Shaping low-thrust trajectories with thrust-handling feature

Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum $\mathrm{\Delta }V$. A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated.     

Three dimensional investigation of the shock train structure in a convergent–divergent nozzle

Three-dimensional computational fluid dynamics analyses have been employed to study the compressible and turbulent flow of the shock train in a convergent–divergent nozzle. The primary goal is to determine the behavior, location, and number of shocks. In this context, full multi-grid initialization, Reynolds stress turbulence model (RSM), and the grid adaption techniques in the Fluent software are utilized under the 3D investigation. The results showed that RSM solution matches with the experimental data suitably. The effects of applying heat generation sources and changing inlet flow total temperature have been investigated. Our simulations showed that changes in the heat generation rate and total temperature of the intake flow influence on the starting point of shock, shock strength, minimum pressure, as well as the maximum flow Mach number.     

Design of an innovative multi-stage forming process for a complex aeronautical thin-walled part with very small radii

In this paper, an aeronautical thin-walled part with a complex geometry which has several sharp bends and curvatures in different directions was investigated. This kind of part is difficult to be manufactured only in one stage. Therefore, an innovative multi-stage active hydroforming process assisted by the rigid forming method was designed. In addition, an optimized blank geometry is obtained. In fact, the main focused point of this paper is to propose a new small radius rounded corner forming technique and analyze the mechanism. Two kinds of forming modes of changing a big rounded corner into a small one, which are related to different tangential positions of the die in the process of calibration, are analyzed theoretically. Meanwhile, the stress and strain states of the deformation region are compared. The relationships between the minimum relative radii of rounded corners I and II in the first stage and the hydraulic pressure are calculated by the bending theory. Finally, the influences of the tensile-bulging effect and the interface condition of the double-layer sheet on the forming quality of the specimen are investigated. The achieved results can make a foundation for utilizing the proposed method in forming of thin-walled parts with very small radii.