A nuclear reactor system (200, 300, 400), comprising: a reactor vessel (70, 210, 310, 410) that comprises an interior volume; a core (20, 220, 320, 420) that comprises one or more nuclear fuel assemblies; a riser that extends from a top portion of the core through the interior volume of the reactor vessel towards an upper half of the reactor vessel; a neutron reflector (15, 215, 335, 435) that comprises an inner face that surrounds lateral sides of the core and an outer face opposite the inner face; a core support structure that comprises one or more support posts (350, 440) that extend from near a bottom portion of the reactor vessel (70, 210, 310, 410) towards the core to support the one or more nuclear fuel assemblies; and a primary coolant flow path contained within the reactor vessel that extends from the riser toward the upper half of the reactor vessel (70, 210, 310, 410), from the upper half of the reactor vessel in a downflow toward the bottom portion of the reactor vessel between the outer face of the neutron reflector (15, 215, 335, 435) and the reactor vessel, and from the bottom portion of the reactor vessel around the one or more support posts (350, 440) through the core and to the riser, wherein the core support structure further comprises a core barrel (230, 330) that is positioned between the neutron reflector (15, 215, 335, 435) and the reactor vessel (70, 210, 310, 410), and the primary coolant flow path extends in the downflow toward the bottom portion of the reactor vessel through an annulus between the outer face of the neutron reflector (15, 215, 335, 435) and an inner surface of the core barrel (230, 330). a reactor vessel (70, 210, 310, 410) that comprises an interior volume; a core (20, 220, 320, 420) that comprises one or more nuclear fuel assemblies; a riser that extends from a top portion of the core through the interior volume of the reactor vessel towards an upper half of the reactor vessel; a neutron reflector (15, 215, 335, 435) that comprises an inner face that surrounds lateral sides of the core and an outer face opposite the inner face; a core support structure that comprises one or more support posts (350, 440) that extend from near a bottom portion of the reactor vessel (70, 210, 310, 410) towards the core to support the one or more nuclear fuel assemblies; and a primary coolant flow path contained within the reactor vessel that extends from the riser toward the upper half of the reactor vessel (70, 210, 310, 410), from the upper half of the reactor vessel in a downflow toward the bottom portion of the reactor vessel between the outer face of the neutron reflector (15, 215, 335, 435) and the reactor vessel, and from the bottom portion of the reactor vessel around the one or more support posts (350, 440) through the core and to the riser, wherein the core support structure further comprises a core barrel (230, 330) that is positioned between the neutron reflector (15, 215, 335, 435) and the reactor vessel (70, 210, 310, 410), and the primary coolant flow path extends in the downflow toward the bottom portion of the reactor vessel through an annulus between the outer face of the neutron reflector (15, 215, 335, 435) and an inner surface of the core barrel (230, 330).