Stability analysis of Poiseuille flow in an annulus partially filled with porous medium

Abstract

The linear stability analysis of fluid flow, driven by an axial pressure gradient, inside the annular region partially filled with porous medium is investigated. The porous layer is attached to the inner cylinder. The flow is governed by the unsteady Darcy model in the porous region and the Navier–Stokes equation in the viscous region. The effect of the curvature parameter C (ratio of the inner cylinder radius to the gap between cylinders), the ratio of the fluid to the porous layer thickness (t̂), and the Darcy number (Da) on the stability characteristics are explored. In addition, the help of the radial velocity contours and the kinetic energy balance is taken to get an insight into the mode and the cause of instability, respectively. The results show that depending upon the value of t̂, a decrease in the value of C causes a shift in the neutral stability curve from bimodal to trimodal. For low values of t̂, when the onset of instability is dominated by a porous mode, C destabilizes the flow, whereas it has a stabilizing impact on the flow stability for the odd-fluid mode and the even-fluid mode. At high values of t̂, C has again destabilizing characteristics and instability is dominated by even-fluid mode. When axisymmetric disturbances are dominant, it is observed that the value of t̂ for which similar instability characteristics are found varies directly as the square root of Da. However, the correlation between t̂ and Da does not hold when the non-axisymmetric disturbances are least stable. Contrary to the unconditional stability of the annular Poiseuille flow under non-axisymmetric disturbances for C < 0.1325, the present system is unstable even for C = 0.005 and t̂≤1. This shows the significant impact of the curved fluid–porous interface on the stability characteristics.