Exploring the beta distribution in variable-density turbulent mixing

Physics – Fluid Dynamics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Added two paragraphs to Introduction + minor changes, Accepted in Journal of Turbulence, July 19, 2010

Scientific paper

10.1080/14685248.2010.510843

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Exploring the beta distribution in variable-density turbulent mixing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exploring the beta distribution in variable-density turbulent mixing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exploring the beta distribution in variable-density turbulent mixing will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-205890

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.