Optimization of cathodic protection for complicated structures using fast multipole boundary element method and equivalent boundary condition

利用快速多极边界元法和等效边界条件优化复杂结构阴极保护

基本信息

批准号：
11555028
负责人：
AOKI Shigeru
金额：
$ 8万
依托单位：
Tokyo Institute of technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

This research consists of three parts.In the first part, boundary element methods (BEM) to analyze the cathodic protection for complicated structures were reviewed. At first an experimental verification of BEM solusion was shown for an actual seawater pump with zinc sacrificial anodes. where the dependence of polarization curves on flow rate and time must be taken into account. Then, an effective BEM based on a concept "macroscopic polarization curve" was presented, and a heat exchanger having thousands of stainless steel tubes and naval brass tube-holder plates with zinc sacrificial anodes was analyzed using this method. Optimization of the impressed current and location of electrodes in impressed current cathodic protection was performed using the BEM for an underground long pipeline. An inverse and optimization problems in impressed current cathodic protection for a large ship were also solved.In the second part, application of the fast multipole boundary element method (FMBEM) to c … More orrosion problems was studied. It was found that this method can be successfully applied to corrosion analysis by employing the previous research results on the potential problems together with the following procedures ; (1) use of M^O_O of the root cell (which is obtained in the process of multipole expansion) for the infinite region problems, and (2) modification of the residual calculation formula in the Bi-CGSTAB iterative method to cope with the nonlinearity caused by polarization curves. A pipe element which is suitable to the FMBEM was also developed to increase the efficiency of calculation for pipelines. A few examples were shown to demonstrate the applicability of the FMBEM to corrosion problems.In the third part, an effective optimization technique for cathodic protection design was developed. To cope with the large amount of memory and calculation, FMBEM is applied. To achieve an effective optimization, the initial values of the design variables, i.e., the location and current of each electrode, are determined by solving an inverse problem. In the inverse problem both of the potential and the current density on the metal surfaces to be protected are given as the ideal values, i.e., the protection potential and its corresponding current density. The inverse problem is solved effectively by using FMBEM.Using thus obtained initial values, the optimization problem is solved by the symplex method. A couple of example problems were solved to demonstrate the effectiveness and usefulness of the present method. Less

本研究由三个部分组成。第一部分回顾了分析复杂结构阴极保护的边界元方法(BEM)。首先对带有锌牺牲阳极的实际海水泵进行了BEM解决方案的实验验证。然后，提出了一种基于“宏观极化曲线”概念的有效边界元法，以及具有数千个不锈钢管和海军黄铜的热交换器。利用该方法对地下长管道外加电流阴极保护中的外加电流和电极位置进行了优化分析。第二部分研究了快速多极边界元法（FMBEM）在腐蚀问题中的应用，发现该方法可以成功地应用于腐蚀分析。先前关于潜在问题的研究结果以及以下过程；（1）使用根单元的M^O_O（在多极展开过程中获得）来解决无限区域问题，以及（2）修改并提出了Bi-CGSTAB迭代法中的残差计算公式，以应对极化曲线引起的非线性问题，并开发了适用于FMBEM的管道单元，以提高管道的计算效率。的第三部分，开发了一种有效的阴极保护设计优化技术，以应对大量的内存和计算，应用FMBEM来实现有效的优化。设计变量，即每个电极的位置和电流，是通过求解反演问题来确定的，在反演问题中，待保护的金属表面上的电势和电流密度都给出为理想值，即保护电位及其相应电流利用FMBEM有效地求解了反问题。利用由此获得的初始值，通过复杂方法求解了几个示例问题，以证明该方法的有效性和实用性。