Damping forces of vibrating cylinder in confined viscous fluid by a simplified analytical method

Abstract

The simplified analytical solutions for viscous damping have been formulated, considering the results obtained by an existing numerical method, for relatively narrow annular configurations: (i) when a rigid cylinder executes translational oscillation in the plane of symmetry, and (ii) a flexible cylinder vibrates in its first mode as a clamped-clamped beam subject to axial flow. For narrow annular passages, the viscous damping has significant effects on fluid-dynamic forces. In such a case, an inviscid fluid model is acceptable for estimating added mass. This theory is developed for both relatively high and low oscillatory Reynolds numbers. In terms of computational efficiency, it is useful to obtain the viscous damping forces using this approximate method. Also this method has important benefit for the future study of stability analysis of system; since, the viscous damping forces obtained by the present method can be expressed in terms of the oscillatory Reynolds number explicitly. To validate this theory, the results are compared with the ones obtained by the full viscous theories in the previous works. These results were found to be in reasonably good agreement with the results of the full theories.