Exhaust Drone

[Joe in NY]

Alas I have a direction in which to go in an attempt to rid of the drone due to my new muffler! Since installing a new muffler I have an undesirable drone in the 2,000 to 3,000 rpm range. This is because our factory mufflers were designed to deconstructively resonate with this specific drone where as my new muffler is not. The worst is around 2,400 RPM which is me doing 75MPH on the highway. Not cool to have a drone there.. So here is some math to explain what is going on and how I want to tackle some solutions.

So exhaust drone is cause by the exhaust piping matching up to the harmonics of our engines and causing constructive resonance. So for a V8:

4 Stroke Engine
8 Cylinders
1 Revolution = 2 Strokes
4 Exhaust strokes per Revolution (follow? 1 Rev = 2 Strokes, 8 Cyl / 4 Strokes = 2 Cyl doing the same thing at same time, 2 * 2 = 4)

My Drone: 2,000 to 3,000 RPM.
Recorded while driving and threw into Audacity. FFT showed huge spike at 155Hz.

So,
155Hz = 155 1/Seconds * 60 Seconds/Minute = 9300 Cycles/Minute (Cycle = One Full Wavelength)

9300 C/M / 4 = 2325 RPM (4 pulses in one revolution)

And yup that's right about where my drone is the worst! This was just to confirm the drone I hear with engine rpm.

So now wavelength:
WL = Velocity / Frequency
WL = 1125.33FT/s / 155Hz (1125.33FT/s is at sea level at 20*C for normal Oxygen and Nitrogen atmosphere.. Important!)

WL = 7.26FT * 12IN/FT = 87.1 Inches

This is where so many people go WRONG! This is the wavelength for NORMAL AIR... Not an EXHAUST SYSTEM!

Exhaust system:
CO2 (mostly)
H2O (where do you think the steam comes from?)
300*F + (At tailpipe can be over 600*F coming out of engine)

So the corrected velocity for 300*F CO2 is 1046.59FT/s.

WL = 1046.59 / 155 = 6.75FT * 12 = 81 Inches.

600*:
WL = 1237.21 / 155 = 7.98 *12 = 95.8 Inches

So if I want to go the route of using a J Pipe resonator (Closed end 1/4 wavelength pipe resonator) I would be aiming for something between 20.25" to 23.95". This is why for some people J pipe resonators work perfectly for some people and others just not what they hoped for. Because people are not taking into account the different mediums and temperatures!

Now another aspect to this is that my tail pipe must be in resonance with the 155Hz. An open pipe has resonant frequencies of 1/2WL*n. n = whole integer. So, 81 / 2 = 40.5". So the entire exhaust system now comes into play with this.

The whole length of you system, length of your muffler, and length of the tail pipe all play into this. This is why when people add short glass packs as resonators it breaks down the resonance of the solid one piece piping that the sound waves resonate with and build on. But it also why you can just cut off some of your tail pipe, or lengthen it to change the resonant frequency of your exhaust system.

If there are blatant errors let me know! This is coming together from 4 physics classes, internet, and my dad. (We're engineers, we do math lol)

So what I'm going to do is measure from the 3rd cat to the end of the tail pipe and see what kind of lengths I come up with to see if the whole system is at fault or mostly the tailpipe. I *should* be able to simply lop off 3" of tail pipe to change the resonance of the tail pipe. To drastically change it would be to cut 6 inches.

Say it was 40.5", 40.5" - 3 = 37.5", new F=166Hz. Too close to the 155Hz.

40.5 - 6 = 34.5", new F= 182Hz. Far enough from the resonance that it should not allow the 155Hz to constructively build into a horrid drone!

 

[TechGuru]

@imp might be able to help you with that stuff.

What muffler did you buy? Why not just get a proper silent OEM muffler?

I'd give this one a try: WALKER 21422 Premium Quiet-Flow Stainless Steel Muffler | http://www.rockauto.com/en/moreinfo.php?pk=995779

If you went with a loud exhaust on purpose, well you got what you asked for, lol. I would use a silent OEM and install electronic controlled cut outs if you want loud.

 

[Joe in NY]

@imp might be able to help you with that stuff.

What muffler did you buy? Why not just get a proper silent OEM muffler?

I'd give this one a try: WALKER 21422 Premium Quiet-Flow Stainless Steel Muffler | http://www.rockauto.com/en/moreinfo.php?pk=995779

If you went with a loud exhaust on purpose, well you got what you asked for, lol. I would use a silent OEM and install electronic controlled cut outs if you want loud.

I was looking to make this sound more like a V8 and give it back some of it's man hood haha. I mean I've never heard any other V8 this quiet before! Honestly looking to give about the some sound/loudness as our 2007 Suburban. It's got just enough rumble at idle and the right amount of sound when you step on it. The muffler I did pick is actually not that loud. My dad reported after following me that it sounds like a quiet straight pipe. But the system is droning and resonating with the interior which have stated above the natural frequency is actually 151Hz. (I made a typo with the 155Hz but carried the math through for 155 cause its close enough).

I really should have gone with my gut and bought a Dynomax 17236 Ultra Flo™ Welded. That would have given the deep tone and let a little more sound out then stock. But I wanted to be different and try out a Classic Chambered Powerstick. TUNDRA model.

Oh well live and learn..

Also, the stock mufflers and silent mufflers, otherwise known as turbo style mufflers, are TERRIBLE for exhaust flow! The exhaust gets forced to change direction multiple times and has to go through all sorts of different sized cavities. That just puts a major stink in keeping exhaust momentum to actually help with expelling exhaust from the engine. These explorers with the undersized single 2.25" exhaust and terrible flow muffler, the motors actually have to work to get the exhaust out.

 

[imp]

@Joe in NY
Very interesting work-up! Thought before I study it, I'd at least let you know we're watching you. As both a theoretician and plumber, I've learned that reality often throws "ringers" into the mathematically-predicted physical results. For example, have you ever heard "water-hammer" in pipes? NYC must have plenty (just being nasty....). Premise was, each location of a faucet had a vertical pipe rising upwards a foot or two inside the wall, capped at the top. In theory, trapped air in that pipe acts as an accumulator, and returns energy back into the system to blunt the inertial effect of suddenly stopping water flow when abruptly shutting off the faucet. Know what happens in reality? Works for a short time, then stops working.

Not an example related to harmonics generated by flowing fluids, exactly. Before offering any ideas for solution of your dilemma, if I can even do that at all, I will go back over your calculations. One of my required Engineering courses at UNLV was labeled simply "Fliuid Mechanics". Great course. Do you recall Froude's Number theory? See: https://en.wikipedia.org/wiki/Froude_number#Walking_Froude_number

There may be some value lurking therein with respect to Exhaust Drone. Could we also consider that a form of "Beating", akin to two or more repetitive cyclic actions of differing wavelengths creating "beats"? imp

 

[Joe in NY]

@Joe in NY
Very interesting work-up! Thought before I study it, I'd at least let you know we're watching you. As both a theoretician and plumber, I've learned that reality often throws "ringers" into the mathematically-predicted physical results. For example, have you ever heard "water-hammer" in pipes? NYC must have plenty (just being nasty....). Premise was, each location of a faucet had a vertical pipe rising upwards a foot or two inside the wall, capped at the top. In theory, trapped air in that pipe acts as an accumulator, and returns energy back into the system to blunt the inertial effect of suddenly stopping water flow when abruptly shutting off the faucet. Know what happens in reality? Works for a short time, then stops working.

Not an example related to harmonics generated by flowing fluids, exactly. Before offering any ideas for solution of your dilemma, if I can even do that at all, I will go back over your calculations. One of my required Engineering courses at UNLV was labeled simply "Fliuid Mechanics". Great course. Do you recall Froude's Number theory? See: https://en.wikipedia.org/wiki/Froude_number#Walking_Froude_number

There may be some value lurking therein with respect to Exhaust Drone. Could we also consider that a form of "Beating", akin to two or more repetitive cyclic actions of differing wavelengths creating "beats"? imp

Well luckily I'm not in NYC! We live on 3 acres and have only 3 neighbors on top of a hill in upstate. Also, we have a well, a well that is 800ft deep! I am well acquainted with water hammer. Do you know why those vertical pipes stop working? The theory is no tthat the extra length of pipe will stop the hammer. It is instead that the vertical riser will hold a pocket of air. Air compresses and expands, water doesn't. That is why when they are first installed they work. There is a little pocket of air that compresses when you shut the valve off and the water goes surging past. Then expands when the water bounces back. The air compressing and expanding provides the cushion (Like a shock absorber for a car) and turns it into heat when compressed then absorbs heat when expanding. All about turning that Kinetic Energy into heat!

I actually made a water hammer arrestor for a hot tub last fall! This old California Cooperage Cedar Hot Tub from the 80s has a remote pump/filter/heater. The line set is easily 30FT of 1.5" PVC and goes from the back deck/hot tub down into the basement. There is a two speed pump and when ever you go from HI to LOW you blow the lid of the pump basket.(literally break the tabs that hold the lid down and it pops off) Why? Well Unless you close the valves right down so it's barely moving any water, the momentum of water in 30FT of 1.5" pipe doesn't want to stop immediately. That is roughly 45 GPM at roughly 8FT/s. So I put a Tee in at the pump basket inlet, if the water were to go straight through the piping it runs through the Tee, into a 90* elbow pointed toward the ceiling, then to 1.5" to 3" reducer, and then there is 2FT of 3" pipe with a cap. Works beautifully! Go from high to low, and the water-hammer-arrestor shakes some and you can hear the water slosh around inside. And each time you use it, you can feel the warmth of where the water level in the absorber. It slowly creeps its way up because water absorbs air and with every cycle from low to high you pull air out as that same 30FT doesn't want to speed up immediately either. Due to the installation every-time you close the valves in the basement to clean the basket out the lines in the basement drain and fill with air. So this recharges the arrestor with air each time.

Any who..... Back to the topic at hand. Last night I lopped off 9" of tailpipe and went for a drive. To my ear it sounds like the peak of the drone moved up a bit... So going to my spreadsheet and messing around it seems that my previous 151Hz might actually an over tone and the whole length of the system is coming into play.

 

[imp]

....Any who..... Back to the topic at hand. Last night I lopped off 9" of tailpipe and went for a drive. To my ear it sounds like the peak of the drone moved up a bit... So going to my spreadsheet and messing around it seems that my previous 151Hz might actually an over tone and the whole length of the system is coming into play.

@Joe in NY
You are an interesting guy! Your drone reminded me of the old front-engined school buses which had a very long tailpipe reaching clear to the back end. Upon releasing the throttle to coast, especially at highway speed, those pipes made the most god-awful rapping racket!

Another comparative thought came to mind. Incompressibility of liquids vs. gases. When proof-testing boilers, they are filled with water, plum full, then pressurized for test purposes. On the outside chance the unit under test fails, ruptures, the stored energy is released as a dull "thunk", as the only stresses being relieved are those of the "stretched" boiler structure. Gas in a boiler, OTOH, can create a devastating explosion with disastrous results as the compressed gas, suddenly released, hurls broken parts at high speed. Steam boiler explosions are a well-documented example.

BTW, any idea why boiler-users insist that distilled water is acidic, having Ph < 7.0 ? imp