Intrinsic low-dimensional manifold

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In chemical kinetics, an intrinsic low-dimensional manifold is a technique to simplify the study of reaction mechanisms using dynamical systems, first proposed in 1992. [1] [2] [3]

The ILDM approach fixes a low dimensional surface which describes well the slow dynamics and assumes that after a short time the fast dynamics are less important and the system can be described in the lower-dimensional space. [4]

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Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While activation energy must be supplied to initiate combustion, the heat from a flame may provide enough energy to make the reaction self-sustaining.

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In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (Ea) of a reaction is measured in joules per mole (J/mol), kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Activation energy can be thought of as the magnitude of the potential barrier (sometimes called the energy barrier) separating minima of the potential energy surface pertaining to the initial and final thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy. The term "activation energy" was introduced in 1889 by the Swedish scientist Svante Arrhenius.

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In mathematics, inertial manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth, invariant manifolds that contain the global attractor and attract all solutions exponentially quickly. Since an inertial manifold is finite-dimensional even if the original system is infinite-dimensional, and because most of the dynamics for the system takes place on the inertial manifold, studying the dynamics on an inertial manifold produces a considerable simplification in the study of the dynamics of the original system.

Combustion models for CFD refers to combustion models for computational fluid dynamics. Combustion is defined as a chemical reaction in which a hydrocarbon fuel reacts with an oxidant to form products, accompanied with the release of energy in the form of heat. Being the integral part of various engineering applications like: internal combustion engines, aircraft engines, rocket engines, furnaces, and power station combustors, combustion manifests itself as a wide domain during the design, analysis and performance characteristics stages of the above-mentioned applications. With the added complexity of chemical kinetics and achieving reacting flow mixture environment, proper modeling physics has to be incorporated during computational fluid dynamic (CFD) simulations of combustion. Hence the following discussion presents a general outline of the various adequate models incorporated with the Computational fluid dynamic code to model the process of combustion.

References

  1. Maas, U.; Pope, S. B. (1992). "Implementation of simplified chemical kinetics based on intrinsic low-dimensional manifolds" (PDF). Symposium (International) on Combustion. 24: 103–112. doi:10.1016/S0082-0784(06)80017-2.
  2. Maas, U.; Pope, S. B. (1992). "Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space" (PDF). Combustion and Flame. 88 (3–4): 239. doi:10.1016/0010-2180(92)90034-M.
  3. Bongers, H.; Van Oijen, J. A.; De Goey, L. P. H. (2002). "Intrinsic low-dimensional manifold method extended with diffusion". Proceedings of the Combustion Institute. 29: 1371–1378. doi:10.1016/S1540-7489(02)80168-7.
  4. Tomlin, A. S.; Whitehouse, L.; Lowe, R. (2002). "The Estimation of Intrinsic Low Dimensional Manifold Dimension in Atmospheric Chemical Reaction Systems". Air Pollution Modelling and Simulation. p. 245. doi:10.1007/978-3-662-04956-3_25. ISBN   978-3-642-07637-4.