Abstract
Probability density function (pdf) methods provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. Turbulent convection and finite-rate chemistry can be treated in closed and exact form with pdfs in contrast to methods based on statistical moments. The equations for pdfs at a finite number of points are indeterminate due to molecular transport and pressure-gradient terms which require pdfs of higher order. The theoretical foundation of pdfs methods are developed in this paper starting from the exact and linear equations on the functional level. The closure problem for single-point pdf equations is treated in detail and several closure models are analyzed. Turbulent combustion at low Mach numbers constitutes an important area of application and selected results for a turbulent methane flame are presented as an example. The extension of pdf methods to supersonic turbulent flows with and without chemical reactions are outlined. Progress in the numerical solution of pdf equations is reviewed briefly. In the concluding remarks, both the advantages and disadvantages of pdf methods are evaluated.
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