Journal Article

Chemical Equilibrium Analysis with Adjoint Derivatives for Propulsion Cycle Analysis


J. S. Gray, J. Chin, T. Hearn, E. Hendricks, T. Lavelle, and J. R. R. A. Martins


Journal of Propulsion and Power, 33(5):1041–1052, 2017



The design optimization of aircraft engines considering their integration with the airframe has been limited by challenges with existing propulsion modeling tools. Gradient-based optimization with derivatives computed using adjoint methods has been successful in solving aerodynamic and structural shape optimization problems but has not yet been applied to coupled propulsion–airframe optimization, partly because existing tools lack analytic derivative computation. As a step toward obtaining a full cycle analysis with efficient analytic derivative computation, a new chemical-equilibrium thermodynamics solver is developed for propulsion applications. This solver provides a continuous formulation that enables analytic derivative computation using a coupled adjoint approach. The results from this solver are verified against a well-established chemical-equilibrium code. The analytic derivatives are also verified by comparing them with finite-difference approximations. The performance of the analytic derivative computations is tested using two optimizations: combustion temperature maximization with respect to equivalence ratio, and combustion temperature maximization with respect to air pressure. The results show clear speed and numerical stability benefits when comparing the proposed method against finite-difference approximations. It is now possible to use this new solver as the foundation for further development of a complete propulsion analysis for integrated propulsion–airframe design optimization.