Stability analysis of a pipe conveying periodically pulsating fluid using finite element method

It is well known that the constant velocity of the fluid in a pipe which makes the lowest natural frequency zero is called critical velocity. The pipe becomes unstable when the fluid in a pipe is faster than the critical velocity. If the velocity of the fluid in a pipe varies with time, however, the instability of a pipe will occur even though the mean velocity of the fluid is below the critical velocity. In this paper, a new method for the stability analysis of a pipe conveying fluid which pulsates periodically is presented. The finite element model is formulated to solve the governing equation numerically. The coupled effects of several harmonic components in the velocity of fluid to a pipe is discussed. A new unstable region is shown in this paper which will not appear in the stability analysis of single pulsating frequency. The results of the stability analysis presented in this paper are verified by the time domain anlysis.