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

CFD Forums

In order to obtain complete control over the "commercial" blackbox codes, it is imperative that users discuss the finer details of the code implementation (user functions) so as to maximize the benefits ..the code has to offer. As most of the readers know, CFD-online has the primary source for many of us. Given that, several other forums such as

Fluent University Forums:

http://university.fluent.com/forum/viewtopic.php?p=385&sid=a4c100c125bf479c72bcc07e6c117432

http://university.fluent.com/forum/viewtopic.php?p=2934&sid=98f99ad4d91f615f7be6fcd74a7665c6

CommentPortals: http://commentportal.com/search/udf-compile-error--cfd-online-discussion-forums

can provide elaborate discussions on certain stuff that may be missing in CFD-online.

I, in fact, strongly recommend Fluent users to become a part of the Fluent University Forum community. Besides getting answers from fellow CFD users, sometimes the developers themselves post results to queries which just makes it perfect ;) - straight from the source. Search for other topics (anything in Fluent) and errors/bugs that you think exists within the code can be discussed here. In fact, this portal serves as a nice forum to let Fluent guys know your exact problems.

Website providing tips for CFD modeling (especially multiphase flows such those using VOF etc) are also very helpful

http://www.cfluid.com/bbs/archiver/?tid-42834.html

I came across this site where manuals for different softwares and discussions pertaining to their usage are available.

http://www.cadfamily.com/downlist/s_115_1.html

VOF Modeling / Applications : Sprays / Droplet Breakup-Deformation-Coalescence .....

One the important problems where more academic fellows look to employ multiphase-VOF approach concerns the breakup of droplets (bunch of stuff can be investigated here : effect of shear, liquid/gas density ratios, velocity of impact etc). They keep publishing stuff back and forth so that they can honor their "commitment to publications!" either during tenure period or post-tenure (this time, the grad students are made to kill the problem !)

Anyways, being beaten down time to time or not, droplet simulations is something I have personally grown fond of ..especially the use of VOF in creating almost real droplets is simply artistic nonetheless !From studies on droplets, emerge, more sophisticated studies such as spray breakup, spray impingement problems etc that are of vast interest in real-world applications.

Having said that, it still becomes essential to find lot of literature in this special field so as to improve one's understanding of the phenomena and the applied numerical methods.

In this edition of the blog, I am going to share some of the droplet dynamics (breakup coalescence) studies that I have bookmarked and read over the years. Hopefully, someone may find it useful to read further into these nicely written work.

I came across this nice presentation sometime ago,

http://cfdcre5.org/cfdcre5-Dietsche.pdf

detailing aspects of droplet breakup from an industrial point of view. The presentation infact shows how droplet entering into a matrix of obstacles gets torn apart ! Mechanisms such as "stick and pull", spreading, etc are nicely indicated. Effect of viscosity ratios on the breakup rates are also available.

Dr. Renardy's work in VOF flows is well known. Their group site has a complete list of VOF papers including their PROST model.

http://www.math.vt.edu/people/renardyy/Research/Publications/

All kind of publications dealing with droplet oscillations, shear flow (droplet dynamics), deformation due to strain in both 2D/3D approximation are available for download.

Also, you can find the PROST model here

http://www.ann.jussieu.fr/~frey/papers/stokes/Renardy%20Y.,%20Prost-%20a%20parabolic%20reconstruction%20of%20surface%20tension%20for%20the%20volume-of-fluid%20method.pdf

How could I not include the famous openFoam based VOF studies: (fundamental presentation by Dr. Jasak)

http://powerlab.fsb.hr/ped/kturbo/openfoam/slides/UniDarmstadt_12Jan2005.pdf

Droplet sedimentation simulation using Finite Element - Level Set Methods - interesting one !

http://www.igpm.rwth-aachen.de/Download/reports/reusken/ARpaper55.pdf

Simulation of the dynamics of insoluble surfactant from Univ of Minnesota !

http://static.msi.umn.edu/rreports/2004/291.pdf

The above publication has extensive details of the numerical approach. The modeling includes surface tension force term represented by a linear/non-linear function of surfactant concentration using the continuum surface force (CSF) model. Nice read for developers and new onlookers.

How about DNS of droplets in a closed channel:

http://www.fusion.ucla.edu/neil/Publications/DirectSimulationOfFalling.pdf

The presentation below is litte off from the VOF topic: NEvertheless, you can see the application of VOF in inkJET print heads !!

http://www.coventor.com/pdfs/inkjet_design_for_web.pdf

A study on droplet deformation through a micro-fluidic orifice can be downloaded here.

http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/viewFile/953/791

Some VOF papers using different approaches (other than conventional VOF type)

1. Buoyancy driven droplets simulated using hybrid vof - LEVEL SET approach

http://ame-www.usc.edu/cf/Volterra2009/PROGRAM/PAPERS/Paper-62.pdf

2. Simulations of droplet flows using Lattice Boltzmann approach (just to make sure I do not shun LB approach ;)

http://staff.aist.go.jp/naoki-takada/fedsm2003-45166.pdf

3. A good article on jet breakup using particle method

http://www.nmri.go.jp/act/staff/k_shibata/Paper/SHIBATA_JetBreakup,%20.pdf

Shared Presentation of the Day: http://conferences.npl.co.uk/nmaet/downloads/presentations/costa.pdf
(Nice work VOF methods in Spray modeling !)

Multiphase Applications - Spray Breakup Simulations using VOF

From time to time, I come across some nice articles on VOF applications - also call them "cool multiphase applications" since most VOF runs typically try representing an "actual physical process". Note that the requirements for VOF are similar to DNS in the sense that as the mesh refinement is increased, better and better approximation of the physical phenomena is reached. Isnt it? Think about applications of VOF?

-Spray breakup modeling - when you actually animate the VOF runs - seems like there is a real spray started ..!!

- Droplet splash - now this has been beaten down several times and authors have proven that with nice refinement, one can present results which really puts the user in a stiff situation..which one is the experiment and which one represents simulation !! (Well, after properly rendering the volume fraction iso-surfaces etc )

-Boiling ...a very nice application - still researchers use this as standard benchmarking

-Sloshing, Spilling etc...VOF has been found to be an excellent tool to get these process nicely re-constructed in the virtual environment ..

I could keep adding to the links here ...VOF applications although, at times, forces the computers burn their guts out ...often end with some nice results which, at the end, prove heart warming.

I have been following several VOF applications - being a developer myself - and use of VOF in Spray breakup (primary breakup part) has been quite thrilling. I am posting some videos of Spray breakup using VOF (using openFoam). I contacted several authors long time ago to see if they have any images / videos that they could provide - just to get a glimpse of their research.

Some nice work I have been following

1. Dr. Hermann's work : http://multiphase.asu.edu/publications.shtml

Check out the images in http://multiphase.asu.edu/open_jic.shtml (liquid jet atomization in cross flows).

LES of Atomization using VOF techniques

http://multiphase.asu.edu/open_les.shtml


2. I came across this paper "Numerical investigation on the disintegration of round turbulent liquid jets using LES/VOF techniques", Srinivasan et al., Atomization & Sprays, 2008.

Based on their work, using openFoam, I found some movies that I post here for guests view :)

Case - liquid jet velocity = 20 m/s in staganant gas



Case - Liquid Jet Velocity = 5 m/s in Stagnant gas



I will post some more videos of other breakup modeling work by researchers. Browsing along, one may be easily able to find vof simulations of droplet splashing, boiling etc which is why I left it out of the current discussion.

Kindly let me know your thoughts and comments. If you have something to share, kindly post your comments.