Systems and methods for an exhaust system for a gas turbine engine are provided. The exhaust system includes an eductor system adapted to receive a primary exhaust fluid. The eductor system includes a body that extends along a first axis, with a plurality of ducts spaced apart about a circumference of the body. Each of the plurality of ducts extend from the body along a second axis transverse to the first axis to define a plurality of eductor primary flow paths that terminate in a mixing chamber. The mixing chamber is adapted to receive a secondary cooling fluid and to mix the primary exhaust fluid with the secondary cooling fluid to create a mixed fluid flow.