Applications of similitude to the structural mechanics of reactors

Abstract

The structural mechanics of a reactor involves the prediction of the behavior of the components of the reactor and the entire reactor system under a combination of gravitational and other force fields, electrical and magnetic fields, thermal fields and radiation fields. The nature of the materials and components is such that under the operational conditions imposed, the behavior is often nonlinear, with the result that the application of the usual techniques of mathematical analysis to predict behavior often results in lengthy computations based on assumptions that are somewhat subjective. Although computer techniques have proven very helpful in many instances, they are often limited in scope through size of available computer storage. The direct approach, that of cut-and-try design, is often not appropriate because of the possibility of release of radioactive materials in the event of a faulty design or a failure of the containment or other materials. In addition, economics, as well as safety, usually precludes construction of a complete operating unit without preliminary analysis Under these conditions of complex mathematical analysis and expensive construction the use of small scale models is suggested as a method of obtaining data from which realistic predictions may be made. In the design of small scale models the theory of similitude is used in the same way that it has been used in many fields of engineering. It is also pertinent to consider current power reactors in the 400-MW range as models of projected reactors in the 2000-MW range. Direct application of the principles of similitude leads to a series of design conditions that cannot be satisfied simultaneously. In such a situation the application of distorted model theory is mandatory. The application of distorted model theory requires the determination of the prediction factors associated with the pertinent distortion factors derived from the significant parameters that are distorted. Evaluation of the prediction factors as functions of the distortion factors may be accomplished experimentally or analytically, and the remainder of the presentation is devoted to consideration of the applicable methods and procedures for determining the prediction factors. The analytical procedures may be classed as those based on well established laws and those based on fundamental principles. Specific illustrations of the application of the principles includes fuel element containment, distortion of primary containment, performance of containment shells as a result of sudden release of energy within or from external disturbances, and thermal strains resulting from loss of coolant and subsequent sudden cooling. As the numerical examples will illustrate, distorted model theory often enables one to make practical judgments concerning which distortions are significant and which will have a trivial influence upon the results.