Abstract

Linear and weakly nonlinear stability analyses of Darcy-Benard convection of a Newtonian fluid undergoing combustion are investigated in the paper using a zeroth-order chemi-cal reaction model . The Frank-Kamenetskii-Vadasz-Lorenz model that has in it the influ-ence of combustion is derived and transformed into a Ginzburg-Landau equation using a method of multiscales. An analytical expression for the Frank-Kamenetskii-Darcy-Rayleigh number and the Hopf-Frank-Kamenetskii-Darcy-Rayleigh number is reported. In the limit -ing case, these expressions are validated with the results of previous investigations . Using an analytical solution of the Ginzburg-Landau equation, heat transport in the combust-ing fluid is studied. The clear blow-up of the Nusselt number in the post-ignition regime is shown. The overall effect of combustion is to advance the onset of regular convec-tive and chaotic motions and to enhance the heat transport. The symmetry in the Frank-Kamenetskii-Vadasz-Lorenz model and its Hamiltonian nature are shown. The appearance of chaotic/periodic motion in the system for large values of the eigenvalue (with the but-terfly diagram being trapped in an ellipsoidal region) are highlighted in the paper. One new feature in the problem is the favouring of prolonged periodic convection in a larger range of values of the scaled Darcy-Frank-Kamenetskii-Rayleigh number compared with no combustion. The exact nature of the influence of combustion on Darcy-Benard convection is visualized with the help of a bivariate, least-squares surface fit of the data and some important conclusions are drawn.(c) 2022 Elsevier Inc. All rights reserved.