dynamic modeling of a strip valve

[Graham C. Williams]

Dear Forrest.
I'm sorry for this stupid question but this work is important (at least to me)!
Using Your Graph for w/wn=0.3 as an example and telling you that the colours for p12 and Theta are similar on my monitor.
Is the Lower of the two lines the Reed action and the upper the Pressure drop or is it the other way around (as it appears to me)?
Either way there appears to be a time difference between the pressure drop going to zero and the reed closing. In this example that time is small but in the case of w/wn = 0.4 it seems extreme.
Why the lag; is it a result of the inertia of the gas? I can see this may be the case when opening but when closing should the function become discontinuous?

Regards
Graham.

[WebPilot]

Using Your Graph for w/wn=0.3 as an example and telling you that the colours for p12 and Theta are similar on my monitor.
Is the Lower of the two lines the Reed action and the upper the Pressure drop or is it the other way around (as it appears to me)?

You need to adjust your monitor/graphics card settings. The lower is the valve's theta value [html #C000FF] and the upper is p12 [html #0080FF].

Either way there appears to be a time difference between the pressure drop going to zero and the reed closing. In this example that time is small but in the case of w/wn = 0.4 it seems extreme.
Why the lag; is it a result of the inertia of the gas? I can see this may be the case when opening but when closing should the function become discontinuous?

Actually the pressure drop going to zero leads the closing of the valve. I don't understand your use of the word, discontinuous, here, but that doesn't matter. It's probably due to your color confusion.

The explanation is simple, if you understand elementary circuit theory. The flow resistances here are not equal. The same current (in this case, flow) travels through both resistances in a series circuit.

The voltage (pressure) drop is greatest across the higher resistance, Vdrop = I × R . You knew that.

The strip valve 'lifting' from its seat is a variable flow resistance as I've drawn in my analogous circuit diagram, found on page 1 of this thread.

Continuing ...

I wanted to post these, to complete my display for this model.


View entire image

After counting the 'humps and bumps', it looks like I should have included another one between these two.


View entire image

As I posted in the last model, the strip wiggling may not be good from an engineering point of view. It subjects the valve to an increase in the number of 'cyclic stresses' in the valve material. If that stress exceeds the endurance limit of the material, the valve will only withstand a certain (statistically determined) number of cycles before failure.

It is one more thing for the designer to determine.

[larry cottrill]

Forrest -

Are you going to look at whether (and if so, how much) the valve bounces back off the valve seat?

"They always want more ... " - Roger Otis, electrical engineer / programmer

L Cottrill

[WebPilot]

L.,

I have included this capability in my numerical model and can turn it back on with a simple edit and recompile. However, I have elected not to discuss 'valve bounce' at this juncture of the thread.

I am trying to keep the model simple; thus, making it far easier for the reader to digest what I have to say.

[WebPilot]

On my reference thread, Mode 1/0 , I posted this 77 quadrilateral finite element model of the DynaJet petal valve.



The driving vibrational frequency (wd) of a DynaJet is 200 Hz. The dfr for each of the modes is:

1. wd/w1 = 0.8097
2. wd/w2 = 0.1765
3. wd/w3 = 0.1076

All of these will make contributions to the final response of the vibrating petal valve, with Mode 0/0 (or wd/w1) dominating, of course.

What I am not happy with is the number 0.8097. It is far greater than 0.59, my magic number for driving frequency ratio. I have shown any dfr greater than this and the valve is open when it should not be, and being burnt. This and the fact that higher vibrational amplitude magnifications occur in dfr's approaching 1, causing higher stresses in the root area of the valve, resulting in a shorter 'fatigue' life.

With the success of Grim and his G59er, see his thread, External Valve Grid, I am reluctant to believe there is a serious problem in my dynamic model of a strip valve.

I suspect the problem is in the modeling of a DynaJet petal valve. I have not included the effect of the backing plate (valve retainer). The strip is vibrating between a "rock and a hard place" and is thrashing itself to death twice as fast as one without.

If the 'bouncing' provides a higher average speed over one cycle for the valve, then the time for one cycle will diminish. This will result in a higher valve frequency, sending the dfr down. Of course, this is presently just 'wishful thinking'. (editor's note: more complications and I am trying to keep the model simple?.)

So, a backing plate feature needs to be added to my dynamic strip model in order to analyze properly, DynaJet type valves.

[larry cottrill]

I have not included the effect of the backing plate (valve retainer). The strip is vibrating between a "rock and a hard place" and is thrashing itself to death twice as fast as one without.

However, I (and Jerry, I think) believe this is not as bad as you make it sound. The action is meant to be a "rolling out" onto the retainer's curved surface (not a spherical segment, but a circular-ended oval rotated around a central axis). It may be between a rock and a hard place, but the hard place is designed to cushion the blow as effectively as possible. Of course, it could be argued that the desired action can't actually happen as predicted, but that is another road.

Essentially, the valve petal is never allowed to vibrate freely around its "root". As soon as it opens even slightly, the "fulcrum" point moves farther out, and this (theoretically) continues throughout the valve travel. The free section of the valve is shortened (and stiffened!) throughout its entire range of motion. The incredible smoothness and uniformity of this effect on the standard (factory) valve is attested to by the wear pattern on the back side (I wish I had a photo of that, but sadly, I don't -- the front of the valve shows an elliptical track corresponding to the valve port; the rear face show a long T-shaped track where it contacts the curved retainer surface and the retainer edge).

My old not-to-scale drawing shows the action, in admittedly exaggerated form. The little moving black arrow shows the point delimiting the "free" part of the valve. Going from bottom to top (the direction I intended), the free end of the valve is gradually shortened, and the stiffness increases due to the ever increasing width of the valve at the contact point.

L Cottrill

[Viv]

Interesting graphic Larry but one of the problems of that rolling out and shifting fulcrum point is the shortening of the reed and its effect on the frequency and mode of vibration as per Forrest's models, my own mind turns towards predicting the destructive modes and how to avoid them.

Viv

[larry cottrill]

... one of the problems of that rolling out and shifting fulcrum point is the shortening of the reed and its effect on the frequency and mode of vibration ...

That's exactly why I presented this originally.

... predicting the destructive modes and how to avoid them.

That's exactly why the retainer is shaped the way it is.

Of course it's useful to see what Forrest has done and learn from it. In some valve sets, like most of the ones salvaged from marine outboard engines, the retainer is a "crash stop" that the widest part of the valve slams into at whatever the designer wanted to be the maximum allowed deflection. In that mode, you're relying on the behavior that Forrest's calculations would suggest. But in the real Dynajet, the valve is not allowed to behave in that "wild" fashion. I'll bet Jerry would tell us that those valves lasted a lot fewer cycles before that domed retainer was devised and perfected.

The Dynajet retainer is not just a stop -- it is not even just a stop and a blast shield; it is also a bearing.

L Cottrill

[dynajetjerry]

Hi, Guys,

You've pulled my chain so I'll inject several comments.

I have no information on the various steps that led to the final design of the D-J valve retainer but can assure you that it incorporated a simple radius on the valve side, about 1.1 in., I think. That is NOT to say it is a spherical surface. The central 11/16 in. diameter of that surface is, as most of you know, flat, with the center of the 1.1 in. radii also being at that 11/16 position.

While trying to "soup up" my D-J, I machined many retainers of aluminum and, when many of them melted, stainless steel. Rather than trying to generate true radii, I chose to nibble at the retainers while they were in the lathe, using a standard cutter and various files. I would properly position a good valve against the retainer--whose outer edge had already been cut to the desired "lift"--and hold it with a valve head. Using a pencil (eraser end against the valve petal,) inserted through one of the ports, I pushed the petal against the retainer and carefully examined the contact between them. High spots acted a fulcrums that stressed the petals so I carefully filed or cut them lower. It sometimes required many, many such trimmings but eventually, the petal appeared to make contact with the retainer all the way to the outer edge, lifting off at no point. At that time, I would assemble and run the engine for a short period then dismantle and examine the petals and retainer. The markings on them would indicate the degree of contact between the petals and retainer and whether or not further trimming was advisable. Most of my efforts were successful but, as has been mentioned before, greater thrust led to much shorter valve life.

I must point out that the curve I generated in this way was not a radius or any mathematically-generated and repeatable shape. I don't know what it was but intended its radius to be smaller at the center and gradually increasing toward the edge of the retainer. This reduced stress where the petals were widest.

I have a few experimental retainer/valve sets that were evaluated at Aeromarine during their years of production but have no idea as to their exact shapes. Perhaps I'll make some measurements, sometime.

Jerry

[larry cottrill]

You've pulled my chain so I'll inject several comments.

Any time, Jerry, you can thank me later ;-)

I have no information on the various steps that led to the final design of the D-J valve retainer but can assure you that it incorporated a simple radius on the valve side, about 1.1 in., I think. That is NOT to say it is a spherical surface. The central 11/16 in. diameter of that surface is, as most of you know, flat, with the center of the 1.1 in. radii also being at that 11/16 position.

My wife says I am carried away with trivia, but this strikes me as a very important detail to understand. The surface of the retainer is NOT a sphere, and it is NOT a sphere with a flat spot ground onto it. Instead, a cross-section through the flat central zone is TANGENTIAL to the circular curve beyond it. The idea was obviously to avoid any concentration of stress on any point of the valve during its travel. This is the action I refer to as the "rolling out of the valve on the retainer", and it cannot happen properly without this tengential relationship between the flat and the curve of revolution beyond.

What you're implying next is that even a circular curve doesn't do that perfectly, because of the widening plan form of the valve petal; there are zones where the petal "lifts off" the curved surface of the standard retainer. You attempted to produce a better-contoured retainer that would act as a perfect bearing throughout the entire travel of the valve. Cool. A crude example of the "lift off" your talking about is shown in the topmost detail of my drawing, posted above.

I must point out that the curve I generated in this way was not a radius or any mathematically-generated and repeatable shape. I don't know what it was but intended its radius to be smaller at the center and gradually increasing toward the edge of the retainer. This reduced stress where the petals were widest.

Here I'll point out that you or I might not be able to mathematically generate the perfect curve, but Forrest (with his present state of knowledge of the valve petal) probably could. It would simply take a more complex incremental approach than you can use if you assume the valve bends starting at the root without restraint until it hits a stop.

I have a few experimental retainer/valve sets that were evaluated at Aeromarine during their years of production but have no idea as to their exact shapes. Perhaps I'll make some measurements, sometime.

Now, THAT would be fascinating, especially if Forrest would figure out the "ideal" curve for us and we could compare that with what you achieved on the lathe. One question: Did you actually try to achieve wider-open valving, and that's why thrust improved? Or did improved thrust just "come with the territory" as you worked out a smoother-bearing retainer?

L Cottrill

[WebPilot]

Geeze Louise. What have I started? Thanks for the input.

That's a very nice drawing, Larry, but ... I'm afraid I'm going to have to 'rain on your parade'.

The incredible smoothness and uniformity of this effect on the standard (factory) valve is attested to by the wear pattern on the back side (I wish I had a photo of that, but sadly, I don't -- the front of the valve shows an elliptical track corresponding to the valve port; the rear face show a long T-shaped track where it contacts the curved retainer surface and the retainer edge).

I don't have qualms about these "wear lines". Too bad you cannot come up with a picture. What I have qualms about is your interpretation of them.

Essentially, the valve petal is never allowed to vibrate freely around its "root". As soon as it opens even slightly, the "fulcrum" point moves farther out, and this (theoretically) continues throughout the valve travel. The free section of the valve is shortened (and stiffened!) throughout its entire range of motion.

Nonsense. You forgot the other face. One side of the valve is restrained but the other face is open to chamber pressure. Your supposed "fulcrum" isn't a moving 'clamp boundary'. That's the only way a valve could be shortened and thus stiffened.

The Dynajet retainer is not just a stop -- it is not even just a stop and a blast shield; it is also a bearing.

I'll agree it is a bearing surface/stop and partial blast shield, but no more.

I'll bet Jerry would tell us that those valves lasted a lot fewer cycles before that domed retainer was devised and perfected.

If the valve was designed to maintain its maximum cyclic stresses to BELOW the endurance limit of the material from which it was cut, you'll lose your bet!

I still maintain what I wrote before,

I have not included the effect of the backing plate (valve retainer). The strip is vibrating between a "rock and a hard place" and is thrashing itself to death twice as fast as one without.

Apparently Bruce and I have independently come up with the same conclusion. Check out the telling and dramatic pictures of failure for a petal valve on Bruce's site. They are cracking at the tip (high velocities and g forces due to decelerations) and at the root due to cyclic fatigue stresses.

Somewhere I saw a pic of a petal valve that cracked one of its petals in half lengthwise. The petal valve is subject to high velocities and g-forces as it thrashes between the stops. This is due to the petal valve 'wrapping' around the curvature of the stop as it crashes into it, the bending stresses cracking it along a 'grain' line.





I have some thoughts on the 'why of this stop' and may not have to alter my model as I first thought. That will have to wait since I am involved with determining the fundamental frequency of the Argus V-1 valve.

First results for that analysis is that the dfr for the Argus is only 0.3 and of course, the V-1 uses NO back stop!

[larry cottrill]

I have not included the effect of the backing plate (valve retainer). The strip is vibrating between a "rock and a hard place" and is thrashing itself to death twice as fast as one without.

Apparently Bruce and I have independently come up with the same conclusion. Check out the telling and dramatic pictures of failure for a petal valve on Bruce's site. They are cracking at the tip (high velocities and g forces due to decelerations) and at the root due to cyclic fatigue stresses.

Somewhere I saw a pic of a petal valve that cracked one of its petals in half lengthwise. The petal valve is subject to high velocities and g-forces as it thrashes between the stops. This is due to the petal valve 'wrapping' around the curvature of the stop as it crashes into it, the bending stresses cracking it along a 'grain' line.

Forrest, I'm not buying it. Bruce's example of fatigue failure does not picture a standard Dynajet valve, AND he does not claim that a standard Dynajet retainer was behind it! In my book, that picture is interesting, but bogus evidence when applied to the standard Dynajet.

Now, having said that, I admit that I HAVE seen a Dynajet valve (which I believed to be original) with cracks at the root, i.e. at the very deepest part of the interpetal notch. However, I have no idea as to whether the retainer was original. This would be cracking within the fully clamped zone, which should be utterly impossible, at least in terms of metal fatigue in the valve!

I have some thoughts on the 'why of this stop' and may not have to alter my model as I first thought. That will have to wait since I am involved with determining the fundamental frequency of the Argus V-1 valve.

Fair enough.

First results for that analysis is that the dfr for the Argus is only 0.3 and of course, the V-1 uses NO back stop!

True enough, of course. However, these valves lie in a 'streamlined' orientation. It is entirely possible that they never do open as fully as you could push them with a small tool, for example; i.e. they may be "self stopping" or it might be better to say that their motion may be constrained by fluid forces. They don't "crash" on the open side, they just "flap in the breeze" (not to be taken too literally. Ha).

L Cottrill

[dynajetjerry]

Larry,

My apologies for not answering your question of yesterday, so here goes.

I chose maximum lifts for the reed valve based on hoped-for increases in thrust over the as-mfd. Dyna-Jet valve retainer. They were approx. .015-.100 inches greater than stock and were developed by turning and filing the retainers on the lathe, then testing in a complete, gasoline-fueled D-J.

What I also failed to mention was that, for some, I deepened the slots between petals, permitting a smaller-than-stock flat on the valve surface of the retainer. This permitted a slightly greater lift of the petals while keeping stresses reasonably low. The stainless retainer I loaned to Ned Morris was for such a modified valve. Observing the poor match between that retainer and his stock reed valve, Ned sanded the retainer until the flat was near stock. Of course, this increased stress on the reeds because of the too-small radius at their roots. Even so, he was able to attain model speeds that were more than any others he had previously tried. He never told me how much, if any, his valve lives were reduced. In any case, he was very happy with the results. I still have that retainer, somewhere.

Being retired, I no longer have access to a machine shop and can't do much cobbling of my pulse-jets. When I win the Reader's Digest(TM) giveaway, maybe I'll rig up my own complete shop and resume playing with these noise-makers.

Jerry

[WebPilot]

At this point, considering everything else in the last few posts as extraneous to my thread topic ...

I have already admitted that my present strip model does NOT incorporate a backing plate. Thus, in its present form, it should not be used as a design guide for pulse jets equipped with such devices.

However, since you have brought to my attention as to how you think the said valve retainer operates, I have shot a big hole in your sliding fulcrum theory.

I wrote:

Essentially, the valve petal is never allowed to vibrate freely around its "root". As soon as it opens even slightly, the "fulcrum" point moves farther out, and this (theoretically) continues throughout the valve travel. The free section of the valve is shortened (and stiffened!) throughout its entire range of motion.

Nonsense. You forgot the other face. One side of the valve is restrained but the other face is open to chamber pressure. Your supposed "fulcrum" isn't a moving 'clamp boundary'. That's the only way a valve could be shortened and thus stiffened.

As an engineer, I am politely telling you, my friend, that you are 'barking up the wrong tree' and need a new theory.

If you fail to understand what I am trying to tell you (and the reader), then you (and the reader) need to brush up on your understanding of

1. engineering mechanics
2. vibration theory

[larry cottrill]

Well, of course, there is the slim, remote, outside chance that I'm just wrong again ...

(I mean, I guess it has happened ;-)

L Cottrill