Core-annular flow in a periodically constricted circular tube. I: Steady-state, linear stability and energy analysis (Q2718401)

The authors study a concentric flow of two immiscible fluids in a tube of sinusoidally varying cross-section. The governing equations (neglecting gravitational effects) depend on five dimensionless parameters: Reynolds and Weber numbers, and the ratios of density, viscosity and volume for two fluids. These model equations are solved numerically by using the pseudo-spectral method, and Arnoldi algorithm is applied for computing the most critical eigenvalues that correspond to axisymmetric disturbances. Stationary solutions are obtained for a wide range of parameters. In most cases the stability loss takes place through Hopf bifurcations.