A class of discontinuous dynamical systems I. An ideal gas–liquid system

When a liquid and a gas are sent into a closed system and withdrawn through a single outlet, discontinuous behaviour results. Two different models are applicable to this system depending on whether the liquid or the gas flows out. The system switches between the gas flow and the liquid flow incessan...

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Bibliographic Details
Published in:Chemical engineering science 2001-06, Vol.56 (11), p.3595-3609
Main Authors: Moudgalya, Kannan M., Ryali, Venkatarao
Format: Article
Language:English
Subjects:
Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization
Applied sciences
Chemical engineering
Discontinuous systems
Dynamic simulation
Exact sciences and technology
Long time behaviour
Mathematical modelling
Organic polymers
Physicochemistry of polymers
Polymerization
Preparation, kinetics, thermodynamics, mechanism and catalysts
Reaction engineering
Sliding motion
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Summary:When a liquid and a gas are sent into a closed system and withdrawn through a single outlet, discontinuous behaviour results. Two different models are applicable to this system depending on whether the liquid or the gas flows out. The system switches between the gas flow and the liquid flow incessantly, reaching a state of sliding motion (Filippov, Differential Equations with Discontinuous Righthand Sides. Mathematics and its Applications (Soviet Series), Kluwer, Dordrecht, 1988). It is shown that the state of sliding motion is reached from all starting positions. The sliding motion is also shown to be stable. The steady state of the sliding motion can also be considered as a time-averaged steady state. Simulation results support these predictions. Similar results are obtained in the presence of a control valve.
ISSN:0009-2509
1873-4405
DOI:10.1016/S0009-2509(01)00043-4