화학공학소재연구정보센터
Chemical Engineering Science, Vol.98, 255-264, 2013
Analysis on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated uniformly from below
The onset of convective motion in an initially quiescent, horizontal isotropic porous layer is analyzed theoretically. Using linear theory, the stability equations are obtained with and without the quasi-steady state approximation (QSSA). They are solved by expanding the disturbances as a series of orthogonal functions. Initial value problem analyses also are conducted, and their results are compared with the eigenanalysis and the QSSA. For the large Darcy-Rayleigh number Ra-D, the critical time of the onset of convection is found to be tau(c) = 11.74Ra(D)(-1) with the critical wavenumber k(c) = 0.29Ra(D)(1/2). Based on linear analyses, numerical simulations are conducted to consider nonlinear effects. The nonlinear analysis using the Fourier spectral method and the finite volume method reproduces the linear stability limit obtained theoretically. From the present nonlinear analysis, it is shown that manifest convection is observed experimentally from tau(m) = 51.42Ra(D)(-1). (C) 2013 Elsevier Ltd. All rights reserved.