Abstract
We present a method of direct quadrature conditional moment closure (DQCMC) for the treatment of realistic turbulence-chemistry interaction in computational fluid dynamics (CFD) software. The method which is based on the direct quadrature method of moments (DQMOM) coupled with the conditional moment closure (CMC) equations is in simplified form and easily implementable in existing CMC formulation for CFD. The observed fluctuations of scalar dissipation around the conditional mean values are captured by the treatment of a set of mixing environments, each with its pre-defined weight. Unlike the early versions of the DQCMC method the resulting equations are similar to that of the first-order CMC, and the “diffusion” term is strictly positive and no correction factors are used. We present results for two mixing environments where the resulting matrices of the DQCMC can be inverted analytically. We have performed this analysis for a simple hydrogen flame using a multi species chemical scheme containing nine species. The effects of the fluctuations around the conditional means are captured accurately and the predicted results are in very good agreement with observed trends from direct numerical simulations. Furthermore, the differences between the first order CMC and DQCMC are discussed.
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References
Peters, N.B.: Turbulent Combustion. Cambridge University Press, Cambridge, UK (2000)
Klimenko, A.Y., Bilger, R.W.: Conditional moment closure for turbulent combustion. Progr. Energy Combustion. Sci. 25, 595–687 (1999)
Mastorakos, E., Baritaud, T.B., Poinsot, T.J.: Numerical simulations of autoignition in turbulent mixing flows. Combust. Flame 109(1–2), 198–223 (1997)
Løvås, T., Lowe, A., Cant, R.S., Mastorakos, E.: Three-dimensional direct numerical simulations of autoignition in turbulent non-premixed flows with simple and complex chemistry. FEDSM2006-98109, ASME Joint US-European FESM (2006)
Kronenburg, A.: Double conditioning of reactive scalar transport equations in turbulent nonpremixed flames. Phys. Fluids 16, 2640 (2004)
Mastorakos, E., Bilger, R.W.: Second-order conditional moment closure for the autoignition of turbulent flows. Phys. Fluids 10, 1246 (1998)
Pitsch, H., Cha, C.M., Fedotov, S.: Flamelet modelling of non-premixed turbulent combustion with local extinction and re-ignition. Combust. Theory Model. 7, 317 (2003)
Mitarai, S., Kosály, G., Riley, J.J.: A new Lagrangian flamelet model for local flame extinction and reignition. Combust. Flame 137, 306 (2004)
Kronenburg, A., Cleary, M.J.: Multiple mapping conditioning for flames with partial premixing. Combust. Flame 155, 215–231 (2008)
Wright, Y.M., de Paola, G., Boulouchos, K., Mastorakos, E.: Simulations of spray autoignition and flame establishment with two-dimensional CMC. Combust. Flame 143, 402–419 (2005)
Fox, R.O., Raman, V.: A multienvironment conditional probability density function model for turbulent reacting flows. Phys. Fluids 16(12), 4551–4565 (2004)
Fox, R.O.: Computational Models for Turbulent Reacting Flows. Cambridge University Press, Cambridge, UK (2003)
Marchisio, D.L., Fox, R.O.: Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 36, 43–73 (2005)
Smith, S.T., Fox, R.O.: A term-by-term direct numerical simulation validation study of the multi-environment conditional probability-density-function model for turbulent reacting flows. Phys. Fluids 19, 085102-1 (2007)
Pope, S.B.: Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. Combust. Theory Model. 1, 41–63 (1997)
Tang, Q., Zhao, W., Bockelie, M., Fox, R.O.: Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics. Combust. Theory Model. 11, 889–907 (2007)
Brown, P.N., Hindmarsh, A.C.: Reduced storage matrix methods in stiff ODE systems. J. Appl. Math. Comput. 31, 40–91 (1989)
Hindmarsh, A.C.: LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM-SIGNUM 15(4), 10–11 (1980)
Warnatz, J.: In: Gardiner, W.C. (eds.) Combustion Chemistry. Springer, New York (1984)
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This paper was submitted to Flow, Turbulence and Combustion special issue for COCCFEA final workshop papers.
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Ali, S., Vikhansky, A. & Løvås, T. Direct Quadrature Conditional Moment Closure for Modelling of Turbulent Combustion. Flow Turbulence Combust 87, 493–509 (2011). https://doi.org/10.1007/s10494-010-9318-8
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DOI: https://doi.org/10.1007/s10494-010-9318-8