A cooling system includes a first conduit positioned within a cavity and extends from a radially inner casing aperture to a radially outer casing aperture. The cooling system also includes a second conduit coupled in flow communication with the first conduit and extending into the cavity. The cooling system further includes at least one valve positioned within the first conduit and the second conduit. The at least one valve and the first conduit are configured to channel a first fluid from the radially inner casing aperture to the radially outer casing aperture during a first mode of operation. The at least one valve, the second conduit, and the first conduit are configured to channel a second fluid from the radially outer casing aperture to the cavity during a second mode of operation.