Optimal Cruise Altitude for Aircraft Thermal Management

Mission-planning algorithms and trajectory optimization methods for aircraft that use fuel as a heat sink must ensure that fuel temperature limits are not violated at any point in a flight. The problem of determining the cruise altitude that minimizes final fuel tank temperature for jet aircraft that use recirculating fuel to remove waste thermal energy from the aircraft is considered. A heat exchanger transfers energy from the aircraft subsystems to the fuel. A portion of the fuel is burned in a turbojet engine, whereas the remaining unburned fuel is passed through a cooler that transfers some heat from the fuel to the atmosphere. A differential equation that describes the time rate of change of fuel tank temperature is derived based on the principles of conservation of mass and energy. Specific conditions are derived for the cruise altitude that minimizes final tank temperature for flight conditions associated with maximum endurance and range. Expressions are also derived that provide estimates of time and range to a temperature limit. Numerical examples are provided to illustrate the utility of the conditions and to assess the impact of the assumptions made in the derivation of the analytic models. The conditions also provide a relationship between aircraft performance parameters, the standard atmosphere, and the heat transfer characteristics of the fuel recirculation loop.