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, the turbomachine further comprising a sensor;
• a fuel system comprising a hydrogen delivery assembly positioned in thermal communication with the exhaust assembly and in fluid communication with the combustion section;
• and
• a controller comprising a non-transitory memory and one or more processors, the non-transitory memory storing instructions that, when executed by the one or more processors, cause the gas turbine engine to perform operations, the operations comprising:
• receiving data indicative of a state of the exhaust assembly using the sensor of the turbomachine;
• determining an amount of a hydrogen fuel in a liquid phase to provide to the hydrogen delivery assembly in response to receiving data indicative of the state of the exhaust assembly;
• and
• directing one or more components to provide the determined amount of the hydrogen fuel in the liquid phase to the hydrogen delivery assembly;
• converting, with the hydrogen deliver assembly, the determined amount of hydrogen fuel in the liquid phase to hydrogen fuel in a gaseous phase;
• determining an amount of hydrogen fuel converted to the gaseous phase;
• and
• comparing the amount of hydrogen fuel converted to the gaseous phase to a desired amount of hydrogen fuel in the gaseous phase.