Quote:
Originally Posted by drmiller100
Right now, I don't think ANYONE has a good way to actually calculate the losses due to throttling.
Once you can calculate it, then you should be able to explain it.
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Hi drmiller100,
Interesting. I use this fact: the amount of power to pump past a restriction is the mass flow times the force. To make an estimate, I use the intake manifold pressure minus 1 atm, or measure the manifold vacuum and convert to psi as the force. I figure the mass flow by taking the fuel flow and multiply by the A/F. This is my back of the envelope formula, you can just about do it in your head. I've been accused of missing compressibility. I'll discuss that at the end.
You can compute the exact power to pump across a restriction, given the properties and operation of the engine in question.
HP = mass flow (corrected for compressibility) times force (corrected for compressibility) times conversion factors.
This can be computed from the displacement of the engine in cubic inches, the engine speed, and the absolute manifold pressure in psi, you get this:
HP = D * RPM * Pm * (k / k - 1) / (12 * 2) * ((Pa / Pm) ^ (k - 1 / k) - 1) * (1 / 33000)
Pa is 1 atm, 14.7 psi.
k is 1.41 for air (adiabatic index or ratio of specific heats)
That is (cu in) * rpm * (lb /sq in) * (compressibility correction) times (1 / inches per foot * revs per displacement) * pressure ratio ^ (compressibility correction) * units conversion
(ft lb / min) * (hp / (ft lb / min))
I have a Volvo 240 with the b23 engine. Disp = 140 cu in. At 750 rpm idle the manifold vacuum is 20 in hg = 9.8 psi
HP = (140 * 750 * 4.9 * 3.44 / 24) * ((14.7 / 4.9) ^ .29) - 1)) / 33000
Throttling HP = 0.838
Now you can calculate pumping power across the throttle.
You'll also notice this is almost the same formula given by the
air compressor page except that that page is for compressing 1 atm to higher pressure, and my formula sucks 1 atm in to a lower pressure.
In my back of the envelope formula I estimate mass from the A/F and fuel flow which automatically compensates for compressibility because it is the actual mass of air. Measured psi is the actual force. Notice in the exact formula that correcting the mass term for compressibility involves multiplying by (k / (k - 1)) and correcting the pressure ratio you raise the ratio to the power of (k - 1) / k)) and subtract 1. When the pressure ratio is 2.406 these factors cancel. That happens at manifold vacuum pressure of 6.1 psi. That's not far from the range of manifold vacuum for part throttle operation.
Note "Figure C-3 ...For flow rates less than about 60 percent of the choked flow, the effects of compressibility on the mass flow rate are less than 5 percent." Internal Combustion Engine Fundamentals - John Heywood
Heywood also has this graph, for his test engine: pumping is less than friction.
In that graph the 200 kPa bmep is about 11 HP, the pumping power is about 3 hp and the rubbing friction is over 5 HP
-mort