A centrifugal separator for removing particles from a fluid stream includes an angular velocity increaser configured to increase the angular velocity of a fluid stream, a flow splitter configured to split the fluid stream to form a concentrated-particle stream and a reduced-particle stream, and an exit conduit configured to receive the reduced-particle stream. An inducer assembly for a turbine engine includes an inducer with a flow passage having an inducer inlet and an inducer outlet in fluid communication with a turbine section of the engine, and a particle separator, which includes a particle concentrator that receives a compressed stream from a compressor section of the engine and a flow splitter. A turbine engine includes a cooling air flow circuit which supplies a fluid stream to a turbine section of the engine for cooling, a particle separator located within the cooling air flow circuit, and an inducer forming a portion of the cooling air flow circuit in fluid communication with the particle separator. A method of cooling a rotating blade of a turbine engine having an inducer includes directing a cooling fluid stream from a portion of turbine engine toward the rotating blade, separating particles from the cooling fluid stream by passing the cooling fluid stream through a inertial separator, accelerating a reduced-particle stream emitted from the inertial separator to the speed of the rotating blade, and orienting the reduced-particle stream by emitting the reduced-particle stream from the inertial separator into a cooling passage in the inducer.