A powerplant includes a turbine engine core configured to power a mechanical load. The turbine engine core includes a core compressor section, a core combustor section and a core turbine section. A recovery system includes a condenser and an evaporator. A core flowpath extends sequentially through the core compressor section, the core combustor section, the core turbine section, the evaporator and the condenser from an inlet into the core flowpath to an exhaust from the core flowpath. The recovery system is configured to condense water vapor flowing through the core flowpath into water using the condenser. The recovery system is configured to evaporate the water into steam using the evaporator and to provide the steam to the turbine engine core during a first mode of operation. The recovery system is configured to flow the water through the evaporator during a second mode of operation.