INSTABILITY OF POISEUILLE FLOW IN A CHANNEL FILLED WITH MULTILAYER POROUS MEDIA

We performed a linear stability analysis of Poiseuille flow in a parallel-plate channel filled with fluid-saturated multilayer porous media. To investigate the effect of the porous layer number, n(p), two ways of increasing the number of porous layers have been considered based on an identical three-layer model, which are referred to as the constant Re and psi conditions, respectively. When the inertial effects are ignored, the numerical results show that at the constant Re condition, with an increase in the value of dimensionless permeability, sigma, the number of migration paths for the upper wall modes on the left branch in Orr-Sommerfeld spectra for n(p) = 1, 2, 3, and 4 is identical to the number of open fluid layers, while the number of new inducing lower wall modes is just twice the number of porous layers placed in the channel. The number of modes on the lower-left branch also depends on the positions of the porous layers. In addition, we present the behaviors of the critical Re number against wave number alpha, and n(p) for the constant Re and constant psi conditions. By comparing the stability characteristics between the two conditions, we observed that both have less stability as the number of porous layers increases. At the same number of porous layers, n(p) the value of Re-c at the constant psi condition is much less than that at the constant Re condition.