Modeling PCP Valve Lift and Dwell
Steve in NC inspired me to make up a simple spreadsheet to do this.... The numbers mean nothing, they are just relative to one another.... The basis is the two equations he recently published on the Green....
Quote:
From Steve in NC:
Dwell time = 2 x hammer momentum / closing force.
Lift = hammer kinetic energy / closing force.
Note that, in both eqn's, the relevant numbers for energy and momentum relate to what's left of the hammer's original velocity, after the work has been done that's required to lift the valve head off the seat (i.e., "crack" the valve) against the force of static pressure multiplied by the elasticity (i.e., "give") of the stem and seat.
First, the relationship of Lift and Dwell to Mass and Velocity....
http://i378.photobucket.com/albums/o...ps2fe4f599.jpg
Blue line is Mass M and Velocity V.... baseline....
Red line is double the Mass, original Velocity.... Doubles the Energy and Momentum.... Doubles the Lift and Dwell.... 4 times the area under the curve....
Black line is the original Mass, double the Velocity.... Four times the Energy and Lift.... Twice the Momentum and Dwell.... 8 times the area under the curve....
Green line has the same ENERGY (and therefore Lift) as the red line, but the original hammer Mass.... This is what happens (comparing the red and green lines) if you leave the hammer spring and travel alone, and change the weight.... The Momentum (and hence the dwell) change by the square root of the change in Mass.... Half the Mass, 70.7% of the Momentum (and dwell).... Twice the Mass, 1.414 times the Momentum (and dwell)....
Now for the second part.... what happens when you leave the hammer strike alone (same weight, travel, spring and preload) and change the pressure inside the valve.... I used a pressure at the beginning of the string of twice what it was at the end, and I neglected the valve spring and drag around the poppet.... The closing Force I used, is therefore 100% at the beginning, 75% in the middle, and 50% at the end of the string.... That should be pretty close for the main closing force, which is the air pressure working on the Stem area....
http://i378.photobucket.com/albums/o...ps214bd75a.jpg
So, as far as the Lift and Dwell go, they should be twice as great at the end of the string as at the beginning (as observed, how about that!).... In the middle of the string (or more properly at mid-pressure) they are both almost exactly 2/3rds of the maximum (pretty close to what I have observed).... The area under the curves is in the ratio of 1 : 1.78 : 4.... So, you might reason that is also the amount of flow through the valve, right?.... WRONG !!!
Notice the black horizontal line on the graph?.... I conveniently chose a value equal to the lift at high pressure.... The reason I did that is that once you open a poppet valve to 1/4 the diameter of the throat, the area (and in theory the flow rate) no longer increases.... This is because the "curtain area" (perimeter area under the seat) equals the area of the throat at 1/4 lift....
Curtain Area = Circumference times Lift = Diameter times PI times Lift....
Throat Area = Radius squared times PI = Diameter squared times PI over 4....
for Lift = Diameter/4, Curtain Area = Diameter squared times PI over 4.... same value as the Throat Area....
For a stock Disco valve, where the throat is 7/32" (0.219"), once it opens 0.055" the flow rate won't increase.... That's close enough to the actual lift measured for our purposes.... So, in practical terms, you can ignore what the valve is doing when it is above that black line.... That extra Lift is only adding Dwell, not Flow Rate.... The "curtain area limit" is "clipping" the flow rate through the valve.... To put it another way, for a typical PCP, while the lift and dwell both increase as the pressure drops, because of "clipping" the additional Lift has little or no direct effect on the volume of air released.... However, the Dwell (which also increases as the pressure drops) DOES increase the volume of air delivered.... From my chicken scratches about 2.8 times as much volume of air (at half the pressure) flows through the valve at the end of the string as at the beginning.... In barCC, it should amount to about 1.4 times, or in other words the efficiency should drop to about 70% at the end of the string of what it was at the beginning.... just from that effect alone....
Possible sources of error in the above?.... Well first of all, it is based on the RESIDUAL energy left over after cracking the valve off the seat.... As we know, when the pressure drops, less energy will be lost there, so the Lift and Dwell should increase even more IF there is a 50% pressure drop during the string.... However, not many PCPs can manage that, it is closer to 40% of the fill pressure, sometimes less.... so maybe a wash?.... Next, it ignores the additional closing forces from the valve spring, and from air friction / pressure differential across the head of the poppet.... and how that changes when the poppet is close to the seat.... Those are likely the major problems with trying to quantify what is happening, which is why I used "generic" numbers.... All I am attempting to do is allow you (and me) to visualize what is happening to valve lift and dwell (and ultimately flow rate and volume) as the major variables are changed....
Bob
