Instability analysis of some fluid–structure interaction problems

Abstract

In this paper, we present instability analysis of two fluid–structure interaction (FSI) problems in the papermaking process. The first mathematical model is related to a pipe mixing unit which involves the submerged and inclined concentric pipes with different lengths. In the case of steady flow, both buckling and flutter instabilities are investigated. In the case of pulsatile flow, we use the numerical Floquet method to compute the eigenvalues of the monodromy matrix derived from the discretized linear system with periodic coefficients. In addition, for a special case, in which the concentric pipes have the same length, we also introduce a traditional Bolotin approach for comparison. The second mathematical model is derived from a vane/fluid interaction system within the papermachine headbox in which high-speed flows are separated by long flexible vanes. It is shown that for both laminar and turbulent flow conditions, the steady results derived from such analytical approaches match the corresponding computational solutions obtained using a general-purpose FSI computational package. Although, for certain cases, when geometries of fluid or solid domains are complex, it is very advantageous to use such a general-purpose program, we also point out, through the discussion of the selection of the critical time step in the numerical Floquet analysis and the dynamic stability analysis involving pulsatile flows, that there is still a need for analytical approaches as discussed in this paper.