A gas turbine engine includes a compressor section having rotor shaft assembly and a stator shroud assembly including a stator shroud casing surrounding the compressor rotor shaft assembly, a compressor flow passage being defined between the compressor rotor shaft assembly and the stator shroud casing. A compressor bleed air system includes a compressor bleed air duct that includes a sloped inlet portion, such as a NACA submerged inlet portion, in the stator shroud casing. Alternatively, stator vanes at a compressor bleed air passage may have a NACA inlet scoop and an airflow passage through the stator vane providing a bleed airflow to a cavity, which has airflow passages providing bleed air to an upstream side of the bleed air passage.