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Fluid Dynamics Seminar

Monday, Oct 1st, 2007, 4 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

The cascade structure of linear stability in collapsible channel flows

Xiaoyu Luo

Department of Mathematics, University of Glasgow

Abstract

Flow in collapsible tubes has been extensively studied in the last few decades, not only for its relevance to physiological applications, but also for its rich dynamic behaviour.

In this talk, I will focus on the linear stability of flows in collapsible channel. This is studied using both the full unsteady numerical solver and the eigenvalue solver for the Navier-Stokes equations coupled with two dimensional large deformation small strain elastic beam equations. It is found that the neutral stability of this system appears in a cascade structure consisting of different response modes. This cascade structure shows that in the Reynolds number-wall stiffness space, depending on the inlet boundary condition, the system may first lost stability to mode-1 or mode-2 perturbations as the wall stiffness is lowered to a critical value. However, as the wall stiffness is further reduced, the system is surprisingly re-stabilized first before going through a sequence of higher mode unstable zones. Extensive comparisons are made with earlier models, and differences are discussed.

A possible physical interpretation of the cascade structure is proposed. Although this study applies to two-dimensional collapsible channel flows, it is expected that similar cascade structures exist in possibly many other slender body fluid-structure interactive problems.