Harmonic modelling of nonlinear fluid forces in finite length, cylindrical squeeze films

Abstract

Flow-induced vibration in shell-and-tube heat exchangers can result in excessive wear of the tubes at the support plates. The main source of damping for the case of liquid shell-side flow is the squeeze film damping caused by the motion of the liquid in the clearances between the tubes and the support plates. As a tube oscillates within a clearance space, liquid is squeezed in and out both axially and circumferentially. The pressure field within the squeeze film results in a damping force opposing the tube velocity and an inertia force opposing the acceleration. This paper presents the results of a series of measurements of the squeeze film force components for planar sinusoidal motions. For relatively large amplitude motions or when the initial eccentricity is large, the time waveform of the squeeze force shows significant contributions from higher harmonics. The amplitude and phase angle of each harmonic has been measured using a two-channel FFT analyzer. The force components in-phase and out-of-phase with the displacement are computed to give coefficients for each harmonic. Measurements have been made to show how these coefficients vary with frequency, amplitude, length to diameter ratio, and initial in-plane or out-of-plane eccentricity. Semi-empirical formulas have been developed to predict the values of the coefficients. The fundamental frequency coefficients are compared with the mass and damping models of others and show reasonable agreement. The nonlinear squeeze force waveform for most test conditions can be synthesized satisfactorily. The results of simultaneous rocking and lateral motions indicate that rocking has little effect on the lateral hydrodynamic mass and damping coefficients.