Turbulence and Combustion Group

Dimension reduction of combustion chemistry

In numerical simulations of combustion processes, the use of dimension reduction to simplify the description of the chemical system has the advantage of reducing the computational cost, but it is important also to retain accuracy and adequate detail. In current research, dimension reduction of combustion chemistry is performed by using the ICE-PIC method. The ICE-PIC method is developed based on three major ingredients: constrained equilibrium; trajectory-generated manifolds; and, the pre-image curve method. The low-dimensional manifold identified, the ICE manifold, is invariant, continuous and piecewise smooth. The ICE-PIC method achieves local species reconstruction based on the constrained-equilibrium pre-image curve. In comparison to other existing methods such as QSSA, RCCE and ILDM, this method is the first approach that locally determines compositions on a low-dimensional invariant manifold.

The accuracy of the ICE-PIC method has been examined in autoignition and in one-dimensional laminar flames of hydrogen/air and methane/air mixtures. Studies demonstrate that the local errors incurred by ICE-PIC (e.g., the errors in the reconstructed composition) are well controlled. The capability of the ICE-PIC method for the reduced description of reactive flows is demonstrated through the calculation of the oxidation of CO/H2 in a CSTR. The reduced description provided by the ICE-PIC method is capable of quantitatively reproducing the complex dynamics.

The final goal is to develop an efficient and accurate algorithm - In Situ Adaptive Tabulation with Dimension Reduction (the ICE-PIC method) to incorporate detailed chemistry in turbulent combustion simulations.

Comparison at different ambient temperatures Ta with P=25Torr between the full description (solid lines) and the reduced description (dashed lines) of the complex dynamics exhibited by the reaction of a CO/H2/O2 mixture in an isobaric continuously stirred tank reactor (CSTR). The full description incorporates the full set of 11 chemical species. The reduced description is provided by the ICE-PIC method with H2, O2, CO, H, and O being the represented species.

Schematic of ISAT in combination with dimension reduction (via species reduction and reconstruction) used in the reaction fractional step of a CFD computation

Transport-chemistry coupling

When chemistry-based manifolds are employed to describe inhomogeneous reactive flows, three different mechanisms "non-invariance", "dissipation-curvature" and "differential diffusion" pull compositions off the chemistry-based manifold. The corresponding perturbations introduce three usually non-trivial terms, referred to as transport-chemistry coupling, in the evolution equation of the reduced composition variables. The "first approximation", which simply neglects the perturbations and therefore neglects the transport-chemistry coupling in the evolution equation of the reduced composition variables, is in general inaccurate. In current research, the transport-chemistry coupling is accurately accounted for by the "close-parallel" approach, which assumes that the compositions lie on a low-dimensional manifold which is close to and parallel to the chemistry-based slow manifold.

Selected Publications on Dimension Reduction of Combustion Chemistry
	Z. Ren and S.B. Pope, (2007) ``Reduced description of complex dynamics in reactive systems'', Journal of Physical Chemistry A 111 (34), 8464 -8474.
	Z. Ren and S.B. Pope, (2007) ``Transport-chemistry coupling in the reduced description of reactive flows'', Combustion Theory and Modelling 11 (5), 715-739.
	Z. Ren and S.B. Pope, (2006) ``The use of slow manifold in reactive flows'', Combustion and Flame 147, 243-261.
	Z. Ren, S.B. Pope, A. Vladimirsky and J.M. Guckenheimer (2007) ``Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport'', Proceeding of the Combustion Institute, 31 473-481.
	Z. Ren, S.B. Pope, A. Vladimirsky and J.M. Guckenheimer (2006) ``The ICE-PIC method for the dimension reduction of chemical kinetics'', Journal of Chemical Physics , 124, 114111.
	Z. Ren and S.B. Pope (2006) ``The geometry of reaction trajectories and attracting manifolds in composition space,'' Combustion Theory and Modelling , 10 (3), 361-388.
	Z. Ren and S.B. Pope (2005) ``Species reconstruction using pre-image curves,'' Proceeding of the Combustion Institute, 30, 1293-1300.