The University of Queensland
Combustion is turbulent in most practical applications. Turbulence and combustion interact at different scales making modelling of this process very difficult and computationally expensive. This page offers possible solutions for the problem.
Conditional methods in general and CMC in particular study how to derive, close and use equations for conditional expectations in application to reactive transport in fluid flows. CMC became a popular and computationally inexpensive model that preserves conservation integrals, is consistent with the mixture fraction PDF, correctly incorporates the convective terms into conditional equations and possesses a number of other useful properties.
- A. Y. Klimenko, Multicomponent diffusion of various admixtures in turbulent flows, Fluid Dynamics, 25(3), pp. 327-334, 1990. (Paper introducing the first conditional model, which later was developed into the CMC approach)
- A. Y. Klimenko, Note on the conditional moment closure in turbulent shear flows, Physics of Fluids, 7(2), pp. 446-448, 1995. (Applying boundary layer asymptotic analysis to conditional expectations -- very different from the unconditional boundary layer equations)
- A. Y. Klimenko & R. W. Bilger, Conditional moment closure for turbulent combustion, Progress in Energy and Combustion Science, 25(6), pp. 595-687, 1999. (major review of CMC and conditional methods)
- A. Y. Klimenko, On the relation between the conditional moment closure and unsteady flamelets, Combustion Theory and Modelling, 5(3), pp. 275-294, 2001. (introducing the coordinate-invariant version of the Flamelet model, which possesses a special property of consistency with CMC).
Modelling fundamentals
Relating CMC equations to fundamental possibility of reversing Brownian motion in time
- A. Y. Klimenko, On the inverse parabolicity of PDF equations in turbulent flowsg, Quarterly Journal of Mechanics and Applied Mathematics, 57(1), pp. 79-93, 2004. || preprint: Stanford University CTR Research Briefs , pp. 53--61, 2002
Analysis of numerical diffusion, stochastic errors and stochastic dependencies related to the use of Pope particles and demonstrating their advantages over elementary particles. Treatment of the stochastic dependencies in the last paper resembles the Bogolubov–Born–Green–Kirkwood–Yvon chain of equations known in statistical physics
- A. Y. Klimenko, On simulating scalar transport by mixing between Lagrangian particles, Physics of Fluids, 19(3), 031702, 2007.
- A. Y.Klimenko Random walk, diffusion and mixing in simulations of scalar transport in fluid flows Physica Scripta, T132 , 014037, 2008
- A. Y. Klimenko, Lagrangian particles with mixing. I. Simulating scalar transport, Physics of Fluids, 21(6), 065101, 2009.
Multiple Mapping Conditioning (MMC)
MMC effectively unifies CMC with PDF methods into single and flexible methodology. Deterministic version of the model is a generalisation of the Mapping Closure. Development of MMC progressed towards stochastic interpretation of the model, which is a full-capacity PDF model retaining some features of CMC.
- A. Y. Klimenko and S. B. Pope, The modelling of turbulent reactive flows based on multiple mapping conditioning, Physics of Fluids, 15(7), pp. 1907-1925, 2003. (major work introducing deterministic and stochastic MMC)
- A. Y. Klimenko, MMC modelling and fluctuations of scalar dissipatin , Aust. Comb. Symposium, PO20, 2003 (MMC with conditioning on scalar dissipation)
- A. Y. Klimenko, Matching the conditional variance as a criterion for selecting parameters in the simplest multiple mapping conditioning models, Physics of Fluids, 16(12), pp. 4754-4757, 2004.
- A. P. Wandel & A. Y. Klimenko, Testing multiple mapping conditioning mixing for Monte Carlo probability density function simulations, Physics of Fluids, 17(12), 128105, 2005.
- L. Dialameh, M. J. Cleary, and A. Y. Klimenko A multiple mapping conditioning model for differential diffusion , Physics of Fluids, 26, 025107, 2014.
Generalised MMC and Sparse-Lagrangian methods
Generalised MMC removes restrictions of the original MMC and allows us to perform conditioning of mixing operator on virtually any properties (which in MMC are traditionally referred to as reference variables), which nevertheless should be carefully selected to be instrumental for the model performance. This conditioning corresponds to enforcing the conditional properties simulated by the reference variables on mixing.
Sparse-Lagrangian methods are not attached to Eulerian cells and allow to have significantly fewer particles than cells in FDF-LES simulations. Sandia flame D was simulated with as few as 10000 particles, although more complex cases may need a more intensive system of particles but, overall, Sparse-Lagrangian methods achieve high quality simulations at a dramatically reduced computational cost. The "secret" of thousandfold decrease of the computational cost is not as much in reduction of the number of particles (which is quite obvious) as in high efficiency of MMC mixing, which allows for this reduction. The task of FDF-LES with realistic CH4 chemistry, which was previously suitable only for supercomputers, is now performed in the CMM group on personal workstations. Unlike many models, the MMC model has evolved to become more simple, albeit very efficient.
- A. Y. Klimenko, Matching conditional moments in PDF modelling of nonpremixed combustion, Combustion and Flame, 143(4), (special issue dedicated to R.W.Bilger) pp. 369-385, 2005,
- A. Y. Klimenko, Lagrangian particles with mixing. II. Sparse-Lagrangian methods in application for turbulent reacting flows, Physics of Fluids, 21(6), 065102, 2009.
- M. J. Cleary, A. Y. Klimenko, J. Janicka & M. Pfitzner, A sparse-Lagrangian multiple mapping conditioning model for turbulent diffusion flames, Proceedings of the Combustion Institute, 32, pp. 1499-1507, 2009.
- M. J. Cleary & A. Y. Klimenko, A generalised multiple mapping conditioning approach for turbulent combustion, Flow, Turbulence and Combustion, 82(4), pp. 477-491, 2009.
- A. Y. Klimenko & M. J. Cleary, Convergence to a model in sparse-Lagrangian FDF simulations, Flow, Turbulence and Combustion, 85(3-4) (special issue dedicated to S.B.Pope), pp. 567-591, 2010.
- M. J. Cleary & A. Y. Klimenko, A detailed quantitative analysis of sparse-Lagrangian filtered density function simulations in constant and variable density reacting jet flows, Physics of Fluids, 23(11), 115102, 2011.
- Y. Ge, M. J. Cleary & A. Y. Klimenko, Sparse-Lagrangian FDF simulations of Sandia flame E with density coupling, Proceedings of the Combustion Institute, 33, pp. 1401-1409, 2011.
- Y. Ge, M. J. Cleary & A. Y. Klimenko, A comparative study of Sandia flame series (D-F) using sparse-Lagrangian MMC modelling, Proceedings of the Combustion Institute, 34, 2013.
- L. Dialameh, B. Sundaram, M. J. Cleary and A. Y. Klimenko Differential diffusion of passive scalars with MMC mixing model in isotropic turbulent flow , Aust. Fluid Mech. Conf., paper 318, 2012
- B. Sundaram, A. Y. Klimenko, M. J. Cleary and Y. Ge A direct approach to generalised Multiple Mapping Conditioning for selected turbulent diffusion flame cases , Combustion Theory and Modelling, 2016, 20, 4: 735-764 A new direct and simple introduction into MMC
methodology + some examples.
- B. Sundaram, A. Y. Klimenko, M. J. Cleary and L. Dialameh Recent trends in modelling of turbulent combustion , The 53rd Symposium (Japanese) on Combustion, Sept. 2015, University of Tsukuba, paper B221 A brief review of MMC
Generalised MMC in application to premixed flames
- B. Sundaram, A.Y. Klimenko, M.J. Cleary, U. Maas, Prediction of NOx in premixed high-pressure lean methane flames with a MMC-partially stirred reactor, Proceedings of the Combustion Institute, Vol. 35, 2, 2015, 1517-1525
- B. Sundaram and A. Y. Klimenko, A PDF approach to thin premixed flamelets using multiple mapping
conditioning , Proceedings of the Combustion Institute, Vol. 36, 2, 2017, 1937–1945
- A. Y. Klimenko, The convergence of combustion models
and compliance with the Kolmogorov scaling of turbulence Phys. Fluids 33, 025112 (2021)
Trends in developing turbulent combustion models; the 4/7 power law for turbulent premixed combustion.
Links
back to the index
back to Klimenko's web page
back to the CMM Research Group web page