Phase Change Heat Transfer Problems, Sensitivity Analysis And Optimal Design Method

There are many heat conduction problems with phase change (HCPPC) in nature and industry. This thesis studied the temperature sensitivity analysis and design optimization method of HCPPC. The studies are accomplished in JIFEX, general software for the analysis and design optimization of structures. The research consists of two major parts. The first part is the numerical method to solve HCPPC. The second research includes the sensitivity analysis of the temperature field of HCPPC and the optimization of HCPPC. The research work will be introduced with the following chapters.In chapter 1, the background and research developments of HCPPC are surveyed. Then, the platform of this work is introduced. In the last section, the brief description of the research in this thesis is presented.In chapter 2, the analytical method of HCPPC is surveyed. Then, two classical examples are introduced to explain the method.In chapter 3, the numerical methods of HCPPC are discussed. Four models of fixed grid technique are surveyed. They are total enthalpy method, apparent heat capacity method, effective heat capacity method and the fictitious heat flow method. Then the finite element equations are derived with the effective heat capacity method. Common time-stepping method and precise time integration (PTI) method are used to solve the equation. The results of the example indicate that the accuracy of this algorithm is very high.In chapter 4, sensitivity analysis of HCPPC is investigated. The sensitivity equations are deduced based on the discrete model by direct method and adjoint method respectively. The conventional time difference solutions methods are given. The semi-analytical method for sensitivity analysis is presented.In chapter 5, the design optimization method of HCPPC is investigated. The optimization model and the solution methods are presented. Some improved techniques are applied to approximate programming method. The last section gives some numerical examples. The results indicate the validity of these methods.In Chapter 6, main contributions of the thesis are summarized and the further work is suggested.National Natural Science Foundation of China (No.10032030) and the Special Funds of National Key Basic Research of China (Gl999032805) support this thesis.