(# of cylinders/2)
Drone wave length=SOSmps/Drone Freq
Quarter wave tube length=Drone wave length/4+(applied 1/4 wave tube dia*.4)
Quarter wave Freq Hz=Drone Freq Hz*4

Where:
SOSmps = Speed of sound in meters per second and length output is in meters

[Dust Buster]

Ah! I have found the error in my thinking in part. With the length being a quarter of the pulse wave, when it is reflected / bounces back, it will have travelled twice the quarter length when it returns to the “T”. That is, the half length wave will be 180 degrees shifted out of phase. This anti-phase will cause the destructive interference that I am seeking.

To calculate the required size of the donut, I need the area of the end plate of a 57mm diameter, which is 2552 square mm (pi * radius squared). The donut is missing the 57mm hole in the middle. So, I need 5104 square mm of area minus the 2552 square mm area. Therefore, I need a 80.615mm pipe to fit over.

@ptuomov To answer your question, it is a 1.5 litre diesel and the current exhaust system is a straight through oval absorptive “free flow” silencer / muffler before the rear axle and an offset oval absorptive silencer after the rear axle with no tip.

My understanding of the Helmholtz function is that it is for the volumetric calculation of a sphere and includes the cross-sectional area of the neck, static pressure and volume of the cavity and specific heats of diatomic gases.

However, I like the idea of the muffler clamp and hollow capped tube. Perhaps a 57mm tube (outside diameter) will just fit inside the 57mm pipe (nominal size), depending upon the thickness.

[ptuomov]

Another alternative to try first is to attach a small weight, like a lead sheet with clamps, to the exhaust pipe.

[ptuomov]

@ptuomov To answer your question, it is a 1.5 litre diesel and the current exhaust system is a straight through oval absorptive “free flow” silencer / muffler before the rear axle and an offset oval absorptive silencer after the rear axle with no tip.

Four cylinder engine I assume? Trying to make sense of the engine orders at which the exhaust might produce noise.

[Rick!]

You will be partaking in an exercise called "stepping on the balloon."
For a single frequency you are trying to attenuate, a few others will step up in spite of your best efforts and you end up with nearly the same noise level, in my experience. If you google intake helmholtz resonators and look at the images, you'll see that they consist of multiple volumes attached to the main duct. Typically one ends up attenuating several frequencies in order to achieve the desired outcome.
Will the Helmholtz tube be just enough to prevent the cab from being excited (which is really the structure/air volume being excited by airborne noise)? Only rigorous testing will determine that.
If you purchase a sound analyzer for your phone, you can determine whether it is a single frequency spike or one with a wide base that is actually a range of rpms that create the offending noise.
There are other experiments to you can do to tell if the exhaust pipe is resonating or if the noise is structure borne.
Simply suspending the exhaust with rubber bungee cords should break the structural connection between the exhaust and the body/frame.
If that results in reduced drone, then create a durable mounting system with j-hooks and rubber donuts/rings.
What happens when you open a rear side window at the drone rpm? Worse or better?
What shape are the body to frame mounts in?
Anyway, creating an annular Helmholtz tube is novel, I'll give you that.
In my experience, scrubbing energy off of the sound and using volume in a muffler/resonator is much more successful than treatments after the fact.
If NVH was easy, everybody would be doing it.

Good luck.

This guy didn't give up...

[Dust Buster]

Yes, @ptuomov, four cylinder

@Rick! - I have a spectrum analyser app for my phone. It hunts, but keeps returning to between 170 and 176 Hz and stays there for several sweeps before briefly finding other frequencies, usually harmonics (340 Hz, etc). The only thing that has changed is the new exhaust system. I had previously deadened any body panel that failed the thump test. The average noise level on my test road at the same speed is 61 dB. On the topic of speed, as I'm accelerating through the gears, 1750 to 2000 rpm sounds great. I'm in full boost at 1750 rpm. It's just when I'm on the freeway doing a constant speed in this rpm range that I see the sound meter measure more dB. Don't laugh, but when I hum in harmony, the spectrum analyser app also says 170 Hz. It's a fairly new vehicle (I find warranties a bit overrated) and I inspected the rubber hangars before the new exhaust install. Also, I installed a new long flex tube at the DP's flange. The j-hooks on the exhaust don't touch the body at any point other than via the suspended hangars. I need to try opening a window when it drones. Maybe I can get the same wind throb that Helmhotz got when he blew across the empty bottle necks.

[stealth]

Holy smokes... that's a lot of words leading off into the weeds...

OP,

What is the issue you are trying to solve?

[Dust Buster]

I'm trying to tame the annoying drone, but can't choose between the two ways of calculating the drone frequency.

[ptuomov]

One more packaging thought. You could do a tuned side branch resonator with a smaller pipe inside a bigger pipe. Like this:



Insertion loss would be something like what is shown on slide 24 of this slide deck:

http://web.engr.uky.edu/~dherrin/ME510_ ... _Ducts.pdf

I think this might package well and it can be fabricated from a cheap empty-can resonator/muffler.