Accession Number

N20120013787

Title

Ensemble Averaged Probability Density Function (APDF) for Compressible Turbulent Reacting Flows.

Publication Date

Aug 2012

Media Count

26p

Personal Author

N. S. Liu T. H. Shih

Abstract

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 (FGPDF) 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 FGPDF, 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 NavierStokes 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 NavierStokes 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.

Keywords

Large eddy simulation Navierstokes equation Probability theory Reacting flow Reynolds averaging Spatial filtering Steady flow Turbulent flow


Source Agency

National Aeronautics and Space Administration

NTIS Subject Category

72B  Algebra, Analysis, Geometry, & Mathematical Logic

Corporate Author

National Aeronautics and Space Administration, Cleveland, OH. NASA John H. Glenn Research Center at Lewis Field.

Document Type

Technical report

Title Note

N/A

NTIS Issue Number

1306

Contract Number

N/A
