213 research outputs found
On inhibiting runaway in catalytic reactors
We consider the problem of heat and mass transfer in porous catalyst pellets. Both the steady and time dependent operating characteristics are studied. Accurate approximate equations are derived from the basic governing equations of motion. A nonlinear stability analysis is employed to account for the observation that under certain conditions reactions on catalyst pellets can pass transiently stably into a region which would correspond to instability in the steady state. One consequence of our analysis is a possible control mechanism which inhibits temperature runaway by extending the stable operating characteristics desirable in modern reactors
Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames
We describe spatial and temporal patterns in cylindrical premixed flames in
the cellular regime, , where the Lewis number is the ratio of
thermal to mass diffusivity of a deficient component of the combustible
mixture. A transition from stationary, axisymmetric flames to stationary
cellular flames is predicted analytically if is decreased below a critical
value. We present the results of numerical computations to show that as is
further decreased traveling waves (TWs) along the flame front arise via an
infinite-period bifurcation which breaks the reflection symmetry of the
cellular array. Upon further decreasing different kinds of periodically
modulated traveling waves (MTWs) as well as a branch of quasiperiodically
modulated traveling waves (QPMTWs) arise. These transitions are accompanied by
the development of different spatial and temporal symmetries including period
doublings and period halvings. We also observe the apparently chaotic temporal
behavior of a disordered cellular pattern involving creation and annihilation
of cells. We analytically describe the stability of the TW solution near its
onset+ using suitable phase-amplitude equations. Within this framework one of
the MTW's can be identified as a localized wave traveling through an underlying
stationary, spatially periodic structure. We study the Eckhaus instability of
the TW and find that in general they are unstable at onset in infinite systems.
They can, however, become stable for larger amplitudes.Comment: to appear in Physica D 28 pages (LaTeX), 11 figures (2MB postscript
file
An adaptive pseudo-spectral method for reaction diffusion problems
The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions
Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension
AbstractWe consider the Saffman-Taylor problem describing the displacement of one fluid by another having a smaller viscosity, in a porous medium or in a Hele-Shaw configuration, and the Taylor-Saffman problem of a bubble moving in a channel containing moving fluid. Each problem is known to possess a family of solutions, the former corresponding to propagating fingers and the latter to propagating bubbles, with each member characterized by its own velocity and each occupying a different fraction of the porous channel through which it propagates. To select the correct member of the family of solutions, the conventional approach has been to add surface tension σ and then take the limit σ → 0. We propose a selection criterion that does not rely on surface tension arguments
On the Birth of Isolas
Isolas are isolated, closed curves of solution branches of nonlinear problems. They have been observed to occur in the buckling of elastic shells, the equilibrium states of chemical reactors and other problems. In this paper we present a theory to describe analytically the structure of a class of isolas. Specifically, we consider isolas that shrink to a point as a parameter Ï„ of the problem, approaches a critical value Ï„_0. The point is referred to as an isola center. Equations that characterize the isola centers are given. Then solutions are constructed in a neighborhood of the isola centers by perturbation expansions in a small
parameter ε that is proportional to (τ-τo), with a appropriately determined. The theory is applied to a
chemical reactor problem
A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points : (prepublication)
Spiral flames
AbstractWe describe computations of periodic and meandering spiral patterns in a reaction-diffusion model of flames
- …