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
3 жыл бұрын
Please, make a video on Variational multiscale turbulence modelling
@anupamdas8277
3 жыл бұрын
Why is it necessary to do time averaging to original NS equation??
@fluidmechanics101
3 жыл бұрын
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
2 жыл бұрын
@@fluidmechanics101 That's so cool
@parasghumare8067
Жыл бұрын
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
Жыл бұрын
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
Жыл бұрын
Thank you so much, I really appreciate it
@productivity_station
5 күн бұрын
This is by far the best video on turbulence. Can’t thank you enough!
@AliMostafazadeAbolmaali
25 күн бұрын
You solved some of my longstanding problems with turbulence with this absolutely fantastic video. I can't thank you enough.
@engineeringarts4509
3 жыл бұрын
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
3 жыл бұрын
Great points! Thanks for your help 🙂
@arthurwittmann6242
2 жыл бұрын
Far and wide the best explanation i have seen.
@brandongleeson9903
2 жыл бұрын
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.
@CalvinoBear
9 ай бұрын
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.
@leminhduy8368
Жыл бұрын
You save my life!!! As a beginner in CFD simulation, I am so confused with equations. Your lecture do enlighten me. Thanks so much
@brunaveras734
3 жыл бұрын
What an amazing lecture... Thank you so much for preparing this material and for sharing it with us.
@lenacaban4178
3 жыл бұрын
I don't need any books anymore :) Everything is clear after your videos. I love your style and diagrams!
@sudhanshumaurya2860
3 жыл бұрын
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!
@cronos864
Жыл бұрын
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!
@EngLhag
3 жыл бұрын
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.
@wonsungjin
3 жыл бұрын
Thanks for your clear explanation for the derivation of the eddy viscosity model
@realkanavdhawan
Жыл бұрын
FM101 is *Digital Gold* for CFD Community
@AmitMishraUP43
Жыл бұрын
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 😃
@bijendersingh43
Жыл бұрын
This was the best explanation what is the basis of the 2 eqn model. Simply amazing, precise and concise
@atakan716
Жыл бұрын
thank you for filling all the empty slots in my brain with these beautiful derivations :D helped me massively!
@sangal666
3 жыл бұрын
That was unbelievable. I understand it perfectly now. Your Lectures are greatly appreciated.
@idreeskhan-zp5ey
8 ай бұрын
Amazingly simple and to the point explanations!
@prestonr6348
Жыл бұрын
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
@andrewgibson7797
3 жыл бұрын
I'm a graduate student in CFD and machine learning -- thank you for this!!
@pritampriyadarshi4530
Жыл бұрын
Thanks Dr Aidan for these wonderful insights
@vivekkhantwal8346
Жыл бұрын
concise and quality content. you are one of the rarest🙌. thanks for the tutorial.
@davidwang8270
3 жыл бұрын
Thanks a lot. I did a bit research recently on this but wasn't successful. Thank you for lay out this so clearly.
@VishalSingh-os5oj
2 ай бұрын
Great Explanations!!! Thanks mate
@leslienovihoho4658
2 жыл бұрын
Great Lecture, I always love your practical explanations and insights into the theoretical models
@mustafamarvat863
2 жыл бұрын
Simply immpecable. Believe me I haven't have enough words to praise your efforts.
@narenbharatwaj7854
3 ай бұрын
One amazing lecture! Thank you so much, Dr. Aidan!
@vsjhade
3 жыл бұрын
Really Helpful ..and how you addressed it from very basic to advanced. It is really really an informative presentation. Thank you very much
@meshalnafea5200
3 жыл бұрын
brilliant, Thank you from KSA, Riyadh.
@michaelmello42
Жыл бұрын
The clearest physical explanation and mathematical derivation you'll find anywhere on eddy viscosity models applied to RANS modeling
@solaadekoya9836
2 жыл бұрын
This is an amazing job, well-done Doc.
@hamedheydari989
8 ай бұрын
Thank you very much. It was amazing 👏👏👏👏
@reza1815
3 жыл бұрын
Perfecto! Your les series chapter is outstanding! Keep up the good work!
@jack-buckhilll5428
3 жыл бұрын
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?
@scugglebottom
3 жыл бұрын
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.
@stophercry
Жыл бұрын
Amazing work, your videos have been helping me so much lately.
@jimdeligiannakis6314
3 жыл бұрын
Clear and concise. Excellent.
@colonelManyBears
3 жыл бұрын
Brilliantly clear explanations. Thank you!
@yazanatrash
3 жыл бұрын
Best explanation, it captures everything needed to understand eddy viscosity
@JAYasankarPillai7
2 жыл бұрын
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
2 жыл бұрын
Thank you very much for your kind words 🙂
@Thescavenger4
3 жыл бұрын
Keep on that good work ! Many thanks from a Fluid Mechanics lover
@Darkkenfox
3 жыл бұрын
I love your work and your videos! Keep this incredible work 🙏
@nikhildarekar672
3 жыл бұрын
Really great session. Thanks.
@nwsteg2610
Жыл бұрын
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
Жыл бұрын
Exactly
@MalcolmAkner
3 жыл бұрын
Yes, this is exactly what I was looking for! :D
@dodo19961375320
2 жыл бұрын
youtube needs more content like this. very useful
@francescoindolfo
Жыл бұрын
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
@БабичЕлена-б6ш
Жыл бұрын
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
Жыл бұрын
I think the same and thus going forward certain equations will have a missing factor of 2.
@NavneetKumarnab
Жыл бұрын
Thank you Sir!!
@turalsuleymanov4529
2 жыл бұрын
Amazing explanation!
@sauravpanda1380
3 жыл бұрын
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 👏
@averyswarthout6428
24 күн бұрын
I am preparing for my Viva and you are my god (I do applied CFD lol i cant do fundamentals for shit)
@Thonix94
3 жыл бұрын
Thanks for another great lecture
@jhongoulart9493
3 жыл бұрын
Parabéns! I am always looking forward to see your videos.
@MG-hm9bh
3 жыл бұрын
Really great! Thanks for everything!
@asifjaved9797
3 жыл бұрын
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.
@MalcolmAkner
3 жыл бұрын
At 27 minutes, isn't there an error there in the notation? Either it should be: -rho*u'_i*u'_i on the LHS, or a factor of 2 need to appear on the RHS. What am I missing here?
@yazanatrash
3 жыл бұрын
I had the same thought
@fluidmechanics101
3 жыл бұрын
Ahhh yes! The factor of 2 has gone missing somewhere along the way 😩let me look into this and correct it
@ilyassebouatou3161
3 жыл бұрын
can someone please explain to me how we got equation 9, in my understanding we should divide the term on the right by 2
@arpitdwivedi4577
2 жыл бұрын
nice one!!!
@pawejedrejko7398
3 жыл бұрын
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
3 жыл бұрын
Amazing explanation! Much appreciated
@TheAmitsch
3 жыл бұрын
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
3 жыл бұрын
Yes. A typo.
@hishamlotfy3942
2 жыл бұрын
good job
@alexandergillespie6381
3 жыл бұрын
This was really great, thanks.
@orlandopalone80
3 жыл бұрын
Perfect, as always
@esraisk5109
3 жыл бұрын
Thanks for the lessons
@adamgregor4359
3 жыл бұрын
Thanks Aidan!
@Mr230306
3 жыл бұрын
Thanks
@Aao_Baat_Krenge
3 жыл бұрын
Thanks Sir Its too useful
@bartoszstachowicz6978
2 жыл бұрын
Great Work! Thanks!
@ИгорьШелякин-ь4д
3 жыл бұрын
Thank's man! You are the best!
@diwasbajracharya3745
3 жыл бұрын
New guru in town.
@kartikkhanna5063
2 жыл бұрын
Had there been a feature which allowed 1 'super like' per user account, i would have given to you...thanks a lot sir...
@itsnotwhatuc3147
10 ай бұрын
You look very cool man
@kristianions8052
2 жыл бұрын
So good, cheers
@martinleskovec430
Жыл бұрын
Thanks for this. Could you do a video on turbulence models that are not eddy viscosity models, like cubic k-epsilon?
@abzrg
9 ай бұрын
Ok, the pinned comment is correct as OpenFOAM has a documentation page on Linear eddy viscosity models that shows that as well, but if that is the case then something will definitely be wrong in the early eqns of 8 or 9 I guess.
@alexz26389
2 жыл бұрын
Thanks for the video. It did clear up a few conceptual issues, but I'm still left with one. You have shown that to calculate how U, V, W change with time, it is not necessary to know , and
@fluidmechanics101
2 жыл бұрын
Cmu = 0.09 ( an empirical constant). K and epsilon are the calculated by solving 2 transport equations. This is the basis of the k epsilon model!
@alexz26389
2 жыл бұрын
@@fluidmechanics101 Thanks. Is there another video I can reference for how to do that?
@fluidmechanics101
2 жыл бұрын
Yep, just check out my video on 'The K Epsilon model'
@Glistenable
3 жыл бұрын
Mark, and going to watch this video later
@NITESHKSAHU
Жыл бұрын
The eq. (36) points out that closure requires modeling of turbulent kinetic energy and turbulent viscosity both. Isn't it so. As the focus is only laid on the latter.
@abzrg
9 ай бұрын
Thanks for the fantastic lecture. 13:03 isn't the momentum transported in the opposite direction of gradient? this is confusing to me. If considering the direction of gradient, the direction in which the function increases most quickly from, then the momentum like other transport quantities like mass and heat points toward the opposite of gradient of a quantity (velocity, temperature and mass respectively).
@priyankadhiman6142
3 жыл бұрын
It was awesome!!
@rogerdemo6344
Жыл бұрын
Great video and very clear explanations. However, I can't get past eqns 7 and 9. How can both equations be simultaneously true unless one of the velocity gradients is equal to zero. To come up with eqn 9, I thought you would add eqns 7 and 8 together. If that is true, then there would be a factor of 1/2 on the RHS of eqn. 9. What am I missing??
@MalcolmAkner
3 жыл бұрын
I would love to see a video on why the limitations pop up and what we can do about that. I have a model where all three of the cases you warned about show up all over the model (bending tubes, baffles, conical reducers etc.). Are there any models that can handle that? K-omega SST seems to give physical results, but how accurate can the data be?
@fluidmechanics101
3 жыл бұрын
The best you can really do is to compare to experimental measurements and see which gives the closest agreement. It is hard to say which will be most accurate until you have some results that you know are true (for comparison). Personally, k omega SST always seems to be a solid choice for me and it's what I normally pick if I am unsure
@rishikeshmishra9485
2 жыл бұрын
At 20:12 , by the logic of Eqs (7) and (8), shouldn't Eq.(9) have a factor of 2 (or half)? This would then translate into the uu components described in the next slid (eq. 10 onwards). Perhaps something else needs to be factored in rather than just symmetricity?
@fluidmechanics101
2 жыл бұрын
I think this is part of the error which I have noted in the pinned comment. Well spotted! There is indeed a factor of 2 missing
@abhishekganguly7695
3 жыл бұрын
Thank You!!!
@pavankumarkv4920
3 жыл бұрын
Elegant
@felizbanking2951
2 жыл бұрын
Hello can you discuss DELAYED DETACHED LARGE EDDY SIMULATIONS. can you make videos on how to understand DDES
@ssss4391
3 жыл бұрын
Correction @12:53: Since dU/dy is positive, the direction of velocity gradient is upward. So should the statement not be "momentum is transported in the direction of negative velocity gradient"?
@fluidmechanics101
3 жыл бұрын
Hmmm yes that does make sense 🤔
@ilhantalih9949
3 жыл бұрын
Thanks sir
@prakashthirunavukkarasu29
3 жыл бұрын
Hi Dr. Aidan!. Thank you once again for the wonderful lecture. At 12:49, isn't the gradient supposed to point towards the maximum? Please correct me if I am wrong.
@fluidmechanics101
3 жыл бұрын
Yes you are correct. Sorry if I wasn't clear! Momentum is transported down to the lower particles, which have lower momentum. This is transport from high to low (towards the minimum). This is why there is the minus sign in the front of the Reynolds stress, because the momentum is transported in the direction of negative gradient. Pesky minus signs always catch me out 😅
@prakashthirunavukkarasu29
3 жыл бұрын
@@fluidmechanics101 Hahaha... I would like to request you to continue the series of LES. Thank you!
@uttamcp5016
5 ай бұрын
I have a question - it is more of an OpenFOAM one but since you mentioned OpenFOAM here, I am tempted to ask it. Apologies if it is not relevant. In the momentum equation of say simpleFOAM for example, i notice this term turbulence->divDevReff(fvc::grad(U)) which is the deviatoric part of the stress tensor without the 2/3 TKE. Now when I use a turbulence model such as SA model where k is not explicitly calculated, I need to use a postProcessing utility (such os simpleFoam -postProcess -func R). But i get the message that TKE is not defined for SA and hence I get the Reynolds stress tensor WITHOUT the subtraction of the TKE (I know this because if I take the trace of the obtained Reynolds stress tensor, it comes out to be zero, same as the start of the video which resulted in the mathematical manipulation). I suppose I have two questions - firstly, is this Reynolds stress tensor even correct? Secondly, is it true that to get TKE, one must run a two equation turbulence model such as k epsilon or k omega SST and cant obtain it from a post Processing step? I got these questions only after watching your video.
@elganaelmehdi1697
Жыл бұрын
Hi , Thanks for the video , its very helpfull . Can we told us how to calculate turbulence kinetic energy , because we still have u prime ... with the k
@fluidmechanics101
Жыл бұрын
That will depend on your turbulence model. If you are using k epsilon or k omega SST or SGS turbulent kinetic energy, you should have these. If you are using Smagorinsky then you will need to look in the user manual
@elganaelmehdi1697
Жыл бұрын
@@fluidmechanics101 Thank you very much, do you have a video explaining this ?? thanks
@loudcloud1499
2 жыл бұрын
yung tenure 😌
@mehranjangh
2 жыл бұрын
Thanks for the awesome video, I didn't understand two things though: 1) in eq.9 why did you sum the RHS but did not sum the LHS of the equation, should we not have 2*rho*u*v on the LHS? 2) in eq.11, why has the definition of u^prime changed from du/dy to du/dx?
@Ethan-mi1wj
Жыл бұрын
I have difficulties to see the step from equation 10 to 11, why does de gradient change from Y to X? To me the obvious step would be =2mu(dU/dy)
@ferasalgafary9063
Жыл бұрын
Hi Dr Aidan I have a question in equation number 9 should the eddy viscosity multiply by 0.5? see the video in 20.00 Because we add equation numbers 8 and 7 to get equation 9. Am I right?
@jeremyloustau
Жыл бұрын
A big Thanks for this Masterclass. However I have a question about equation 39. We have 2 in factor, then we get 2/3 of ∇ . U instead of 1/3. Isn't it a pb ? Maybe I will find my answer after writing my comment but i take the risk
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