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[CFD] Eddy Viscosity Models for RANS and LES 

Fluid Mechanics 101
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An introduction to eddy viscosity models, which are a class of turbulence models used in RANS and LES. Popular eddy viscosity models include the k epsilon model and the k omega SST model.
The talk is broken down into the following sections:
1) 03:50 Which turbulence models are eddy viscosity models?
2) 05:27 A complete derivation of the eddy viscosity formula for the Reynolds stresses
3) 37:50 Limitations of eddy viscosity turbulence models
#eddyViscosity #cfd #fluidmechanics101
============================================
Some useful references:
1) T. J. Craft, B. E. Launder, and K. Suga, 'Development and application of a cubic
eddy-viscosity model of turbulence', Int. J. Heat and Fluid Flow 17: 108-115, 1996.
www.researchgate.net/publicat...
2) M. Leschziner. 'Statistical Turbulence Modelling For Fluid Dynamics - Demystified: An Introductory Text For Graduate Engineering Students', August 2015.
www.amazon.co.uk/Statistical-...
3) S. Pope. 'Turbulent Flows', Cambridge Univeristy Press, 2000.
www.amazon.co.uk/Turbulent-Fl...
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Disclaimer
==================================
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.

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30 июн 2024

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Комментарии : 211   
@fluidmechanics101
@fluidmechanics101 3 года назад
Hi everyone. I would just like to thank everyone who noticed the typo in Equation 30. I wanted to confirm that the term in the brackets should be -2/3 dU_k / dx_ k and not -1/3 dU_k / dx_k. This error has been carried forward into equations 32, 34 and 36 but is correct in equations 39 and 40. I have left the video up in its original form and have pinned this comment, so that you are all aware of the typo. For my patrons on Patreon, the lecture slides have been corrected and you can find the correct version of the lecture slides there to download. Thanks again everyone for spotting the typo!
@anurajmaurya7256
@anurajmaurya7256 3 года назад
Please, make a video on Variational multiscale turbulence modelling
@anupamdas8277
@anupamdas8277 2 года назад
Why is it necessary to do time averaging to original NS equation??
@fluidmechanics101
@fluidmechanics101 2 года назад
For high Reynolds number flows, resolving the fluctuations in time is too expensive, even with a big computer. A common approach is to time average the NS equations and model the effect of the high frequency oscillations, rather than resolve them. Time averaging is really only necessary because computers aren't fast enough to resolve turbulence at high Reynolds numbers 🙂
@leslienovihoho4658
@leslienovihoho4658 2 года назад
@@fluidmechanics101 That's so cool
@parasghumare8067
@parasghumare8067 Год назад
I don't think -1/3 dU_k / dx_k is incorrect. Infact there should a term 1/2 outside mu_t x {dU_i / dx_j + dU_j / dx_i -2/3 dU_k / dx_k}. This is because you missed a 1/2 on the RHS of equation 9. This changes eqs 39 and 40 as well. Probably that is the reason why OF doesn't have 2 in front of (nut_)*dev.
@ana.scarabino
@ana.scarabino Год назад
Have you ever wanted to clap and cheer in the middle of a movie or a concert, thrilled by the quality of what you are experiencing? As a teacher, this was my feeling as this lecture was going on. Wow, I wish I could explain things as this lad! Aidan, you are definitively gifted. Thank you very much for generating and sharing this invaluable material.
@fluidmechanics101
@fluidmechanics101 Год назад
Thank you so much, I really appreciate it
@scugglebottom
@scugglebottom 3 года назад
Continue to be impressed by your clear and well spoken lectures on everything around CFD. A fantastic resource & setting a standard. This collection will no doubt add fantastic high end quality to the currently available study aids and theory across the topic of CFD.
@gerhardbekker646
@gerhardbekker646 3 года назад
I also went down the turbulence modelling rabbit hole for my Master's. Thank you for the effort to convert your research into useful and understandable slides. This is a considerable amount of work!
@sangeeth49
@sangeeth49 Год назад
This video and his explanations are as beautiful as the physical phenomenon and math modelling he is trying to explain! This is a gift to humanity! :) Please keeping more of these videos Dr. Aidan.
@fluidmechanics101
@fluidmechanics101 Год назад
Thank you so much for your kind words, I really appreciate them
@narenbharatwaj7854
@narenbharatwaj7854 29 дней назад
One amazing lecture! Thank you so much, Dr. Aidan!
@reza1815
@reza1815 3 года назад
Perfecto! Your les series chapter is outstanding! Keep up the good work!
@brandongleeson9903
@brandongleeson9903 Год назад
Another 5-star lecture, thank you so much for sharing your knowledge! I now see that the eddy viscosity model is a key enabler beneath the turbulence models we so often rely upon; you filled in an important missing component in my understanding of RANS formulation.
@jessbuildstech
@jessbuildstech 3 года назад
I'm really enjoying the video series, thank you posting this Dr Aidan!
@lenacaban4178
@lenacaban4178 3 года назад
I don't need any books anymore :) Everything is clear after your videos. I love your style and diagrams!
@VishalSingh-os5oj
@VishalSingh-os5oj День назад
Great Explanations!!! Thanks mate
@engineeringarts4509
@engineeringarts4509 3 года назад
Hi Dr. Aidan, may I add some remarks for the Boussinesq approximation here: 1. Reynolds stress (RS) term is sub-divided into isotropic and anisotropic components. 2. For the isotropic component of RS term: the axial components of the RS term are summed up and related to turbulent kinetic energy. The assumption is that: this part of the turbulence is assumed to be isotropic!! It somehow makes sense since it is on the isotropic component of RS. 3. For the anisotropic component of RS term (which is subtracting the full RS term by its isotropic component), this component is analogue to the diffusion term of the N-S equations while the eddy viscosity is introduced to replace the dynamic viscosity. In most of the RANS turbulence models (except the RS model), the eddy viscosity is the same in all the axial and shear components of this anisotropic component of RS term. Again, isotropic turbulence is assumed. But this time - isotropic turbulence assumption is on the anisotropic component of RS!! This is a plausible reason why RANS model is not that accurate in some situations where turbulence is very anisotropic!!
@fluidmechanics101
@fluidmechanics101 3 года назад
Great points! Thanks for your help 🙂
@brunaveras734
@brunaveras734 2 года назад
What an amazing lecture... Thank you so much for preparing this material and for sharing it with us.
@sangal666
@sangal666 3 года назад
That was unbelievable. I understand it perfectly now. Your Lectures are greatly appreciated.
@leminhduy8368
@leminhduy8368 Год назад
You save my life!!! As a beginner in CFD simulation, I am so confused with equations. Your lecture do enlighten me. Thanks so much
@CalvinoBear
@CalvinoBear 6 месяцев назад
You have given me so much more confidence in my work. I have been working in electronics packaging design for aircraft, and often need CFD to understand and define system performance. I have a mechanical engineering background, but not much in fluids. With each video, a new corner of Fluent is demystified. You have my thanks and respect for making these excellent videos which present complex concepts in a highly digestible formats.
@leslienovihoho4658
@leslienovihoho4658 2 года назад
Great Lecture, I always love your practical explanations and insights into the theoretical models
@14johnnymarques
@14johnnymarques Год назад
Awesome lecture Dr. Aidan ... Thanks a lot for the time and effort to make this amazing content available for free here in youtube!
@sudhanshumaurya2860
@sudhanshumaurya2860 3 года назад
great work man, I have been working on my engineering project in CFD and after a week of exploration on the internet found your videos on various CFD models and their basics. it's helping me a lot in better comprehension of basics. thanks, man!
@sienliu663
@sienliu663 3 года назад
the best intro of eddy viscosity model online, thanks
@wonsungjin
@wonsungjin 3 года назад
Thanks for your clear explanation for the derivation of the eddy viscosity model
@atakan716
@atakan716 Год назад
thank you for filling all the empty slots in my brain with these beautiful derivations :D helped me massively!
@solaadekoya9836
@solaadekoya9836 2 года назад
This is an amazing job, well-done Doc.
@mustafamarvat863
@mustafamarvat863 2 года назад
Simply immpecable. Believe me I haven't have enough words to praise your efforts.
@EngLhag
@EngLhag 3 года назад
Great job. I had studied this stuff last semester during my PhD. That 1/3 thing is tricky because depending on the source I have seen, they use the same notation for S and S* (only S for example), then we ask ourselves "where the hell this 1/3 comes from?". Again, great job. It was really nice to rediscover this and refresh my memory.
@cronos864
@cronos864 Год назад
In the end of this video you stated what you wanted to achieve with this video, and let me assure you that you did accomplish just that. Thanks for the incredible content!
@vivekkhantwal8346
@vivekkhantwal8346 Год назад
concise and quality content. you are one of the rarest🙌. thanks for the tutorial.
@colonelManyBears
@colonelManyBears 3 года назад
Brilliantly clear explanations. Thank you!
@yazanatrash
@yazanatrash 3 года назад
Best explanation, it captures everything needed to understand eddy viscosity
@idreeskhan-zp5ey
@idreeskhan-zp5ey 5 месяцев назад
Amazingly simple and to the point explanations!
@arthurwittmann6242
@arthurwittmann6242 2 года назад
Far and wide the best explanation i have seen.
@Darkkenfox
@Darkkenfox 3 года назад
I love your work and your videos! Keep this incredible work 🙏
@vsjhade
@vsjhade 3 года назад
Really Helpful ..and how you addressed it from very basic to advanced. It is really really an informative presentation. Thank you very much
@davidwang8270
@davidwang8270 3 года назад
Thanks a lot. I did a bit research recently on this but wasn't successful. Thank you for lay out this so clearly.
@realkanavdhawan
@realkanavdhawan Год назад
FM101 is *Digital Gold* for CFD Community
@andrewgibson7797
@andrewgibson7797 3 года назад
I'm a graduate student in CFD and machine learning -- thank you for this!!
@AmitMishraUP43
@AmitMishraUP43 Год назад
Thank you Dr. for this excellent lecture. Explanation was pretty lucid and comforting despite lot of mathematics involved. This lecture has certainly helped in building a strong foundation for further learning the turbulence modeling. Thank you again 😃
@jimdeligiannakis6314
@jimdeligiannakis6314 3 года назад
Clear and concise. Excellent.
@Thescavenger4
@Thescavenger4 3 года назад
Keep on that good work ! Many thanks from a Fluid Mechanics lover
@stophercry
@stophercry Год назад
Amazing work, your videos have been helping me so much lately.
@j.gordonleishman6401
@j.gordonleishman6401 5 месяцев назад
Excellent job in sorting this all out!
@bijendersingh43
@bijendersingh43 Год назад
This was the best explanation what is the basis of the 2 eqn model. Simply amazing, precise and concise
@sauravpanda1380
@sauravpanda1380 3 года назад
Wow... you always come up with some great videos... and rightly said it will help me immensely in my master thesis which i am doing now 😛 Great admirer of your work 👏
@prestonr6348
@prestonr6348 Год назад
Finally after 3 years of modelling CFD, I finally understand! Thanks Dr. Aiden. However I must admit that I did struggle in understanding the first few slides. I had to refer to Dr. Steve Brunton's YT derivation to prepare me to understand your initial slides
@francescomadonia4922
@francescomadonia4922 3 года назад
Great explanation! Very clear as usual
@sitrakaforler8696
@sitrakaforler8696 Год назад
Really great content and so clear explanations. Bravo !! And thanks !
@pritampriyadarshi4530
@pritampriyadarshi4530 10 месяцев назад
Thanks Dr Aidan for these wonderful insights
@MalcolmAkner
@MalcolmAkner 3 года назад
Yes, this is exactly what I was looking for! :D
@user-it1qu2on5l
@user-it1qu2on5l 3 года назад
Thank you for high quality video! I'm also waiting for your Reynolds stress model video :)
@nikhildarekar672
@nikhildarekar672 3 года назад
Really great session. Thanks.
@jack-buckhilll5428
@jack-buckhilll5428 3 года назад
Very impressive, Sir! I have now understood very well on eddy viscosity modelling and its derivation to obtain a correct value to solve the momentum equation for the velocity field from your presentation, fantastic effort with complete clarity in your presentation!...keep doing this Sir, you are a blessing to many who venture into CFD. Would your be able to do one on Coupling of Level-set method and VOF model for two-phase flow interface tracking technique?
@gabrielpinananaharro7154
@gabrielpinananaharro7154 5 месяцев назад
Masive help for my aero class! Will probably buy your course
@michaelmello42
@michaelmello42 Год назад
The clearest physical explanation and mathematical derivation you'll find anywhere on eddy viscosity models applied to RANS modeling
@shobob29
@shobob29 3 года назад
Thank you for a wonderful lecture!!!
@meshalnafea5200
@meshalnafea5200 3 года назад
brilliant, Thank you from KSA, Riyadh.
@jhongoulart9493
@jhongoulart9493 3 года назад
Parabéns! I am always looking forward to see your videos.
@dodo19961375320
@dodo19961375320 2 года назад
youtube needs more content like this. very useful
@slim590
@slim590 Год назад
Thank you very much for your hard work and effort.
@Thonix94
@Thonix94 3 года назад
Thanks for another great lecture
@MG-hm9bh
@MG-hm9bh 3 года назад
Really great! Thanks for everything!
@orlandopalone80
@orlandopalone80 3 года назад
Perfect, as always
@goodday276
@goodday276 3 года назад
Very good and useful as always 👌
@roubert1979
@roubert1979 2 года назад
You did a wonderful job deriving the eddy viscosity formula. Thanks very much! You made it very easy to understand. I should say you nailed it! PS. I noticed that other people mentioned it and you pinned it as well but would like to emphasize that the missing "2" on the left side of equation 9 or "1/2" on the right side, affects the proceeding equations. If you consider OpenFOAM formulation, that is the reason there is no "2" behind (nut)*dev ...
@fluidmechanics101
@fluidmechanics101 2 года назад
Such an annoying typo for me to make 😅
@roubert1979
@roubert1979 2 года назад
Typo is sort of a curse, never goes away, always follow us, lol. As I said earlier, you have done a great job explaining behind-the-scenes of CFD codes. Good luck!
@parasghumare8067
@parasghumare8067 Год назад
@@fluidmechanics101 Well if that is true then it changes some equations going ahead.
@turalsuleymanov4529
@turalsuleymanov4529 Год назад
Amazing explanation!
@alexandergillespie6381
@alexandergillespie6381 3 года назад
This was really great, thanks.
@troyanych1
@troyanych1 2 года назад
Big thanks for video! That's awesome.
@hamedheydari989
@hamedheydari989 5 месяцев назад
Thank you very much. It was amazing 👏👏👏👏
@bartoszstachowicz6978
@bartoszstachowicz6978 2 года назад
Great Work! Thanks!
@asifjaved9797
@asifjaved9797 3 года назад
Really appreciate your work Sir. Could you please make a video on Navier stokes equation? This would help those who are beginner in the field of CFD. Looking forward for the video.
@nwsteg2610
@nwsteg2610 Год назад
You rock! Thanks It strikes me that the Reynolds normal stress "correction" is a bit ad-hoc and not exactly physically motivated. Oh well, seems to work!
@fluidmechanics101
@fluidmechanics101 Год назад
Exactly
@user-cs4zq6cb8v
@user-cs4zq6cb8v 3 года назад
Thank's man! You are the best!
@DiegoAndrade
@DiegoAndrade Год назад
Bravo thanks what a great lecture you’re really an amazing lecturer teacher, commentor RU-vidr Thank you.
@fluidmechanics101
@fluidmechanics101 Год назад
Thank you for your kind words, I really appreciate it
@esraisk5109
@esraisk5109 3 года назад
Thanks for the lessons
@Aao_Baat_Krenge
@Aao_Baat_Krenge 3 года назад
Thanks Sir Its too useful
@HolzmannCFD
@HolzmannCFD Год назад
Thank you for your effort preparing these nice talks. Refreshing my mind and is in correlation with my book :)
@NavneetKumarnab
@NavneetKumarnab Год назад
Thank you Sir!!
@priyankadhiman6142
@priyankadhiman6142 3 года назад
It was awesome!!
@jasonchu852
@jasonchu852 2 года назад
very useful !
@JAYasankarPillai7
@JAYasankarPillai7 2 года назад
You have to kiss a lot of frog videos to have your prince video. You have just made my life easy, this is the best video lecturer on this topic that I have watched. I am saying it after watching somewhere around 15 other videos.
@fluidmechanics101
@fluidmechanics101 2 года назад
Thank you very much for your kind words 🙂
@CarlosEduardo-xr8eu
@CarlosEduardo-xr8eu 3 года назад
Great video, as always! Indeed, finding consistency notation in CFD Turbulence modeling is challenging , especially at the beginning of the study. Associated with "magical jumps" from one equation to other (not only in papers), it was really a problem. Until now, for my dissertation I've been using the notation present in the book "Turbulence Modeling for CFD" from D. C. Wilcox.
@fluidmechanics101
@fluidmechanics101 3 года назад
It's a great book! I think sticking with that notation is a good approach. Good luck with your dissertation
@CarlosEduardo-xr8eu
@CarlosEduardo-xr8eu 3 года назад
@@fluidmechanics101 Thank you! :D
@kristianions8052
@kristianions8052 2 года назад
So good, cheers
@francescoindolfo
@francescoindolfo Год назад
Hi Aidan, you said at about 12:50 that momentum is transferred in the direction of the velocity gradient but it should point upwards and not down so I think is more correct to say that momentum is transported against the velocity gradient
@abhishekganguly7695
@abhishekganguly7695 3 года назад
Thank You!!!
@arpitdwivedi4577
@arpitdwivedi4577 2 года назад
nice one!!!
@adamgregor4359
@adamgregor4359 3 года назад
Thanks Aidan!
@diwasbajracharya3745
@diwasbajracharya3745 3 года назад
New guru in town.
@chenghui620001
@chenghui620001 3 года назад
Thank you for this very impressive and informative video. I think there is a small typo in Eq (30): the normal stresses on the left side should be -puiui :)
@fluidmechanics101
@fluidmechanics101 3 года назад
Hmmm yes, I suppose this is a typo. As I am trying to combine the equations together I have left this expressed as -puiuj but you could also write -puiui if you wanted to be clearer. Good to see you are paying close attention 😂
@user-zg8qx1gw8w
@user-zg8qx1gw8w Год назад
Thanks, the lecture perfectly reveals the idea of ​​turbulence modeling :) But I've a little misunderstanding. At the 19th minute, we equate the symmetric components of the Reynolds stress tensor and obtain formula (9). But if they are equal, then when they are added, we should get 1/2*mu_t(dU/dy+dV/dx). I would be grateful if someone could explain this issue.
@parasghumare8067
@parasghumare8067 Год назад
I think the same and thus going forward certain equations will have a missing factor of 2.
@TheAmitsch
@TheAmitsch 3 года назад
Thanks for the video! @20.19 if eq. 9 is derived by adding eq. 7 and eq. 8, then shouldn't we have 2 in the denominator on RHS?
@Luiferhoyos
@Luiferhoyos 3 года назад
Yes. A typo.
@ilhantalih9949
@ilhantalih9949 3 года назад
Thanks sir
@hishamlotfy3942
@hishamlotfy3942 Год назад
good job
@martinleskovec430
@martinleskovec430 Год назад
Thanks for this. Could you do a video on turbulence models that are not eddy viscosity models, like cubic k-epsilon?
@Mr230306
@Mr230306 3 года назад
Thanks
@nonokbh
@nonokbh Год назад
Do you have a video with an explanation of the physical meaning / relative importance of the different terms of the Reynolds stresses ? Like, how is the magnitude of the pressure term -2/3 rho. k compared to 2.mut.dU/dz, and also their respective signs ? Thanks a lot, great lecture.
@reverseila4363
@reverseila4363 Год назад
I can only reach to the following relation for equation 32: - ho u_i u_j = mu_t ( 0.5 (dU_i/dx_j + dU_j/dx_i) - 1/3dU_k/dx_k \delta_{i,j} ) - 2/3 ho k \delta_{i,j} Thanks for the video!
@parasghumare8067
@parasghumare8067 Год назад
that is correct.
@pawejedrejko7398
@pawejedrejko7398 3 года назад
Actually, the deviatoric part of rate of strain tensor has a meaning. It's more often mentioned in the context of the von Misses hipothesis in strength of materials/elasticity theory (of course, in these fields, the strain tensor instead of the rate of strain tensor is used). It represents only this part of (rate of) deformation of infinitesimal fluid percel that changes its shape (changes the angles). The remaining rest, represents the 'resizing' of the percel - change of its volume (btw. thats why they sum up to divergence) without affecting its shape. It can be shown that pure 'resize' is represented by the average of the diagonal terms of velocity gradient. In 3D thats (du/dx+dv/dy+dw/dz)/3 or in 2D: (du/dx+dv/dy)/2. When you subtract it from the rate of strain tensor, then voila, you have the deviatoric part.
@fluidmechanics101
@fluidmechanics101 3 года назад
Amazing explanation! Much appreciated
@hkm3933
@hkm3933 2 года назад
Great video !!!! But a small doubt isn't momentum transported opposite to the direction of velocity gradient?
@ilyassebouatou3161
@ilyassebouatou3161 3 года назад
can someone please explain to me how we got equation 9, in my understanding we should divide the term on the right by 2
@raffaellavuolo8389
@raffaellavuolo8389 2 года назад
Great explanation, thank you very much Aidan! I'm just wondering if around minute 12 there is a little error about the direction of the gradient of U that you mention (downwards). I understand that the gradient is rather pointing upwards and the transfer of momentum, which is counter-gradient, is pointing downwards. Looking fotward to your feedback!
@fluidmechanics101
@fluidmechanics101 2 года назад
You could be right. It has been a while since I put together this talk and I remember this bit being really confusing!
@Hollowguy1603
@Hollowguy1603 5 месяцев назад
You told turbulent viscosity isn't actually random I said this in my class and everybody laughed, please reply to this asap so I can tell my professor
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