A turbine casing includes at least one shell adapted to enclose one or more turbine stages in a gas turbine engine; an air inlet in the at least one shell; a flow sleeve secured to an inside surface of the at least one shell, the flow sleeve comprising at least two arcuate segments. Each arcuate segment includes an arcuate base, a pair of sidewalls extending radially outwardly of the base thereby forming a circumferentially-extending flow channel defined by the base, the sidewalls and the inside surface. The air inlet is aligned with the flow channel and the sleeve is configured to distribute air flowing in the channel into spaces proximate the one or more turbine stages in circumferential, radial and axial directions, including along the inside surface of the at least one shell.