Cooling air extracted from a gas turbine engine compressor is sent to nozzle vane cooling passage inlets, through the cooling passages, and to purge tubes of a set of two or more vanes. A mixing chamber formed between the purge tubes in a diaphragm cavity receives fluid from the purge tubes and directs it through exit passage(s) formed through a wall of the mixing chamber to a surface of the diaphragm. The exit passage(s) can be inclined to induce a fluid velocity component substantially parallel to the surface and/or in a rotation direction of a turbine wheel.