Industrial & Engineering Chemistry Research, Vol.50, No.8, 4335-4344, 2011
Dynamics of Mixing-Limited Pattern Formation in Non isothermal Homogeneous Autocatalytic Reactors: A Low-Dimensional Computational Analysis
This work studies the temporal evolution of concentration and temperature patterns in fast, homogeneous, nonisothermal, autocatalytic, adiabatic tubular reactors. Transverse patterns are simulated using a two-dimensional unsteady state model, called the regularized model, obtained by averaging the 3-D convection-diffusion-reaction equations axially using a Liapunov-Schmidt based averaging technique, followed by regularization. Steady state bifurcation and linear stability analysis show that the patterns emerge from the unstable middle branch of the S-shaped steady state bifurcation diagrams of concentration/temperature versus reactor Damkohler number. This unstable steady state is then slightly perturbed to analyze the evolution dynamics of various symmetric and asymmetric concentration and temperature patterns. Our simulations show how zones with slightly differing concentrations and temperature evolve over time into intensely segregated patterns that slowly diffuse into the homogeneous ignited branch of the steady state curve. Our parametric analysis quantifies the effects of process parameters such as transverse and axial Peclet numbers, Damkohler number, Zeldovich number, and Lewis number on the dynamics and intensity of pattern formation and dissolution. Interesting differences between the mechanics of pattern formation in isothermal and nonisothermal autocatalysis are also discussed.