Hydrodynamic instability of thermal fronts in reactive porous media: spinning patterns.

The interaction of convection and reaction front propagation is known to exhibit a nonlinear phenomenons in the case of an adverse flow, i.e., when the gas velocity (V=[u,v]') and the front velocity (Vf) are of opposite directions. This was demonstrated both experimentally and analytically under isothermal conditions with Vf constant independent of V. Here we analyze thermal reaction front propagation in a porous medium in which an exothermic reaction of Arrhenius kinetics occurs. Numerical simulations of a packed-bed reactor model accounting for variable temperature, concentration, and hydrodynamic fields following the Euler-Darcy equations revealed emergence of spinning transversal patterns. Such solution cannot emerge in a two-variable (C,T) model, assuming "frozen" hydrodynamics, within a feasible domain of parameters. Two models are employed for analysis: a qualitative model based on a learning one-tube and two-tube consideration and an extended Landau-Darries instability analysis to account for the momentum losses and for a variable front propagation velocity. Both models revealed the important role of the Vf(u) dependence which can be presented as Vf=u-Vch, where the chemical component of the front velocity (Vch) depends on the main governing parameters such as the adiabatic temperature rise (ΔTa) and the inlet velocity (uin). The instability takes place if the parameter β=∂Vch/∂u<1. The effect of ΔTa, uin on the instability domain obtained in simulations can be translated to the effect of the parameter β.