A spectral approach to reaction/diffusion kinetics in chaotic flows

A classical spectral approach based on the set of eigenfunctions of the Laplacian operator is proposed for the numerical solution of advection/diffusion/reaction equations for reactive mixing in 2-D laminar chaotic flows. This approach overcomes numerical diffusion problems and provides accurate spatiotemporal concentration fields in reasonable computer time up to very high values of Pe, such as Pe=105 and higher. Moreover, a pseudo-spectral approach, combining spectral expansion with an FFT algorithm, provides an efficient computational strategy for both polynomial and non-polynomial nonlinearities such as those arising in non-isothermal reactive mixing problems with Arrhenius dependence of kinetic rates on temperature.

[1]  S. Wiggins,et al.  An analytical study of transport, mixing and chaos in an unsteady vortical flow , 1990, Journal of Fluid Mechanics.

[2]  Fernando J. Muzzio,et al.  The geometry of mixing in time-periodic chaotic flows.: I. asymptotic directionality in physically realizable flows and global invariant properties , 1999 .

[3]  J. M. Zalc,et al.  Parallel-competitive reactions in a two-dimensional chaotic flow , 1999 .

[4]  S. W. Jones.  Interaction of chaotic advection and diffusion , 1994 .

[5]  Julio M. Ottino,et al.  A case study of chaotic mixing in deterministic flows: The partitioned-pipe mixer , 1987 .

[6]  R. Temam.  Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[7]  Ottino,et al.  Diffusion and reaction in a lamellar system: Self-similarity with finite rates of reaction. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[8]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[9]  Julio M. Ottino,et al.  Potentialities and limitations of mixing simulations , 1995 .

[10]  H. Aref.  Stirring by chaotic advection , 1984, Journal of Fluid Mechanics.

[11]  Patrick Patrick Anderson,et al.  Mixing of non-Newtonian fluids in time-periodic cavity flows , 2000 .

[12]  Andrew C. Poje,et al.  Universal properties of chaotic transport in the presence of diffusion , 1999 .

[13]  Hsueh-Chia Chang,et al.  Instability of a Criminale-Ericksen-Filbey fluid in a disk-and-cylinder system , 1990 .

[14]  S. Wiggins,et al.  Invariant manifold templates for chaotic advection , 1994 .

[15]  Spatial organization in the A+B→0 reaction under confined-scale mixing , 1997 .

[16]  O. S. Galaktionov,et al.  A mapping approach for three-dimensional distributive mixing analysis , 2001 .

[17]  Julio M. Ottino,et al.  Conversion and selectivity modifications due to mixing in unpremixed reactors , 1982 .

[18]  F. Muzzio,et al.  The Kenics Static Mixer : a Three-dimensional Chaotic Flow , 1997 .

[19]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[20]  Bidkar,et al.  Collision rates in chaotic flows: Dilute suspensions. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[21]  Hsueh-Chia Chang,et al.  Flow in periodically constricted tubes: Transition to inertial and nonsteady flows , 1986 .

[22]  Ottino,et al.  Visualization of three-dimensional chaos , 1998, Science.

[23]  Julio M. Ottino,et al.  Experiments on mixing due to chaotic advection in a cavity , 1989, Journal of Fluid Mechanics.

[24]  Jerzy Bałdyga,et al.  Turbulent Mixing and Chemical Reactions , 1999 .

[25]  Sokolov,et al.  Diffusion-controlled reactions in lamellar systems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[26]  Scott W. Jones,et al.  The enhancement of mixing by chaotic advection , 1991 .

[27]  Fernando J. Muzzio,et al.  Quantification of mixing in aperiodic chaotic flows , 1994 .

[28]  Kinetics of the A+B --> 0 reaction under steady and turbulent flows , 1996 .

[29]  R. Roberts,et al.  Wave-enhanced interfacial transfer , 2000 .

[30]  Sokolov,et al.  Distribution of striation thicknesses in reacting lamellar systems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[31]  An orthonormal basis of solenoidal vector functions vanishing on a cylinder , 1990 .

[32]  Hsueh-Chia Chang,et al.  Effect of chaotic interfacial stretching on bimolecular chemical reaction in helical-coil reactors , 1996 .

[33]  J. Ottino.  Mixing, chaotic advection, and turbulence , 1990 .

[34]  Metcalfe,et al.  Autocatalytic processes in mixing flows. , 1994, Physical review letters.

[35]  Hassan Peerhossaini,et al.  The effects of chaotic advection on heat transfer , 1997 .

[36]  Hsueh-Chia Chang,et al.  Heat transfer enhancement in three-dimensional corrugated channel flow , 1998 .

[37]  F. Muzzio,et al.  Structure of the stretching field in chaotic cavity flows , 1994 .

[38]  F. Muzzio,et al.  Chemical reactions in chaotic flows , 1996 .

[39]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[40]  Fernando J. Muzzio,et al.  The geometry of mixing in 2-d time-periodic chaotic flows , 2000 .

[41]  M. Sen,et al.  Application of chaotic advection to heat transfer , 1994 .

[42]  Ottino,et al.  Evolution of a lamellar system with diffusion and reaction: A scaling approach. , 1989, Physical review letters.

[43]  Florence Raynal,et al.  Energy saving in chaotic laminar mixing , 1997 .