Research Papers: Fundamental Issues and Canonical Flows

Advanced Quasi-Steady State Approximation for Chemical Kinetics

[+] Author and Article Information
Sharath S. Girimaji

e-mail: girimaji@aero.tamu.edu

Ashraf A. Ibrahim

e-mail: ashraf235@tamu.edu
Aerospace Engineering Department,
Texas A&M University,
College Station, TX 77843

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 29, 2012; final manuscript received August 30, 2013; published online December 24, 2013. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(3), 031201 (Dec 24, 2013) (9 pages) Paper No: FE-12-1265; doi: 10.1115/1.4026015 History: Received May 29, 2012; Revised August 30, 2013

The computational feasibility of many systems with large degrees of freedom such as chemically reacting systems hinges on the reduction of the set to a manageable size with a minimal loss of relevant information. Several sophisticated reduction techniques based on different rationales have been proposed; however, there is no consensus on the best approach or method. While the search for simple but accurate schemes continues, the classical quasi-steady state assumption (QSSA), despite serious shortcomings, remains popular due to its conceptual and computational simplicity. Invoking the similarity between a reduced invariant manifold and a streamline in fluid flow, we develop an advanced QSSA procedure which yields the accuracy of more complex reduction schemes. This flow-physics inspired approach also serves to reconcile the classical QSSA approach with recent methods such as functional equation truncation (FET) and intrinsic low dimensional manifold (ILDM) approaches.

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Fig. 1

The system trajectories tend rapidly to the slow manifold

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Fig. 2

The exact manifold and the different approximations of it

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Fig. 3

The trajectories of the Michaelis–Menten system for η = 0.5 and ɛ = 10.0. The trajectories tend to a one-dimensional manifold and they converge along the manifold to the equilibrium point (0,0).

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Fig. 4

The QSSA, LLA, and ILDM manifolds of the Michaelis–Menten system with η = 0.5 and ɛ = 10.0. The LLA and ILDM manifolds (solid line) are identical

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Fig. 5

The competitive inhibition system trajectories for L1 = 0.99, L2 = 1.0, L3 = 0.05, L4 = 0.10, and μ = 1.00. The trajectories converge to a two-dimensional manifold before reaching the equilibrium state.

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Fig. 6

The QSSA approximation of the two-dimensional slow manifold of the the competitive inhibition system

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Fig. 7

The LLA approximation of the two-dimensional slow manifold of the competitive inhibition system

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Fig. 8

A cross section for the LLA, ILDM, and QSSA manifolds at x = 0.2

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Fig. 9

The intersection of the LLA, ILDM, and QSSA manifolds with the plane x = y




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