Advances In Modeling Mixing And Molecular Transport In Probability Density Function Methods Of Turbulent Reacting Flows

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Abstract
Modeling of turbulent reacting flow problems using Probability Density Function (PDF) methods yields transport and reaction in closed form while the processes related to the conditional dissipation of species compositions need to be closed using mixing models. First, we study the dispersion from line sources in decaying grid turbulence using a modified form of the Interaction by Exchange with the Conditional Mean (IECM) mixing model. These flows pose a significant challenge to statistical models, because the scalar length scale (of the initial plume) is much smaller than the turbulence integral scale. Consequently, this necessitates incorporating the effects of molecular diffusion in order to model laboratory experiments. The effects of molecular diffusion are modeled by adding a conditional mean scalar drift term and a laminar wake model is used to obtain an analytic expression for the mixing timescale at small times which is subsequently used as part of a general specification of the mixing timescale. Based on this modeling, PDF calculations are performed, and comparison is made primarily with existing experimental and numerical data on single and multiple line sources. A heated mandoline is also considered. This establishes the validity of the proposed model and the significant effect of molecular diffusion on the decay of scalar fluctuations. Next, various numerical implementations of mixing and molecular transport in LES/PDF studies of turbulent reacting flows are evaluated for accuracy using the Method of Manufactured Solutions (MMS). Mixing is modeled using the Interaction by Exchange with the Mean (IEM) model and the effects of molecular transport are incorporated as a mean drift term in the mixing step. This methodology avoids spurious production of scalar variance and also allows direct incorporation of differential diffusion effects. The implementation of the mixing model is shown to be successful in capturing the effects of differential diffusion accurately with the additional property of satisfying detailed conservation and realizability of species mass fractions. Additionally, we present a new variance reduction technique by way of an implicit smoothing methodology. This smoothing scheme is shown to satisfy conservation, boundedness and regularity criteria. Moreover, for an appropriate choice of the smoothing length scale, significant improvements in accuracy can be achieved for an incremental increase in computational cost. Also, it is shown that with smoothing, the bias and statistical errors due to finite number of particles in the Lagrangian Monte Carlo simulations now scale as N[-]1 and tot N[-]1/2 respectively, where Ntot is the total number of particles in the computatot tional domain. Finally, the numerical implementations described are applied to the study of a turbulent reacting jet flame (Sandia Flame D). It is shown that this implementation yields a consistent formulation between the LES and the PDF methods. Further, cross-validation is presented as a numerical technique to assist in the automatic choice of the smoothing length scale and the application of crossvalidation to smoothing of PDF fields is shown to improve the consistency between the LES and PDF fields.
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2011-01-31
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pdf methods; turbulent reacting flows; mixing models; turbulent dispersion; differential diffusion; smoothing
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Pope, Stephen Bailey
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Caughey, David Alan
Guckenheimer, John Mark
Degree Discipline
Mechanical Engineering
Degree Name
Ph. D., Mechanical Engineering
Degree Level
Doctor of Philosophy
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dissertation or thesis
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