TY - JOUR
T1 - Prediction of 3D transversal patterns in packed-bed reactors using a reduced 2D model
T2 - Oscillatory kinetics
AU - Nekhamkina, Olga
AU - Sheintuch, Moshe
PY - 2010/11/3
Y1 - 2010/11/3
N2 - We have recently showed the formation of transversal patterns in a 3D cylindrical reactor in which an exothermic first-order reaction of Arrhenius kinetics occurs with variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution, with the front position oscillating in the axial direction, while in the 3D case, three types of transversal patterns can emerge: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating-oscillating fronts. In the present study, we analyze the possible reduction of the 3D model to a 2D cylindrical shell model to predict patterns. We map bifurcation diagrams showing domains of different modes using the reactor radius (R) as a bifurcation parameter and show that the front divergence and the domains of the kn-mode pattern in the 3D model [corresponding to the transversal eigenfunction Jk(μknr) exp(ikθ), in which Jk is the Bessel function of the first kind] can be predicted by those of the one wave in the 2D model using the linear transformation R 3D = μknR2D.
AB - We have recently showed the formation of transversal patterns in a 3D cylindrical reactor in which an exothermic first-order reaction of Arrhenius kinetics occurs with variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution, with the front position oscillating in the axial direction, while in the 3D case, three types of transversal patterns can emerge: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating-oscillating fronts. In the present study, we analyze the possible reduction of the 3D model to a 2D cylindrical shell model to predict patterns. We map bifurcation diagrams showing domains of different modes using the reactor radius (R) as a bifurcation parameter and show that the front divergence and the domains of the kn-mode pattern in the 3D model [corresponding to the transversal eigenfunction Jk(μknr) exp(ikθ), in which Jk is the Bessel function of the first kind] can be predicted by those of the one wave in the 2D model using the linear transformation R 3D = μknR2D.
UR - http://www.scopus.com/inward/record.url?scp=78049355091&partnerID=8YFLogxK
U2 - 10.1021/ie100531e
DO - 10.1021/ie100531e
M3 - 文章
AN - SCOPUS:78049355091
SN - 0888-5885
VL - 49
SP - 10558
EP - 10564
JO - Industrial and Engineering Chemistry Research
JF - Industrial and Engineering Chemistry Research
IS - 21
ER -