Optimizing progress variable definition in flamelet-based dimension reduction in combustion

doi:10.1007/s10483-015-1997-7

Abstract

Abstract: An automated method to optimize the definition of the progress variables in the flamelet-based dimension reduction is proposed. The performance of these optimized progress variables in coupling the flamelets and flow solver is presented. In the proposed method, the progress variables are defined according to the first two principal components (PCs) from the principal component analysis (PCA) or kernel-density-weighted PCA (KEDPCA) of a set of flamelets. These flamelets can then be mapped to these new progress variables instead of the mixture fraction/conventional progress variables. Thus, a new chemistry look-up table is constructed. A priori validation of these optimized progress variables and the new chemistry table is implemented in a CH₄/N₂/air lift-off flame. The reconstruction of the lift-off flame shows that the optimized progress variables perform better than the conventional ones, especially in the high temperature area. The coefficient determinations (R2 statistics) show that the KEDPCA performs slightly better than the PCA except for some minor species. The main advantage of the KEDPCA is that it is less sensitive to the database. Meanwhile, the criteria for the optimization are proposed and discussed. The constraint that the progress variables should monotonically evolve from fresh gas to burnt gas is analyzed in detail.

Key words: principal component analysis (PCA), dimension reduction, progress variable, flamelet-based model

2010 MSC Number:

TK16

Jing CHEN, Minghou LIU, Yiliang CHEN. Optimizing progress variable definition in flamelet-based dimension reduction in combustion. Applied Mathematics and Mechanics (English Edition), 2015, 36(11): 1481-1498.

TrendMD

References

[1] Rabitz, H., Kramer, M., and Dacol, D. Sensitivity analysis in chemical kinetics. Annual Review of Physical Chemistry, 34, 419-461 (1983)
[2] Lutz, A. E., Kee, R. J., and Miller, J. A. Senkin: A Fortran Program for Predicting Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis, Sandia National Laboratories, Livermere (1988)
[3] Lu, T. and Law, C. K. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30, 1333-1341 (2005)
[4] Sun, W., Chen, Z., and Gou, X. A path flux analysis method for the reduction of detailed chemical kinetic mechanisms. Combustion and Flame, 157, 1298-1307 (2010)
[5] Rao, C. V. and Arkin, A. P. Stochastic chemical kinetics and the quasi-steady-state assumption: application to the gillespie algorithm. The Journal of Chemical Physics, 118, 4999-5010 (2003)
[6] Rein, M. The partial equilibrium approximation in reacting flows. Physics of Fluids, A: Fluid Dynamics, 4, 873-886 (1992)
[7] Pierce, C. D. and Moin, P. Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. Journal of Fluid Mechanics, 504, 73-97 (2004)
[8] Vreman, A., Albrecht, B., and van Oijen, J. Premixed and nonpremixed generated manifolds in large-eddy simulation of sandia flame d and f. Combustion and Flame, 153, 394-416 (2008)
[9] Gicquel, O., Darabiha, N., and Thévenin, D. Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion. Proceedings of the Combustion Institute, 28, 1901-1908 (2000)
[10] Bilger, R. W., Pope, S. B., and Bray, K. N. C. Paradigms in turbulent combustion research. Proceedings of the Combustion Institute, 30, 21-42 (2005)
[11] Vegendla, S. N. P. and Hasse, C. Steady flamelet progress-variable (FPV) modeling and simulation of a high-pressure gasifier. Energy and Fuels, 27, 7772-7777 (2013)
[12] Vegendla, S., Messig, D., and Weise, S. Flamelet-based time-scale analysis of a high-pressure gasifier. Energy and Fuels, 25, 3892-3899 (2011)
[13] Yilmaz, B., Ozdogan, S., and Gokalp, I. Numerical study on flame-front characteristics of conical turbulent lean premixed methane/air flames. Energy and Fuels, 23, 1843-1848 (2008)
[14] Albrecht, B., Zahirovic, S., and Bastiaans, R. A premixed flamelet-PDF model for biomass combustion in a grate furnace. Energy and Fuels, 22, 1570-1580 (2008)
[15] Ihme, M. and See, Y. C. LES flamelet modeling of a three-stream mild combustor: analysis of flame sensitivity to scalar inflow conditions. Proceedings of the Combustion Institute, 33, 1309- 1317 (2011)
[16] Vervisch, L., Hauguel, R., and Domingo, P. Three facets of turbulent combustion modelling: DNS of premixed v-flame, LES of lifted nonpremixed flame and RANS of jet-flame. Journal of Turbulence, 5, 1-8 (2004)
[17] Ihme, M., Shunn, L., and Zhang, J. Regularization of reaction progress variable for application to flamelet-based combustion models. Journal of Computational Physics, 231, 7715-7721 (2012)
[18] Niu, Y. S., Vervisch, L., and Tao, P. D. An optimization-based approach to detailed chemistry tabulation: automated progress variable definition. Combustion and Flame, 160, 776-785 (2013)
[19] Farcy, B., Abou-Taouk, A., Vervisch, L., Domingo, P., and Perret, N. Two approaches of chemistry downsizing for simulating selective noncatalytic reduction DeNO_x process. Fuel, 118, 291-299 (2014)
[20] Ribert, G., Vervisch, L., and Domingo, P. Hybrid transported-tabulated strategy to downsize detailed chemistry for numerical simulation of premixed flames. Flow, Turbulence and Combustion, 92, 175-200 (2014)
[21] Abdi, H. and Williams, L. J. Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 433-459 (2010)
[22] Moore, B. Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Transactions on Automatic Control, 26, 17-32 (1981)
[23] Parente, A., Sutherland, J. C., and Tognotti, L. Identification of low-dimensional manifolds in turbulent flames. Proceedings of the Combustion Institute, 32, 1579-1586 (2009)
[24] Parente, A., Sutherland, J., and Dally, B. B. Investigation of the mild combustion regime via principal component analysis. Proceedings of the Combustion Institute, 33, 3333-3341 (2011)
[25] Sutherland, J. C. and Parente, A. Combustion modeling using principal component analysis. Proceedings of the Combustion Institute, 32, 1563-1570 (2009)
[26] Isaac, B., Parente, A., Smith, P., Fru, G., and Thevenin, D. Source term parameterization for PCA combustion modelling. Proceedings of the European Combustion Meeting, Lund University Press, Sweden (2013)
[27] Biglari, A. and Sutherland, J. C. A filter-independent model identification technique for turbulent combustion modeling. Combustion and Flame, 159, 1960-1970 (2012)
[28] Coussement, A., Gicquel, O., and Parente, A. MG-local-PCA method for reduced order combustion modeling. Proceedings of the Combustion Institute, 34, 1117-1123 (2013)
[29] Najafi-Yazdi, A., Cuenot, B., and Mongeau, L. Systematic definition of progress variables and intrinsically low-dimensional, flamelet generated manifolds for chemistry tabulation. Combustion and Flame, 159, 1197-1204 (2012)
[30] Coussement, A., Gicquel, O., and Parente, A. Kernel density weighted principal component analysis of combustion processes. Combustion and Flame, 159, 2844-2855 (2012)
[31] Mirgolbabaei, H., Echekki, T., and Smaoui, N. A nonlinear principal component analysis approach for turbulent combustion composition space. International Journal of Hydrogen Energy, 39, 4622- 4633 (2014)
[32] Schlkopf, B., Smola, A., and Mjller, K. R. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10, 1299-1319 (1998)
[33] Parzen, E. On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33, 1065-1076 (1962)
[34] Schlkopf, B., Tsuda, K., and Vert, J. P. Kernel Methods in Computational Biology, MIT Press, Cambridge (2004)
[35] Silverman, B. W. Density Estimation for Statistics and Data Analysis, CRC Press, Boca Raton, Florida (1986)
[36] Jha, P. K. and Groth, C. P. T. Tabulated chemistry approaches for laminar flames: evaluation of flame-prolongation of ILDM and flamelet methods. Combustion Theory and Modelling, 16, 31-57 (2011)
[37] Bennett, B. A. V., Mcenally, C. S., Pfefferle, L. D., and Smooke, M. D. Computational and experimental study of axisymmetric coflow partially premixed methane/air flames. Combustion and Flame, 123, 522-546 (2000)
[38] Schwer, D. A., Lu, P., and Green, W. H., Jr. An adaptive chemistry approach to modeling complex kinetics in reacting flows. Combustion and Flame, 133, 451-465 (2003)
[39] Ray, J., Najm, H, N., and Mildne, R. B. Triple flame structure and dynamics at the stabilization point of an unsteady lifted jet diffusion flame. Proceedings of the Combustion Institute, 28, 219-226 (2000)
[40] Grtzbach, G. Spatial resolution requirements for direct numerical simulation of the RayleighBWnard convection. Journal of Computational Physics, 49, 241-264 (1983)
[41] Smith, G. P., Golden, D. M., and Frenklach, M. GRI-MECH: an Optimized Detailed Chemical Reaction Mechanism for Methane Combustion, Sandia National Laboratories Report, SAND-898009B, New Mexico (1999)
[42] Kee, R. J., Rupley, F. M., and Meeks, E. Chemkin-III: a FORTRAN Chemical Kinetics Package for the Analysis of Gas-phase Chemical and Plasma Kinetics, Sandia National Laboratories, New Mexico (1996)
[43] Bilger, R. W., Starner, S. H., and Kee, R. J. On reduced mechanisms for methane air combustion in nonpremixed flames. Combustion and Flame, 80, 135-149 (1990)