TITLE:
Effects of the Reynolds and Weissenberg’s Numbers on the Stability of Linear Pipe Flow of Viscous Fluid
AUTHORS:
Ibrahima Kama, Mamadou Lamine Sow, Kodjo Kpode, Cheikh Mbow
KEYWORDS:
Viscoelastic Fluids, Oldroyd-B Model, Linear Stability, Petrov-Galerkin, Generalized Eigenvalue Problem
JOURNAL NAME:
Modern Mechanical Engineering,
Vol.8 No.4,
November
30,
2018
ABSTRACT: A
Fourier-Chebyshev Petrov-Galerkin spectral method is described for high
accuracy computation of linearized dynamics for flow in a circular pipe. The
code used here is based on solenoidal velocity variables and is written in
FORTRAN. Systematic studies are presented of the dependence of eigenval-ues and
other quantities on the axial and azimuthal wave numbers; the Reyn-olds’ number
of up to 107 and the Weissenberg’s number that is considered lower here. The
flow will be considered stable if all the real parts of the ei-genvalues
obtained are negative and unstable if only one of these values is positive.