金属结构航天器陨落过程三维瞬态传热有限元算法研究

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。     

轻质多层热防护结构的一体化优化设计研究

大面积防热结构在航天航空领域应用广泛, 其创新结构设计是关键技术之一. 航天飞行器的工作条件要求热防护材料与结构同时具备轻质、隔热、抗冲击的特点, 因此热防护材料与结构正在朝着一体化的方向发展. 基于这种发展趋势, 提出了一种轻质多层热防护结构设计方案. 以一体化多层防热结构在航天器再入过程中的传热为研究对象, 引入大面积防热结构的一维传热假设, 依照航天器再入大气层的温度条件, 建立了防热结构一维非稳态传热的物理模型和封闭的控制方程, 使用差分方法求解方程, 进行一维非稳态的传热分析, 并采用商业有限元软件ABAQUS的传热分析进行验证. 得到了航天器再入大气过程中多层防热结构的各层温度分布, 提出了在满足一定的热约束要求的条件下, 以轻质多层热防护结构的总重量为目标函数的优化设计方法, 得到了多层结构的最优几何参数, 并将优化后的结构进行了有限元承载分析.     

基于全隐式无分裂算法求解三维N-S方程

基于多块结构网格,本文研究和发展了三维N-S方程的全隐式无分裂算法.对流项的离散运用Roe格式,粘性项的离散利用中心型格式.在每一次隐式时间迭代中,运用GMRES方法直接求解隐式离散引起的大型稀疏线性方组.为了降低内存需求以及矩阵与向量之间的运算操作数,Jacobian矩阵的一种逼近方法被应用在本文的算法之中.计算结果与实验结果基本吻合,表明本文的全隐式无分裂方法是有效和可行的.     

再入飞行仿真的几个力学问题

本文针对航天器再入飞行仿真的研究。就仿真中的几个力学问题，讨论了如何建立合理的物理模型和数学模型。再入飞行仿真主要涉及刚体运动的飞行轨迹计算模型，涉及激波，表面压力。摩擦阻力。粘性干扰等因素的气动力计算模型；涉及边界层厚度，转捩，传热和物面粗糙度，辐射传热等因素的气动热计算模型；涉及结构强度，动态特性，稳定性，热应力等因素的有限元计算模型；涉及硅基和碳基防热材料，防热层温度分布等因素的热化学烧蚀模型；涉及天气严重环境指数，粒子与激波层干扰，粒子运动特性等因素的粒子侵蚀模型。涉及瞬时外形变化。气动特性变化。累积质量损失等因素的总体参数计算模型；其中要特别注意把握好对绕流流场计算，转捩准则选择，结构响应跟踪，瞬时外形圆整等问题的处理。才能使再入飞行仿真顺利进行到再入落地，而且仿真结果具有很好的可信度。     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法,建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型.在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性.研究结果表明:(1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下,而其计算效率比有限元全阶模型提高2～3个数量级,并且自由度数量(DOFs)愈大提高的幅度也愈加显著;(2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题,即使是在DOFs比较小的时候也能够明显提高计算效率;(3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型,并对其传热过程和温度场进行快速准确的分析与预测,具有很好的工程应用价值.     

相变传热问题的灵敏度分析与优化设计方法

研究了相变传热问题的优化设计及其灵敏度分析方法. 在有限元-时间差分和等效热容 法求解相变温度场的基础上，提出了相变温度场对设计变量一阶灵敏度的计算方法，给出直 接法和伴随法两种计算格式并分析了它们的特点，建立了相变温度场优化的模型和算法，在有限元分析与优化设计软件JIFEX中实现了该方法. 数值算例表明了灵敏度计算的精度和优 化方法的有效性.     

充液弯管连续/离散模型振动的动刚度解法

由充液弯管三维振动模型切入，应用动刚度法构建了弯管及直管单元的振动求解方法，进而用于组装求解充液管系的振动，可同时适用于含弯管单元的连续模型或只含直管单元的离散模型；通过算例对比，证明动刚度法比传递矩阵法和有限元法在计算效率和精度上有所提升；与充液L型管道振动实验测得的加速度频响曲线对比，验证了本文对于管道组装的计算方法的有效性，此外还分析了连续模型和离散模型的区别及适用范围。     

有限元分析快速解法

基于结构分析有限元方程组的特征，提出了在刚度矩阵及其因子的超方程概念下的细胞稀疏索引存贮方案。与传统的稀疏索引存贮方案相比，它可以减少磁盘空间和内存的占用量约30％。同时，这一存贮方案也可以减少关于索引的操作.结合双向循环展开技术，发展了一种适合于多维有限元分析的快速稀疏直接静力求解方法。工程算例表明，所建议的方案在存贮量和速度方面显著地改进了直接求解法的效率。     

瞬态空化泡演变过程的数值模拟

采用边界积分方程方法，对无粘流体中三个空化泡以及自由面附近二个空化泡相互作用的演变过程进行了数值模拟。计算中边界用二阶有限元离散，影响系数矩阵非对角线元素用六点高斯数值积分方法计算，对第一类、第二类完全椭圆积分用高次多项式近似，对计算系数矩阵对角线元素中遇到的奇异积分进行了特殊处理。结果表明，在不同的给定参数下，空化泡的溃灭形态各异，柱状射流和环形射流都有可能发生，使空化泡演变成双泡或环形泡。     

ELEMENT－BY－ELEMENT MATRIX DECOMPOSITION ANDSTEP－BY－STEP INTEGRATION METHOD FOR TRANSIENTDYNAMIC PROBLEMS

ＥＬＥＭＥＮＴ－ＢＹ－ＥＬＥＭＥＮＴＭＡＴＲＩＸＤＥＣＯＭＰＯＳＩＴＩＯＮＡＮＤＳＴＥＰ－ＢＹ－ＳＴＥＰＩＮＴＥＧＲＡＴＩＯＮＭＥＴＨＯＤＦＯＲＴＲＡＮＳＩＥＮＴＤＹＮＡＭＩＣＰＲＯＢＬＥＭＳＷａｎｇＨｕａｉｚｈｏｎｇ（王怀忠）（ＲｅｃｅｉｖｅｄＪｕ...     

Convective drying analysis of three-dimensional porous solid by mass lumping finite element technique

A numerical analysis of convective drying of a 3D porous solid of brick material is carried out using the finite element method and mass lumping technique. The energy equation and moisture transport equations for the porous solid are derived based on continuum approach following Whitaker’s theory of drying. The governing equations are solved using the Galerkin’s weighted residual method, which convert the governing equations into discretized form of matrix equations. The resulting capacitance matrices are made diagonal matrices by following the classical row-sum mass lumping technique. Hence with the use of the Eulerian time marching scheme, the final equations are reduced to simple algebraic equations, which can be solved directly without using an equation solver. The proposed numerical scheme is initially validated with experimental results for 1D drying problem and then tested by application to convective drying of 3D porous solid of brick material for four different aspect ratios obtained by varying the cross section of the solid. The mass lumping technique could correctly predict the wet bulb temperature of the solid under evaporative drying conditions. A parametric study carried out for three different values of convective heat transfer coefficients, 15, 30 and 45 W/m² K shows an increased drying rate with increase in area of cross section and convective heat transfer coefficient. The proposed numerical scheme could correctly predict the drying behavior shown in the form of temperature and moisture evolutions.     

Transient radiative and conductive heat transfer in non-gray semitransparent two-dimensional media with mixed boundary conditions

This paper is devoted to transient heat transfer involving radiation and conduction. Considering a non-gray purely absorbing media, the radiative heat transfer equation (RTE) is solved iteratively with the Discrete Ordinates Method (DOM) using an exponential differencing scheme. The energy balance equation is used to compute temperature at each time step with the Crank–Nicholson technique. Energy equation is coupled to the RTE through the radiative source term. Both equations are discretized with finite differencing schemes. The energy conservation leads to the sparse system of linear equations A× T=B which is solved with a bi-conjugate stabilized gradient technique (BCSG). Validation of the model with different test cases is achieved and application to transient heating of glass is also studied.     

Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length

In this paper a thick hollow cylinder with finite length made of two dimensional functionally graded material (2D-FGM) subjected to transient thermal boundary conditions is considered. The volume fraction distribution of materials, geometry and thermal boundary conditions are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure and the Crank–Nicolson finite difference method is implemented to solve time dependent equations of the heat transfer problem. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder are investigated. Effects of variation of material distribution in two radial and axial directions on the temperature distribution and time response are studied. The achieved results show that using two-dimensional FGM leads to a more flexible design so that transient temperature, maximum amplitude and uniformity of temperature distributions can be modified to achieve required specifications by selecting a suitable material distribution profile in two directions.     

Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics

Deformable components in multibody systems are subject to kinematic constraints that represent mechanical joints and specified motion trajectories. These constraints can, in general, be described using a set of nonlinear algebraic equations that depend on the system generalized coordinates and time. When the kinematic constraints are augmented to the differential equations of motion of the system, it is desirable to have a formulation that leads to a minimum number of non-zero coefficients for the unknown accelerations and constraint forces in order to be able to exploit efficient sparse matrix algorithms. This paper describes procedures for the computer implementation of the absolute nodal coordinate formulation' for flexible multibody applications. In the absolute nodal coordinate formulation, no infinitesimal or finite rotations are used as nodal coordinates. The configuration of the finite element is defined using global displacement coordinates and slopes. By using this mixed set of coordinates, beam and plate elements can be treated as isoparametric elements. As a consequence, the dynamic formulation of these widely used elements using the absolute nodal coordinate formulation leads to a constant mass matrix. It is the objective of this study to develop computational procedures that exploit this feature. In one of these procedures, an optimum sparse matrix structure is obtained for the deformable bodies using the QR decomposition. Using the fact that the element mass matrix is constant, a QR decomposition of a modified constant connectivity Jacobian matrix is obtained for the deformable body. A constant velocity transformation is used to obtain an identity generalized inertia matrix associated with the second derivatives of the generalized coordinates, thereby minimizing the number of non-zero entries of the coefficient matrix that appears in the augmented Lagrangian formulation of the equations of motion of the flexible multibody systems. An alternate computational procedure based on Cholesky decomposition is also presented in this paper. This alternate procedure, which has the same computational advantages as the one based on the QR decomposition, leads to a square velocity transformation matrix. The computational procedures proposed in this investigation can be used for the treatment of large deformation problems in flexible multibody systems. They have also the advantages of the algorithms based on the floating frame of reference formulations since they allow for easy addition of general nonlinear constraint and force functions.     

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

A review on transient test techniques for obtaining heat transfer design data of compact heat exchanger surfaces

Accurate and reliable dimensionless heat transfer characteristic is very essential for the analysis of heat exchangers. It is also required for the rating and sizing problems of heat exchangers. One of the important experimental methods used to determine the heat transfer coefficient between the heat transfer surface of the heat exchanger and the flowing fluid is transient test techniques. The transient test techniques are usually employed to establish Colburn factor versus Reynolds number characteristics of a high NTU heat exchanger surfaces like compact or matrix heat exchangers. In those situations, a single-blow test, where only one fluid is used, is employed to conduct the transient test. The transient technique may have the fluid inlet temperature having a step change, periodic or an arbitrary rise/drop. In this paper, various transient test techniques that are used for the determination of heat transfer characteristics of high NTU heat exchanger surfaces are discussed.     

磁悬浮飞轮转子组件温度场分析与研究

磁悬浮飞轮作为一种航天器的姿态控制执行机构当其工作在高真空环境下时，散热条件差，系统温度过高，导致转子组件热膨胀，产生热应力或改变磁轴承及电机的间隙，则会降低系统的可靠性。利用有限元软件ANSYS对一种磁悬浮飞轮系统的转子组件进行了温度场仿真，考虑了传导及辐射的传热方式，得到了飞轮转子组件的温度场分布，并且分析了组件材料属性对温度场分布的影响，最后对飞轮系统的强化传热进行了研究。分析所得温度值与实验测值相符，为磁悬浮飞轮系统的热设计及总体结构设计提供了重要依据。     

Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns

Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non-symmetric matrix systems are described. A certain level of fill-in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient-like methods and tested on finite element discretized scalar convection-diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill-in corresponding to about 50% of the number of original non-zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill-in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.