The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1017/S1446181100013389.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1023/B:JOMC.0000014308.66514.e7.
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.
M.I. Nelson and H.S. Sidhu. Bifurcation phenomena for an oxidation reaction in a continuously stirred tank reactor. II Diabatic operation. The Anziam Journal, 45, 303-326, 2004. http://dx.doi.org/10.1017/S1446181100013389.
Abstract
It is often numerically convenient to reduce models in two-dimensions
to one-dimension. This can be done formally through the use of
centre manifold techniques, or informally using physical reasoning.
We investigate the extent to which flammability limits in a
two-dimensional slab are
accurately represented by the values in the corresponding
one-dimensional slab.
We use a simple chemical
mechanism containing exothermic and endothermic reactions that has been used
to model the combustion of hydrocarbon fragments produced by polymer pyrolysis.
M.I. Nelson and H.S. Sidhu. Flammability limits of an oxidation reaction in a batch reactor. II The Rychlý mechanism. Journal of Mathematical Chemistry, 35(2), 119-129, February 2004.
The DOI (Digital Object Identifier) link for this article is http://dx.doi.org/10.1023/B:JOMC.0000014308.66514.e7.
Abstract
The problem of heat and mass transfer within a porous catalytic pellet
in which an irreversible first-order exothermic reaction occurs is
a much studied problem in chemical reactor engineering. The system is
described by two coupled reaction-diffusion equations for the temperature
and the degree of reactant conversion.
The Galerkin method is used to obtain a semi-analytical model for the pellet
problem with both one and two-dimensional slab geometries. This
involves approximating the spatial structure of the temperature and
reactant conversion profiles in the pellet using trial functions.
The semi-analytical model is obtained by averaging the governing partial
differential equations. As the Arrhenius law cannot be integrated
explicitly, the semi-analytical model is given by a system of
integro-differential equations.
The semi-analytical model allows both steady-state temperature and
conversion profiles and steady-state diagrams to be obtained
as the solution to sets of transcendental equations (the integrals
are evaluated using quadrature rules). Both the static and dynamic
multiplicity of the semi-analytical model is investigated using
singularity theory and a local stability anlaysis. An example of a
stable limit-cycle is also considered in detail. Comparison with
numerical solutions of the governing reaction-diffusion equations and with
other results in the literature shows that the semi-analytical solutions
are extremely accurate.
T.R. Marchant and M.I. Nelson. Semi-analytical solutions for one and two-dimensional pellet problems. Proceedings of the Royal Society of London A, 460, 2381-2394, 2004.