Research On Adaptive Pseudospectral Trajectory Optimization Method Based On Density Function

The dissertation aims at the development of a new optimization algorithm, used in thetrajectory optimization problem of air-breathing hypersonic vehicle. This paper establishes aparametric physical model of air-breathing hypersonic vehicle, and uses the FLUENT software toanalyse the aerodynamic and propulsion performance. A mesh refinement algorithm based ondensity function is reasonably added to the pseudospectral method. Finally, hp adaptive gausspseudospectral method is used to slove glide phase and dive phase trajectory optimization.Thenumerical simulation results are analyzed. The main results achieved in this dissertation aresummarized as follows:(1) There is coupling between aerodynamic and propulsion system, and it is caused by thescramjet engine exhaust plume pushing aftbody; thrust increases with the angle of attack increaseduntil the best point; the higher is fuel equivalence ratio, the wider is the residual thrust range;variable cowl geometry compared to a fixed cowl, can generate additional thrust in non-designangle of attack.(2) Based on curvature density function, a new mesh refinement algorithm determines gridnode distribution of the next iteration. It is demonstrated by the mesh refinement algorithm thathigh accuracy solutions to problems do not require high-degree polynomials. The highest degreepolynomial used by the mesh refinement algorithm is eighth order. If exponential convergence isexpected in a particular interval, a high-degree polynomial approximation should not be required.Furthermore, because low and mid-degree polynomials are used, the mesh refinement algorithmresults in an NLP that is sparse. Moreover, it specifically refines only parts of an approximationwith the largest errors. Compared to the global Gauss pseudospectral method, it costs lesscomputation time and memory, can greatly improve the effectiveness of the global Gausspseudospectral method, and obtain more accurate solution.(3) Unpowered glide phase and dive phase trajectory are sloved by optimization algorithmdeveloped in this paper; the solutions satisfy the dynamics, process and terminal constraint, thesimulation results have certain reliability.