Quarter Wave Resonator vs Drone

[ptuomov]

If one is the magic number, then =(3.182^2-2.25^2)/2.25^2 [or =((3.182*3.182)-(2.25*2.25))/(2.25*2.25)] gets close.

So, the length of the side branch is irrelevant or longer increases the attenuation? If this is so, then there must be a formula for this relationship.

The length determines the resonant frequency, I think. It’s just like a side branch resonator in that sense.

The side branch resonator formulas should be directly applicable to the pipe-in-pipe resonator as long as that are ratio is approximately one.

If you are calibrating the length by trial and error, then I think the resonator should work with area ratio greater than one, too, just the formula for the resonant frequency may be different. May, I don’t know for sure.

[ptuomov]

By the way, if you make the first resonator version maximum length that fits, say 0.8m, you can make the resonator adjustable by moving the far-end end cap further inside the pipe to make the resonator shorter than that. I haven’t ever done this, but epoxying the end cap temporarily into a location might work for tests?

[Dust Buster]

Both of my boxes are 0.69m which has caused me to consider either they are really suppressing something horrendously loud or are really trying to suppress it. Although both are the same length, the second one should be dealing with a slower sound wave due to it being colder. See the calculations below (note the length).

I see now that your perforated pipe is referring to Helmholtz's resistive acoustic liner, but it is actually just the volume that matters as the inner pipe is acoustically invisible.

https://en.wikipedia.org/wiki/Acoustic_ ... r_(vented)

Furthermore, although considered inconsequential, let's include the adjustment of a quarter of the diameter:

f = (n * v) / (4 * (L + 0.4 d ))
where:
f = resonant sound frequency
n = 1 for just the first order harmonic
v = speed of sound, which increases with temperature
4 = quarter wave where one end of the pipe is closed
L = length of the resonant tube
d = diameter of the tube

L + 0.4 d = nv / 4f
L = nv / 4f - 0.4 d
L = 460.6 / 4 (170) – 0.4 (0.057)
L = 0.65m and 0.63m for the 176 Hz from the original 0.68m and 0.65m respectively

[pcnsd]

I don't know if this spreadsheet will help you, but you are free to amuse yourself. I chased my tail on this subject before concluding it wasn't going to do what I wanted and I needed to build a bigger muffler if I wanted to pass sound at the track.
You are dealing with the third harmonic of your primary frequency at 1750rpm in a 4 cylinder. ~175 Hz. It may well be a resonance that is driven by but occurring outside your exhaust system. Not sure which frequency to target in a suppression scheme but I think the primary (driving frequency) would be my first target.

Quarterwave drone.xlsx

[Dust Buster]

I was just starting to think of that possibility (resonance occurring outside of my exhaust system).

I've just read ptuomov's “Countermeasures to Reduce Muffler Shell Radiation Noise”. My box shell is embossed and crimped on the side (not in the middle). I didn't see any baffles, but it is packed with glass wool. However, I don't know how stiff the shell is for preventing resonance. The article mentions placing 2mm ceramic paper between shell layers, but that's too much bother.

There is also a suspended heat shield between the box and the bottom of the vehicle, which could also now be vibrating.

I haven't found silencer bandages to be of much use for repairing holes, but was wondering if this could be used to dampen the vibration or some other cheap solution (bitumen perhaps, when I don't plan driving over dry grass or perhaps just on top of the heat shield). I was thinking that just placing a finger on a small bell will stop it from tinkling.

[Dust Buster]

So, if I “T”ed off the 57mm with a 57mm (neck diameter) for potential maximum out-of-phase destructive interference for 15cm to allow clearing the box before bending, then extended that with 76.2mm pipe for 52cm, the Helmholtz resonator would be tuned to 173.21 Hz. In this way I'd be combining the ¼ wave (length requirement of 67cm, being the 15cm + 52cm) and Helmholtz resonators. Perhaps now I don't need the bell-shaped mouth at the “T”.

Helmholtz.PNG

I'm assuming that in the cc equation:
FH=SOS mps*100/(2*PI())*SQRT(((Neck dia/2)^2)*PI()/(Cavity Vol cc*(Neck length+(Neck Dia*0.75))))
that I don't have to calculate the volume of the neck and that the volume of the main cavity (Cavity Vol cc) is a quarter of the pi * diameter squared * height of the 76mm pipe only.

If I kept the start of the 76mm pipe square, it might be adding a secondary bounce wave / vibration. Therefore, I should probably angle it (at the donut) – not unlike the original Helmholtz flask.

[ptuomov]

Do you have photos or diagrams of the exhaust system that you currently have in the car and that is droning?

[pcnsd]

So, if I “T”ed off the 57mm with a 57mm (neck diameter) for potential maximum out-of-phase destructive interference for 15cm to allow clearing the box before bending, then extended that with 76.2mm pipe for 52cm, the Helmholtz resonator would be tuned to 173.21 Hz. In this way I'd be combining the ¼ wave (length requirement of 67cm, being the 15cm + 52cm) and Helmholtz resonators. Perhaps now I don't need the bell-shaped mouth at the “T”.

Helmholtz.PNG

I'm assuming that in the cc equation:
FH=SOS mps*100/(2*PI())*SQRT(((Neck dia/2)^2)*PI()/(Cavity Vol cc*(Neck length+(Neck Dia*0.75))))
that I don't have to calculate the volume of the neck and that the volume of the main cavity (Cavity Vol cc) is a quarter of the pi * diameter squared * height of the 76mm pipe only.

If I kept the start of the 76mm pipe square, it might be adding a secondary bounce wave / vibration. Therefore, I should probably angle it (at the donut) – not unlike the original Helmholtz flask.

You do not need to calculate neck volume, it is calculated from the neck length and diameter inputs.
Remember the suppression frequency is 4 times the target frequency or 692 Hz for a 173hz target. The higher frequency target makes for a very small chamber and short neck. Are you sure you don't want to target the driving frequency at ~57.6 Hz. Its suppression frequency should be ~230.6 Hz.

Helmholtz inputs and freq relations:
Increasing neck diameter increases frequency
Increasing neck length decreases frequency
Increasing cavity volume decreases frequency

[Rick!]

Do you have photos or diagrams of the exhaust system that you currently have in the car and that is droning?

Been thinking this for a while - we know nothing about the stock system, the aftermarket system, make of the vehicle, etc.
Another unknown is how sophisticated the phone sound measurement is. Free ones typically measure just dB(A). Better ones can perform FFTs or PSDs to understand all prominent frequencies (not to be confused with prominence, which is a comparative measurement).
Once a guy gets a glimpse of what's going on, "A duck with a glass eye could have seen that coming" could be one response...
There are far too numerous examples that can be searched where someone bolts on a shiny new system looking for performance and a throaty sound and end up with "the drone".
Source, Path, Receiver - with usually three paths: airborne, structure borne, or fluid borne. Sources rarely change so the solution is in the path or receiver. Mitigation can be addressed many ways but usually one needs to cut some steel or make several tests with lead or butyl rubber blankets and create some test results. You can math the crap out of an issue but by the time you think you are ready to make the solution, the guy with the dirty fingernails already is putting his solution into production.

Suggestion below from pcnsd:
You do not need to calculate neck volume, it is calculated from the neck length and diameter inputs.
Remember the suppression frequency is 4 times the target frequency or 692 Hz for a 173hz target. The higher frequency target makes for a very small chamber and short neck. Are you sure you don't want to target the driving frequency at ~57.6 Hz. Its suppression frequency should be ~230.6 Hz.

Helmholtz inputs and freq relations:
Increasing neck diameter increases frequency
Increasing neck length decreases frequency
Increasing cavity volume decreases frequency

I'd make a resonator for both target frequencies though a 57.6Hz solution will take up a bit of real estate due to its wavelength (almost 6m).
Except for the NASA paper, most Helmholtz math is based on white noise and pink noise inputs. Use pulsed inputs from an engine and a transmission loss can be measured but not in the magnitude that a spreadsheet calc may give.

YMMV

[Dust Buster]

Do you have photos or diagrams of the exhaust system that you currently have in the car and that is droning?

Duster_New_Exhaust_Tailpipe.PNG

Pic of current system as requested. The OEM system's pipe sizes were all over the place. The flange at the bottom of the DP is 57mm, but was probably closer to 50mm inside and full of soot. The pre-CAT pipe from the flange was 54mm, but the flex pipe restricted down to 38mm leading to the CAT / DPF. The pipe from the DPF to the OEM silencer was 43.5mm. The tailpipe from the silencer was 50mm. The current system is 57mm from DP back and consists of an oval absorptive “free flow” silencer / muffler before the rear axle and an offset oval absorptive silencer after the rear axle with no tip, although my old tip looks like it will fit.

Pity the vent wasn't one the other side. Otherwise, the piping would have been shorter.

I did want it to exit to the side and down as diesel fumes are not very pleasant.

[Dust Buster]

I'm assuming that in the cc equation:
FH=SOS mps*100/(2*PI())*SQRT(((Neck dia/2)^2)*PI()/(Cavity Vol cc*(Neck length+(Neck Dia*0.75))))
that I don't have to calculate the volume of the neck and that the volume of the main cavity (Cavity Vol cc) is a quarter of the pi * diameter squared * height of the 76mm pipe only...

You do not need to calculate neck volume, it is calculated from the neck length and diameter inputs...

Yes, I meant that it didn't appear that I needed to add the volume of the neck as the equation seemed to take care of this already.

[Dust Buster]

Been thinking this for a while - we know nothing about the stock system, the aftermarket system, make of the vehicle, etc.
Another unknown is how sophisticated the phone sound measurement is. Free ones typically measure just dB(A). Better ones can perform FFTs or PSDs to understand all prominent frequencies (not to be confused with prominence, which is a comparative measurement).
Once a guy gets a glimpse of what's going on, "A duck with a glass eye could have seen that coming" could be one response...
There are far too numerous examples that can be searched where someone bolts on a shiny new system looking for performance and a throaty sound and end up with "the drone".
Source, Path, Receiver - with usually three paths: airborne, structure borne, or fluid borne. Sources rarely change so the solution is in the path or receiver. Mitigation can be addressed many ways but usually one needs to cut some steel or make several tests with lead or butyl rubber blankets and create some test results. You can math the crap out of an issue but by the time you think you are ready to make the solution, the guy with the dirty fingernails already is putting his solution into production.
...
I'd make a resonator for both target frequencies though a 57.6Hz solution will take up a bit of real estate due to its wavelength (almost 6m).
Except for the NASA paper, most Helmholtz math is based on white noise and pink noise inputs. Use pulsed inputs from an engine and a transmission loss can be measured but not in the magnitude that a spreadsheet calc may give.

YMMV

The vehicle is a 2014 / 15 Renault / Dacia Duster 1.5 litre dCi (diesel) 4WD. The stock system is described two posts above. The aftermarket piping is bespoke without mandrel bending facilities, which is one reason I went a size larger (than one size larger). The boxes are built locally by Powerflow.

The app does FFT size, range, resolution and length and does various calculations: A3, A4, A5, A6, B5, B6, C4, C5, C7, D4, D5, E5, F4, F5, G4, G5 giving average, peak and max Hz. I use another app to just give dB(A). However, the mic has not been calibrated and perhaps that is my glass eye. My other eye might be blinded by a research paper on in-pipe temp.

Agreed, I don't have 6m of spare real estate. I do go off-road and need to maintain the ground clearance.

I decided to do some dirty fingernail work before taking my chosen design to an exhaust fabricator by applying a roofing product to the top of the heat shield over the boxes. I don't think the shells are too thin, but the two sections of heat shield closer to the engine seem to be metal without any absorptive material backing (unlike the one over the boxes). These two heat shield sections thud around 350 Hz when finger tapped while one section of pipe actually rings at 1249 Hz. I wasn't expected the ringing, but I am prone to a bit of serendipity.

I'll take a long drive through some nearby mountain passes tomorrow and let the co-pilot drive sections so that I can measure under load at various rpm, which I can't do on my own today.

From ptuomov's “Chapter 10 Sound in Ducts”
The side-branch resonator is analogous to the tuned dynamic absorber.
Resonators used as side branches attenuate sound in the main duct or pipe.
The transmission loss is confined over a relatively narrow band of frequencies centered at the natural frequency of the resonator.

From “Engine Exhaust Noise Control”
Insertion loss (IL) is defined as the reduction of noise level that occurs when a silencing element is inserted into the system.
Engine Firing Rate (EFR) = number of cylinders * Cylinder Firing Rate (CFR)
CFR = rpm / 120
EFR = 4 * 1750 / 120
EFR = 58 1/3 Hz (primary harmonic)

[ptuomov]

Nice phone of it can handle those apps. Does it have a camera?

[Dust Buster]

Nice phone of it can handle those apps. Does it have a camera?

yes, but it doesn't do temps in the range needed.

[ptuomov]

Is this the stock exhaust?

BE13EA25-FAFB-4C49-B2D7-DE5CE00ACCF6.jpeg