therm8

Warning, lots of equations in here, may cause a headache :D

I just perused it, but the article talks of using an audio speaker to shift the resonant frequency of a Helmholtz resonator in real time. Maybe those who know more of resonance tuning could determine if it is viable.

A Smart Helmholtz Resonator

rotarygod

Just to simplify that entire areticle and put it into english, they are basically saying that Helmholtz resonant tuning is dependent upon plenum volume, intake pipe length, and diameter. This we all knew. What they propose is a system that constantly retunes itself based on engine requirements. Their way of doing it would be to replace 1 wall of the plenum with a movable one that would adjust the size of the plenum. Yes this would work. They are not using a speaker in the system. Since the inlet pipe resonance also corresponds to the volume of the plenum, the resonance would change. This seems like a very complex way to do it though.

Helmholtz plenum sizing works exactly the opposite of engine requirements. Typically for better low end power (in a Helmholtz system) you want a larger plenum and for better high end power, you want a smaller one. However this is entrirely backwards from what we do when we do not use Helmholtz tuning. Better power is made with a larger plenum up high and a smaller one down low. The rules all change when you use resonant tuning in the plenum.

In a perfect world, the plenum volume would change in a continuously variable manner, the inlet pipe would change length, and it would change diameter. This would enable it to always keep the same air inlet veolitcy, and maintain the same tuning for every rpm. This isn't practical though. Fortunately just adjusting the tuning of the system by itself by altering only one aspect does work nearly as well. In the case or the article, they want to adjust the plenum volume. Another way to do it would be to adjust the inlet pipe length. this is so much easier. The adjustment of the plenum volume could have an affect over a larger rpm range though but we rally run into a host of other problems. The length of the intake pipe would have to adjust over a pretty large area. In a Helmholtz tuned system, this inlet pipe will shift the power peak by 1000 rpm's per every 1.7" change in length. Also remember that for every spot that acoustics helps, there are also spots that it hurts. This is why constant adjustment would be so nice. In a fixed system, you get gains at the tune point as well as at every harmonic point of that tuning. In between these however power may be hurt somewhat. The goal is to make it help where you need it the most and hurt where it isn't as critical.

Another way to retune the system is throught what is already standard on the RX-8. By having a tuned length inlet pipe such as the long inlet pipe on the RX-8, the system is tuned to a spot lower in the powerband. By opening the pipe with the flapper door, the resonance point is raised and so is the boost. The autop RX-8 has a single pipe that is medium length. It is designed to provide a good boost in the mid range where that engine stays at the most.

This article merely shows another alternative way to tune the system. The 787B 4 rotor engine had varible length intake runners that kept torque flat in it's powerband. It's the same principle here. It's all about tuning and there is more than 1 way to do it.

shelleys_man_06

Does anyone remember the Wave Equation from PDE? The Helmholtz equation gets thrown around here a lot. I believe rotarygod best explains it, but I would like to simplify things in terms of mathematics.

The Helmholtz equation, I believe, is an extension of Laplace's Equation, described by



My PDE book describes it in a similar fashion, but using variables u and n, with n=(omega/c), the index of refraction. With the Helmholtz equation, you're assuming a slowly varying medium, in which the medium varies over a much longer distance than typical wave lengths, so that

n^2=n^2(ex,ey,ez)

This may back up rotarygod's point of design parameters regarding the Helmholtz-tuned plenum. I hope someone can understand how the PDE works. Personally, most of this is beyond my understanding except changing omega, which I believe is the frequency of the wave, and e, which is some sort of perturbation coefficient, can have adverse effects, since it is part of a coefficient regarding u. You can play around with the equation to obtain the results you want. Also, I discovered setting k=0 from the Helmholtz equation leads to Laplace's equation, which is really fun to solve.

Aoshi Shinomori

What in God's name does that first formula say!?!? It looks like a bunch of weird symbols thrown around, haha. I can make out a + and an = but that's about it. Anyway, I probably wouldn't understand the formulas anyway, as I am in the lowly Physics 140. (Only a freshman) But in the future I might understand all of this a little bit better. But if you could post the formula in the normal font I would really appreciate it. Thanks

shelleys_man_06

I think it depends on what background you have. You're probably running the plasma setting. :p

Okay, here's the equation in my own words:

The Helmholtz equation is,

(del)^2*u+n^2*u=0

where (del)^2*u is the gradient of the function u (you'll learn this in you cal III class), and n is (omega/c), the index of refraction. This coefficient is what I consider a weighting factor in the equation.

If n=0, you'll get Laplace's equation, which my teacher explained is for thin films. If n<0, the Helmholtz equation turns into the diffusion equation, which I think is the basis for Fick's 1st Law , which explains diffusion flux. I've gone overboard with mathematical insanity.

Gomez

Correct.

Aoshi Shinomori

Makes a little more sense now that I understand what the formula says, but I've never worked with this kind of stuff, could be interesting. Thanks though for the explanation, and yes you are are insane :D

RX8_Buckeye

What article were you reading? They definitely are using a speaker to continuously vary the Helmholtz resonant frequency, and the concepts discussed actually have nothing to do with tuning for increased engine performance. Rather, the purpose of a Helmholtz resonator in this context is to act as an "acoustic vibration absorber". The speaker essentially acts as a piston at one end of the Helmholtz resonator--it's complex impedence is adjusted by the flow of electrical current. Helmholtz resonators are often used in air induction systems to cancel out annoying tonal frequencies generated by acoustic pulsations in the channel (tubing). Any given section of tubing has its own resonant acoustic frequency, and adding a Helmholtz resonator, which is essentially a closed branch off the main section of tubing, eliminates this single-tone resonance and reduces the amplitude of dynamic particle velocity, and thus overall sound pressure levels.

FYI, The Helmholtz resonance can often be a VERY annoying phenomenon. This is the case with my wife's SUV with moonroof open. There is no wind deflector for the moonroof, so the entire vehicle cabin acts as a Helmholtz resonator. There is a loud rumble at a low frequency when cruising at 25-30 mph. It really hurts the human ear. For those unfamiliar with a Helmholtz resonator, just think of it as a spring-mass system. The air inside the vehicle cabin is compressible, so it acts as a spring. The air in the cavity opening, in this case the moon roof, acts as a mass that bounces up and down on the "acoustic spring". The driving force the sets off the resonance is the air flow across the roof of the vehicle--it excites the small mass of air in the moonroof opening. We are forunate that our RX-8 has a moonroof that does not retract into the roof, because it becomes an obstacle that prevents a boundary layer from forming in the airflow around the car.

shelleys_man_06

With the equation, we're assuming the slowly varying medium is air. I assume the thing hurting your ears is the resonant frequency omega[n]?

The Celica GT-S also has a moonroof that retracts over the roof of the car.

Does the Helmholtz equation go to the Wave equation under certain conditions?

rotarygod

You made me go back and look at it again. The first time I just skimmed it. Yeah, you're right about it being a "speaker".

RX8_Buckeye

The thing hurting your ears is large fluctuations in air pressure--hard on the ear drums. As you know, sound is basically pressure waves traveling through any medium, like air. The amplitude of the air particle motion is what we perceive as loudness, and the rate at which the particles oscillate dictates the frequency of the sound. So, to put it simply, the frequency (pitch) of the rumble heard in the vehicle cabin is the resonant frequency of the Helmholtz resonator, and the amplitude of the particle motion determines how loud it is.

The Helmholtz equation is derived from the wave equation, if I recall correctly, but it has been a couple of years since my acoustics class! I don't like differential equations, except for simple 2nd-order ODEs (vibration).

shelleys_man_06

Hmm. I came upon the Helmholtz equation through my PDE book. Yes it comes from the wave equation.