TY - JOUR
T1 - Kinetic effects on transversal instability of planar fronts in packed-bed reactors
AU - Nekhamkina, Olga
AU - Sheintuch, Moshe
N1 - Funding Information:
This work is supported by Israel Science Foundation. ON is partially supported by the Center for Absorption in Science, Ministry of Immigrant Absorption State of Israel. MS is a member of the Minerva Center of Nonlinear Dynamics and Complex Systems.
PY - 2014/1/15
Y1 - 2014/1/15
N2 - We derive a new criterion for transversal instability of planar fronts in packed bed reactors (PBR's) in which nth order or Langmuir-Hinshelwood kinetics reaction occurs using a pseudo-homogeneous two-variables (C,T)-model. The derivation follows the analysis of combustion of reaction-diffusion systems by Sivashinsky, Comb. Sci. Tech. 15 (1977). The new criterion is expressed as a complicated relation of the ratio of the heat to mass dispersivities on the kinetic parameters. A necessary (but not sufficient) condition for emerging patterns in the reactor cross-section for the kinetic models studied is that (δTad/δTm)/(PeC/PeT)>1, where δTad and δTm are the adiabatic and the maximal temperature rise, respectively, PeC and PeT are the mass and the heat Peclet numbers, respectively. This condition agrees with our previous results that were limited to first order kinetics and is unlikely to be satisfied in PBR's. Also, unlike the previous condition, the new criterion allows to determine the critical wave number (minimal reactor radius) that can exhibit transversal patterns. The new criterion is verified by comparison with the linear stability results and with 3-D simulations.
AB - We derive a new criterion for transversal instability of planar fronts in packed bed reactors (PBR's) in which nth order or Langmuir-Hinshelwood kinetics reaction occurs using a pseudo-homogeneous two-variables (C,T)-model. The derivation follows the analysis of combustion of reaction-diffusion systems by Sivashinsky, Comb. Sci. Tech. 15 (1977). The new criterion is expressed as a complicated relation of the ratio of the heat to mass dispersivities on the kinetic parameters. A necessary (but not sufficient) condition for emerging patterns in the reactor cross-section for the kinetic models studied is that (δTad/δTm)/(PeC/PeT)>1, where δTad and δTm are the adiabatic and the maximal temperature rise, respectively, PeC and PeT are the mass and the heat Peclet numbers, respectively. This condition agrees with our previous results that were limited to first order kinetics and is unlikely to be satisfied in PBR's. Also, unlike the previous condition, the new criterion allows to determine the critical wave number (minimal reactor radius) that can exhibit transversal patterns. The new criterion is verified by comparison with the linear stability results and with 3-D simulations.
KW - Bifurcation criterion
KW - Mathematical modeling and simulations
KW - Nonlinear dynamics
KW - Packed bed
KW - Stability
KW - Transversal patterns
UR - http://www.scopus.com/inward/record.url?scp=84886685373&partnerID=8YFLogxK
U2 - 10.1016/j.cej.2013.09.050
DO - 10.1016/j.cej.2013.09.050
M3 - 文章
AN - SCOPUS:84886685373
SN - 1385-8947
VL - 236
SP - 212
EP - 222
JO - Chemical Engineering Journal
JF - Chemical Engineering Journal
ER -