A gas core engine was tried at least on standby power levels in sixties. The experiment was called "Baikal 2" and made for testing of RD-600 and EU-610, not much info on them in English.
I myself don't think that economising on fuel is that much important. Back in sixties, enriched uranium and plutonium were still though of as extremely pricey to be expended with propellant, thus the development went an extra mile to get as much oomph out of the fuel as possible.
But thanks to few decades of military industry making u235 and plutonium production cheaper, an option with expendable fuel looks easier.
My own thinking: get a conventional expander cycle rocket engine and add hexafluoride injection past the turbine. Then, you add moderator and reflectors into the combustion chamber. Voila, a much easier solution. Even easier than a solid core reactor as your don't have to think much about reactor not melting, and reactor control — just adjust the tap on the heaxafluoride.
I myself don't think that economising on fuel is that much important. Back in sixties, enriched uranium and plutonium were still though of as extremely pricey to be expended with propellant, thus the development went an extra mile to get as much oomph out of the fuel as possible.
But thanks to few decades of military industry making u235 and plutonium production cheaper, an option with expendable fuel looks easier.
My own thinking: get a conventional expander cycle rocket engine and add hexafluoride injection past the turbine. Then, you add moderator and reflectors into the combustion chamber. Voila, a much easier solution. Even easier than a solid core reactor as your don't have to think much about reactor not melting, and reactor control — just adjust the tap on the heaxafluoride.