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Wednesday, February 17, 2010

Eulerian Multi-fluid modeling: Developer and User Perspective

Understanding and implementing a multi-fluid model in any software code is a tedious and strenous process. The complication, not only arises owing to coding the procedure, rather to make sure that the system is stable after being washed with multiple "stablizing" approaches such as treatment of implicit drag terms to indicate a few. Often, CFD vendors have a single route for multiphase solution and it takes different forms based on the approach required: such as VOF, Eulerian or mixture type approaches. So, basically a given multiphase code assumes different formulations for fluxes, source / sink terms and induces the need for coupling (only in eulerian multifluid approach) based on the user specification.
Although, most of the users are not quite interested in the "background coding" involved in the blackbox tool, sometimes it becomes essential that they understand the physical significance of the methodology employed.

For example, let me indicate an off the shelf trick to make your eulerian multi-fluid runs much stable. Increasing the drag terms, involved between the phases, results in higher coupling and hence stable runs. Lowering the interaction terms makes the system (or the involved fluids) decoupled and may pose problems for mass convergence. Well, while writing papers people indicate, "enhancement in convergence was obtained by improving the interaction terms between the fluids" - which essentially a developer would read, the left hand side diagonal terms were made dominant :) !!! Such is the essence of CFD - both the user with a physical representation of the phenomena and the developer in a mathematical state of mind can mingle together talking about the same stuff!!

For those who are interested in the formulation part: I am presenting some nice lectures/notes on multi-fluid formulation.

Ofcourse, if you have any comments on the algorithms or suggest different approaches, please feel free to comment - i would be very interested in getting to know new techniques !

Take a look at this website for a decent understanding of the multi-fluid approach
http://www.tnw.tudelft.nl/live/pagina.jsp?id=abc4209a-4a5f-4a77-9121-54850566f33f〈=en

For detailed understanding of the Multi-fluid approach, one can always lean to the Fluent presentation

www.bakker.org/dartmouth06/engs150/18-eulmp.ppt

Modeling of Gas-fluidized systems require very detailed investigation of the drag formulations (although, people tend to think of it more in a physical manner- the truth is ..such systems are extremely unstable owing to the multiple interaction terms and hence a good implicit approach is required to enhance convergence!)

http://www.wpi.edu/Academics/Depts/CHE/Research/HMTL/CFD_in_CRE_IV/vanderHoef.pdf

http://www.princeton.edu/~jsun/docs/Sun06fb.pdf (Formulations in MFIX explained)

A nice presentation of gas-liquid reactor simulation with multiple bubble size distribution

http://cfdcre5.org/cfdcre5-Petitti.pdf with discussion on moments, breakup and coalescence rates ..definitely something worth investigating..

CFD modeling of particulate flows (from the Stanford institute) http://web.engr.oregonstate.edu/~sva/archive/apte_ARB_2003b.pdf

http://www.stanford.edu/group/ctr/Summer/SP08/4_5_Massot2_new.pdf (turbulent combustion part)

Eulerian models for polydisperse evaporating sprays: http://hal.archives-ouvertes.fr/docs/00/44/98/66/PDF/Kah_etal_Pope_final.pdf

I tend to use the keywords such as polydisperse models, dilute sprays, etc so that if one is searching for these keywords over the web, the blog presented here may be useful in finding some relevant papers.

A very nice use of Eulerian multi-fluid modeling for biological transport:

http://www.personal.psu.edu/rfk102/PUBS/BIOMED2003Paper.pdf

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