Hydrogen fuel system for a gas turbine engine

A gas turbine engine comprising:

• a turbomachine comprising a combustion section and an exhaust assembly arranged in serial flow order and collectively defining a working gas flow path through the turbomachine, wherein the exhaust assembly includes a tail cone;
• a fuel system fluidly coupled to the combustion section, the fuel system comprising:
• a hydrogen fuel tank for holding a hydrogen fuel;
• a pump fluidly coupled to the hydrogen fuel tank for generating a flow of the hydrogen fuel;
• and
• a heat exchanger, at least a portion of the heat exchanger positioned radially within the tail cone, the heat exchanger extending axially downstream from an aft end of the tail cone, the heat exchanger comprising:
• a first axial flow path in flow communication with the hydrogen fuel tank;
• a second axial flow path in flow communication with the combustion section of the gas turbine engine;
• and
• a radial flow path in thermal communication with the working gas flow path,
• wherein the heat exchanger comprises an inner wall and an outer wall circumferentially surrounding the inner wall, wherein the inner wall defines the first axial flow path, and wherein the inner wall and the outer wall together define the second axial flow path,
• wherein the first axial flow path, the radial flow path, and the second axial flow path are fluidly coupled in serial flow order, and wherein the first axial flow path extends in a first axial direction, and the second axial flow path extends in a second axial direction opposite the first axial direction.