Scale modelling in LMFBR safety

Abstract

This paper reviews scale modelling techniques used in studying the structural response of LMFBR vessels to HCDA loads. The geometric, material, and dynamic similarity parameters are presented and identified using the methods of dimensional analysis. Complete similarity of the structural response requires that each similarity parameter be the same in the model as in the prototype. The paper then focuses on the methods, limitations, and problems of duplicating these parameters in scale models and mentions an experimental technique for verifying the scaling. Geometric similarity requires that all linear dimensions of the prototype be reduced in proportion to the ratio of a characteristic dimension of the model to that of the prototype. The overall size of the model depends on the structural detail required, the size of instrumentation, and the costs of machining and assemblying the model. Material similarity requires that the ratio of the density, bulk modulus, and constitutive relations for the structure and fluid be the same in the model as in the prototype. A practical choice of a material for the model is one with the same density and stress-strain relationship as the operating temperature. Ni-200 and water are good simulant materials for the 304 SS vessel and the liquid sodium coolant, respectively. Scaling of the strain rate sensitivity and fracture toughness of materials is very difficult, but may not be required if these effects do not influence the structural response of the reactor components. Dynamic similarity requires that the characteristic pressure of a simulant loading source equal that of the prototype HCDA for geometrically similar volume changes. The energy source is calibrated in the geometry and environment in which it will be used to assure that heat transfer between high temperature loading sources and the coolant simulant and that non-equilibrium effects in two-phase sources are accounted for. For the geometry and flow conditions of interest, the viscous and gravity forces are usually negligible compared with pressure forces and, therefore, are not scaled.