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Exploring the beta-pdf in variable-density turbulent mixing | | J. Bakosi
; J. R. Ristorcelli
; | | Date: |
22 Mar 2010 | | Abstract: | In assumed probability density function (pdf) methods of turbulent
combustion, the shape of the scalar pdf is assumed a priori and the pdf is
parametrized by its moments for which model equations are solved. In
non-premixed flows the beta distribution has been a convenient choice to
represent the mixture fraction in binary mixtures or a progress variable in
combustion. Here the beta-pdf approach is extended to variable-density mixing:
mixing between materials that have very large density differences and thus the
scalar fields are active. As a consequence, new mixing phenomena arise due to
1) cubic non-linearities in the Navier-Stokes equation, 2) additional
non-linearities in the molecular diffusion terms and 3) the appearance of the
specific volume as a dynamical variable. The assumed beta-pdf approach is
extended to transported pdf methods by giving the associated stochastic
differential equation (SDE). The beta distribution is shown to be a realizable,
consistent and sufficiently general representation of the marginal pdf of the
fluid density, an active scalar, in non-premixed variable-density turbulent
mixing. The moment equations derived from mass conservation are compared to the
moment equations derived from the governing SDE. This yields a series of
relations between the non-stationary coefficients of the SDE and the mixing
physics. Our treatment of this problem is general: the mixing is mathematically
represented by the divergence of the velocity field which can only be specified
once the problem is defined. In this paper we seek to describe a theoretical
framework to subsequent applications. We report and document several rigorous
mathematical results, necessary for forthcoming work that deals with the
applications of the current results to model specification, computation and
validation of binary mixing of inert fluids. | | Source: | arXiv, 1003.4046 | | Services: | Forum | Review | PDF | Favorites | |
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