New RL10C-3 engines for SLS

[bknight]

I was browsing NASA's web page this morning and amd across this

http://www.nasa.gov/exploration/systems/sls/proven-engine-packs-big-in-space-punch-for-nasa-s-sls-rocket.html

Wiki  https://en.wikipedia.org/wiki/RL10

Since this engine has been around since the sixties, it does not have a closed loop system such as the RD-180 (and all its predecessors).
My question is simple: Can the closed loop system be used with cryogenics  like the use of RP-1?  Or would that design not work?  Has it been tried?

[QuietElite]

As far as I know the RL-10 uses a closed expander cycle. It offers a similar high efficiency as staged combustion (which is the engine cycle of the RD-180 that you mentioned). Closed expander cycles however can only be used for engines with low thrust, according to Wikipedia 300kN is the maximum for this cycle.
Yes there are cyro rocket engines that also have a staged combustion cycle. Probably the most famous is the RS-25, also known as SSME (Space Shuttle main engine).