Phase Lag Model for Fluidelastic Instability in Square Cylinder Arrangement

International audienceIn this paper, a phase lag model is proposed in order to pre-dict the fluid velocity threshold for fluidelastic dynamic instabil-ity of a square cylinder arrangement under cross flow. A theoret-ical formulation of a total damping, including the added damp-ing in still fluid, the damping due to fluid flow and the dampingderived from the phase shift between the fluid force and tube dis-placement, is given. A function of fluid and structure parameters,such as reduced velocity, pitch ratio and Scruton number, is thusobtained. It is shown that this function, taken as function of thereduced velocity variable, vanishes at the critical reduced ve-locity from which the fluidelastic dynamic instability of the tubeoccurs. Obviously, the value of the critical velocity is depend-ing on other fluid-structure parameters. The obtained results arecompared to experimental ones and those obtained from othertheoretical models