Predicting the eigenmodes of a cavity containing an array of circular pipes

An array of pipes inside a cavity, as found, for example, in a shell-and-tube heat exchanger, changes the eigenfrequencies of the cavity. It can be tedious to determine the shifted eigenfrequencies with a finite-element model. Based on previous work by Meyer and Neumann, Parker proposed a simple relationship for predicting the shifted eigenfrequencies. In this paper, results obtained from this relationship are compared with eigenfrequencies obtained from very accurate finite element simulations. From the results it can be concluded that Parker's relationship gives fairly good predictions of the eigenfrequencies for the first few modes in a cavity with pipes arranged in a rectangular configuration. The predictions are not so accurate for pipes arranged in a diamond configuration, and a modified version of the relationship is suggested for this configuration. If the number of pipes in the cavity is small, the simple relationship is no longer valid.