I find it difficult to know exactly what the author has in mind. The section refers to an Otto cycle. Which is an internal combustion engine cycle (as far as I know always) the expansion and compression in an IC engine are decidedly "adiabatic". The ignition (heat addition" is "constant volume" at TDC.Bumpkin wrote: ↑Tue Sep 26, 2023 8:28 pm “As the gas is transferred at zero total volume change from the cold
space to the hot space the pressure rises. This pressure rise results in a
temperature increase in the gas due to adiabatic compression.
Therefore, at the end of the transfer process the mixed mean gas temperature
in the hot space will be higher than 900 K. Point 3 is calculated for all the
gas to be exactly 900 K. Adiabatic expansion then takes place. Then by the
same process as just described, the transfer of the expanded gas back into the
cold space results in a lower gas temperature than 300 K at the end of this
stroke. The computational process must be carried through for a few cycles
until this process repeats accurately enough. This effect will be discussed
further in Section 5.1.6.”
OK Martini is a big shot so I’m open to persuasion, but —
I’ve always thought the power piston compression/expansion is mostly prior to the displacer shift, so you can only transfer half of your available temperature difference before you run out of difference. The rest is already taken by the pressure change. So for instance for a 300K to 600K source/sink (100% difference) you would only want at most a 50% volume change engine. — But I dunno.
Bumpkin
So, it seems he is relating a Stirling cycle to an IC engine type compression/expansion heat addition scenario.
This does seem to relate to what has been discussed here lately as far as trying to make a Stirling engine more IC-like.
From my observations, in a gamma Stirling, the displacer lifts off the hot plate 90° ahead of the piston reaching TDC, so heat input (ignition-like event) and full compression take place, more or less simultaneously, allowing for a slight delay for the time necessary for heat to actually transfer from the exposed hot plate to the working fluid.
At TDC then, you have the combination of the heat input from the hot plate and the "heat of compression" peaking, more or less simultaneously at TDC.
That was the general idea I was pursuing in the "aligning heat vectors" thread I started recently: viewtopic.php?f=1&t=5556
I don't really know what type of Stirling the author of that paper has in mind.
There is that graph I've often posted showing the elevation in temperature in a Stirling engine above the temperature of the "heat exchanger", again, it's not entirely clear if that refers to the heat source hot plate or the internal regenerator, but I assume, the heat input heat exchanger, though thermally, in at least some configurations, there isn't much difference. Heat comes from the hot plate and/or regenerator. Either way, the combination of heat input just prior to full compression or heat concentration adds up to creating a temperature that exceeds the heat source temperature in either the hot heat exchanger or regenerator.
Similar to how the convergence of the crest of two waves results in a much larger wave, the "alignment of heat vectors" results in a higher peak temperature at TDC.
In the above quote, I assume he's talking about an Alpha when both pistons are moving and gas is being transfered through the regenerator from the cold to hot cylinder or vice versa.
Since one piston is going up and the other down the volume is sort of "constant" at times.