eprintid: 158
rev_number: 4
eprint_status: archive
userid: 6
dir: disk0/00/00/01/58
datestamp: 2008-10-07
lastmod: 2015-05-29 19:48:22
status_changed: 2009-04-08 16:54:58
type: report
metadata_visibility: show
item_issues_count: 0
creators_name: Myers, Tim
creators_name: Brannan, Jim
contributors_name: Cumberbatch, Ellis
contributors_name: Moodie, Bryant
contributors_name: O'Connell, Gordon
contributors_name: Pickering, Douglas
title: Density Driven Turbulent Mixing at Batch Interfaces
ispublished: pub
subjects: utilities
studygroups: ipsw3
companyname: Enbridge Incorporated
full_text_status: public
abstract: Models are developed for the turbulent mixing and growth at a batch interface. These models depend crucially on the choice of diffusion coefficient $D$. 

The model where $D$ is the harmonic average of the mixing coefficients of the two pure fluids is analysed in detail, since this is likely to be a good approximation when the density difference between the two fluids is small.

When the density difference is large, the laminar flow regime fingering will occur and there will be a relatively sharp interface between the fluids. However, in the turbulent case, as gravity drives the denser fluid into the less dense one the invading fluid is immediately mixed by turbulent diffusion. This means that sharp interfaces do not exist. Instead there will be a finite mixing region where the volume fraction of each fluid changes from $0$ to $1$. In this case $D$ will depend upon the relative concentration of the fluids. This approach leads to a degenerate diffusion problem.
problem_statement: Petroleum products are most economically shipped in long distance pipelines. There can be significant differences between the characteristics of the various petroleum products that are shipped, so they are shipped in batches of fluids with like characteristics.

The purpose of the workshop is to explore the mechanisms by which the bi-fluid vertical interface deforms with time when two fluids flow through a pipe of cylindrical geometry under the driving force of a constant pressure gradient. These differing fluids may have different viscosity or different densities or both.
date: 1999
date_type: published
pages: 11
citation:   Myers, Tim and Brannan, Jim  (1999) Density Driven Turbulent Mixing at Batch Interfaces.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/158/1/turbulent_mixing.pdf