ANZIAM J.
45 (2004), 303-326
|
Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation.
|
M. I. Nelson
School of Mathematics and Applied Statistics
The University of Wollongong
Wollongong, NSW 2522
Australia
mnelson@uow.edu.au
|
|
|
H. S. Sidhu
School of Physical, Environmental
and Mathematical Sciences
University College
University of New South Wales
Australian Defence Force Academy
Canberra 2600
Australia
|
|
|
Abstract
|
We extend an investigation into the
bifurcation phenomena exhibited by an oxidation
reaction in an adiabatic reactor to the case of a
diabatic reactor. The primary bifurcation
parameter is the fuel fraction; the inflow
pressure and inflow temperature are the secondary
bifurcation parameters. The inclusion of heat
loss in the model does not change the static
steady-state bifurcation diagram; the organising
centre is a pitchfork singularity for both the
adiabatic and diabatic reactors. However, unlike
the adiabatic reactor, Hopf bifurcations may
occur in the diabatic reactor. We construct the
degenerate Hopf bifurcation curve by determining
the double-Hopf locus. When the steady-state and
degenerate Hopf bifurcation diagrams are combined
it is found that there are 23 generic
steady-state diagrams over the parameter region
of interest. The implications of these structures
from the perspective of flammability in the CSTR
are discussed.
|
Download the article in PDF format (size 496 Kb)
|
|
|
|