Simultaneous Propulsion System and Trajectory Optimization

Abstract

A number of new aircraft concepts have recently been proposed which tightly couple the propulsion system design and operation with the overall vehicle design and performance characteristics. These concepts include propulsion technologies such as boundary layer ingestion, hybrid electric propulsion systems, distributed propulsion systems and variable cycle engines. Initial studies examining these concepts have typically used a traditional decoupled approach to aircraft design where the aerodynamics and propulsion designs are done a-priori and tabular data is used to provide inexpensive look up tables to the trajectory analysis. However the cost of generating the tabular data begins to grow exponentially when newer aircraft concepts require consideration of additional operational parameters such as multiple throttle settings, angle-of-attack effects on the propulsion system, or propulsion throttle setting effects on aerodynamics. This paper proposes a new modeling approach that eliminates the need to generate tabular data, instead allowing an expensive propulsion or aerodynamic analysis to be directly integrated into the trajectory analysis model enabling the entire design problem to be optimized in a fully coupled manner. The new method is demonstrated by implementing a canonical optimal control problem, the F-4 minimum time-to-climb trajectory optimization, using three relatively new analysis tools: OpenMDAO, PyCycle and Pointer. PyCycle and Pointer both provide analytic derivatives and OpenMDAO enables the two tools to be combined into a coupled model that can be run in an efficient parallel manner to offset the increased cost of the more expensive propulsion analysis. Results generated with this model serve as a validation of the tightly coupled design method and guide future studies to examine aircraft concepts with more complex operational dependencies for the aerodynamic and propulsion models. Nomenclature C Aerodynamic cross force D Drag F n Net thrust L Lift M Mach number r Radius T Temperature T SF C Thrust-specific fuel consumption v Airspeed α Angle of attack β Sideslip angle γ Flight path angle λ Azimuth angle µ ⊕ Gravitational parameter of Earth ω ⊕ Rotation rate of Earth φ Latitude σ Bank angle θ Longitude * Aerospace Engineer, Propulsion Systems Analysis Branch.

A Review of Concepts, Benefits, and Challenges for Future Electrical Propulsion-Based Aircraft

“…PyMission, as mission analysis tool, produces analytic derivative for the trajectory analysis when integrated with other disciplines and enables an adjoint-based optimization in the aircraft mission analysis [158]. Hendricks et al [159] assessed the aircraft concepts with a view towards coupled interaction in the aero-propulsion system, with a negotiation with the flown trajectory. In the proposed environment, the PyCycle tool [160] is used to generate the thermodynamic cycle and the trajectory analysis is implemented using the Pointer tool.…”

Multipoint Variable Cycle Engine Design Using Gradient-Based Optimization

“…pyCycle uses chemical equilibrium analysis [20] for its underlying thermodynamic library and uses a system of nested Newton solvers to converge complex engine cycles efficiently. pyCycle has been used for propulsion-mission optimization [21] and boundary layer ingestion studies [22,23,13].…”

How Certain Physical Considerations Impact Aerostructural Wing Optimization

“…OpenMDAO was developed at NASA Glenn and uses the modular analysis and unified derivatives theory to allow for modular construction and execution of complicated models [20]. OpenMDAO has been used to optimize a variety of problems, including wind turbines [21,22], boundary layer ingestion aircraft [23,24], thermodynamic engine cycles [25,26], and coupled thermal-mission problems [6,27].…”