Stability analysis of a tube group in cross flows, (1)

The vibration of plural column structures placed closely due to the interference with flow is an important problem, for example in case of the tube bundles of heat exchangers and the fuel assemblies of nuclear reactors. Heretofore, the vibration of this type has been understood as the forced vibration due to Karman's vortices, but now, the analysis taking the change of flow pattern due to the movement of tubes and the accompanying change of fluid force into consideration is required. In this study, the general method of analyzing the vibration of tube groups in ideal fluid is shown, and the stability of its solution is examined. Also analysis is made about the case in which disturbance is assumed as small periodic velocity variation as well as the case of constant upstream flow velocity, and the stability of tube groups in the coupled vibration due to the added stiffness of fluid is investigated. The model for analysis, the fluid force acting on a stationary tube group, quasi-steady fluid force, the equation of motion, the stability in steady flow, the stability in varying flow, and the example of numerical calculation on a group of three tubes arranged in triangular form are explained. (Kako, I.)