集成单元边界元法及其在主动冷却热防护系统分析中的应用

随着高超声速飞行器的快速发展，飞行器及发动机所面临的热防护压力越来越大. 传统的被动热防护系统已很难满足设计要求，因此主动冷却热防护系统受到了越来越多的关注. 主动冷却热防护系统因为管道密布、结构复杂，传统的分析方法需要花费大量的精力和时间来建模和计算分析. 针对管道阵列排布的主动冷却系统，提出了一种用边界元法求解空间周期性结构的集成单元法，并将其用来分析具有冷却通道的热防护系统的传热与受力变形问题. 此方法求解空间周期性结构问题，仅需要针对一个胞元建立边界元胞元方程，并由其形成由指定胞元数组成的集成单元，然后由集成单元组集成总体系统方程组. 提出的集成单元法既有常规子结构法的消元思想，又有传统有限单元、边界单元易于组集的特征，便于大型空间周期性结构的快速分析. 由于集成单元的系数矩阵只需形成一次，且最终方程只含边界节点未知量，计算效率显著提高. 论文最后用功能梯度平板和主动冷却燃烧室算例验证了本文所述算法的正确性和计算效率. 

INTEGRATED UNIT BEM AND ITS APPLICATION IN ANALYSIS OF ACTIVELY COOLING TPS

With the fast development of hypersonic aircrafts, the traditional passive thermal protection system (TPS) can't a ord the increasing demand of the thermal protection for aircrafts and engines. As a result, the actively cooling TPS has received more and more attentions. The commonly used technologies do require a substantially much more time due to the complexity of the structures. In this paper, the integrated unit method is proposed for solving spatially periodical structural problems using the boundary element method (BEM) and it is used to solve the thermal and mechanical problems appearing in the TPS with actively cooling channels. In this method, the BEM cell equation only needs to be established for one computational cell and the integrated unit can be formed by a specified number of cell equations. The equations of final system can be formed by the integrated unit equations. The proposed integrated unit method inherits the variableelimination idea of the sub-structure technique and assimilates the easy assembling characteristic of the conventional finite and boundary elements, and therefore is suitable for fast analysis of large-scale spatially periodical structural problems. As the coefficient matrices of the integrated unit only needs to be established once and the equations of final system only includes boundary nodal variables, the computational efficiency can be improved considerably. Three numerical examples for actively cooling combustors of scramjet engine are given to demonstrate the computational accuracy and efficiency of the proposed method.