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On slow manifolds of chemically reactive systems

J. Chem. Phys. 117, 1482 (2002); doi:10.1063/1.1485959

Issue Date: 22 July 2002

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Sandeep Singh, Joseph M. Powers, and Samuel Paolucci
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556-5637
This work addresses the construction of slow manifolds for chemically reactive flows. This construction relies on the same decomposition of a local eigensystem that is used in formation of what are known as Intrinsic Low Dimensional Manifolds (ILDMs). We first clarify the accuracy of the standard ILDM approximation to the set of ordinary differential equations which model spatially homogeneous reactive systems. It is shown that the ILDM is actually only an approximation of the more fundamental Slow Invariant Manifold (SIM) for the same system. Subsequently, we give an improved extension of the standard ILDM method to systems where reaction couples with convection and diffusion. Reduced model equations are obtained by equilibrating the fast dynamics of a closely coupled reaction/convection/diffusion system and resolving only the slow dynamics of the same system in order to reduce computational costs, while maintaining a desired level of accuracy. The improvement is realized through formulation of an elliptic system of partial differential equations which describe the infinite-dimensional Approximate Slow Invariant Manifold (ASIM) for the reactive flow system. This is demonstrated on a simple reaction-diffusion system, where we show that the error incurred when using the ASIM is less than that incurred by use of the Maas-Pope Projection (MPP) of the diffusion effects onto the ILDM. This comparison is further done for ozone decomposition in a premixed laminar flame where an error analysis shows a similar trend. ©2002 American Institute of Physics.
History: Received 13 November 2001; accepted 23 April 2002
Permalink: http://link.aip.org/link/?JCPSA6/117/1482/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.70.Fw
    Fluid dynamics Reactive, radiative, or nonequilibrium flows Chemically reactive flows
  • 82.40.Ck
    Physical chemistry and chemical physics Chemical kinetics and reactions: special regimes and techniques Pattern formation in reactions with diffusion, flow and heat transfer
  • 02.10.Ud
    Mathematical methods in physics Logic, set theory, and algebra Linear algebra
  • 02.30.Jr
    Mathematical methods in physics Function theory, analysis Partial differential equations
  • 47.27.Te
    Fluid dynamics Turbulent flows, convection, and heat transfer Convection and heat transfer
  • YEAR: 2002

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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