Turbine shroud assembly with carrier cooling holes for carrier aft flange

A method, comprising

• arranging a blade track segment made of ceramic matrix composite materials and arranged circumferentially at least partway around an axis to define a portion of a gas path of a turbine shroud assembly, the blade track segment having a shroud wall that extends circumferentially partway around the axis,
• arranging a carrier segment made of metallic materials circumferentially at least partway around the axis, the carrier segment supporting the blade track segment to locate the blade track segment radially outward of the axis, the carrier segment including an outer wall, a forward support wall that extends radially inward from the outer wall, and an aft support wall that extends radially inward from the outer wall that is located axially aft of the forward support wall, the aft support wall including at least one axially aft-facing surface,
• forming at least one cooling air plenum in the aft support wall of the carrier segment, and
• forming at least one cooling air passageway in the carrier segment, the at least one cooling air passageway being in fluid communication with and extending away from the at least one cooling air plenum through the aft support wall, the at least one cooling air passageway opening at the at least one axially aft-facing surface of the aft support wall such that the at least one cooling air passageway is configured to conduct cooling air through the carrier segment and direct the cooling air out of the carrier segment so as to cool at least one portion of the aft support wall.