Yep, the plot thickens. Tom has chosen to ignore conv'l thermo, but not me. Here's an update on that last graphic for those who wonder what I'm babbling about. Only a rudimentary thermo knowledge is req'd, especially PV=nRT where I'll use PV=mT since R doesn't matter and I prefer m vs n, even tho I'll be using m to denote gas mass, not gas moles. OK, here's a detail of above expansion stage...
- hot PP detail.png (26.85 KiB) Viewed 561 times
This is same as previous graphic except that I've used cc for volume (vs v) and shrunk down those lofty pressure values. So, what's happening here ??? Let's continue with previous ideal assumptions where all dead volumes are zero (clearance, regen & conduits) and where DP and PP have separate dwells. During any isothermal expansion or compression, internal energy is constant, and internal energy is linear T. So, during B1-2 hot PP expansion, gas expands 1:2 (100cc>>>200cc) and isothermal input equals work output (ignoring charge vs buffer pressure issue). Meanwhile, during S1-2 cold PP expansion, gas expands 1:1.5 (100cc>>>150cc) thru regenerator. Note that during both expansions, the same gas flow occurs, but that the results are different. If we consider both PP identical except for B has 2x the area, we can easily conclude that B hot PP produced 2x the output of S cold PP.
The question is how much heat was used for B vs S, especially since there's no simple method to measure heating while expanding thru a regenerator like Cv and Cp heats. So far, all we know is that hot 100cc B PP produced 2x cold 50cc S PP, and that both 100cc DP had the same internal energy at B1 and S1 when both were 100cc, 600k and 6m (prior expansion). Some might suggest that B simply used more heat during expansion, but if B used 2x the heat during expansion than S, then S regenerator would have no heat to remove to allow cooling for cold S PP. So, even if we 'simply' calculated heat flows for B, how would we know heat flows for S ??? Hmmm, saved by thermo basics, again !!! Recall that internal energy is constant for any isothermal expansion or compression AND that internal energy is linear T, and we can easily deduce that each 3m gas flow req'd the same source input, but that S lost 1/2 this 'isothermal' input passing thru S regenerator.
This ratio will vary depending upon thermal cycle and volume ratios, but losing 50% during just expansion phase likely explains why SE never live up to expectations. As Fool, Nobody and others have noted, energy is path dependent...
BTW, both cycles have the same total gas flow thru regenerator, just a different sequence. Interestingly, S regen heat in this example equals 300-600k Cv heat (like alpha regen) despite massive PV variation.