Hydrodynamic instability of the coflow filtration combustion: Numerical simulation

Abstract

The stability of the front to infinitely small distor� tions was analyzed under the assumption that the reac� tor channel width is infinitely large in comparison with the combustion zone thickness (5). It was concluded that the plane filtration combustion wave may be unstable. The experimental investigation of the filtra� tion combustion wave stability confirmed (6) that the propagation of a plane filtration combustion front may be unstable and may be accompanied by the formation of structures similar to Saffman-Taylor fingers, which were observed as a highviscosity liquid was displaced by a lowviscosity liquid (7). In this work, for the first time, we made mathemat� ical modeling of twodimensional unsteady filtration combustion during the forced oxidant filtration in the combustion wave direction. The purposes of the study was to determine the conditions for the occurrence of filtration combustion with a stable plane front in chan� nels of finite width and investigate the filtration com� bustion wave propagation modes in the range of insta� bility of the plane reaction front. The physical formulation of the problem is the fol� lowing. A gas mixture with oxidant concentration a0 is fed to a reactor filled with a porous mixture containing a fuel component. The gas flow rate at the inlet (x = 0) is maintained constant (G0). Reaction initiation with a hightemperature source leads to reaction front prop� agation in the х direction at rate u. As the fuel is burned out, the structure of the porous medium changes, because of which the porosity, thermal diffusivity, and permeability of the combustion products may differ from the respective characteristics of the initial reac� tion mixture. The problem is considered in the plane geometry under the assumption that the reactor is shaped as a thin slitlike channel. If the reaction front propagation velocities are low, which is characteristic of filtration combustion waves, the difference between the temperatures of the parti� cles and the gas can be ignored and the porous medium can be considered locally uniform in temper� ature and concentration. Under this assumption, the dimensionless system of equations describing filtra� tion combustion has the form (1, 2)