Development of multiple mapping conditioning (MMC) for application to turbulent combustion

Wandel, Andrew P. (2005). Development of multiple mapping conditioning (MMC) for application to turbulent combustion PhD Thesis, School of Mechanical and Mining Engineering, The University of Queensland.

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Author Wandel, Andrew P.
Thesis Title Development of multiple mapping conditioning (MMC) for application to turbulent combustion
School, Centre or Institute School of Mechanical and Mining Engineering
Institution The University of Queensland
Publication date 2005
Thesis type PhD Thesis
Supervisor Unknown
Total pages 355
Language eng
Subjects L
290501 Mechanical Engineering
Formatted abstract

The majority of the world's energy is currently generated via heat release using chemical reaction-combustion of fossil fuels (which have questionable reserves). To minimise pollution and wastage, accurate computational modelling is a vital tool.

This thesis focusses on non-premixed combustion of gasses, where the mixing and combustion of fuel and oxidiser (generally gas containing oxygen) both occur in the combustion chamber. "Turbulent combustion modelling" is considered, where the transport of chemical species through physical space is not significantly faster than the chemical reactions.

The goal is the development, implementation and validation of the new turbulent combustion model Multiple Mapping Conditioning (MMC), introduced by Klimenko and Pope (Phys. Fluids, 15:1907 (2003)). Elements of probability density function (pdf) modelling [Pope, Progress Energy Comb. Sci., 11:119 (1985)] and Conditional Moment Closure (CMC) [Klimenko and Bilger, Progress Energy Comb. Sci., 25:595 (1999)] are used in MMC to define a model that resolves the turbulent fluctuations of important species, while neglecting fluctuations for species deemed unimportant. Thus available computational resources may be utilised effectively. Klimenko and Pope validated the model for a physically homogeneous, two dimensional conserved scalar case, but the model has not previously been implemented or validated for physically inhomogeneous conserved scalar transport, nor combustion. These are not trivial matters and general principles for implementation procedures are the major contributions of this thesis.

Part I details various statistical tools used throughout the thesis.

The Markov hypothesis, that scalar processes develop more rapidly than physical space processes, is an underlying principle upon which much of turbulent combustion modelling is founded. For pdf models, which are generally implemented using stochastic methods, this is implicit in the assumption that stochastic methods can be used to describe deterministic processes. The Markov hypothesis was fundamental in the original derivation of CMC.

Part II introduces the salient turbulent combustion models: pdf modelling, CMC and MMC. Chapter 6 concludes with derivations of MMC for cases with simplified transport in physical space, used for the combustion modelling in Part V. Chapter 7 concludes Part II with Direct Numerical Simulation (DNS) results to check the Markov hypothesis.

For turbulent combustion models that are implemented in stochastic form, the model for the scalar dissipation is treated as an independent substep to the transport in physical space, and is implemented as locally homogeneous. Part III includes further modelling procedures to those detailed by Klimenko and Pope for stochastic implementation of the Conditional MMC, which ignores conditional fluctuations (deviations from conditional means). Stochastic and deterministic methods are compared. Models for Probabilistic MMC (Klimenko, in Clean Air 1, p. 14.4 {2003)], which models these deviations from the conditional means, are described in Chapter 11. There are some implementation issues that are crucial to successful modelling using Probabilistic MMC that are introduced in this thesis and elsewhere summarised [Wandel and Klimenko, Phys. Fluids, Accepted]. These were identified and resolved as a consequence of experience with the behaviour observed from numerical implementations. The Probabilistic MMC is validated for passive scalar mixing, with results for the limit of minimal conditional fluctuations matching CMC and those for substantial conditional fluctuations following DNS closely.

Part IV contains implementation details for inhomogeneous transport using deterministic, Conditional MMC and results for the scalar pdf are compared against experiment [Batt, J. Fluid Mech., 82:53 (1977)]. W hile results from MMC are not substantially different from those produced by simpler models, the consequence of these simulations is that it has been shown that when the stochastic inhomogeneous form of MMC is applied, reasonable pdfs are inherently produced.

The final simulations (Part V) are for the validation of MMC in a combustion case (Wandel and Klimenko), comparing against results obtained by Mitarai, Riley and Kosaly [Phys. Fluids, 17:047101 (2005)]. It is apparent that MMC p erforms favourably and displays physical behaviour for a case with combustion close to extinction/ reignition.

The goal of this thesis has been achieved: development of the new turbulent combustion model MMC so it could be implemented and validated. Further work may be performed with MMC in similar combustion cases to those performed here to check the universality of parameters for Probabilistic MMC as well as inhomogeneous combustion and/or scalar dissipation-like modelling.

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Document type: Thesis
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