Research On Adaptive Reanalysis For Structures With Close Frequencies And Near Defective Structures And Study Of Double Chamber Impingement Cooling

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.