Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium

Abstract

A study of instabilities in planar flows produced by the presence of a parallel penetrable porous obstruction is presented. The case considered is a flow between parallel plates partially obstructed by a porous medium. The most unstable perturbation modes are obtained solving numerically the eigenvalue problem derived from the linear stability analysis of the two-dimensional Navier-Stokes equations applied to the geometry of interest. The analysis leads to an extended Orr-Sommerfeld equation including a porous term. It was found that the ratios of the permeability and depth of the obstruction with respect to the free flow layer depth are the relevant parameters influencing the stability margin and the structure of the most unstable modes. To validate the conclusions of the theoretical analysis, an experiment with air flowing through a channel semi-obstructed by a regular array of cylindrical wires was performed. The critical Reynolds number, which was determined by measuring the amplitude of velocity fluctuations at the interface of the porous medium, agrees with the theoretical predictions. The dominant instability mode was characterized by the cross-section profile of the root mean square of the velocity perturbations, which matches reasonable well with the eigenfunction of the most unstable eigenvalue. Also, the wavenumber was determined by correlating the velocity measurements in two sequential locations along the channel, which compares well with the theoretical value.

Aplication of the Lattice Boltzmann Method to the Simulation of Easily Penetrable Complex Obstructions

“…Del cálculo de estabilidad lineal se obtuvieron los números de Reynolds críticos (Re h =ρh 3 /8µ 2 (-dp/dx) [7]), resultando 90 para el canal asimétrico y 71 para el simétrico. A continuación se presentan resultados numéricos y experimentales para casos subcríticos y supercríticos.…”

“…al. [7]. De esta forma se obtiene una ecuación diferencial ordinaria de cuarto orden muy similar a la ecuación de Orr-Sommerfeld pero con un término adicional que representa la amortiguación introducida por el medio poroso.…”

“…De esta forma se obtiene una ecuación diferencial ordinaria de cuarto orden muy similar a la ecuación de Orr-Sommerfeld pero con un término adicional que representa la amortiguación introducida por el medio poroso. Cabe aclarar que la presencia del medio poroso se refleja también en la forma del perfil de velocidad U(y) [7].…”

“…La solución de esta ecuación puede obtenerse de diversas maneras; en nuestro caso se utilizó un set de herramientas llamado Derivation Matrix Suite, que utiliza interpolantes de Chevishev para discretizar el problema y resolverlo numéricamente [7].…”

Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

“…Interestingly, the theoretical results reported by Socio et al [14] shows no bi-or tri-modal behavior in the neutral stability curve. The experimental data obtained by Silin et al [15] also showed no sign of bi-modal stability curve. Tilton and Cortelezzi [16] argued that the prediction of bi-and tri-modal neutral stability curves in Refs.…”