Effect of vertically varying permeability on the onset of convection in a porous medium

• Published in: The Korean journal of chemical engineering Vol. 35; no. 6; pp. 1247 - 1256
• Main Authors: Ryoo, Won Sun, Kim, Min Chan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2018; Springer Nature B.V; 한국화학공학회
• Subjects: Biotechnology; Buoyancy; Catalysis; Chemistry; Chemistry and Materials Science; Computational fluid dynamics; Computer simulation; Convection; Fluid flow; Heterogeneity; Industrial Chemistry/Chemical Engineering; Linear analysis; Mass transfer; Materials Science; Motion stability; Nonlinear analysis; Parameters; Permeability; Porous media; Simulation; Stability analysis; Transport Phenomena; 화학공학; Onset Condition; Buoyancy-driven Convection; Linear Stability Analysis; Vertically Heterogeneous Porous Medium; Direct Numerical Simulation
• ISSN: 0256-1115; 1975-7220
• DOI: 10.1007/s11814-018-0045-5

Considering the vertically varying permeability of a porous medium, we conducted theoretical and numerical analyses on the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law was employed to explain the fluid flow through a porous medium and linear and nonlinear analyses are conducted. In the semi-infinite domain, the growth of disturbance and the onset of convection were analyzed with and without the quasi-steady state approximation. The present analysis of initial growth rate shows that the system is initially unconditionally stable regardless of a vertical heterogeneity parameter. The onset conditions of buoyancy-driven instabilities were investigated as a function of the Darcy-Rayleigh number and the heterogeneity parameter. To find the effect of a vertical heterogeneity on the flow after the onset of convection, nonlinear numerical simulations also were conducted using the result of the linear analysis as a starting point. Nonlinear numerical simulations show that the finger-like instability motion is not readily observable at a critical time and it becomes visible approximately when a mass transfer rate substantially increases.