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Study on finite element algorithm for three dimensional transient heat transfer during falling reentry of spacecraft with metal truss structure[J].计算力学学报,2019,36(2):219~225

Study on finite element algorithm for three dimensional transient heat transfer during falling reentry of spacecraft with metal truss structure
Study on finite element algorithm for three dimensional transient heat transfer during falling reentry of spacecraft with metal truss structure

DOI：10.7511/jslx20171129003

 作者 单位 E-mail 石卫波 中国空气动力研究与发展中心, 绵阳 621000 孙海浩 中国空气动力研究与发展中心, 绵阳 621000 唐小伟 中国空气动力研究与发展中心, 绵阳 621000 马强 四川大学 数学学院, 成都 610043 李志辉 中国空气动力研究与发展中心, 绵阳 621000国家计算流体力学实验室, 北京 100191 zhli0097@x263.net

构建金属桁架结构航天器陨落再入气动热环境有限元传热模型，是准确预测在轨服役期满大型航天器陨落再入解体过程温度分布的关键。本文采用四节点四面体单元对空间进行离散，依据泛函理论，将传热控制方程离散为代数方程组；利用有限单元法总体合成得到具有对称正定、高度稀疏和非0元素分布的规则性刚度矩阵，发展一维变带宽压缩存贮技术，有效解决大型稀疏矩阵的数据存贮问题；为有效抑制求解过程出现的温度在时间和空间上的振荡问题，发展集中热容矩阵系数处理方法，将热容矩阵的同行或同列元素相加代替对角线元素，使非对角线元素化为0，构造求解三维瞬态温度场的两点向后差分格式、Crank-Nicolson格式和Galerkin格式。通过对正方体瞬态传热计算验证分析，在相同条件下，采用以上三种格式均可获得一致稳定的温度解，并得到与现有ANSYS有限元软件较为吻合的计算结果，验证了所建立三维瞬态传热有限元计算模型的准确可靠性。在此基础上，对铝合金低轨航天器薄壳结构进行了传热计算，给出了类天宫飞行器两舱体陨落飞行107.5 km~90 km不同高度的瞬态温度分布，为这类寿命末期航天器陨落再入解体预报提供理论支撑与可计算模型。

To construct the finite element model for the heat transfer of large-scale complex spacecraft with a metal truss structure during in reentry in aerothermodynamic environment,is the key to accurately predict the temperature distribution of the end-of-life spacecraft during the process of falling reentry and disintegration.In this paper,the four-node tetrahedron element is used to discretize the space,and the heat transfer equation is discretized into a set of algebraic equations.The symmetric positive-definite stiffness matrix with a highly sparse and non-zero element distribution is obtained by the overall synthesis of the finite element method.The one-dimensional variable bandwidth storage technique is developed to effectively resolve the data storage of large sparse matrix.To effectively depress the temperature oscillations appearing in time and space in the solving process,the centralized heat capacity matrix coefficient method is developed.The elements on the same row or column elements of the heat capacity matrix are summed to replace the diagonal elements,so that only the diagonal elements of the new heat capacity matrix are non-zero,and the remaining elements are zero.The two-point backward difference scheme,Crank-Nicolson scheme and Galerkin scheme are constructed to solve the three-dimensional transient temperature field.By computational analysis of transient heat transfer of a rectangular cylinder body,the converged temperature solutions of the above-said three schemes are found to be in good agreement,and the results are consistent with those of the existing finite-element software ANSYS,which confirms the precision and reliability of the present 3D finite-element model for transient heat transfer.The heat transfer computation is carried on the shell structure of a low-orbit spacecraft made of aluminium alloy,and the transient temperature distribution of the Tiangong's two-capsule structure is simulated and analyzed from the flight altitude of 107.5 km~90 km,which provides the theoretical support and computable model for the forecast of disintegration of the end-of-life spacecraft during falling reentry.