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Accession Number
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N20120013787
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Title
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Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows.
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Publication Date
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Aug 2012
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Media Count
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26p
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Personal Author
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N. S. Liu T. H. Shih
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Abstract
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In this paper, we present a concept of the averaged probability density function (APDF) for studying compressible turbulent reacting flows. The APDF is defined as an ensemble average of the fine grained probability density function (FG-PDF) with a mass density weighting. It can be used to exactly deduce the mass density weighted, ensemble averaged turbulent mean variables. The transport equation for APDF can be derived in two ways. One is the traditional way that starts from the transport equation of FG-PDF, in which the compressible Navier- Stokes equations are embedded. The resulting transport equation of APDF is then in a traditional form that contains conditional means of all terms from the right hand side of the Navier-Stokes equations except for the chemical reaction term. These conditional means are new unknown quantities that need to be modeled. Another way of deriving the transport equation of APDF is to start directly from the ensemble averaged Navier-Stokes equations. The resulting transport equation of APDF derived from this approach appears in a closed form without any need for additional modeling. The methodology of ensemble averaging presented in this paper can be extended to other averaging procedures: for example, the Reynolds time averaging for statistically steady flow and the Reynolds spatial averaging for statistically homogeneous flow. It can also be extended to a time or spatial filtering procedure to construct the filtered density function (FDF) for the large eddy simulation (LES) of compressible turbulent reacting flows.
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Keywords
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Large eddy simulation
Navier-stokes equation
Probability theory
Reacting flow
Reynolds averaging
Spatial filtering
Steady flow
Turbulent flow
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Source Agency
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National Aeronautics and Space Administration
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NTIS Subject Category
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72B - Algebra, Analysis, Geometry, & Mathematical Logic
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Corporate Author
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National Aeronautics and Space Administration, Cleveland, OH. NASA John H. Glenn Research Center at Lewis Field.
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Document Type
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Technical report
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Title Note
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N/A
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NTIS Issue Number
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1306
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Contract Number
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N/A
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