[ilyagr]

Perhaps https://news.ycombinator.com/item?id=42428537 or its parent will make sense to you: connecting 3 or more perfect constant-temperature regenerative heat exchangers in a series would make the ones at the ends work at a higher/lower temperature (of the constant-temperature heat sink for those exchangers) than the one in the middle, increasing efficiency of the overall system.

I'm not proposing this as a practical design, but it convinces me that 50% efficiency is not the limit.

[benj111]

Maybe? but doesn't that just become a poor mans counter flow heat exchanger?

[ilyagr]

It's closer to a counter-flow heat exchanger, but you could still have air only go in one direction at a time. Say your indoor temperature is 20 degrees and the 3 heat exchangers are at 25, 30, and 35 degrees, and outside is 40 degrees (I'm thinking in Celsius, though 40 is a bit extreme). You blow air out until they cool to 20, 25, and 30 degrees. Then you blow air the other way until they heat back up to 25, 30, and 35 degrees, with the air coming in being somewhere in the 20-25 degree range instead of 40 degrees that the outside air is at.

This assumes that the heat exchanger has just enough thermal capacity so that raising/lowering its temperature by 5 degrees would get the air to the same temperature. In fact, it might be easier to imagine if the air doesn't blow continuously. Each chamber could fill up with air and wait for the heat exchanger and the air to get to the same temperature, before moving the air to the next chamber.