Intercooled cooling air with dual pass heat exchanger

A gas turbine engine comprising;

• a main compressor section having a downstream most end, and more upstream locations;
• a turbine section having a high pressure turbine;
• a tap tapping air from at least one of said more upstream locations in said compressor section, and where said air is at a pressure that is lower than a pressure at said downstream most end, passing said tapped air through a heat exchanger and then to a cooling compressor, said cooling compressor compressing air downstream of said heat exchanger, and delivering air into said high pressure turbine;
• and
• said heat exchanger having at least two passes, with one of said passes passing air radially outwardly, and a second of said passes returning the air radially inwardly to the cooling compressor.