Moving transversal hot zones in adiabatic, shallow packed‐bed reactors

Viswanathan, Ganesh A.; Luss, Dan

doi:10.1002/aic.10647

Cited by 18 publications

(40 citation statements)

References 49 publications

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“…This behavior is of academic and practical importance, as the PBR is the workhorse of the chemical‐producing and pollutant abatement industry, and here we tried to address the academic interest. Of the practical implications we should point out just a few: Transversal patterns can emerge with Pe C ≫ Pe T (even for 1/ Pe C = 0), as was shown for other 2D versions with oscillatory kinetics 12, 29, 30. This condition is valid in most systems.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 76%

“…Previous studies were focused on linear analysis of the first four modes (see Figure 1 with the corresponding μ mn ) in either 3D16, 27, 28 or shallow reactor models15, 16, 29, 30 and did not simulate patterns. Linear analysis suggests formation of moving nonrotating patterns of the form (2) while the unstable domains of certain modes were quite similar in 3D and SR models.…”

Section: Introductionmentioning

confidence: 99%

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Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Nekhamkina¹,

Sheintuch²

2010

AIChE Journal

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in Wiley Online Library (wileyonlinelibrary.com).Formation of transversal patterns in a 3D cylindrical reactor is studied with a catalytic reactor model in which an exothermic first-order reaction of Arrhenius kinetics occurs with a variable catalytic activity. Under these oscillatory kinetics, the system exhibits a planar front (1D) solution with the front position oscillating in the axial direction. Three types of patterns were simulated in the 3D system: rotating fronts, oscillating fronts with superimposed transversal (nonrotating) oscillations, and mixed rotating-oscillating fronts. These solutions coexist with the planar front solution and require special initial conditions. We map bifurcation diagrams showing domains of different modes using the reactor radius as a bifurcation parameter. The possible reduction of the 3D model to the 2D cylindrical shell model is discussed.

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Section: Discussion and Concluding Remarksmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Nekhamkina¹,

Sheintuch²

2010

AIChE Journal

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“…Sheintuch and Nekhamkina [19] analyzed the pattern formation in homogeneous model of a fixed catalytic bed for reactions with oscillatory kinetics. Viswanathan and Luss [20][21][22] ied the conditions for the existence of hot zones in a uniformly active shallow as well as long adiabatic packed bed reactors using a two-phase model. Mathematical models developed to study chemical reactors are derived from balances of species, energy, momentum and continuity in conjunction with various constitutive relationships, and they form a set of unsteady state three-dimensional partial differential equations containing a large set of physiochemical parameters.…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in homogeneous autocatalytic reactors

Gupta

Chakraborty

2009

Chemical Engineering Journal

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“…40 ] This approach has been demonstrated successfully for models of reactor operated under adiabatic conditions. [27][28][29]41 We extend this to nonadiabatic reactor model. The pseudo-homogeneous model of the shallow, non-adiabatic packed-bed reactor (SNAR) is (12) with the corresponding boundary conditions being…”

Section: ■ Calculations and Modelingmentioning

confidence: 98%

“…27,29 Therefore, to gain useful insights into the formation and dynamics of hot zones, we first study the shallow reactor model under nonadiabatic conditions, which is a limiting form of the full model 14 and can be obtained using the Liapunov−Schmidt reduction of the full model (eqs 2−9). 38,39 [Details of the method have been described by Viswanathan.…”

Section: ■ Calculations and Modelingmentioning

confidence: 99%

Impact of Wall Heat Transport on Formation of Transversal Hot Zones in Shallow, Non-adiabatic Packed-Bed Reactors

Narendiran

Viswanathan

2015

Ind. Eng. Chem. Res.

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Transversal hot zones have been reported to form in packed-bed reactors used to conduct exothermic reactions. Packed-bed reactors are usually operated under non-adiabatic conditions. Previous attempts to predict the formation of transversal hot zones have been made on both shallow and long reactors under adiabatic conditions; that is, wall heat transport is zero. We show that a rich variety of slowly oscillating transversal hot zones, such as rotating patterns, targets, and spirals, may form in shallow, non-adiabatic reactors. Under certain conditions, azimuthally symmetric target patterns coexist with azimuthally non-symmetric rotating patterns. Surprisingly, a small wall heat transport can force a traveling wave or band motion observed under adiabatic conditions into a rotating pattern. A transition from the rotating patterns and/or target patterns to spiral waves depends on the residence time, the reactor length scale, and the wall heat transfer coefficient. A shallow reactor model predicts that the spatiotemporal patterns oscillate at a very low frequency (order of 10 −5 Hz), which is in agreement with predictions based on laboratory experiments.

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Moving transversal hot zones in adiabatic, shallow packed‐bed reactors

Cited by 18 publications

References 49 publications

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Transversal patterns in three‐dimensional packed bed reactors: Oscillatory kinetics

Linear stability analysis of high- and low-dimensional models for describing mixing-limited pattern formation in homogeneous autocatalytic reactors

Impact of Wall Heat Transport on Formation of Transversal Hot Zones in Shallow, Non-adiabatic Packed-Bed Reactors

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