Valve Dwell, Lift, and Total Flow

[rsterne]

I've been giving some thought to what might be happening in our PCPs.... specifically what increasing the hammer strike, and therefore the lift and the dwell does to the amount of flow.... A while back I posted this drawing about what might be happening to the amount of flow through a valve as we increase hammer strike.... I used as an example a Sine wave, as follows:



I was basically saying that as we hit the valve harder, increasing the lift, we are also increasing the dwell.... I think everyone pretty much agrees with that.... The smallest curve above has lift "x" and dwell "y", and the area under the curve, which represents the amount of air flowed, is area "A".... The next curve has x and y increased by 41%, and the area doubles.... The largest curve has a lift of "2x", a dwell of "2y", and an area of "4A".... If the flow rate was proportional to the lift, those are probably a reasonable indication of what happens....

However, with a poppet valve, once the lift is 1/4 the diameter, the limiting factor to flow becomes the throat diameter of the valve, not the "curtain area" between the head and the seat.... If you lift the valve more than that, the dwell still increases, because the valve head is lifting further and taking more time to peak and return to the seat.... However, the flow is "clipped" at a maximum value when the lift is really quite low, on the order of 1/16" on a 1/4" diameter valve.... Therefore, I propose the following diagram to cover that situation....



For clarity, I chose to make the limiting lift "x" (ie the valve diameter was "4x").... During the period of time when the valve is open "x" distance or more, the flow is at maximum rate.... represented by the straight line at that height.... You can see that some of the middle curve is missing, leaving the total flow area maybe "1.6 A" instead of "2 A".... With the largest curve.... a very large part of it is missing.... It no longer has an area of "4 A", but something of around "2.4 A".... Not only that, but the waveform is beginning to approach our ideal "square wave" that we "think" might be better.... The valve opening sharply, holding during all of its dwell, and then closing abruptly....

I suggest that perhaps we should be thinking of the flow RATE through our valves as "clipped" by the diameter.... and therefore the total VOLUME flowed through the valve is more in direct proportion to the dwell than to the square of the dwell as I suggested previously....

Bob

[ericw]

There is another big factor in there too.  The flow rate is directly proportional to the square root of the pressure differential across the valve and directly proportional to the effective area of the opening.  That is during the time when the valve is operating with reynolds number >= the critical reynolds number which is valve design dependent.  For Re< Re critical it is directly proportional to both area and pressure difference (no square root).  So, I believe your graph would have some drop off in the clipped region plus some ripples due to the pressure shock wave leaving the valve and bouncing to and from the load end (the pellet).  The missing information to be able to accurately graph what it looks like includes stuff like the critical reynolds number (where laminar goes to turbulent flow) and a flow discharge coefficient which which are valve design dependent.   The discharge coef.   basically just scales things up and down (kind of like a valve efficiency number).    I like your thinking on this and by taking it further I bet an end to end theoretical solution can be done that matches closely with the experimental results.   Figuring out what the valve exit pressure profile looks like would be a next step. 
Thanks for the post, interesting stuff.

[PakProtector]

So for a valve like the marauder uses, the lift of ~.15" is giving us performance in the 'clipped' regime, and we lift it so high( OTO dia/2 ) in order to increase dwell. Seems like an increase in diameter would both increase power and efficiency( due to reduction of the pulse bubble length at a given flowed volume).
cheers,
Douglas

[rsterne]

Seems like an increase in diameter would both increase power and efficiency (due to reduction of the pulse bubble length at a given flowed volume).

Exactly, Douglas.... Keep the area under the curve the same, shorten the curve and make it higher.... The downside is the hammer striking force to open the valve goes up by the square of the diameter.... You remember Lloyd's spreadsheet I keep referring to?.... It has an "Efficiency factor" that must be adjusted and coordinated with the dwell to make the output match reality (ie known test results).... Generally, as we increase port sizes the efficiency increases.... ie the FPE/CI goes up for a given pressure and dwell.... or for a given FPE you can reduce the dwell and/or pressure required to produce it.... The limiting factor would, in general terms, be the bore size.... and related pellet loading considerations....

ericw.... RE your comments regarding precise modelling of the flow, that was never my intention.... You are correct that the factors you mention would need to be considered, as well as the possibility of transonic/supersonic flow in what might be (ideally) a convergent/divergent nozzle system (like a rocket nozzle).... That is wayyyyyyyyyy beyond my ability, and likely most of the others here on the Forum, and as you say, is case specific.... I am trying to generate lines of thinking and comments such as Douglas' above.... hopefully simple, effective solutions applicable in general terms.... We have to walk before we can run.... In my case, pretty much stumble.... *grin*

Bob

[Motorhead]

While I follow the MECHANICS real well, the Physics & Math parts of all this loses me pretty quickly 
Case in point being somewhat surprised with my current M-rod hammer experiment that with Nothing changed other than a hammer HALF the weight still operates valve so close to the OEM heavier hammer it kind of stumps me WHY such a heavy hammer is there in the first place ?

Always Very interesting reading never the less while the brain pool here at GTA continually scratches the heads wondering WHY 

[Rescue35]

While I follow the MECHANICS real well, the Physics & Math parts of all this loses me pretty quickly 
Case in point being somewhat surprised with my current M-rod hammer experiment that with Nothing changed other than a hammer HALF the weight still operates valve so close to the OEM heavier hammer it kind of stumps me WHY such a heavy hammer is there in the first place ?

Always Very interesting reading never the less while the brain pool here at GTA continually scratches the heads wondering WHY 

Similar to me making a hammer that is 50% heavier and only getting a 1.5% increase in FPS.

I have a feeling fluid dynamics has more to do with it than mass/inertia. time to dust off some books.

[rsterne]

Similar to me making a hammer that is 50% heavier and only getting a 1.5% increase in FPS.

If you already had the valve closing when the pellet had travelled more than half the length of the barrel, that is pretty much on the money.... In addition, if you didn't change the hammer spring preload, you didn't change the hammer energy by installing a heavier hammer.... only the momentum.... If the hammer strike was pretty much sufficient to do the job with the lighter hammer, even doubling the weight may make no difference....

Bob