Transversal thermal patterns in packed‐bed reactors with simple kinetics: Bifurcation criterion and simulations

We derive a new criterion for transversal instability of planar fronts based on the bifurcation condition dV_f/dK|_K=0 = 0, where V_f and K are the front velocity and its curvature, respectively. This refines our previously obtained condition, which was formulated as α = (ΔT_adPe_T)/(ΔT_mPe_C) > 1 to α > 1 + |δ|, where ΔT_ad and ΔT_m are the adiabatic and maximal temperature rise, respectively, Pe_C and Pe_T are the axial mass and the heat Pe numbers, respectively, and δ is a small parameter. The criterion is based on approximate relations for ΔT_m and V_f, which account for the local curvature of a propagating front in a packed bed reactor with a first‐order activated kinetics. The obtained relations are verified by linear stability analysis of planar fronts. Simulations of a simplified 2D model in the form of a thin cylindrical shell are in good agreement with the critical parameters predicted by dispersion relations. Three types of patterns were detected in simulations: “frozen” multiwave patterns, spinning waves, and complex rotating–oscillating patterns. We map bifurcation diagrams showing domains of different modes using the shell radius as the bifurcation parameter. The possible translation of the 2D cylindrical shell model results to the 3D case is discussed. © 2010 American Institute of Chemical Engineers AIChE J, 2011