Dynamic behaviour of coupled CSTRs operating under different conditions
01 Jan 1983-Chemical Engineering Science (Pergamon)-Vol. 38, Iss: 5, pp 673-686
TL;DR: In this article, the consequences of coupling two independent CSTRs operating under different stability conditions are analyzed, and a variety of behavioural patterns of the coupled system have been shown to exist for different types of reactor combinations.
About: This article is published in Chemical Engineering Science.The article was published on 1983-01-01. It has received 18 citations till now. The article focuses on the topics: Distributed parameter system.
TL;DR: The characteristics of the different coupling strategies and scenarios that lead to amplitude death in a variety of different situations are discussed, and several open issues and challenging problems for further study are drawn attention.
Abstract: When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.
TL;DR: In this article, the authors discuss the characteristics of different coupling strategies and scenarios that lead to amplitude death in a variety of different situations, and draw attention to several open issues and challenging problems for further study.
TL;DR: In this paper, a review brings attention to much of the recent literature describing these developments and their applications, particularly regarding complex and chaotic oscillations, as well as reported experimental observations which, in many cases, have provided support for prior theory and in many others, have led to new theoretical developments.
TL;DR: In this paper, it is shown that with an increase in the amplitude of the forcing that quasiperiodic behaviour occurs, followed by a sequence of period doubling bifurcations leading to chaos.
TL;DR: In this article, a polycrystalline Pt wire loop was used to measure the rate of CO oxidation in a gas flow reactor over a range of gas temperatures and CO partial pressures, and the reaction rate was measured using a thermocouple spotwelded to the loop.
TL;DR: In this article, the types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites.
TL;DR: Under appropriate conditions the cerium catalyzed oxidation of malonic acid by bromate in acid medium exhibits a numer of interesting phenomena, including sustained periodic the coexistence of alternative stable steady states, and the conditions for periodic “echo” waves in an excitable medium.
Abstract: Under appropriate conditions the cerium catalyzed oxidation of malonic acid by bromate in acid medium exhibits a numer of interesting phenomena, including sustained periodic the coexistence of alternative stable steady states,i4 nonperiodic (“chaotic”) oscillation^,^^^ and spatiotemporal waves of chemical Some insight into the mechanism that generates such diverse behavior can be gained by examining simple models of this reaction. Because of the wide separation of time scales, which occurs naturally in this problem, it is possible to derive analytic expressions in terms of system parameters for characteristic properties of models, such as the waveform and period of oscillations, the domain of existence of multiple steady states, and the conditions for periodic “echo” waves in an excitable medium.
TL;DR: In this article, it was shown that screw-type chaos is possible in the Zhabotinskii reaction with a simple Bonhoeffer-van der Pol circuit, which can be run as both an astable and a monostable "flip-flop".
Abstract: THE Belousov–Zhabotinskii reaction is a chemical Bonhoeffer–van der Pol circuit, that is, a relaxation oscillator that can be run as both an astable and a monostable ‘flip-flop’1–3. Apparently the reaction also belongs to the slightly more complicated class of‘universal circuits’4 as introduced by Khaikin5–6. Oscillators of this type not only show ‘smooth’ and ‘relaxation type’ oscillations5–6, but also ‘chaotic’ oscillations4. As evidenced by the simplest equation of this type7, both ‘spiral type’ and ‘screw type’ chaos20 are possible in such systems. We present here preliminary evidence for the occurrence of screw-type chaos in the Zhabotinskii reaction.
TL;DR: The chemical reactor is the heart of any chemical process, as it is here that the chemical transformation takes place for which the whole plant was designed as discussed by the authors, and it does not work in isolation: a great deal of ancillary equipment may be needed to prepare and deliver the raw materials and to separate or purify the products.
Abstract: The chemical reactor is the heart of any chemical process, as it is here that the chemical transformation takes place for which the whole plant was designed. Like the biological heart, it does not work in isolation: a great deal of ancillary equipment may be needed to prepare and deliver the raw materials and to separate or purify the products. Though the reactor cannot be considered in isolation from its surroundings, it still remains the locus of the transformation from less valuable inputs to more valuable outputs. In crass economic terms it is where the profit is made. and this alone would command a certain attention from the engineer. But from a scientific, rather than technological, point of view its claims are no less; for chemical reactor theory is the source of some of the most varied and interesting models in the whole of engineering science while the analytical understanding of the natural chemical reactors of the biological sciences is still in its infancy. Chemical reactors come in all shapes and sizes. Sulfur dioxide for sulfuric acid is sometimes made by the reaction of anhydrite, shale, and coke in a rotating kiln 230 feet long and 1 1 feet in diameter, built to withstand a firing temperature of I600'C near the inlet. On the other hand, a superphosphate fertilizer is ammoniated in a 3by 3-foot drum, which granulates the product at the same time. The Fischer-Tropsch synthesis of fuel requires a vertical cylinder 30 feet high and 3 feet in diameter containing 7 tons of catalyst at some 500°F and 350 psi. This bed of catalyst is kept in suspension by the mixture of synthesis gas and cooling oil that is the feed. I n other processes, such as the catalytic cracking of crude oil, the catalyst bed may be fully fluidized: a bubbling bed of fine particles with many fluid characteristics. An important part of the reaction may take place in the transfer pipes by which the reactor is fed-a surprise perhaps to the first designers, but something they were quick to take advantage of. There are self-operating reactors in which changes are not intended or perhaps cannot be controlled. No doubt certain reactions will take place in the Alaska pipeline, making it the largest man-made reactor of all: but these will be incidental and so slow as to be unimportant. One challenge for the biochemical engineer might be to breed a bug that would improve crude oil, say by desulfurizing it, so that the long journey from Alaska could be turned to positive advantage. These are continuous processes and require continuous reactors. There are also batch reactors for discontinuous processes, ranging from the beaker or flask used i n the lab to 30.000-gallon fermentors for producing lactic acid from cornstarch. Specialty soaps are made in kettles ranging from 5 to 15 feet in height and 4 to 10 feet in diameter, fitted with steam coils or jackets and stirred with paddles