dynamic modeling of a strip valve

[WebPilot]

I did this back in June of this year to see if something else I was working on made "physical sense". I was hoping it was not just mere science fiction.

It turns out that I found the result for which I was looking.

This is not the only way to do this; but it is A way.

The following is not for the mathematically "faint of heart" but towards the end of my presentation, I am sure you'll all find something to take away with you.

If there is interest, then I shall continue ...



(c.t.)

[Viv]

Hi Forrest

Looks interesting, you have to model a system to understand it and be able to design from it properly.

Viv

[WebPilot]

Hey Viv,

I agree. I was looking for something ... which was the reason for the model.



(c.t.)

[Viv]

Hi Forrest

I was just reading your criteria page and what leapt out at me was the question of what the hysteris loop of pressure to valve movement would look like

Viv

[WebPilot]

Hi Viv,

I didn't but could. Remind me at the end lest I forget.

continuing ...



(c.t.)

[Viv]

Hi Forrest

I love the electrical analogy, it reminds me strongly of a relaxation oscillator and if I remember correctly it was Larry who first put forward that particular circuit as an analogy, correct me if I am wrong Larry, it does strongly suggest (with your other post on valves) that there is a very narrow band of conditions were the combustor will operate.

Viv

[WebPilot]

Hi Viv,

Many years ago, I took an introductory course in System Dynamics and the crux of the course was to convert elements of various disciplines (heat transfer, mechanics, fluids, etc.) to electrical analogs. Why?

In the early days of computation, computers were of the analog type. To solve an equation one applied voltage to array of resistors, capacitors, inductors, diodes, and such and measured out a voltage, probably on an oscilloscope, for the solution. To obtain a solution to an equation from some other field of study than electrical/electronics, one had to properly transform his/her equation to an electrical analogy.

It was one of those things that had to be learned. It is just one more 'trick' in an engineer/scientist's tool bag. Kudos to Larry if he was the first to post. I hope he took the time to solve it, because I'd like to compare results.

Anyways, I solved this problem using a program I wrote for a digital computer. I still used Kirchoff's current and voltage laws in developing the governing equations, though.

[WebPilot]

It's tough picking up where one left off 3 months ago. I now realize I did not model the diode, so I've crossed it out here. I'll fix this image later.

[WebPilot]

click here to see image in its entirety:

Instead of boring you with all the details of the analysis, I have decided to show you some of the more interesting results.

Here is the response with a driving frequency ratio of 5.0. That is the pump is running at a speed 5 times faster than the resonant frequency of the valve strip.

COLOR CODES:

• Psource is the pressure differential generated by the pump or P13,
• p23 is the pressure across the port generated by the moving of the strip valve away from the valve plate and
• p12 is the pressure across the orifice through which air and fuel pass.

Where Psource and p23 'cut' the x-axis will show you the beginning/end of one cycle.

The period, tau, is 2 x pi / (w/wn)= 2 x 3.14 / (5) = 1.257 [no units]

The left y-axis depicts pressure; the right, theta in radians. Theta is the angle the strip valve makes with the vertical, +tive CW.

The purple curve depicts how the valve is moving over one cycle. Notice how small the amplitude is and worse still it is still OPEN when the chamber pressure turns +tive. See arrow.

The valve still hasn't quite closed at the end of the cycle so it leaks!

This valve is not 'stiff enough' for this application.

[WebPilot]

Click here to see image in its entirety.

• dfr is 1.0
• max valve amplitude from the valve plate is greater than when dfr was 5.0
• valve is still open for a time when chamber pressure is +tive but eventually closes before end of cycle (see arrow)
• dfr needs to be made smaller, still

[WebPilot]

Click here to see image in its entirety.

Particulars:
[*]dfr is 0.5
[*]it appears that the valve closes exactly at the end of the -tive portion of the cycle pressure (see arrow)
[*]max amplitude of theta is comparible to that found in dfr=1.0
[*]my problem with this valve is that the movement of the valve 'lags' the pressure across the orifice - in other words, at the end of the -tive portion of the cycle pressure, the valve is still open but the pressure, p12, across the orifice is rapidly approaching zero. UNSAT

[Ape]

This is propably a rather silly question, showing my complete lack of understanding of what you're trying to relate here, but, well, here goes ; How can dfr be >1?
What did I miss?

[WebPilot]

This is propably a rather silly question, showing my complete lack of understanding of what you're trying to relate here, but, well, here goes ; How can dfr be >1?
What did I miss?

Hi Ape,

No harm done in asking.

For the sake of illustration, let's assume my pump runs at 1800 rpm.

f = (1800 rev/min) / (60 sec/min) gives 30 rev/sec

During 1 rev the pump cycles 1 time so

f = 30 cycles/sec for the pump frequency

let fn = resonant frequency of the valve

I have defined driving frequency ratio as

dfr = w / wn = (2pi/2pi) x w / wn = f / fn

So, the dfr is dependent on the resonant frequency of the valve, fn

If fn = 10 cps, then dfr = 30/10 or 3.0

If fn = 30 cps, then dfr = 30/30 or 1.0

If fn = 60 cps, then dfr = 30/60 or 0.5, etc.

One way to change the fn of the valve is to vary its thickness.

CAUTION: I think the fn is proportional to the thickness raised to the 3rd power so it won't take much change in thickness to radically alter its value. IOW if you double the thickness, you will increase its resonant frequency by 8 times!

[Ape]

yes, that makes sense.. .. thinking about it, I realized I assumed cycles meant no flow, but pulses instead, and then just dismissed dfr>1 as an impossibility.
Cheers

p.s. I'm no good at math, but the graphs and your comments makes it almost understandable to me, and in spite of my expectations when you started this ( and the cybernetics), I have come to find it interesting. Just outta curiosity, exactly what do you mean by "a variable speed, reciprocating, positive displacement pump"? Not centrifugal, then, but a diaphagm? or did I get that one wrong as well?

[WebPilot]

Hi Ape,

Welcome aboard. I'm glad you're 'catching my drift'.

The pump I envisioned was more like a miniature air compressor pump working in reverse. When the piston comes down, a check valve stops the flow of air from the environment but another port allows air to be withdrawn from my 'valve box'. When the piston comes up, it pushes some air back into the box, but the majority gets pushed back into the atmosphere since that check valve now opens. A variable speed DC motor could be coupled to this small pump.

continuing my discussion



Click here to see image in its entirety.

Particulars:

• dfr is 0.3
• valve is still open during a portion of the +tive pressure regime (see arrow)
• the valve appears to oscillate 2 times to the pressure cycle's 1 time (this would shorten its lifetime due to an increase in likelihood of cyclic fatigue)
• I find this valve's behavior UNSATISFACTORY.