Fluid-elastic instability of in-line tube arrays in cross-flow

Abstract

Indirect contact heat exchangers usually contain arrays of closely spaced parallel, circular, flexible tubes. Under certain conditions the fluid cross-flow causes the tubes to vibrate, producing noise problems and tube damage due to tube collisions, wear at the supports, or fatigue. A mathematical model is developed for an in-line tube array, using the unsteady fluid force coefficients due to Tanaka and Takahara, in which it is assumed that the fluid forces acting on a tube arise only from its own motion and that of its four nearest neighbors. An iterative solution algorithm, which differs from that of Tanaka and Takahara, is presented to predict the velocity for the onset of whirling vibrations together with the corresponding frequency and mode shape for various array sizes. Two extensions of the model are considered. In the first the effect of the diagonally positioned tube is incorporated; in the second the first row is modelled by using unsteady fluid force coefficients for a single row. It is found that for practical array sizes, both modifications have negligible effect on the velocity for the onset of whirling vibrations.