Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors

Russo, Lucia; Mancusi, Erasmo; Maffettone, Pier Luca; Crescitelli, Silvestro

doi:10.1016/s0009-2509(02)00425-6

Cited by 29 publications

(34 citation statements)

References 45 publications

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“…The analysis of the periodic solution φ 0 (t, y 0 ) reduces to the analysis of the fixed point x 0 = 0 of the Poincaré map P or of the half-period-flip map H, and we have reverted to the previous problem. If x 0 is a point of the periodic orbit of (9) or (17), it is a fixed point of both P and H. The actions of P and H on points neighboring x 0 are illustrated in Fig. 3.…”

Section: Bifurcations With a Z 2 Spatio-temporal Symmetrymentioning

confidence: 99%

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Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry

Marqués

Lopez

Blackburn

2004

Physica D: Nonlinear Phenomena

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Section: Bifurcations With a Z 2 Spatio-temporal Symmetrymentioning

confidence: 99%

“…[14]), and the dynamic consequences of this type of spatio-temporal symmetry have been explored in diverse circumstances (e.g. [11,17]). …”

Section: Introductionmentioning

confidence: 99%

Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry

Marqués

Lopez

Blackburn

2004

Physica D: Nonlinear Phenomena

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“…In this section, the conditions to obtain induced oscillations through the PI 1 and PI 2 controllers are researched (simplified models in which the self-oscillations are used to improve the performance of different kind of reactors can be found in Refs [23][24][25][26]). …”

Section: Induced Oscillations Originated By the Controllers Pi 1 And mentioning

confidence: 99%

Increasing the reactant conversion through induced oscillations in a continuous stirred tank reactor by using PI control

Pérez-Polo

Pérez-Molina

2013

Journal of Process Control

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We report a strategy to increase the reactant conversion in a continuous stirred tank reactor (CSTR) to produce propylene glycol through induced oscillations generated by two controllers PI 1 and PI 2 that manipulate the reactor outlet flow and the coolant flow rate respectively. It is shown that an adequate parameter choice for the PI controllers allows one to derive sustained oscillations in the concentrations and reactor temperature, which in turn allows increasing the propylene glycol production. For a suitable choice of the PI 1 and PI 2 controller parameters, we use a complete reactor model that provides with physically feasible parameters. The issues of external disturbance rejection, self-oscillations and stability have also been discussed. The analytical calculations are verified by means of full numerical simulations.

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“…The considered regimes are symmetric as the corresponding spatiotemporal patterns repeat unchanged during each cycle provided that the sequence of reactor units is appropriately permutated. 15 Moreover, they give rise to sequences (or trains) of temperature waves travelling over the catalytic bed in the flow direction. Each temperature wave results from a hot bed region delimitated by two temperature fronts and separates two consecutive cold bed regions.…”

Section: Model Equationsmentioning

confidence: 99%

Temperature wave‐trains of periodically forced networks of catalytic reactors

Altimari¹,

Mancusi²,

Russo³

et al. 2011

AIChE Journal

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Networks of N identical catalytic reactors with periodically switched inlet and outlet sections are studied for first-order irreversible exothermic reactions. Switching strategies with inlet and outlet sections periodically jumping a fixed number n s of reactors are considered and the mechanisms governing the formation of traveling temperature wave-trains are analyzed as n s and N are varied. To this aim, a geometric approach to the analysis of the network energy balance is developed. Based on this approach, infinite domains of traveling temperature wave-trains are predicted for any n s and N. Analytical approximations are derived for the stability limits and the spatiotemporal patterns of these regimes. Stability boundaries predicted analytically include for any solution the largest part of the stability region computed by numerical simulation. Moreover, good agreement is found between the structure of the spatiotemporal patterns computed numerically and that predicted based on the proposed approach.

show abstract

Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors

Cited by 29 publications

References 45 publications

Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry

Bifurcations in systems with Z2 spatio-temporal and O(2) spatial symmetry

Increasing the reactant conversion through induced oscillations in a continuous stirred tank reactor by using PI control

Temperature wave‐trains of periodically forced networks of catalytic reactors

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