Stability of the Poiseuille Flow in a Compliant Pipe of Elliptic Cross-Section.

A new numerical model for hydrodynamic stability analysis of flows in pipes of constant elliptic cross-section with compliant walls is described. The model is based on the equations governing the propagation of small-amplitude three-dimensional disturbances of the velocity and the pressure as well as Love's equations of two-dimensional shell theory for simulating the viscoelastic properties of the pipe wall. The possible presence of media surrounding the shell is simulated as a set of equidistant springs and dampers. Numerical properties of the model are illustrated with the Poiseuille flow in round and elliptic pipes with compliant walls of constant thickness. [ABSTRACT FROM AUTHOR]