CHAOS IN A PERIODICALLY PERTURBED CSTR

Abstract

The occurrence of chaotic behavior is analyzed in a periodically perturbed dynamic nonisothermal CSTR with first-order exothermic chemical reaction A→B and an Arrhenius expression for the rate constant. When sinusoidal forcing functions for the cooling-fluid temperature and the volumetric feed rate are applied to the unperturbed part of the system, period-doubling behavior leading to a strange attractor is observed as the amplitude of the perturbation in the cooling-fluid temperature is increased. Chaos and period-doubling are also verified through Fourier spectra analysis, adherence to the Feigenbaum Theory, and analysis of the Poincare return map

The basis for obtaining chaotic behavior in the reactor system is the Melnikov theory, which slates that chaos can be obtained in a periodically perturbed system if the phase plot of the unperturbed system closely corresponds to that of a homoclinic orbit (a phase trajectory which contains the stable and unstable separatrices of a saddle). From linear stability analysis of the unperturbed reactor system along with certain geometric considerations, the range of parameter values is obtained wherein a homoclinic orbit is present. For parameter values close to this bifurcation, chaotic behavior is observed when periodic perturbation is applied to the cooling-fluid temperature and volumetric feed rate.

KEYWORDS:

• Chaos
• Nonisothermal CSTR
• Homoclinic orbit
• Strange attractor
• Reactor dynamics

Additional information

Notes on contributors

GERARD T. CANEBA

Department of Chemistry and Chemical Engineering, Michigan Technological University, Houghton, MI 49931.