A nozzle includes a center body and a shroud circumferentially surrounding at least a portion of the center body to define an annular passage between the center body and the shroud. A plurality of apertures pass through the center body to the annular passage, and a plenum extends inside the center body and is in fluid communication with the plurality of apertures. A cooling medium is in fluid communication with the plenum. A method for cooling a nozzle includes flowing a cooling medium through a plenum across a surface of the nozzle.