[CFD] Eulerian Multi-Phase Modelling

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[CFD] Eulerian Multi-Phase Modelling
An introduction to Eulerian multi-phase modelling in CFD. Eulerian multi-phase modelling is available in most mainstream CFD codes (OpenFOAM, Fluent, CFX, Star etc). The following topics are covered in the video:
1) 0:37 What are dispersed-continuous and continuous-continuous phase interactions?
2) 5:02 What are the Eulerian multi-phase model equations?
3) 12:29 What is inter-phase drag and how is it accounted for?
#multiphaseflow #eulerianmultiphase #cfd
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Some Useful References:
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1) ANSYS Fluent Theory Guide
16.5.3 Conservation Equations
www.afs.enea.it/project/neptun...
2) ANSYS CFX Theory Guide
5.5.2 Interphase Drag for Particle Model
www.sharcnet.ca/Software/Ansy...
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Want to learn more?
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Grab a copy of my CFD Fundamentals Course (for beginners):
www.udemy.com/course/computat...
Learn how to write your own CFD code in MATLAB and python (for intermediates):
dr-aidan-wimshurst-s-school.t...
Learn how I draw my figures and diagrams in Inkscape (for everyone):
dr-aidan-wimshurst-s-school.t...
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Did you like the video?
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Download the lecture slides from my website:
www.fluidmechanics101.com/pag...
Buy me a coffee to say thanks:
www.buymeacoffee.com/NKEZrhvg0
Support the channel on Patreon (and get useful extras for your CFD studies):
/ fluidmechanics101
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Donations:
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1) PayPal
www.paypal.me/fluidmechanics101
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Disclaimer
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The methods, algorithms, equations, formulae, diagrams and explanations in this talk are for educational and demonstrative purposes only. They should never be used to analyse, design, accredit or validate real scientific / engineering / mathematical structures and flow systems. For such applications, appropriate trained, qualified and accredited (SQEP) engineers / scientists should be consulted along with the appropriate documentation, procedures and engineering standards. Furthermore, the information contained within this talk has not been verified, peer reviewed or checked in any way and is likely to contain several errors. It is therefore not appropriate to use this talk itself (or any of the algorithms, equations, formulae, diagrams and explanations contained within this talk) as an academic or technical reference. The reader should consult the original references and follow the verification and validation processes adopted by your company / institution when carrying out engineering calculations and analyses. Fluid Mechanics 101 and Dr. Aidan Wimshurst are not accountable or liable in any form for the use or misuse of the information contained in this talk beyond the specific educational and demonstrative purposes for which it was intended.

Пікірлер: 125

@hamedmehrvlogs 3 жыл бұрын

That's an amazing video mate! Especially that mention that, the dispersed-continuous and continuous-continuous interaction differs in how we define the interfacial area per unit volume. It was super helpful.

@HaithamAhmed-kr8yl 4 жыл бұрын

Really, Thank you for this valuable video. Go ahead ! We are waiting your new videos.

@mihirmakwana2026 4 жыл бұрын

Hi Aidan. This video was very informative. A video on Lagrangian Multiphase model along with a comparison to Eulerian will be good sequel to this one. Cheers :)

@MalcolmAkner 3 ай бұрын

Damn, you are such an expert in explaining this in a way where it feels simple and approachable. Excellent pedagogic skills Aiden!

@engineersacademy4137 3 жыл бұрын

Appreciate alot.. One of the best CFD masters on KZfaq. Really very informative and clear

@RichardDuneSJTU Жыл бұрын

Thanks for your very detailed introduction.

@ricardoguzman9844 5 жыл бұрын

Congratulations! Great work!

@ryanlin5101 4 жыл бұрын

Thanks for your good teaching really. It's very literally. hope for next video about VOF model!

@tusharthorat5925 Жыл бұрын

Great video. Simple and effective. It would be great if you can post a video on combustion models.

@abdelaal2 4 жыл бұрын

that was really informative and helpful thanks and great job

@nabekary 4 жыл бұрын

Very nice explanation. Thanks a lot.

@sanjaykumaryadav3186 Жыл бұрын

Amazing explanation. Thanks a lot.

@juancamilorojasvalencia9294 3 жыл бұрын

Very thanks , your content is very useful.

@anjanmevanrajapakse1511 3 жыл бұрын

Great lecture mate

@akhileshwarsingh4054 3 жыл бұрын

Today, I watched this lecture and subscribed your channel. Your lecture was compact with quality. I am hoping some lecture related to interface tracking in multi-phase. I mean VOF model with explicit function. Thanks for this video.

@shubhamphysicist 3 жыл бұрын

Simply awesome

@syedimran1052 2 жыл бұрын

very informative video... thank you very much!!

@oneuniverse6679 4 жыл бұрын

dude you are god for us. thanks. :D

@ashishtiwari1912 5 жыл бұрын

Good work. Your explanations are simple enough to understand. Keep continuing with the good work. I am a masters student in CFD so it sounds familiar. I would request you to make videos on hybrid RANS LES models and probably on parameters such as q criterion and vorticity.

@fluidmechanics101 5 жыл бұрын

Thanks Ashish! Ive got lots of videos to come. I hope you find them all useful and easy enough to understand 😊

@toptentop1019 5 жыл бұрын

Thanks for good teaching

@fluidmechanics101 5 жыл бұрын

Thanks 😊 glad you liked it!

@kaushalsorte9870 3 жыл бұрын

Hello Aiden. This explanation was very helpful. Thanks. Could you please make a video on Volume of Fluid approach as well? Thanks in anticipation.

@hydrokbar2019 2 жыл бұрын

i think thanking is not sufficient for your efforts...i really mean it

@ikacar 9 ай бұрын

Thank you.

@nikhilnick8886 5 жыл бұрын

Found useful🙂 Thks

@fluidmechanics101 5 жыл бұрын

Great! Glad you found it useful Nikhil

@edithlee6221 2 жыл бұрын

thank you alot

@sergeianpilov5222 5 жыл бұрын

Wow, that is an unexpected leap - right into multiphase! Great lection again :> PS I know it's too much to ask for - but .. any plans for lections on evaportaion/condensation/boiling , break-up/coalescence, solid dispersed (granular temeprature etc)?

@fluidmechanics101 5 жыл бұрын

😄 im glad you liked it! I havent looked into any phase change processes yet (they are quite hard) but it is something im going to look into in the future! General multiphase is the best place to start for sure with mass and heat transfer terms

@ehsanheshmati5842 3 жыл бұрын

Perfect

@matiasbarron949 5 жыл бұрын

Thanks !

@fluidmechanics101 5 жыл бұрын

Glad you liked it 😄

@hassanazizi8412 5 жыл бұрын

Great explanation. I would request you to kindly give an insight to the modelling of mass transfer mechanisms between the different phases in your next video.

@fluidmechanics101 5 жыл бұрын

Hi Hassan, the mass transfer mechanisms are very tricky and im going to have to put some careful thought in before making a video. The essence of mass transfer is equal and opposite source terms in the volume fraction equations so that you get an effective transfer of mass between phases where you want it. For now i hope you have enough to help out with your CFD, while i research the video 😄

@water5825 3 жыл бұрын

@@fluidmechanics101 "The essence of ... source terms in the volume fraction equations ...": this eqn reads partial r_q/partial t+div(r_q U_q)=0 in your video, do you mean in the case of mass transfer between phases, e.g., phase change, we should add source terms on the rhs of the original volume fraction eqn?

@lizarettflavour 5 жыл бұрын

👍👍👍 thank you!

@fluidmechanics101 5 жыл бұрын

😄 No problem, glad you found it useful!

@lizarettflavour 5 жыл бұрын

@@fluidmechanics101 it is! it's very useful 🌞

@manchee23 Жыл бұрын

Hey Aidan great video, any plans of making an dedicated video series of multiphase in focus to mixture models .

@thunder852za 3 жыл бұрын

So in continuous-continuous flows, we don't normally model the ''surface drag'. For two incompressible fluids, the interface velocity is continuous. ie there is no phase velocity difference. However, I am talking about the single-fluid approach - which is the standard approach for fuel/tank slosh - maybe it is different in the multi-fluid approaches. I have never header of using the gradient as a stand-in for the surface area. I mean there is no mathematical reason for the gradient of the volume fraction to be related to the surface area, they are spatially orthogonal quantities. The gradient is used frequently as the interface normal (when normalised). For an algebraic VOF scheme, knowing the surface area of the interface is next to impossible, but for geometric methods, it is implicit in the scheme. Sorry perhaps because I work building these models I am being a bit critical. I love this channel in any case. Please don't take it personally, just a bit of confusion on my side. :D

@fluidmechanics101 3 жыл бұрын

Good comments! I always appreciate feedback from people who actually develop the models, as it really helps clarify the understanding. The best I can ever go for is reading the manuals, equations and trying to make deductions from these 😄

@thunder852za 3 жыл бұрын

@@fluidmechanics101 Thank you so much for taking the comment in good spirit. I was really worried it came across wrong and I really find these videos of great quality and I appreciate the work you do. I have learned a lot, and it's nice to be able to absorb advanced content in related but different areas of CFD. If you need to reach out regarding multi-phase stuff feel free. I am a Post-Doc in InCFD at the University of Cape Town. :D Thanks again for this channel.

@mohamedelbouti6556 3 жыл бұрын

Thank you for this amazing video, i just have a question regarding the VOF and mixture models, in Fluent when choosing VOF model we have also the option to choose dispersed interface , and when choosing mixture model , we have the option to choose sharp/ dispersed interface, could you please give more details about that ? Thanks

@tubaisaha3222 2 жыл бұрын

Hi Aidan, thanks for uploading such an informative video on Multiphase modelling. I have something to ask, i.e is DPM also pronounced as mixture model?

@Rihan_pls 4 жыл бұрын

Nice video👌👌

@naidrenalinadventuresn.a1684 4 жыл бұрын

Hi Adrian. WHat do you use in creating your nice looking CFD lecture notes on patreon?

@fluidmechanics101 4 жыл бұрын

I use latex with the beamer package. If you look through the patreon posts i have put up the template that i use, so you can use it yourself if you like 👍

@Miao_zai 4 жыл бұрын

Hello Aidan At 20:50 in the video, is that continuous-continuous interaction Cd is calculated same as Dispersed-continuous interaction Cd? All using the Schiller model? Thanks

@mateusalves9558 4 жыл бұрын

Thank you for the videos, they are pretty cool. Could you please say to what references do you get to study and maybe make your materials?

@fluidmechanics101 4 жыл бұрын

Mostly, i use the CFD user manuals from ANSYS, the OpenFOAM source code and textbooks. Often these sources arent very good, so i try and work things out for myself as well 😊 I then try and compile everything together in a really clear form for you guys, as there really isnt a great source of CFD information out there. Thats what im trying to make 😄

@mateusalves9558 4 жыл бұрын

@@fluidmechanics101 Thank you for your reply, I asked that becausa I felt the same think as you said and I wanted to confirme. I am doing my course conclusion work and I would like to have some lectures to put on the reference and explain all the things that I have done in my research (that is to develop a tool using OpenFOAM to predict the resistance curve for a ship of the Serie 60 merchant ships) . If you could help in some way with that I would be very thankful, and thank you for your help and your good videos!

@mdkhairulbasharshovon5530 4 жыл бұрын

Hello Aidan, It’s a Very nice video. So multiphase modeling is applied for phase transition between liquid and vapor refrigerant in a small diameter channel with larger length. But why most of the time solution diverge or temperature doesn’t not change? Thank you very much Please leave a suggestion

@Lunamycat34 3 жыл бұрын

Great video Aiden. What model should I use if we have both continuous-continuous and dispersed-continuous interactions in the same flow system?

@fluidmechanics101 3 жыл бұрын

If you are using CFX you should be able to have different interactions for different fluid couples. I am not sure about fluent or openfoam though

@diksharaut6241 2 жыл бұрын

It was a great video, I got this project called modeling of liquid-gas flows using VOF-DBM method and this surely was helpful, so I will be needing more guidance, could you help me out with that?

@samueltorres1322 4 жыл бұрын

Thank you for the clear explanation! For a project I need to simulate the dynamics and concentration profiles of polydispersed nanoparticles in a microfluidic and I was considering to approach the model using the Euler-Euler method in COMSOL (treating them as a dispersed phase), also introducing LES equations. Can this model be considered for nanoparticles? Do you think this approach could work?

@fluidmechanics101 4 жыл бұрын

Hi Samuel, yes your approach seems reasonable and will probably work. Im not sure if LES is necessary though. It depends on what quantities you are interested in studying.

@yi_mix5224 3 жыл бұрын

Can you do an introduction of the interface capturing discretization scheme? Many thanks in advance!!!

@mick74batti 4 жыл бұрын

Nice video, thanks. However, in the drag model, please note that what counts is the frontal area of a sphere, not its surface area. The Cd of a body is generally defined using its frontal area. Therefore, equation 12 turns out to be 3/2*rp/dp, not 6*rp/dp

@fluidmechanics101 4 жыл бұрын

Well spotted! Thanks for the clarification 😊

@mick74batti 3 жыл бұрын

@@water5825 The surface area of a sphere is 4*pi*r^2, the frontal area is the area of a circle, which is pi*r^2. So as you can see, the frontal area is 1/4 of the surface area!!

@arminsh9315 3 жыл бұрын

Thanks a zillion for your awesome videos. Honestly, my CFD knowledge has improved significantly since I started watching your great informative videos. Anyway, there was something that I couldn't understand very well at the penultimate slide which was about Ap/V of the continuos-continuous phases. I was wondering if you could explain it to me how this ratio is equal to the gradient of the volume fraction.

@fluidmechanics101 3 жыл бұрын

I can't remember exactly why this is the case. It is stated in many of the CFD manuals without much explanation. I know that's not very helpful but it's the best I've got at the moment 😅

@arminsh9315 3 жыл бұрын

@@fluidmechanics101 Thank you Aiden. By the way, may I ask you to introduce a source from which I can learn better the discretisation methods for the convection term of the volume fraction equation of the continuous-continuous method? Or if it's possible, could you please make video on them?

@sonyjasonallccarimamunico1990 3 жыл бұрын

Hi bro, could you recommend me a book or bibliography to have a better understanding of this and multiphase flow equations?

@danieltarraf7881 Жыл бұрын

Thank you, may I ask a question ? Assume we are spraying water in hot air (~1000c). some of the water will evaporate. Now, At the beginning of time t=0 we know r_vapor = 0 every where (we don't have vapor yet). If we consider the equation (4), r_vapor will not change as time progress (r_vapor = 0 for every time step). Is this correct ? Should not we add a volume fraction term (representing the transfer from water to vapor) as we did to the continuity equation ?

@vikashkumar-cr7ee 4 жыл бұрын

Could you plz upload more lecture on Multiphase modelling

@amirhosseinparvin2119 3 жыл бұрын

Hi Aidan, Thank you it was really helpful, I have a question. in the solution of volume fraction equations for three-phase (sharp interface), how it avoids overlapping the interfaces? in references the explanations about the interface tracking are all about the two phases condition.

@fluidmechanics101 3 жыл бұрын

Good question. Let me have a think about that one!

@ProjectPhysX 5 жыл бұрын

Thank you, found the talk very useful! I'm currently implementing VOF for free surface LBM (see my YT channel) and the hardest part is surface curvature calculation. A talk about this would be very appreciated!

@fluidmechanics101 5 жыл бұрын

Will see what i can do! This sounds like quite a challenging problem .... 😅

@joseffreebird2372 3 жыл бұрын

Please I need Help how to handle with spray cooling impinging hot flat wall.

@coolguy1652 4 жыл бұрын

Thank you for the video. I had a question though, doesn't the two-phase full eulerian model also have an inequality bound restraint on the phase fractions (i.e. 0

@fluidmechanics101 4 жыл бұрын

Yes, the CFD code uses a limiter to ensure that rq stays bounded in the range of 0 to 1. Limiters are quite complicated, so i havent covered them yet!

@SantiagoMarquezD 3 жыл бұрын

Part of that restraint is imposed in the way you obtain your pressure equation, additionally you have to properly integrate the phase's transport equations.

@michelletramper3025 3 жыл бұрын

Hi! Thanks for another wonderful video. I was wondering, is there a way to know how much governing equations I'm solving in total? If you e.g. have three phases, but they are coupled via drag / the sum of the volume fractions is one. And only considering mass and momentum (no energy and turbulence). I don't quite understand how fluent solves/couples the equations, and thus how many equations you're eventually solving. Cheers! Michelle

@fluidmechanics101 3 жыл бұрын

You could always just check the residuals that fluent writes out? Fluent will write the residuals for every governing equation you are solving, so this is a quick way to check. For example: pressure x-mom y-mom z-mom volf-1 volf-2 would give 6 governing equations? (3 momentum, 1 pressure, 2 volume fractions) which is what I would expect for 3 species

@michelletramper3025 3 жыл бұрын

@@fluidmechanics101 thank you!!

@finophile 10 ай бұрын

good video, but I have some problems with the metaphors. I suspect that you mean "suspension" not "solution" when you discuss Dispersed - Continuous. Specifically this is clear in (c) of sediment transport.

@manusego 2 жыл бұрын

Very good video, teacher.👏👏👏. Could I know the software that you use to draw the figures in the presentation? They are excellent! Lot of thanks in advance💞

@fluidmechanics101 2 жыл бұрын

Yep, they are all made using inkscape. I put together a quick course to show you how do it if you are interested? (Link is in the video description)

@manusego 2 жыл бұрын

@@fluidmechanics101 Thank you very much teacher. I will learn Inkscape from the video link. I have just joined the udemy course. You are the BEST💞👏💞👏💞👏💞

@HENGELWIN 3 жыл бұрын

Hi Aidan, if I want to simulate in Fluent for Moisture diffusion into something (like Electronic Packaging with voids inside them that allow moisture to diffuse in), do I need Multiphase model: Eulerian in this case?

@fluidmechanics101 3 жыл бұрын

For moisture diffusion you can just use a mixture model. In fluent you need to define a custom fluid as a mixture of air and water vapour. Then enable species transport and fluent should solve for the mass fraction of water vapour which you can convert into a humidity. With moisture calculations, there are no distinct free surfaces or interfaces between the water droplets and the air so you don't need an Eulerian / Volume fraction based approach. I hope this helps!

@HENGELWIN 3 жыл бұрын

@@fluidmechanics101 Thanks for the reply Aidan! will try that out.

@ketanganatra2403 Жыл бұрын

Dear sir... I referred to your video... can you add energy equation to eulerian model...??? I have checked the ansys fluent theory guide... there energy equation is not clearly interpreting in nature..in fact the energy equation contains the shear stress tensor and velocity vector....though energy equation should contain temperature or enthalpy term.. it will be helpful for me if you can reply...

@adlinasir2953 4 жыл бұрын

Hello sir, may i ask a few question? Lets say i want to insert diesel fuel in chamber that contain air as their fluid. should i use multi phase model in order to separate the two fluid which is diesel and air to identify the flow of the diesel and if yes which model should i use?.. Thanks sir for answer my question before..

@fluidmechanics101 4 жыл бұрын

Yep, i would use an inhomogeneous multiphase method (seperate momentum equations for diesel and oil). I would only go for a homogenous method if you are sure that the drag forces are only significant near the interface

@oneuniverse6679 4 жыл бұрын

can we model heat pipe wick structure in ansys fluent?

@fluidmechanics101 4 жыл бұрын

Sorry dude, im not sure what you mean. Can you provide a link/example?

@sylwiawrzesien518 3 жыл бұрын

@leonardohenao7646 4 жыл бұрын

Hello Aidan. I Have a question. In air-water multiphase flow CFD simulation's it is common to use a VOF = 0.5 to track or identify the position of interface or free surface. I would like to know why this criteria is used and if it can always be assumed the same. Otherwise, I would like to know if volume fraction can be taken different to 0.5 and, if so, ask you about a methodology to find this volume fraction. In Summary: Which value of volume fraction I can to choose for to identify free surface in an air-water simulation of open channel? What you do is great! Thanks for sharing your knowledge!

@fluidmechanics101 4 жыл бұрын

Hi Leonardo, yes you are right, it is common to use a volume fraction of 0.5 to track the free surface. This choice is arbitrary of course and you could really use any value between 0 and 1. The important thing to remember is that the CFD code can only resolve the free surface to within a cell. So perhaps a better way of defining it would be: the free surface exists in a cell where the volume fraction changes between 0 and 1. We cant say where in the cell it is, only that it is within a cell. So 0.5 is just useful as it is between 0 and 1. Interface compression algorithms usually try and steepen the gradient so that the volume fraction changes within 1 cell (instead of several) so it makes it easier to locate the free surface. I hope this helps 👍

@thunder852za 3 жыл бұрын

In algebraic VoF approaches (CICSAM) this does get used. However, in the actual physics governing equations, there is no distinction, just a region of smoothly varying material properties (its why we do VoF). The 0.5 can help to localise certain terms for example surface tension and evaporation. Although even here typically you don't find 0.5 being used rather volume fraction \in (tole, 1- tole). The geometric methods have a discrete representation of the interface so for them, they 'know' where the interface is. In all, I would say the use of 0.5 is most commonly a post-processing thing.

@leonardohenao7646 3 жыл бұрын

@@thunder852za Very interesting. Do you recommend some book or paper where I can read about algebraic VoF approaches, particularly COMPRESSIVE AND HRIC MODIFIED? Thank you!

@fluidmechanics101 3 жыл бұрын

I would have a read of Unno Ubbinks thesis (you should be able to find it on Google search) from Imperial College London

@totaloverdose3591 3 жыл бұрын

Sir, while modelling flow-boiling how do we decide the first cell size in the mesh accounting for different Reynolds no of different phases?

@fluidmechanics101 3 жыл бұрын

I would estimate the volume fraction of each phase and then calculate the volume averaged material properties (density, viscosity). You can use these to get an estimate of the Reynolds number, friction coefficient and y+

@totaloverdose3591 3 жыл бұрын

@@fluidmechanics101 thank you sir!

@sapyman216 Жыл бұрын

Hi, can you please tell me what are the boundary conditions required to solve the volume fraction equation in VOF model?

@fluidmechanics101 Жыл бұрын

The standard boundary conditions normally work. Fixed values on the velocity inlets and zero gradient on the other surfaces

@sapyman216 Жыл бұрын

@@fluidmechanics101 Thanks Aiden. I have another query. In a dam break simulation using VOF, what will be the bc to be applied on the inner surface of the fluid while solving the volume fraction equation?

@belfodilfarid4515 3 жыл бұрын

Which apraoch we should adopt for spray cooling impinging hot flat plate? thanks guys!

@fluidmechanics101 3 жыл бұрын

A mixture model would probably be best, or you could use Lagrangian particle tracks 👍

@belfodilfarid4515 3 жыл бұрын

@@fluidmechanics101 THANKS SO MUCH

@satishnatarajan 2 жыл бұрын

Why is the mass transfer term 'sink' for the liquid water In case of evaporation?

@fluidmechanics101 2 жыл бұрын

The liquid water phase loses mass, while the gaseous vapour phase gains mass. So the source term is negative for the liquid phase and positive for the vapour phase. Of course if you have condensation, it is the other way around 👍

@satishnatarajan 2 жыл бұрын

@@fluidmechanics101 Thanks a lot, Dr. Wimshurst. Now it's clear to me.

@shahan3596 2 жыл бұрын

Hey Aidan, how should the interaction or water-steam or water-vapor be treated? is it dispersed-continuous or continuous-continuous interaction?

@fluidmechanics101 2 жыл бұрын

I haven't done boiling calcs myself. I am guessing that it depends on the boiling regime? Do you have nucleate boiling?

@shahan3596 2 жыл бұрын

@@fluidmechanics101 yes. Nucleate boiling

@TNDeepuKumarmed 3 жыл бұрын

As it was mentioned that the dispersed particles are dissolved in the continuous fluid (1:53), So my doubt is if it is a solid particle then will it also get dissolved in CFD simulation? If we don't want the solid particle to be dissolved then what type of modeling approach (i.e., Models in CFD) needs to be followed? Thanks in advance

@fluidmechanics101 3 жыл бұрын

If your particles are large, then you probably need to look at Discrete Particle Method / Discrete Element Method. It is available in Fluent or MFIX. Not sure about CFX or OpenFOAM though 👍

@TNDeepuKumarmed 3 жыл бұрын

@@fluidmechanics101 So, you mean Dense discrete phase model (DDPM) with Eulerian phase?

@fluidmechanics101 3 жыл бұрын

Yep

@europa3233 3 жыл бұрын

If I want to simulate LNG dispersion which would u recommend?

@fluidmechanics101 3 жыл бұрын

Hmmm depends on the morphology of the gas bubbles in the fluid. Are they dispersed or continuous. Is there a free surface or do you have slug flow?

@europa3233 3 жыл бұрын

@@fluidmechanics101 dispersion, just trying to recreate falcon series tests

@skhossenali5654 2 жыл бұрын

Sir, can you make another video on the algorithm/procedure to solve these complex equations.like I didn’t get how do we get pressure equation and solve it.

@fluidmechanics101 2 жыл бұрын

Yes, I am working on this at the moment. It is quite confusing and the pressure correction equation is definitely one of the hardest parts to understand in CFD

@skhossenali5654 2 жыл бұрын

@@fluidmechanics101 Sir, if possible can you suggest some references untill you upload the video prefereably for the compressible cases. Thanks.

@fluidmechanics101 2 жыл бұрын

The book by Ferziger and Peric (computational methods for fluid dynamics) is pretty good. I would start there 👍