[CFD] The k - epsilon Turbulence Model
Ғылым және технология
An introduction to the k - epsilon turbulence model that is used by all mainstream CFD codes (OpenFOAM, Fluent, CFX, Star, COMSOL, Saturne). The following topics are covered:
1) 9:30 What is the standard k - epsilon model?
2) 11:05 How has the model evolved over time and what variant am I using?
3) 13:30 What are the damping functions and why are they needed?
4) 17:56 What are high-Re and low-Re formulations of the k - epsilon model?
#kEpsilon #fluidmechanics101 #cfd
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Some useful references:
1) W. P. Jones and B. E. Launder
The prediction of laminarization with a two-equation model of turbulence, Int. Journal of Heat and Mass Transfer, 15, 1972, pp. 301-314.
www.researchgate.net/publicat...
2) B. E. Launder and D. B. Spalding
The numerical computation of turbulent flows, Comp. Methods in App. Mech and Engineering 3, 1974, pp. 269-289.
www.researchgate.net/publicat...
3) B. E. Launder and B. I. Sharma
Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc, Letters in Heat and Mass Transfer, 1974, 1, pp. 131-138.
www.researchgate.net/publicat...
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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: 268
I hold a PhD in physics and have been working on CFD simulations for decades. Even so I still find your lecture very useful and comprehensible! THX a lot!
@sharemarketkoninja6929
2 жыл бұрын
I too understand him well. I have applied phd in ustc, and i watch his lectures to be able to tackle phd interview questions. 😁
@Roselen1993
Жыл бұрын
Hello ! Have you worked on grid independence studies ?
@Geschaeft-lf3pj
Жыл бұрын
@@Roselen1993 I am asking myself if it is possible to achieve a mesh independing TKE-Field. The finer the mesh, the more TKE is produced since the "detected" velocity differences between the cells and thus the shear stress is larger in comparison to large cells?
@prestonr6348
Жыл бұрын
@@Roselen1993 It depends on which field of CFD you are asking about. Every field has its own methodology to achieve grid independence, one has to check the existing literature to find out
This is amazing! I cannot believe that I am watching this video at 4:00 am and understanding everything. Thank you so much!
@fluidmechanics101
4 жыл бұрын
4am! 😂😂
@autonu
4 жыл бұрын
I am at 3:38 AM 😉
@sssandrew2205
3 жыл бұрын
I've watched this video for 10+ times and read a book for several months, until today, I finally understand every question in my head. I'm a slow learner and you really saved me !!!!!
@tumulpurwar8812
3 жыл бұрын
@@sssandrew2205 looks so for..me 2 times
@Kavser
Жыл бұрын
@@sssandrew2205 good learning is always slow. its not you! Expertise requires repetition
your way of explanation is outstanding
These lectures are invaluable
Finally, I am waiting for this for a long time thank you so much Dr. Aidan!!
Explained so well. In depth explanation also covering basics in a way that is easy to understand.
Wow!!! what an amazing lecture, now I can have a far better view of all these factors in CFD modelling. Thanks a million.
Thank you for making this available to us!
Bro you are saving lives with this channel. God bless you!!!
Really Appreciate the efforts you've put in making this. Thanks for sharing your knowledge.
We will support you forever! You are an amazing teacher with excellent explanation. Thank you Aidan
What a wonderful video, beautifully and calmly presented, super clear and well researched, thank you for this! I'm doing my thesis in CFD of a heat exchanger and have been wondering exactly what the magic behind the scene was for these k-eps and k-omega SST models. You've shed some great light on this. Much love! :D
Best lecturer ever! Great job .. time to start adding - "as usual" :>
You are the best, amazing teacher. Using simple content but complete concept! Also, easy to learn!
thank you for your fantastic introduce about k-e! I love it!
Hey man, just approaching a research activity in CFD at my university and this video helped me a lot! So thank you very much, even if with more than a year delay!
amazing man, thanks for the great video, I've just started simulating turbulent models and did not understand what the different models were or how they solver work, the insights have been pretty helpful.
you are doing a wonderful job in your channel man.
Thank you sooooo much! I really appreciate it! This video helped me a lot! Already recommended it to some friends.
This channel is brilliant, thank you very much
you're a saint, i find your lessons very well done
This video was very useful for my project work, thank you
amazing lecture, learning a lot in a lockdown world in 2020, thank you
Thank you so much for this excellent presentation! I have been a practicing engineer for many years. One of our focus points is coupled-physics CFD-Thermal analyses for rotating electric machines.
This guy is good. I would pay for this, thanks a million
As an engineering student, these videos are life saving at times of need. Keep up the awesome work!
I have a CFD exam tomorrow and you have been one of my best buddies this past weekend while studying. Thanks :D
@fluidmechanics101
4 жыл бұрын
Fantastic, im so glad you found my talks useful for revising 😄 good luck for tomorrow! I know you will smash it
Incredible, thank you so much
Amazing channel! Well done. 2 questions 1) would it be possible to give a lecture to summarize the best applications for each turbulence model? 2) could you give a lecture about implicit and explicit models and their applications ? Thank you very much !
Brilliant, thank you very much for this video.
thanks you make the concepts very easy to understand...
This, sir, is perfect!
Thank you! Very clever explanation
Great video!
Thank you very much. It really help to understand easily.
Malgré mon faible niveau d'anglais, j'arrive à te suivre. tu es le meilleur.Merci
Thank your for the references
amazing ,thank you Mr aidan
Amazing lecture!
Nice job, man! Thank you a lot!!!
Thanks you very much.... Now I am somewhere able to understand my CFD simulation!!!
Great lecture. I am doing a CFD project at my university and your videos are helping a lot to catch the theory behind everything! I started with the Wall-Functions, then this one, now going for the k-w SST one!
@fluidmechanics101
4 жыл бұрын
Perfect 👍 good luck with your CFD project 😊
Great work, very lucid...
wonderful lecture! bro you are the best!!!
That was so clear. Thanks!
Such a great video
Amazing explanation, and I hope I become like you one day!
Excellent lecture Aidan!
Excellent. I read the Book《The CFD-FVM》 written by Dr. Versteeg, which combined with your lecture is more impressing.
@fluidmechanics101
4 жыл бұрын
It is a great book! I use it myself every so often
You are doing a good job , go on
wow! really good video! thanks
very useful.Thank you very much
This is amazing
Excellent!
Very good video. Thanks.
As Always great job_ Fan of your work😃
@fluidmechanics101
5 жыл бұрын
Thanks Nikhil 😊 much appreciated!
Thank you very much Sir.
very useful!
Thank you so much.
Thank you
Well done Aidan.
Really Thank You
why this guy doesnt teache fluid mechanics and dynamics from begining ... he is a good teacher
Thanks!
Tell you what mate, I am in one of the best French engineering schools and my professor for CFD is miles away behind of you. It's ashaming that you are not the one I can rely on every Friday morning
great video
Really helpful. Thanks (:
thank you!!
thanks a ton!!!
very good video
good job! =)
Excellent lecture! Always beyond my expectations. Small remark : In minute 7:39, I think that on the mixing length equation (last one), Cmu has an expo of 3/4
@fluidmechanics101
3 жыл бұрын
Yep, typo!
Thank you for the lecture. Wonderfully explained. Is it possible to give another lecture on RNG, Realizable also with the two-layer approach? Then it will be much transparent how the different K- Epsilon models are different from each other. Thanks in advance.
Hello, Mr. Wimshurst. The video is brilliant! Thank you for your time and passion. I have a couple of questions about it. Slide 8. We have coefficients C1, C2 and C3, and Cμ. However, on slide 9 in the table there is only C1, C2, and Cμ. Could you tell us something about C3? Slide 12. You said: “… we have to have some way of damping the dissipation rate close to the wall …” I think we have to increase the dissipation rate to mimic of sublayer, isn’t it? Slide 12. In equation 18 there is no Cμ in the mixing length part. Slide 13. Laminar viscosity equals molecular viscosity, isn’t it? Slide 13. Equation 22. Could you explain how μt from eq. 2 became μ+μt in eq. 22? Slide 17. You said: “… damping functions are effectively reducing the value of epsilon in a similar way to how the mixing length was reduced in earlier models near the wall …” I think the epsilon must increase while approaching the wall. And mixing length must decrease!
A KZread video series made me understand CFD theory better than a £9k/year MSc
Wonderful lecture sir, this as well as your other one base on k-epsilon turbulence model. Could you please spare time to make a lecture about the spalart allmaras turbulence model and why it is widely used in aerospace applications? This would be really helpful for me as well as other aerospace modelling peeps out there. Thanks in advance :)
@luzzyrogue
4 жыл бұрын
Has he done a video for this yet?
@jayanstanite
4 жыл бұрын
@@luzzyrogue kzread.info/dash/bejne/ip2qxZJ-eaqsgdo.html
A highly educated & well-explained content. Can you please deliver an extension lecture of this one on Non-linear k---ε models? As there are too many models out there & usually things get missed up while selecting the right model for the problem.
@fluidmechanics101
2 жыл бұрын
Yep, if I get around to them 😅 there are a lot of models to cover
you save my life
Hi Aidan, best video I've come across. Any chance you give an introduction on realizable k epsilon model?
@fluidmechanics101
4 жыл бұрын
Yep, that one is coming soon. Im currently working on the video for the k-omega model, so that one will be next!
Thank you Dr. Aidan for such simple and concise theory! One question though - should the last term in equation 2 (Reynold Stress) has a nu_t multiplied to it?
@fluidmechanics101 Love the videos they're extremely helpful! Just wondering what website you use to create your sketches?
@fluidmechanics101
4 жыл бұрын
I use inkscape 😊 its free and available on all operating systems
Hello Dr. Aidan, Thanks for this informative lecture. In equations 4 and 5 , to get the graph shown y would have to equal y+, is that correct?
Thank you 谢谢
@fluidmechanics101
5 жыл бұрын
No problem, glad you found it useful 😊
great explaination man ....Big fan !!...Can you elaborate more on history of turbulence and why these two parameters (k, epsilon) are best for turbulence modelling and how we get changes in final velocity and pressure fields due to these equation. That is relation between two turbulence equation to the main momentum equations.
@fluidmechanics101
4 жыл бұрын
Yes of course. The only way that the RANS turbulence fields affect the momentum equations is: 1) through the eddy viscosity which changes the diffusion in each cell 2) increasing the wall shear stress in the cells adjacent to the wall (if the log law wall function approach is used). These effects are manifested as increased mixing and steeper velocity profiles near the wall 👍
Great video! How do you obtain equation 7?
Extremely useful lectures on RANS. Will you consider LES or hybrid RANS-LES in future episodes ?
@fluidmechanics101
4 жыл бұрын
Yes definitely. Im going to start with general LES background and the look at the main methods in turn (the same way that i have done with RANS), so DES, SAS and WMLES and so on 👍
put a video on detailed explanation and formation of Navier stokes equation
Hi Dr. Aidan, please, could you make a video of mixing lenght and how this could impact the values of k, epsilon and omega?
Video regarding the wall distance free turbulence models please
Hello there, first of all i ant to thank you for your great videos. From your eplanation it seems to me as if there is no need for a wall function in low-Re applications, is that right?
Hello Aidan Thank you again for the excellence material, i have purchased the PPT for 1-20 are you going to include this one in 21-30?
@fluidmechanics101
5 жыл бұрын
Yea i was going to release them in sets of 10, so this one will be in 21-30. Alternatively, if you would like to get them all, i release them on patreon as soon as they are uploaded, so you can get them there straight away!
What should I consider to decide that my flow is turbulent ? Is it only Re number ?
Thank you very much Dr Aidan. I have a question about your figures. Are you using pyx?
@fluidmechanics101
4 жыл бұрын
Yep I am using python for all my figures 😊
Hello Dr. Wimshurst, Thank you for your helpful lecture. I want to study more deep on the behavior of flame in a pipeline but I am confused this model is applicable for prediction of behavior of flame or not. One of the biggest problem is that we have a compressible fluid in the pipeline. Can you help me to solve this problem? If you present some references for this goal will be very helpful. Thank you. Best regards, Kazem Lakzian
Hi Aidan, Wonderful video as always. I'm confused with something and I would like to know if you can help me. I understand that the k-e model is best used with 30
@fluidmechanics101
4 жыл бұрын
Yep, looks good to me! I will be looking at RNG and realizable k epsilon models soon, so that should clear this up a bit for you 🙃
@leonardohenao7646
4 жыл бұрын
@@fluidmechanics101 Thanks Aidan. I will also be researching and commenting here the news that I find about it
While substituting for lm in Ret, did u missed the Cu coefficient?
This is a great video! Is there a source for the first general RANS Equation? I am wondering what each term represents in the equation and want to make sure I know what each variable is
@fluidmechanics101
3 жыл бұрын
Most CFD textbooks usually have a pretty good description of the basic RANS equations and their derivation. I would probably look at mixing length models first as they are the most straightforward to understand
thanks for making this awesome lecture. btw I think you have a typo in the eq.2 in your video. It seems you missed the turbulent viscosity in the third term of the RHS of your equation 2.
@fluidmechanics101
4 жыл бұрын
Ahh yes, this is a typo 😅
pls do a application demo of this models in a commercial software guided with the theory. Thanks a lot.
Good lecture please allow videos in 144p it is bit trouble it uses more mobile data