Jump to content


Photo

A Proposal For A Bi-Directional Concertina Reed


  • Please log in to reply
75 replies to this topic

#37 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 182 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 13 February 2015 - 01:29 PM

Hi Lucasz, your observation that the tongue begins vibrating with an amplitude too small for it to enter the slot in the shoe is important.  Years ago, I had noticed that, but I forgot about it when I wrote my previous post.  If indeed this happens all the time during the start transient of the free reed, then the actual situation becomes very difficult to explain in detail, without further experimentation.  It would be nice if someone made a slow motion video of the starting free reed in order to verify this speculation, complete with smoke entrained by the airflow, so that the air stream becomes visible. 

I say the actual situation becomes very difficult because I’m very sure that such “pre-vibration” is inherently unsteady.  I can’t explain the details on how that works.  It may have something to do with turbulence and the shedding of eddies and vortices under the tongue. 

 

It seems I have difficulty convincing you of the difference between unsteady flow and steady flow, and in your explanations, you don’t make distinctions.  When anyone invokes the so-called “Bernoulli” explanation on how a free reed works, they implicitly adopt a quasi-steady assumption, because the Bernoulli equation referred to is the one for steady (and incompressible) flow.  As I wrote before, with this assumption, the gap under the tongue during starting will cause a jet of air, and the pressure all along the bottom surface of the tongue is P2.  This is true in part because the pressure inside a subsonic jet must equal the pressure immediately outside the jet.  In this case, the jet velocity is the maximum velocity that can be obtained by the pressure difference (P1 – P2), and the pressure difference (P1 – P2) is the maximum for the system.

Let me try another way.  Bernoulli can be written:

P1 + 0 = p + 0.5*rho*v^2

The zero is because P1 represents a quiescent reservoir.  We can write this as

P1 – p = 0.5*rho*v^2

I’m saying that p = P2, which is the lowest pressure in the system, and thus, (P1 – P2) is the maximum pressure difference that the air could experience – when unsteady effects are not important.  Thus, when you adopt a quasi-steady approach and say that there must be a pressure force greater than (P1 – P2), you are equivalently saying that p is negative, which is impossible. 

 

I’m in favor of discarding the quasi-steady assumption for the very beginning of the start transient, and to accept that the flow field is inherently unsteady, and I am at a loss to explain the details of that flow field.  The question I asked in my previous post was in the context of the quasi-steady assumption, and when I make that assumption, I cannot explain completely the start mechanism.  And I’m sorry, I don’t understand your explanation.  Perhaps this means that the quasi-steady assumption is inadequate to explain the start transient, simple because this assumption is wrong, and one needs to invoke some principles of unsteady flow in order to understand it.  The “pre-vibration” you describe suggests to me that the quasi-steady assumption is inadequate.  Most other musical instruments contain sound sources that involve unsteady effects, such as the flute, trumpet, and reed instruments, thus, why shouldn’t the free reed?

 

However, for the air motion during periodic motion (speaking), as I mentioned, the quasi-steady assumption may be accurate for the lower frequency reeds.  Indeed theoretical papers have been written that make this assumption.

 

Best regards,

Tom



#38 Chris Ghent

Chris Ghent

    Heavyweight Boxer

  • Members
  • PipPipPipPipPip
  • 1054 posts
  • Gender:Male
  • Location:Blue Mountains NSW

Posted 13 February 2015 - 02:38 PM

The very sharp jumps of the square wave come about because the cutoff and restoration of the air flow is very abrupt in the conventional reed due to the shape of the slot in the reed frame. With the top interior edges of the frame filed down somewhat as i suggested, the cutoff and restoration of the air flow should not be so abrupt... /...Less energy in higher harmonics should mean a more mellow sound.

This cause and effect are well understood here. The inefficiency of the reed with wider clearances brings its own problems ie. the need for more force to create the same volume and slower response. Retaining the close clearances and having a more mellow sound is where the game is.

Edited by Chris Ghent, 13 February 2015 - 02:39 PM.


#39 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 182 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 13 February 2015 - 06:00 PM

Rlgp, I apologize for the flippancy with witch I posted above.  I’ll consider you a real physicist, because you have earned the title.

 

I’ll also concede that ma is not considered to be strictly a force.  The ma term is often loosely regarded, in laymen’s terms, as the “force of inertia,” and when you draw a free body diagram in dynamics, you show all the forces acting on a mass using arrows denoting the direction of the force, and you also draw an arrow at the center of mass, labelling it ma.  This diagram thus shows a dynamically balanced condition.  So I’ll compromise a bit here and call ma an “equivalent force.”  More importantly, and I think you would agree, no description of the dynamics of a vibrating system can be complete without acknowledging this equivalent force of inertia. 

 

Thanks for your note about the progression of higher harmonics in the Fourier analysis of trapezoids and rectangles.  Like you, I’m retired, and it’s been long enough now that I lost track of such details, but I actually do recall those facts.  (So far, for me, it’s a terrible thing to grow old.)

 

The criterion that determines whether or not a fluid flow is incompressible, in steady state, is that the square of the Mach number be much less than unity, M^2 << 1, or M less than about 0.3.  When this is the case, all the terms arising from compressibility can be omitted, and one can still calculate with good accuracy.  For air at ambient conditions, this translates to an air velocity less than about 325 ft/sec.  From the Bernoulli equation, for air, a pressure difference of about 24 inches water column will produce such a flow velocity.  Most accordion and concertina bellows pressures are less than about 10 inches water column.  Thus, the airflow through a free reed can be considered incompressible. 

 

It’s odd that you would say that we cannot consider the higher pressure region to be incompressible, when you do proceed to consider the lower pressure region incompressible.  The two regions are intimately connected, differing only (dynamically speaking) by a very small pressure difference. 

 

It’s incorrect to say that the pressure on the top of the tongue produced by downward flowing air is higher than the pressure the air started out with (P1).  In fact, the dynamic pressure produced by an airstream that impinges on the top surface is its stagnation pressure, which is equal to P1, the static pressure of the air at rest.  From Bernoulli, any air particles originating from quiescent air and experiencing velocity, have a pressure less than P1 by an amount precisely equal to the V^2 term.  In other words, upon stagnation, the air stream restores the pressure it started out with (P1).  This stagnation is thus essentially frictionless and reversible.  Therefore, the pressure on the top surface of the tongue, with the quasi-steady assumption, is P1, and the ordering of pressures that you arrive at is erroneous. 

 

The Bernoulli equation you wrote, P2 = p2 + 1/2 rho*v^2 is incorrect.  It purports to calculate an air velocity without acknowledging the pressure difference that causes it.  The correct equation is P1 – P2 = 0.5*rho*v^2.  And again, the ordering of pressure magnitudes that you write is incorrect. 

 

I’m not sure that a square wave is a “pretty good approximation” of the waveform Cottingham shows.  The jagged edges in the actual pressure waveform may produce more higher harmonics than a square corner.  Would you agree?  Incidentally, in that article, Cottingham mentions my pitch bending invention, and in the references, mentions also a web-published article that I wrote for Concertina.org.  (So I guess I tooted my own horn, as well.) 

 

“…but the frequency will be twice the frequency of the tongue oscillation.”

 

I don’t know why you would insist on asserting this.  I’ve done experiments in this regard, and I’ve read a fair amount on it.  I’m quite sure you have very little experimental experience with free reeds, yet you have no reservations in asserting what you imagine.  I think this communication would be more comfortable if we talked in person and got to know one another, and one another’s experience.  The forum here is valuable, although it can be rigid.  I can’t do much else than again suggest you do the experiment I suggested in my earlier post.  I also suggest in a friendly way that you think more about the need for experimental evidence to support theoretical predictions.

 

Best regards,

Tom



#40 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 13 February 2015 - 07:02 PM

Tom, all theoretical papers I've found on free reed analysis skip the starting period and focus on sound generating properties of steady oscilation. I also think, that slow motion, smoke airflow analysis is the only logical step in verifying my assumptions. Unfortunately I'm bound by the capacities of my workshop here which does not include high speed camera :)

 

I'm also aware, that my explanations weren't as clear as they should be, and there are two main reasons for this: first is the language barrier and the second (more important) is that my times at university are long past and I haven't done serious math for more than a decade now. This is why I can only operate on simple illustrative experiments, observations and intuitions and must withheld from throwing any calculations into this discussion. 

 

Instead I did some digging and I think I have finally found a well-described principle that I was trying to ilustrate with my paper experments. It's called Coanda effect http://en.wikipedia.org/wiki/Coandă_effect and describes the tendency of a fluid jet to be attracted to nearby surfaces and is one of the fundaments for the lift force generation and numerous other fluid flow phenomenons. This combined with the third Newton's law makes the tongue to be atracted towards the jet as well and is what I think draws the tongue into the shoe at an early stage of the oscilation.

The second principle which I have tried to describe with "the paper corner reed" example (in the part of airflow acceleration) is Venturi effect http://en.wikipedia..../Venturi_effect which speeds the airflow and significantly lowers the pressure locally at the gap below P2, and in consequence increases the force generated by Coanda effect.

 

Both of the effects above are generated only dynamically and are significant only when there is fast enough airflow, so as soon as the gap is closed (*) the tongue can spring back upwards against the pressure gradient. Because there will be some time needed for the airflow to reestablish after reopening of the gap, the tongue can have enough time to swing higher than initial position.

 

In my opinion this combined effect is present also at a stable stage of the reed oscilation. This effect can also be present at the second (and third) point in the reed cycle, when the tongue crosses the bottom of the shoe, creating another gap - this time with the force acting upwards. But those both statements heavily depend on whether or not there is enough time for the steady jet to be formed at those later stages of tongue oscilation.

Those effects are of course dependand on pressure difference P1-P2, tongue area and all sort of reed parameters, so they will be proportional to them in some way or another, so those "microscopic" effects may be in fact omitted in "macroscopic" description of the stable phase of reed oscilation, when the focus of description is mainly on acoustics of the free reed (as is done in all reed-related articles I could find on the web). 

 

I hope this time my point of view is finally clear enough to be seriously considered (either as true or false) as a coherent "theory" based on actual physics :)

(*) there will probably be a slight delay between cuting the airflow and upward acceleration of the tongue because of inevitable turbulence below the tongue caused by a sudden cut-off of the airflow.



#41 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 13 February 2015 - 07:07 PM

To be clear - I think that at the later stages of the reed oscilation the effects I have described coexist to some degree with the direct effects that the pressure gradient has on the oscilating reed.



#42 adrian brown

adrian brown

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 457 posts
  • Gender:Male
  • Location:Amsterdam, NL

Posted 14 February 2015 - 02:36 AM

Tom, all theoretical papers I've found on free reed analysis skip the starting period and focus on sound generating properties of steady oscilation. I also think, that slow motion, smoke airflow analysis is the only logical step in verifying my assumptions. Unfortunately I'm bound by the capacities of my workshop here which does not include high speed camera :)

 

Have you ever tried using a strobe light to observe reed motion rather than a high speed camera? By looking at a reed in a tuning bellows in a darkened room under a strobe (disco light) by varying frequency of the strobe you can effectively slow down/stop the reed in all positions of it's cycle and just have a look at what's going on. If you want to add smoke, the same disco light shop can probably help :-)

 

I'd just like to thank the participants of this thread for a fascinating and absorbing discussion, even if I have to admit to it being sometimes completely unfathomable to this particular "acoustically challenged" instrument maker :-) I somehow can't stop myself from remarking though, whether it wouldn't be quicker just to make one to find out if it works, then worry about the theoretical niceties afterwards? However, I really don't want to rock the boat, chaps, so please treat this comment with the humour intended.

 

Adrian



#43 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 182 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 14 February 2015 - 10:36 AM

“I hope this time my point of view is finally clear enough to be seriously considered (either as true or false) as a coherent "theory" based on actual physics :)

 

Lukasz, The bank, Coanda, and venturi effects are not, in themselves, basic physics.  In fact, they can all be explained, at least in part, by an appropriate application of the quasi-steady, incompressible Bernoulli equation, as long as the velocities and time derivatives are not too large, and this equation is basic enough, at least for me. This also goes for the operation of the free reed, which also operates by the same basic principles.  It’s up to us to seek out what the basic principles are and understand how they are applied. 

 

It’s not a valid approach for you to point out a flow phenomenon as if it's a basic principle that reminds you of a vibrating free reed,  then say “Oh look, see, this phenomenon is basic and it is what explains how the free reed works.”  Would it be correct for you to say, alternatively for instance, “the Coanda effect is explained by what happens in the operation of the free reed?”  No.  Adequate explanations must be based on the same fundamental laws of Physics that are at the core of how all phenomenon work. 

 

Best regards,

Tom



#44 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 14 February 2015 - 10:42 AM

I didn't say "basic physics" but "based on actual physics".



#45 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 14 February 2015 - 11:30 AM

@ Tom:  Of course that all those various fluid dynamics effects come from calculations of the same equation, but used at different scales (both spatial and time) resulting in looking at a different geometry and airflow. I think that our missunderstanding comes from looking at the reed tongue at two different scales. You look at the reed as a divider between high pressure reservoire and low pressure reservoire and try to describe it at this "large" scale of an airflow. I on the other hand, focus only on the flow through the gap "magnifying" it. I'm not particularily interested in pressure differences between the bellows and the chamber and the steady oscilation phase, because I try to understand only the first cycle of movement, which we already agreed cannot be explained by this "large" scale (P1-P2)*A approach. It should be clear by now, that I think that the reed would close even when subjected to a very selective jet of air pointed only at the gap (prior to introducing this jet, the reed as a whole subjected only to ambient air pressure, equal both above and below the tongue). 



#46 Dana Johnson

Dana Johnson

    Heavyweight Boxer

  • Members
  • PipPipPipPipPip
  • 662 posts

Posted 14 February 2015 - 11:43 AM

Tom made an interesting observation that I can't find again. There is so much to read, I lost it. going back to his parent child swing analogy, he emphasizes the correct timing of the push. I think it would be a mistake ( not Tom's) to assume that the place where that push occurrs in the reed's cycle is the same regardless of amplitude. It might occur in the same, or close to the same part of the reed's cycle relative to when the reed has come to the top of the swing and is about to start over again, moving farther out of the reed opening as the reed's amplitude increases, just as a parent must move farther back to apply the push to the swing as the child goes higher and higher.
I have tried the strobe thing years ago, but not on a starting reed, since strobes only freeze regular motion. I did find it interesting that the smoke flow was so incredibly smooth regardless of where the reed was in its cycle, like water running down a drain. I couldn't see any turbulence, though that may simply have been an artifact of the strobe. Still , you would expect it on the back side of the reed during the upswing, or at least eddies coming from both edges of the reed similar to the ones that form when you put a flat stick in moviing water. Even though this would be drag on the reed on the upswing, it may need to cease before whatever it is that provides the push can reestablish itself.
Tom sent me a link years ago as a result of a similar conversation where he patiently and clearly explained his thinking, allowing me to understand rather than simply accept my own errors. The link was to experiments of some French scientists with a "water reed". Worth looking into if you don't mind more of the math. ( search ancient threads on reeds )
Regarding the initiation of reed vibration, I did do an experiment near 20 years ago that I found had interesting results. I set my oscilliscope to trigger juat at the start of vibration, and found an interesting image of what was going on. The trace started as aslowly increasing sine wave (from zero) for about 5 or six cyles at very low amplitude. then it increased in amplitude in the next 5-10 cycles dramatically, nearly abrubtly. This seemed to say to me that the initial forces involved were quite weak, especially as the initial tension resulting from the deflection is very small. I Think the reed's inertia washes out given that it is per cycle, and is already accounted for in the period of the reed a little like weight doesn't matter in a pendulum, only length when it comes to period. Anyway, the reed needed to reach a certain amount of deflection before the push force really kicked in.
What this makes me think is that the inital set or starting gap of the reed serves a dual role. first, it begins to build up tension in the reed before it reaches the point where the air flow is more or less cut off, enough to allow it to swing back against the air flow. Second, it biases the reed enough to the top side that it can take advantage of an increading push force that can't establish itself when the reed is nearly shut. REed amkers and repairers will know that a reed's set is a compromise between a set low enough to start at very low pressure, but high enough to beable to reach the reed's full volume potential. A low set reed may start easily but will be quiet. A high set reed may be slow to start and need more pressure to get going, but will reach an much higher final amplitude. Reeds set too low can't return aagainst the bellows pressure and cholke or refuse to start at all. The starting transient curve looked like a trumpet bell, just to give you some idea of how fast it was. The reed itself showed no irregular motion in its starting.
Reeds driven by air flow don't behave the same as reeds driven by other means of inducing oscillation, ( sound waves for instance ). They behave in acoustic ways that aren't always easy to visualize as a simple physical system. They can't be isolated from their surroundings and still operate even close to the way they do in actual use. In an oboe reed, the reflected pressure wave from the open end of the bore is what reopens the closed double reed. Who'da thunk it, certainly not obvious. Reeds will operate with an infinite chamber ( no chamber ) on either side. but at a much lower amplitude than with a chamber of appropriate size range. They are not simple things in action. A theoretical understanding can help tease out problems, but The theory for how reeds work as much as there is one, is so little developed compared to the complexities of practical operation as to be nearly useless to the maker. Thought experiments here, generally fall so far short of reality as to be more likely to lead you away from the truth as towards it. I have had so many hypotheses shot down by practical experiment ( And some by Tom who saved me the work ), that I hardly tend to waste my time with them anymore. Experiments get results so much faster in this field. I made a reed like the one originally proposed here 20 yars ago. couldn't get it to work at all. Does that mean it doesn't work, or that I never found the exact perameters needed. Who knows? But the curreent design works really well, Other working designs I've tried did make a sound, but they were far inferior to the normal version. None had enough promise to persue. They looked good on paper. Some human endeavors have been advanced greatly by science, others have been advanced by trial and error. In the end you have to try things, not just think about them.

#47 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 14 February 2015 - 11:44 AM

Well, as I'm more of an experimental than theoretical person, I have just performed a very quick and simple experiment which you can easily reproduce and which I think proove my approach definitively: I've taken my largest reed (the same I've mentioned earlier, which was choking under typical bellows pressure) and a drinking straw (flattened at the end to improve selectiveness of the jet produced), pointed it at the gap (*) and I blew hardest I could. I did manage to start the reed vibration and got a low volume sound. I was holding the reed in my hand in the ambient air, so there was no perpendicular pressure force on the tongue other than resulting from the jet of fast moving air and those two phenomenons I've mentioned eariler (or some additional turbulent effects on the bottom side of the tongue).

 

(*) you have to hold the straw end with your fingernail very close to the gap and tongue.

 

 



#48 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 14 February 2015 - 03:14 PM

@Dana: your observation may sugest that after those 5-6 cycles the mechanism I seek gives way to the direct acting of the high pressure on the entire area of the tongue pushing it through the shoe. This is also why I was only able to get the reed oscilating above the shoe with the straw blow, getting only a low volume sound.



#49 ttonon

ttonon

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 182 posts
  • Gender:Male
  • Location:New Jersey, USA

Posted 14 February 2015 - 05:28 PM

Hi Dana, it’s always a pleasure to read your posts.  I do think that the kick the tongue gets because of bellows pressure is applied at about the same place in its motion, when moving downward, and that location is when it first enters the slot, because then, the maximum pressure difference always delivers its maximum force, (P1 – P2)*A.  There may be an exception to this if, just before entering the slot, jets form in the small spaces between tongue and reed plate.  With these jets, the pressure on the bottom surface of the tongue will be P2 (as it is when the tongue first enters the slot), producing the same maximum force. 

 

I agree with Lucasz in suggesting that the sudden increase in vibration amplitude you observed during the start transient begins when the tongue is in the positions I mention in the above paragraph.  In fact, I observed this very same thing – or at least, that’s what it appeared to be - when I was looking at the start transientt many years ago, while closely controlling the magnitude of blowing pressure.  It’s amazing how much one can lose track of, until reminded. 

 

With all this discussion, my own conclusions on how the tongue starts vibrating, I think, are a bit clearer.  I would suggest the following.  The very first motion is a small vibration just above the slot, and this motion is inherently unsteady, enabled probably by periodic shredding of eddies and vortices off the bottom surface of the tongue.  I don’t understand the details there, nor why the amplitude of this vibration increases until the tongue enters the slot.  Nevertheless, when the tongue just enters the slot (or a little before, if jets are formed), the tongue experiences the maximum pressure difference, (P1 – P2).  Before this entrance, inertial effects of the oscillatory air motion around the tip of the tongue keeps the pressure on the lower surface of the reed just a little under P1, not all the way down to P2.  With this sudden increase in pressure force, the vibration rapidly builds up to a maximum, where the energy input balances aerodynamic losses and acoustic energy that radiates outward.  Thus the tongue position at the top of the slot is most important, from the standpoint of energy addition.  As the tongue travels further into the slot, the tip of the tongue moves away from the wall of the slot and eventually a jet forms below the tongue.  With this jet, air flows over the top surface of the tongue, and the pressure on that top surface becomes (from Bernoulli) less than P1, reducing the net pressure force on the tongue.  Tapered slots will enhance this latter process.  Thus, the maximum pressure force is applied for only a short instance in the swing cycle, and it is always in the direction of the moving tongue, which means this energy input is balaced by energy losses and periodic motion is achieved. 

 

I do recall our very interesting discussion of the paper by Ricot, et al., and I also recommend others who are so interested in these topics to seek it out.  If anyone has problems finding it, I can provide a link.  One major experimental finding in that paper (and I believe what you also observed in your smoke experiments) is that jets are formed for most of the time that the tongue is near and inside the slot.  Relating to the discussion here, this means that the quasi-steady assumption should be pretty good for vibrating tongues that operate below some maximum frequency. 

 

Best regards,

Tom



#50 Dana Johnson

Dana Johnson

    Heavyweight Boxer

  • Members
  • PipPipPipPipPip
  • 662 posts

Posted 14 February 2015 - 06:09 PM

That does seem clearer, and also blends with Lukasz's experiment. I really had no idea in which part of the swing the increased force occurred, only that the amplitude need to reach a certain amount. It makes more sense to be when the reed closes the window. That has the relatively abrupt change in reed conditions I seemed to see in the trace. It had to be at a point where the return force or its momentum generated was sufficient, which I still would guess is due to the initial bias the set provides. Simply entering the window isn't enough, since a low set reed that chokes enters the window but doesn't come back up. Likewise a high set reed needs lots of Lukasz's straw to begin to enter the window.
One thing I am not clear on is the relative velocity of the reed tip to the air stream. It seems for all but low reeds and or high playing pressures, the reed tip velocity likely exceeds the unimpeded air flow velocity through the gap. If this is the case, the reed doesn't block the downward air flow at all, but pulls it on through. I could figure out the reed tip velocity, but don't know how to work out the air stream velocity. If this is the case, what happens then? Or does the reed tip never exceed the air velocity. ( amplitude always increases to match the feed tip to the air speed)?
Dana

Edited by Dana Johnson, 14 February 2015 - 06:11 PM.


#51 rlgph

rlgph

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 109 posts
  • Gender:Male
  • Location:Western North Carolina

Posted 14 February 2015 - 11:57 PM

1.

The criterion that determines whether or not a fluid flow is incompressible, in steady state, is that the square of the Mach number be much less than unity, M^2 << 1, or M less than about 0.3.  When this is the case, all the terms arising from compressibility can be omitted, and one can still calculate with good accuracy.  For air at ambient conditions, this translates to an air velocity less than about 325 ft/sec.  From the Bernoulli equation, for air, a pressure difference of about 24 inches water column will produce such a flow velocity.  Most accordion and concertina bellows pressures are less than about 10 inches water column.  Thus, the airflow through a free reed can be considered incompressible. 

 

2.

It’s odd that you would say that we cannot consider the higher pressure region to be incompressible, when you do proceed to consider the lower pressure region incompressible.  The two regions are intimately connected, differing only (dynamically speaking) by a very small pressure difference. 

 

3.

The Bernoulli equation you wrote, P2 = p2 + 1/2 rho*v^2 is incorrect.  It purports to calculate an air velocity without acknowledging the pressure difference that causes it.  The correct equation is P1 – P2 = 0.5*rho*v^2.  And again, the ordering of pressure magnitudes that you write is incorrect. 

 

Tom,

 

I've numbered the comments of your post that i'd like to address above.  For simplicity, in what i say below i'm considering the beginning of the operation of a conventional reed, when the air has started flowing but the tongue has not begun to move with any significant velocity.  (The relative masses of the tongue compared to air molecules insures this approximation.)

 

1.  The moving air will have (in addition to its randomly-directed molecular velocities) a drift (or flow) velocity.  This drift velocity is of course not constant at different points above the top of the tongue, but before collision with the tongue, the air's drift velocity will have a downward component.)  Some of this air will collide with the tongue, causing a downward force on the tongue in excess of the force that would occur in the absence of this air flow (i.e., P1*A).  The magnitude of the force in the presence of the air flow is thus greater than P1*A, so the dynamic pressure (p1) at any point on the top surface of the tongue that is struck by air with a non-zero drift velocity will have p1 > P1.  This is the prediction of Newtonian dynamics, in contradiction to what you find by appying the simple form for Bernoulli's equation.  My conclusion is that the simple form of Bernoulli's equation that you have used cannot be true in this region.  I think that the reason is that the air near the top surface of the tongue is significantly denser than the average density at other locations; that is, the incompressibility assumption is invalid.

 

Lukasz's experiment with the straw is consistent with the Newtonian prediction, since unless the flattened end of the straw is below the end of the tongue, some of the air will strike the top surface of the tongue.

 

 

2.  I do not know whether the simple form of Bernoulli's equation is true just below the tongue.  However, the excess collisional affects that occur on the top of the tongue do not occur on the bottom because the vertical component of the drift velocity is either zero or generally away from the tongue, particularly if we look at the region significantly distant from the complicated air movement at the free end.  Since i can see no reason to say otherwise, i accepted your statement that the simple form for Bernoulli's equation is approximately correct in this region.

 

 

3.  On the contrary, I have correctly applied Bernoulli's equation (provided the condition for using the simple form is valid).  As you have noted, the simple form for Bernoulli's equation states that p + 1/2 rho*v^2 = constant for any points along a streamline.  I applied the equation at two points -- one immediately below the fixed end of the tongue (call it a)  and the other at some intermediate point along the tongue, but immediately below it (B). Thus, p_a + 1/2 rho*v_a^2 = p_b + 1/2 rho*v_b^2.  My only additional assumption was that directly under the fixed end of the tongue the air is approximately static so that p_a = P2 and v_a = 0.  The result is the equation that i wrote down, which indicates that p2 < P2.

 

Incidently, this results in a prediction that can be tested empirically:  Air flow directly under the tongue before the tongue has begun to move should be from left to right, at least at some distance from the free end of the tongue.  In testing this, keep in mind that you need to follow the air close to, but under the tongue and well away from the complicated air flow at the free end of the tongue.  If it does not flow from left to right in this region, either my assumption that the air is nearly static at the left end is wrong, or the simple form for Bernoulli's equation does not apply.

 

 

 

BTW, if you prefer to call me by my name, rather than the obscure username of rlgph, it's Ron.  (Sorry for not letting you guys know earlier.)



#52 rlgph

rlgph

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 109 posts
  • Gender:Male
  • Location:Western North Carolina

Posted 15 February 2015 - 12:06 AM

This cause and effect are well understood here. The inefficiency of the reed with wider clearances brings its own problems ie. the need for more force to create the same volume and slower response. Retaining the close clearances and having a more mellow sound is where the game is.


I am not suggesting a reed with wider clearances in general, only at the top edges. The width over most of the slot depth is the same.

#53 Chris Ghent

Chris Ghent

    Heavyweight Boxer

  • Members
  • PipPipPipPipPip
  • 1054 posts
  • Gender:Male
  • Location:Blue Mountains NSW

Posted 15 February 2015 - 05:08 AM

This cause and effect are well understood here. The inefficiency of the reed with wider clearances brings its own problems ie. the need for more force to create the same volume and slower response. Retaining the close clearances and having a more mellow sound is where the game is.


I am not suggesting a reed with wider clearances in general, only at the top edges. The width over most of the slot depth is the same.
I was mystified by your comment until I have looked back through your posting history; I now realise you might never have come across a real concertina reed.

Briefly, there are three common types of reed assembly used in concertinas, traditional reeds, as used in almost every English built concertina, accordion reeds used in hybrid concertinas, and what I term semi-hybrid reeds which have the geometry of accordion reeds but the outward appearance of traditional reeds.

Concertina reeds are only tight at the top, the reed window is relieved underneath, an important part of producing the concertina sound. Accordion reeds have relatively vertical walls in the frame and it is easy to imagine the clearance will be small throughout the downward swing but the reed itself is usually tapered which means as it travels down through the frame window it effectively shortens and increases the clearance. Filing the top edge of either type will decrease the efficiency of the reed.

#54 Łukasz Martynowicz

Łukasz Martynowicz

    Chatty concertinist

  • Members
  • PipPipPipPip
  • 374 posts
  • Gender:Male
  • Location:Poland

Posted 15 February 2015 - 07:55 AM

 

Lukasz's experiment with the straw is consistent with the Newtonian prediction, since unless the flattened end of the straw is below the end of the tongue, some of the air will strike the top surface of the tongue.

 

 

Ron, the whole point of me performing this experiment on the largest reed I have was to try to apply the flow ONLY below to the gap. This reed has a gap of about 1 mm height and tongue thickness at the edge of about 0.5 mm so you can easily flatten the straw below this width.

I have performed this experiment once again, this time with bent straw and a lens, so I could observe reed behaviour a bit more precisely. This time I was varying the straw crossection height and here are some additional observations (the bottom edge of the straw is always touching the shoe):

 

- if the straw height is less than the gap height the reed does nothing.

- when the straw height reaches the combined height of the gap plus the tongue thickness (probably exceding it a tiny bit), the reed starts to vibrate.

- when the straw height exceeds this combined height by a certain amount (but is still lower than double the gap height plus tongue thickness) the reed does not speak (at least not at a highest blow strenght I could achieve) - the assymetry of the flow is to small to propel the tongue.

 

After this experiment my current intuition is that the only part of the reed that is responsible for the ability of the reed to start vibration is the "double V" (*) shaped section just at the tip of the reed and edge of the shoe and the Venturi effect at this small section, combined with bifurcation in the flow caused by the even slightest movement of the tip, deflecting the flow to the upper or lower surface of the tongue. Due to spring forces and tongue momentum this will be an increasing effect.

 

One other thought: until this point we have assumed, that the axis of oscilation is always the same. But I think that it may be false assumption. I think that when the tongue is swinging enough to touch the surface of the shoe and close the gap completely, the pressure acting on the whole tongue surface moves the axis of vibration downwards. And because the pressure acts on the entire surface of the tongue and the initial mechanism acts only on the tip of the tongue, there will be some "wobbliness" in the tongue at this very point - it won't just bend at the mounting pivot point, but also around the center of percussion of the tongue. Think of it: this sudden axis change when the pressure gives the tongue "a kick" occures at the lowest point of the the already established oscilation but is not instantaneous, so the tip is already moving  upwards in relation to center of percussion. So when the pressure pushes the tongue as far as it can (and we know from "choking" reed behavior that this is not a lot further than the thickness of the tongue) the initial oscilation, (this time around this new axis) opens the flow on the bottom, the pressure force acting on the tongue drops and the whole oscilating tongue axis moves upwards again. With few further cycles this initial oscilation wears off because the initial mechanism of bifurcation is no longer present (or significant) and the steady oscilation around the mounting point is established without any significant oscilation around the center of percussion. 

 

(*) "the double V" shape I think of is the crosssection shape at a tip, because the tongue and shoe are not infinitesimaly thin.






0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users