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关键词： Rocket nozzles  

摘要： A nine-nozzle configuration rocket was established for the heating protection problem of the multi-nozzle rocket caused by the plume flow field structure and base heating in the ascent phase. Compared with the wind tunnel test data，the reliability of the numerical method was verified，and the numerical simulations were carried out for the plume flow field and the base heating environment at different altitudes. The results indicated that collisions occurred between gas jets， and there existed circulation vortices，gas backflow and back splash at different altitudes. The higher altitude indicated the greater expansion angle of the jet. At low flight altitudes，the base heating was mainly affected by radiation heating，and as the altitude increased，the effect of convection heating was enhanced. The peak of base heating flow density occurred within the range of 30 to 40 km，with a maximum convective heating flow density of 318.16 kW/m2，a maximum radiant heating flow density of 315.38 kW/m2 and a maximum total heating flow density of 570.31 kW/m2. The temperature gradient of rocket base was the main influence on convection heating，while radiation heating was mainly influenced by the radiation intensity，distance and area of the radiation micro-element. © 2025 Beijing University of Aeronautics and Astronautics (BUAA). All rights reserved.

关键词： 运载火箭   轨迹优化   保辛   伪谱法   序列凸优化  

摘要： 针对运载火箭入轨飞行段轨迹优化问题，为了提高算法的计算效率以及收敛性，本文从拉格朗日力学出发，在离散力学与最优控制计算方法基础上结合伪谱法高精度的优点，推导出伪谱离散拉格朗日方程，并结合序列凸优化方法提出了基于保辛伪谱序列凸优化的轨迹优化方法。保辛伪谱序列凸优化方法使离散动力学系统保留了原连续系统的结构特征，同时使离散系统状态变量的维数大幅度减低，能有效地提高收敛性以及计算效率。仿真结果表明，相比于经典的伪谱序列凸优化方法，保辛伪谱序列凸优化方法在不损失精度的情况下大幅度提高了计算效率，并且对初值扰动具有很好的适应性。