Reduced chemistry models

B. Using Reduced Chemistry Models in Multidimensional Simulations without Introducing Error... 

If one were able to guarantee that the reduced chemistry model reproduced the full-chemistry source term within a tolerance e for all F s in some range Y... 

The challenge is to construct reduced chemistry models which are fast to evaluate, yet which still satisfy the error tolerance Eq. (13). One effective approach to this is the Adaptive Chemistry method (Schwer et al., 2003a, b), where different reduced chemistry models are used under different local reaction conditions. For example, in the 1—d steady premixed flame studied by Oluwole et al. (Oluwole et al., 2006), six different reduced chemistry models were used, and the full chemistry model only had to be used at about 20% of the grid points, Fig. 14. 

C. Constructing Reduced Chemistry Models Satisfying Error Bounds Over Ranges... 

Fig. 15. Computed temperature field for a radially-symmetric partially-premixed methane-air laminar jet flame. The left-hand side shows the temperature field computed using the full chemistry simulation, and the right-hand side shows the temperature field computed using a set of reduced chemistry models that satisfy the error control constraints.

For gaseous flames, the LES/FMDF can be implemented via two combustion models (1) a finite-rate, reduced-chemistry model for nonequilibrium flames and (2) a near-equilibrium model employing detailed kinetics. In (1), a system of nonlinear ordinary differential equations (ODEs) is solved together with the FMDF equation for all the scalars (mass fractions and enthalpy). Finite-rate chemistry effects are explicitly and exactly" included in this procedure since the chemistry is closed in the formulation. In (2). the LES/FMDF is employed in conjunction with the equilibrium fuel-oxidation model. This model is enacted via fiamelet simulations, which consider a laminar counterflow (opposed jet) flame configuration. At low strain rates, the flame is usually close to equilibrium. Thus, the thermochemical variables are determined completely by the mixture fraction variable. A fiamelet library is coupled with the LES/FMDF solver in which transport of the mixture fraction is considered. It is useful to emphasize here that the PDF of the mixture fraction is not assumed a priori (as done in almost all other flamelet-based models), but is calculated explicitly via the FMDF. The LES/FMDF/flamelet solver is computationally less expensive than that described in (1) thus, it can be used for more complex flow configurations. 

Considerable work has already been carried out using ab initio calculations to predict the photodissociation dynamics of gas-phase metal carbonyls (45). This is a fertile area for computational work, given the extensive experimental results available, which include the use of ultrafast methods to characterize the short time behavior in photoexcited states. There is considerable evidence that surface crossings, especially of a spin-forbidden nature, play a considerable part in the dynamics. Much of the theoretical work so far has focused on reduced-dimensionality models of the PESs, which have been used in quantum mechanical smdies of the nonadiabatic nuclear dynamics, in which spin-forbidden transitions are frequently observed (45). Here, too, the potential benefits to be derived from a proper understanding of the spin-state chemistry are considerable, due to the importance of light-induced processes in organometallic and bioinorganic systems. 

Comparison of Eqs. (13) and (11) reveals that if one ran the CFD calculation to a computational to a convergence tolapprox = toltotai — , one could be certain that the resulting Fapprox would be a satisfactory solution of the full chemistry model, i.e. Eq. (11) would be satisfied. Methods for constructing reduced models guaranteed to satisfy Eq. (13) over a known range of conditions are discussed in detail in Section III.C below. The practical effectiveness of this overall error control approach, once one has an approximate source term fflapprox that satisfies Eq. (13) has recently been demonstrated for 1-d and 2-d steady laminar flame simulations. 

This approach makes it easier to satisfy Eq. (13) using small chemistry models, but it requires a method to easily obtain a set of reduced models appropriate for different conditions. In the next section, we present a method for constructing the various reduced models, and for identifying the range of reaction conditions where each should be used. 

Fig. 14. Fraction of the grid points used by various models during a 1-d Adaptive Chemistry simulation of a premixed stoichiometric methane-air flame. The full chemistry model is GRI-Mech 3.0. Reduced models were accurate at about 80% of the grid points.

A free computer service that automatically performs this type of chemistry model-reduction is available through the CMCS Web portal (http // www.cmcs.org). This web software can also provide an interval where the reduced model is guaranteed to replicate the full model to within user-specified tolerances, i.e. a range [Tiow iugh] where the error constraint Eq. (16) is... 

An example The temperature field computed for a partially-premixed radi-ally-symmetric methane/air flame is shown in Fig. 15. This is the same 4> — 2.464 laminar flame simulated by Bennett et al. (2000). We used the same 217 reaction full chemistry model used by Bennett et al. (2000) to compute the temperature field shown on the left-hand side of Fig. 15. On the left-hand side is shown the temperature field computed using the full chemistry model everywhere. On the right-hand side is shown the temperature field computed by the Adaptive Chemistry method using 13 different reduced models ranging in size from zero reactions to 156 reactions. As guaranteed by the error control... 

Hettema H (2012a) Reducing chemistry to physics limits, models, consequences. Createspace Hettema H (2012b) The unity of chemistry and physics absolute reaction rate theory. Hyle 18 145-173... 

Hinne Hettema (1963) is an Honorary Research Fellow in the Department of Philosophy at the University of Auckland. He completed his Ph.D. in theoretical chemistry at the Radboud University in Nijmegen (1993) and his Ph.D. in philosophy at the Rijksuniversiteit Groningen (2012). He lives in Auckland, New Zealand. His research interests are in the philosophy of science, philosophy of chemistry, and philosophy of cyber security. He is the translator of Quantum Chemistry, classical scientific papers, and author of Reducing Chemistry to Physics Limits, Models, Consequences, http //www.arts.auckland.ac.nz/people/hhet001... 

Jones, W.P. Rigopoulos, S. (2007). Reduced chemistry for hydrogen and methanol premixed flames via RCCE, Combustion Theory and Modelling Vol. 11 (5) pp 755-780. 

Soyhan, H., Maufi, R Sorusbay, C. (2002). Chemical kinetic modeling of combustion in internal combustion engines using reduced chemistry. Combustion Science and Technology Vol. 174 (11-12) (2002) 73-91. 

Figure 22.19 (Up) Schematic oxygen dissociation process on the reduced S11O2 (110) surface. The darker atoms in the final state come from the O2 molecule one atom fills the O vacancy (C), and the other is adsorbed on the five-coordinated Sn site (B), reproduced from [115] by permissions of the Royal Society of Chemistry. (In the middle) Distribution of lowest unoccupied orbitals of stoichiometric (top) and reduced surface models (bottom) calculated by using USP pseudopential. Significant localization is observed at the site of the fivefold coordinated surface tin atom, reprinted with permission from [111], cop5uight...

Fish, D.J. The automatic generation of reduced mechanisms for tropospheric chemistry modelling. Atmos. Environ. 34, 1563-1574 (2000)... 

Lam, S.H. Reduced chemistry-diffusion coupling. Combust. Sci. Technol. 179, 767-786 (2006) Lam, S.H. Model reductions with special CSP data. Combust. Flame 160, 2707-2711 (2013) Lam, S.H., Goussis, D.A. Understanding complex chemical kinetics with computational singular perturbation. Proc. Combust. Inst. 22, 931-941 (1988)... 

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