【作者】 程鹏；

【导师】 姚国凤；

【作者基本信息】 吉林大学 ， 固体力学， 2014， 博士

【摘要】 本论文工作分两部分完成。一是基于2009年度国家自然科学基金项目和教育部高校博士点基金项目，研究密频振动系统及接近亏损振动系统快速重分析问题。结构振动分析及应用范围涉及模态识别、振动测试、优化设计等众多领域。在对大型、复杂工程实际结构进行振动分析时，往往会反复修改结构的设计参数，这将导致惊人的计算量，甚至是难以实现的。为解决此问题，可寻求有效的结构重分析理论及方法。探索具有自适应功能的重分析技术，对提高处理工程实际问题的效率、缩短设计周期意义重大。特别，在许多工程实际问题中，如航天飞机等大型柔性复杂结构，还有一些对称或准对称结构，振动形式比较特殊，会出现一种具有较低的、密集分布在一段狭窄频域内的频率系统，称之为密频结构。当结构发生小修改时，由于密频结构特征向量系不稳定，往往易于与亏损、接近亏损系统交织，其变化规律还待深入研究，以寻求解决策略。二是基于2010年度国家“863”重大专项课题“F级中低热值燃料燃气轮机关键技术与整机技术设计研究”的子项目，对燃气轮机燃烧室过渡段简化模型（双腔室模型）壁面冲击冷却进行了深入研究。随着时代的发展以及各行各业对能源、动力、环保与经济性等要求的提高，以高效清洁的发电设备著称的燃气轮机日益受到重视和关注。然而目前耐热材料的性能和研制进程并不能完全满足实际需求，高温部件的冷却技术研究及改进是亟待解决的关键问题之一。为解决燃烧室过渡段等高温部件的冷却问题，提高换热效果，增强流场湍流，寻求有效的冲击冷却手段。探索改进的冲击冷却技术，具有重大意义。通过计算流体力学（CFD）多物理场耦合分析，研究复合冲击冷却条件下流场、热场、应力场等多物理耦合场的分布及相互影响规律，实现提高我国燃气轮机关键部件的自主研发能力。具体研究内容可概述为：（1）振动系统分类、识别及其重分析问题描述。对振动系统按照非亏损、亏损、接近亏损、密频等类别划分，描述了各类振动系统的主要特征和识别方法。介绍了非亏损振动系统和亏损振动系统较常见的重分析理论和算法，为后文推导密频系统和接近亏损系统重分析算法提供理论基础。（2）自适应选取CA算法基向量个数策略。在分析了CA算法与PCG算法之间等价性的基础上，认为可通过计算PCG算法迭代次数来预估计CA算法的基向量个数。根据高等代数理论，推导了系数矩阵的“K条件数”与向量谱范数的关系，实现了系数矩阵的“K条件数”的近似计算，从而可智能地预估计不同结构下CA算法所需要的基向量个数，不仅有效保证了计算精度和计算稳定性，还大幅压缩了计算量、避免缩减后方程出现病态特征，为后文实现密频结构快速重分析提供有力的计算工具。（3）基于弹性修改和自适应CA算法的密频结构重分析。将密频结构重分析问题转化为由真正结构修改引起的重分析问题和由特征值移位引起的结构重分析问题这两部分的叠加。如果出现亏损现象，则基于广义模态理论将亏损系统不完备的特征向量系补齐，构成一组线性无关的广义特征向量系，并引入弹性修改策略来保证状态矩阵的可逆性，从而满足CA算法应用条件，采用本文提出的自适应CA算法快速重分析；如果不存在亏损现象，则直接应用本文提出的自适应CA算法求解。整个分析求解过程具有计算量小、计算稳定性高等优势。数值算例验证了理论的正确性和算法的有效性。（4）基于弹性修改CA算法的接近亏损结构重分析。基于弹性修改概念和CA算法，针对接近亏损振动系统重分析问题提出了一套可行、高效的解决方案。首先计算密集特征值的代数平均值，再将状态矩阵改写为亏损矩阵和误差矩阵之和，随后利用弹性修改CA算法求解N重以及一般亏损系统重分析问题。该算法计算格式整齐，易于实现。数值算例验证了方法的正确性和有效性，可进一步推广至工程实际中快速求解接近亏损振动系统结构修改问题中。（5）双腔室模型冲击冷却研究。针对燃烧室过渡段冷却技术问题，以过渡段简化模型为双腔室模型代表，建立了其流场的数学物理模型，通过计算流体力学（CFD）多物理场耦合分析，研究复合冲击冷却条件下流场、热场、应力场等多物理耦合场的分布及相互影响规律。根据对称性，截取四分之一圆环结构的双腔室模型，用来模拟过渡段的结构和功能特性。进而讨论了改变不同曲率、利用水滴/空气复合冷却介质和添加扰流柱结构对双腔室模型的冲击冷却性能影响。最后通过数值模拟得出在双腔室模型上添加扰流柱和采用水滴/空气复合冷却介质较单一空气更有利于提高模型冲击冷却效果。更多还原

【Abstract】 The thesis work was completed in two parts.First, this paper is supported by the National Natural Science Foundation of China titled“Fast optimization of cross-sectional parameters for simplified car body multi-elements framestructure based on reanalysis theory”, the Specialized Research Fund for the DoctoralProgram of Higher Education titled “The research of adaptive reanalysis algorithm of thedefective vibration system”. The methods for fast solving the eigenproblems of modifiedsystems with close frequencies and near defective systems are investigated.Vibration analysis is a very important theory during the design of large and complexstructures, which can be applied to many fields, such as vibration measurement, modalidentification and so on. When the objective of vibration analysis is a large and complexstructure, the computational complexity caused by modifying the design variables continually,will be huge. One can solve the problem by searching for effective methods of structuralreanalysis. Therefore, it is necessary to explore available algorithms for dynamic reanalysis,which is helpful to improve the computational efficiency and shorten the design cycle. Someactual engineering problems, such as non-proportionally damping system or flutter analysis ofaero-elasticity, sometimes appear defective. Furthermore, large flexible space structures, suchas the space shuttles, symmetrical and quasi-symmetrical structures, usually have low naturalfrequencies closely distributing in a narrow frequency domain. The eigenvectors of thesestructures with close frequencies are extremely instable. When the modification of structure issmall, there is generally a mutual transformation between systems with close frequencies anddefective systems. At this moment, the conventional methods and theories for non-defectivesystems will be invalid. Therefore, effective methods of reanalyzing defectives systems and systems with close frequencies are focused on.Moreover, based on the research of transition piece of gas turbine combustoroptimization design by National High-Tech R&D Program of China (863Program). Thethesis intensively investigates the modeling method and theory of impingement cooling, aswell as the simplified transition piece model (double chamber model).With the development of the requirements of power, environmental protection, flexibilityand economy, the development of high performance turbine engine-especially highperformance gas turbine-has got more attention and concern. Gas turbine power generationhas been paid more and more attention due to its efficiency and cleaning and independentdesign and manufacture of a heavy gas turbine are extremely necessary. As is known to all,improving the temperature of turbine inlet can significantly improve the overall performanceand budget of turbine, but the transition piece can’t keep working in high temperature toolong because the present material cannot meet the practical needs. This paper, focusing on thecooling technology for improving the heat transfer effect and enhancing the turbulent of theflow field, studies the objective low of the distribution and interaction of the multi physicalcoupling fields such as flow field/thermal field/stress field in condition of compoundimpinging cooling by multi physical fields coupling analysis of CFD (computational fluiddynamics). The new cooling method is built to improve the ability of independent researchand development of key parts of gas turbines in our country.The mainly contents can be concluded as follows.(1) Classification, recognition and description for the reanalysis problem ofvibration systems.First, vibration systems are classified as non-defective system, defective system, neardefective system and system with close frequencies. The characteristic and recognitionmethod of each system are described. Finally, the reanalysis method and theories fornon-defective systems and defective systems are introduced respectively, which can providetheoretical basis for this paper.(2) Adaptive technique for calculating the number of basis vectors in CA method. It has been proved that CA method and PCG method provide theoretically identicalresults in the Krylov subspace, which means the number of basis vectors in CA method equalsto the iterations of PCG method. Therefore, based on the present references, the approximatemethod of calculating the K-condition number of CA method is presented after deducing therelationship between K-condition number and spectral norm. At this moment, the number ofbasis vectors can be automatically pre-estimated by the modification of structure. Thistechnique is benefit to improve the efficiency, avoid the sickness of reduced equations andkeep the computation stability of CA method. It is useful for fast reanalysis of systems withclose frequencies.(3) Fast reanalysis for systems with close frequencies based on flexible modificationand adaptive CA method.The reanalysis problem of system with close frequencies can be treated as two parts. Oneis caused by the modification and the other is caused by the shift of eigenvalues. When thesystem with repeated frequencies is defective, the theories of generalized eigenvectors areapplied to expand a complete state space, as well as flexible modification is taken to keep thereversibility of state matrix in order to satisfy the computation condition of CA method.Meanwhile, the adaptive CA technique proposed in this paper is used for solving theperturbed eigenproblem rapidly. When the system with repeated frequencies is non-defective,the adaptive CA technique proposed in this paper can be applied directly. The calculation iseffective and stable. The numerical example demonstrates the correctness and validity forboth the theoretical derivation and the adaptive CA technique in this paper.(4) Reanalysis for near defective system based on flexible modification and CAmethod.A feasible and effective method for near defective system based on flexible modificationand CA method is proposed. First, the average of close frequencies is calculated. Then thestate matrix is rewritten as the add of defective matrix and error matrix. Finally, the reanalysisproblems of both the general defective systems and defective systems with N repeatedeigenvalues can be solved by the relaxation CA method. The numerical example demonstrates the correctness and validity of the method. The method can be effectively solved the practicalreanalysis problems of near defective systems.(5) Research of inpingement cooling in a double chamber modelThis thesis focuses on the cooling technology of a transition piece of this kind ofcombustion chamber and established equations of mathematical physics. This project alsostudies the objective low, by multi physical fields coupling analysis of CFD (computationalfluid dynamics), of the distribution and interaction of the multi physical coupling fields suchas flow field/thermal field/stress field in condition of compound impinging cooling. A model(double chamber model) of a one-fourth cylinder is designed which could simulate thetransition piece structure and performance. Investigation of the effects of impingement coolingfor the different curvatures, mist/air and pin-fins, which were used in the double chamber model.And study of the aerodynamic behavior of a simplified transition piece model (TP) are the twothemes of this paper. Therefore, retrofitting the typical air impingement cooling systems withpin fins and mist/air cooling seems attractive.更多还原