[CFD] The k - epsilon Turbulence Model

[@supernice1977JeffLee]

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]

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]

Hello ! Have you worked on grid independence studies ?

[@Geschaeft-lf3pj]

@@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]

@@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

[@adghawre]

This is amazing! I cannot believe that I am watching this video at 4:00 am and understanding everything. Thank you so much!

[@fluidmechanics101]

4am! 😂😂

[@autonu]

I am at 3:38 AM 😉

[@sssandrew2205]

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]

@@sssandrew2205 looks so for..me 2 times

[@Kavser]

@@sssandrew2205 good learning is always slow. its not you! Expertise requires repetition

[@vahidalavifar1741]

Wow!!! what an amazing lecture, now I can have a far better view of all these factors in CFD modelling. Thanks a million.

[@ashokdarbhe5664]

Explained so well. In depth explanation also covering basics in a way that is easy to understand.

[@JoshuaLorenz-s5s]

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.

[@hesamnaeimi778]

You are the best, amazing teacher. Using simple content but complete concept! Also, easy to learn!

[@teddyokolo4312]

Bro you are saving lives with this channel. God bless you!!!

[@killua9369]

We will support you forever! You are an amazing teacher with excellent explanation. Thank you Aidan

[@firevarun]

As an engineering student, these videos are life saving at times of need. Keep up the awesome work!

[@sapyman216]

your way of explanation is outstanding

[@MalcolmAkner]

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

[@OgamerPro]

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!

[@antoniodesantis556]

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 !

[@xTerpsichore]

I have a CFD exam tomorrow and you have been one of my best buddies this past weekend while studying. Thanks :D

[@fluidmechanics101]

Fantastic, im so glad you found my talks useful for revising 😄 good luck for tomorrow! I know you will smash it

[@Raphael4722]

These lectures are invaluable

[@DaviMonticelli]

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]

Perfect 👍 good luck with your CFD project 😊

[@kennettallgren640]

Thank you for making this available to us!

[@sergeianpilov5222]

Best lecturer ever! Great job .. time to start adding - "as usual" :>

[@giuseppe2716]

you're a saint, i find your lessons very well done

[@sirerwin5881]

This guy is good. I would pay for this, thanks a million

[@920602145509]

Finally, I am waiting for this for a long time thank you so much Dr. Aidan!!

[@theophilusdsouza5993]

Really Appreciate the efforts you've put in making this. Thanks for sharing your knowledge.

[@edithlee6221]

thank you for your fantastic introduce about k-e! I love it!

[@cheikhnatalebmoustaph43]

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]

Yep, typo!

[@andrealiu8650]

Excellent. I read the Book《The CFD-FVM》 written by Dr. Versteeg, which combined with your lecture is more impressing.

[@fluidmechanics101]

It is a great book! I use it myself every so often

[@saeedhabibzadeh749]

you are doing a wonderful job in your channel man.

[@josephapedanou755]

Malgré mon faible niveau d'anglais, j'arrive à te suivre. tu es le meilleur.Merci

[@martin999]

This channel is brilliant, thank you very much

[@lexuslfa4739]

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.

[@manitalks99]

This video was very useful for my project work, thank you

[@jayanstanite]

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]

Has he done a video for this yet?

[@jayanstanite]

@@luzzyrogue kzbin.info/www/bejne/jprZlGN7fqx5h9k

[@elchupaka]

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!

[@mustafamarvat863]

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]

Yep, if I get around to them 😅 there are a lot of models to cover

[@rafaortwein6646]

Very helpful explanations, thanks.

[@lance3865]

Thank you sooooo much! I really appreciate it! This video helped me a lot! Already recommended it to some friends.

[@rohitkeshri5427]

thanks you make the concepts very easy to understand...

[@keshavkothari5489]

why this guy doesnt teache fluid mechanics and dynamics from begining ... he is a good teacher

[@luzzyrogue]

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

[@sedatarslan3994]

Thanks for the video. It is very educational.

[@vineetsingh8047]

Thanks you very much.... Now I am somewhere able to understand my CFD simulation!!!

[@gaetanjamet1477]

Incredible, thank you so much

[@nageshjamge1372]

Thank you very much. It really help to understand easily.

[@cristiandavidcoronadocasti7804]

Muchas gracias, explicas bastante bien !

[@manitalks99]

Thank your for the references

[@anitsen6252]

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.

[@kamiben692]

Brilliant, thank you very much for this video.

[@elmarbouhjawad4259]

amazing ,thank you Mr aidan

[@ranchao3487]

amazing lecture, learning a lot in a lockdown world in 2020, thank you

[@arefhmoalemi5735]

Wow! Man this video is amazing !

[@davidwang8270]

Hi Aidan, best video I've come across. Any chance you give an introduction on realizable k epsilon model?

[@fluidmechanics101]

Yep, that one is coming soon. Im currently working on the video for the k-omega model, so that one will be next!

[@manelaero7709]

You are doing a good job , go on

[@giuseppesalvo5755]

Thank you! Very clever explanation

[@AmitKumar-uw4uu]

Amazing lecture!

[@TheManolis1984]

A KZbin video series made me understand CFD theory better than a £9k/year MSc

[@abhishekthakur-xt7fl]

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]

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 👍

[@maged779]

Amazing explanation, and I hope I become like you one day!

[@qilongren9623]

wonderful lecture! bro you are the best!!!

[@gauravpant8350]

Great work, very lucid...

[@abhishekganguly7695]

This, sir, is perfect!

[@daddysnip6397]

Great video!

[@mattheushenriquemores5693]

Nice job, man! Thank you a lot!!!

[@mariarosales3535]

Thanks a lot for these free lectures prof. Aidan! If possible, please let me share a question: from OpenFOAM simpleFOAM, all the governing equations are divided by rho for simplicity BUT, in k-epsilon model, the production of TKE, G, originally is not directly affected by rho. Does this omition of a rho value different than 1.0 does not lead to a deviation in the solution of both transport equation of k and epsilon, that at the end is a deviation in the solution of nut and finally could impact the velocity solution?

[@fluidmechanics101]

The production term (G) is the double inner product of the Reynolds Stress tensor and velocity gradient tensor (giving a scalar). In incompressible flows, the Reynolds Stress tensor is written per unit density (divided by rho), so there should also be 'density dependence' in G as well. Have I understood your question correctly?

[@mariarosales3535]

@@fluidmechanics101Hi Aidan thanks for your kind and fast reply. You gave me a clue, and I assume now that 'density dependence' in G that comes from RST is implemented with dev() function used in kEpsilon implementation, and let' say that dev() already considers the 1/rho because is based in the continuity eq of incompressible solvers,... am I in the right path? dev()

[@Michallote]

This is amazing

[@mariarosales3535]

Hi Dr. Aidan, please, could you make a video of mixing lenght and how this could impact the values of k, epsilon and omega?

[@katialamer6681]

That was so clear. Thanks!

[@shangguicai211]

Extremely useful lectures on RANS. Will you consider LES or hybrid RANS-LES in future episodes ?

[@fluidmechanics101]

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 👍

[@TahsinEngin-Akademi]

Great explanation again. Would it be better to use "inertial forces" instead of "turbulent forces" in the definition of Re number.

[@fluidmechanics101]

Yes, you are right, it probably would be better to say inertial rather than turbulent forces. Well spotted!

[@sinangoren4803]

Tahsin hocam sizi buralarda görmek beni sevindirdi. Doğru kanalları takip ediyorum anlaşılan :)

[@prestonr6348]

So basically we relate the Reynolds stress terms to the mean velocity gradient by introducing μ_t. To solve μ_t, we introduce transport equations for k and ε. To solve the transport equation k, we need Cμ. To solve the transport equation ε, we need C1, C2 and C3. To solve the issue of boundary layer, we introduce damping factors f1 and f2 to transport equation k, and fμ to transport equation ε. And to solve for fμ, you need to find Re_T, which is the Turbulent Reynolds number. Is there something else that I'm missing?

[@fluidmechanics101]

Yes, that's everything 👍 nice summary

[@prestonr6348]

@@fluidmechanics101 You're the man Aiden! 👍🏻

[@mohsen7514]

Such a great video

[@Justart_jpeg]

Thank you for this amazing video! What is the best model for Fume hood simulation? I see a lot of people using realizable k-e

[@anirudhsingh3507]

Your video helped a lot , thank you so much. why k e model is better on applications away from the wall . Any answer with details regarding an equational term?

[@fluidmechanics101]

There is no specific term that causes this. It mainly comes from people's reported experience with a variety of test cases

[@kostaskouris3198]

very useful.Thank you very much

[@mohammedyousif618]

I hold a Ph.D. thesis and have been working on SolidWorks CFD simulations for heat exchangers, the modified lam-bremhorst k-epsilon method was considered in SolidWorks, and I want to know how can I calculate the values of k and epsilon at the entrance, exit, and middle regions?

[@fluidmechanics101]

Good question. Does the SolidWorks manual give you any help? K and epsilon should be fairly easy to extract from a CFD solution

[@mohammedy.jabbar7052]

I don't find any description in the help. Then, how can i get these values if i don't have any solutions.

[@fluidmechanics101]

Why do you need k and epsilon? solidworks is generally only used for basic flow analysis, if you need to know k and epsilon you should probably be using a better code like Fluent, Star CCM, CFX or OpenFOAM

[@hassannemati7331]

Well done Aidan.

[@SamarSinghal]

Sir recently I have bought all your lectures last year. sir I am trying to simulate a building in an enclosure, but the backflow is preventing convergence. can you make video on that or help me with that problem,. thanking you sir for your great lectures and courses,

[@fluidmechanics101]

What type of flow do you have? Backflow can happen for a variety of reasons, mostly linked to the flow physics and boundary conditions

[@SamarSinghal]

@@fluidmechanics101 thank you sir for noticing my problem, I overcame my problem

[@SamarSinghal]

Sir If possible make lecture on reference values given in ansys. I think it's to make non dimensional analysis

[@j.kuhlmann8765]

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?

[@nikhilnick8886]

As Always great job_ Fan of your work😃

[@fluidmechanics101]

Thanks Nikhil 😊 much appreciated!

[@martinsaravia]

Excellent lecture Aidan!

[@leonardohenao7646]

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]

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]

@@fluidmechanics101 Thanks Aidan. I will also be researching and commenting here the news that I find about it

[@mouradbelamine9064]

Video regarding the wall distance free turbulence models please

[@ketan8069]

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]

Ahh yes, this is a typo 😅

[@TanmayPanchal46]

Can you provide how did you arrive at this form of RANS equation at 2:10 ?

[@fluidmechanics101]

This form of the RANS equations is the full compressible form. You may have seen the simplified form for incompressible (constant density) flows. You should be able to look them up on CFD online wiki, or any other good CFD textbook. For the purpose of the talk is does not really matter which form you use, we just need an understanding of the Reynolds stress and where it comes from 👍

[@Luiferhoyos]

I had the same doubt. That equation and its derivation can be understood if you read chapters 2 and 3 of this book www.gidropraktikum.narod.ru/Moukalled-et-al-FVM-OpenFOAM-Matlab.pdf Then, in chapter 17, they derive RANS equation, which is almost equation 1, but with the added Reynolds stress.

[@orlandopalone80]

Excellent video. My only question is: in which video do you explain the definition of the basic quantities, such as k, epsilon and so on?

[@fluidmechanics101]

I havent made a video for the simple definitions yet. I suppose i was trying to do the difficult videos first 😂 i will make one and upload it soon!

[@orlandopalone80]

@@fluidmechanics101 perfect. I have just started watching your lectures and I really like them. I am starting using ANSYS, but personally I preferi to get a significant grasp on theory before starting simulation. Thank you for your work.

[@JaatLostInFrance]

Amazing explanation, But I find it somewhat confusing sometimes because I see you saying sometimes that near the wall, just like how mixing length needs to be damped, similarly the dissipation needs to be damped as well. I think you should have been more careful because it is the dissipation of the dissipation that needs to be damped and not the dissipation itself. In fact, We would like to increase dissipation near the wall. Just wanted to point out this so that if someone is reading the comments will get crystal clear idea.

[@fluidmechanics101]

Yea I have been thinking about this lately, I think we should say 'the reduction in the dissipation rate' to be clear

[@yogeshnalam1950]

What should I consider to decide that my flow is turbulent ? Is it only Re number ?

[@dabaker22]

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]

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

[@ylustc940]

great video, but i have a question. is Cμ missed in eq.18 and eq.19?

[@fluidmechanics101]

Yep, well spotted

[@knnfatima9]

Excellent!

[@joshuamills7633]

Good content, would be nice to have an overview though, how does this model compare with others (RST, k-w) at a very high level!

[@fluidmechanics101]

Agreed. Especially as the most important question is usually 'which turbulence model do I choose?'

[@joshuamills7633]

@@fluidmechanics101 haha I suspect you have some more content on the way then! I find it quite difficult to translate the intricacies of the theory and explain the practical differences, like why is my RST model so much more unstable than k-epsilon for the same mesh

[@fluidmechanics101]

Good question. All I can tell you is that RST are notorious for being unstable and is part of the reason people love k epsilon and k omega SST so much. We definitely have the computing power these days, the models just don't seem to be very stable. So don't worry, many other people have found the same thing as you! Do you need RST or can you just use k epsilon and accept a small degree of error?

[@joshuamills7633]

​@@fluidmechanics101 Thanks for the response! I am glad to see that its a common trend then. We are trying to model the effect of the rotation of the wheels on the lift induced on a sports car for different speeds. What's interesting is that the lift is always predicted to be lower by the RST than the eddy viscosity models, this is even more pronounced at lower speeds and the RST fluctuates a lot more at lower speeds. Our professor said that in reality the grid is nowhere near refined enough under the car for the RST to be accurate and it would require such a heavy refinement which is out of the scope of our project, so we'll probably just go with k-e/k-w. As you said, it does seem like k-e/k-w are the quick and dirty models that are much easier for predicting global parameters.

[@fluidmechanics101]

Yep, I think your professor is spot on there! Best of luck with your calculations

[@Dr.VikkY_Ph.D._Mr.Ramesh_MBA]

put a video on detailed explanation and formation of Navier stokes equation

[@nikitvhatkar1214]

Good lecture please allow videos in 144p it is bit trouble it uses more mobile data

[@parasghumare8067]

While substituting for mixing length in equation 18 C_mu term is missing.

[@luuunaw103]

Thanks for the lecture. But is the dynamic viscosity different from turbulent viscosity?

[@fluidmechanics101]

Yes! The dynamic viscosity (mu) is a material property of the fluid. Hence, water will have a different dynamic viscosity to air. The turbulent viscosity/eddy viscosity (mu_t) is a made up quantity! We often make the Boussinesq approximation which states that the strength of the turbulence is proportional to the mean velocity gradients. The proportionality constant is the turbulent / eddy viscosity! This approximation allows us to model the effects of turbulence (eith reasonable accuracy) without resolving the fluctuations themselves, as this is expensive and difficult. I hope this helps 😊

[@luuunaw103]

@@fluidmechanics101 Thanks very much for your explanation.

[@Peisari]

wow! really good video! thanks

[@minzhang2848]

This is excellent material! Thank you so much! I am wondering what is the value for C3? In addition, I am wondering whether you could direct me to a reference about how to calculate/approximate the inlet and/or initial values for these turbulence parameters, such as k, epsilon, turbulence intensity, hydraulic diameter, turbulence viscosity ratio, etc. Thanks again for the excellent video!

[@fluidmechanics101]

I have a calculator on my website that calculates the inlet values of k, epsilon, omega and turbulent viscosity ratio (link in the description). You should check it out 🙃

[@minzhang2848]

@@fluidmechanics101 That is toooo awesome! Thank you so much!!

[@Miao_zai]

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]

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!

[@sumitpatil6346]

Nice explanation!! Although I didn't understand the part after mixing length models as I am naive in Fluid Mechanics.Could you please suggest some material to for a beginner in turbulence concepts

[@fluidmechanics101]

Beginner turbulence books are quite difficult to find. You could always have a read of Pope (2000) ‘turbulent flows’

[@sumitpatil6346]

@@fluidmechanics101 thanks, will check this book

[@messaoudnadia7189]

Thank you

[@lupocci]

Great video! How do you obtain equation 7?

[@shalabhks]

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?