This question is a spinoff from here.
To set the context, here is my understanding of the expander cycle:
- Closed expander cycle is very efficient, perhaps more efficient than staged combustion cycle. It also has very little mechanical complexity as compared to other cycles (look at the simplicity of BE-7) which makes it very reliable (look at the longevity of RL-10). But closed expander cycle doesn't scale well, and engines with thrust over 150 kN are not practical.
- Open expander cycle does not have the same scale limitations (BE-3U has 710 kN of thrust, and LE-9 is expected to have close to 1,500 kN of thrust). But it is less efficient because a small portion of the propellant is ejected unburnt. This puts it closer to gas-generator cycle engines in terms of efficiency.
So, why not route the exhaust of the turbine of the open expander cycle back to the tanks to pressurize them autogenously (see diagram and description below)? This should combine the best of both worlds: efficiency of the closed expander cycle with power of the open expander cycle. But, as far as I know, this hasn't been done yet - so, maybe I'm missing something?
The cycle works pretty much in the same way as the open dual expander cycle - but instead of discarding the output of the turbopumps, the propellant is returned to its respective tanks.
As far as I understand, only about 2% of the propellant needs to be diverted to run the pumps. But I have only a single source for this (page 5 from here). So, if anyone has better numbers on how much of the propellant is usually used to run the pumps in an open expander cycle - would really appreciate the info.
As the propellant returns back to the tanks, most of it condenses back into a liquid form as it comes in contact with the subcoold propellant remaining in the tanks (I understand that this is what happens in plain autogenous pressurization as well). Different methods of injecting the propellant back into the tanks can be used to control the rate of condensation.
The temperature of the propellant returned to the tanks is around 400K (this also comes from the same page 5 from here - so, any validation or invalidation of this would be helpful). And since only about 2% of the propellant is returned, it's not enough to significantly heat up the rest of the propellant in the tanks.
The last point is true only while there is a lot of propellant still left in the tanks - but won't be true once the tanks are almost empty. At this point, the exhaust of the turbopumps would need to be largely discarded - as in the regular open expander cycle.