[CFD] The k - omega SST Turbulence Model
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- čas přidán 3. 08. 2024
- [CFD] The k - omega SST Turbulence Model
An introduction to the k - omega SST turbulence model that is used by all mainstream CFD codes (OpenFOAM, Fluent, CFX, Star, COMSOL, Saturne). The following topics are covered:
1) 6:18 How is the k - omega SST model different to the k - omega and k - epsilon models?
2) 9:21 What is the blending function F1?
3) 13:18 What is the difference between the k- omega BST and k - omega SST models?
4) 14:00 What is the viscosity limiter and why is it used?
#kOmegaSST #fluidmechanics101 #cfd
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Some useful references:
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1) Christopher Rumsey
NASA Langley Research Centre - Turbulence Modelling Resource
turbmodels.larc.nasa.gov/sst....
2) Menter, F. R.
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
AIAA Journal, Vol. 32, No. 8, August 1994, pp. 1598-1605.
arc.aiaa.org/doi/10.2514/3.12149
3) Apsley, D. D., Leschziner, M. A.
Advanced turbulence modelling of separated flow in a diffuser
Flow, Turbulence and Combustion 63, (2000), 81--112
link.springer.com/article/10....
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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. - Věda a technologie
![[CFD] The k-omega Turbulence Model](http://i.ytimg.com/vi/26QaCK6wDp8/mqdefault.jpg)
![[CFD] The k-omega Turbulence Model](/img/tr.png)
![[CFD] The k - epsilon Turbulence Model](http://i.ytimg.com/vi/fOB91zQ7HJU/mqdefault.jpg)
![[CFD] What is the difference between Upwind, Linear Upwind and Central Differencing?](/img/n.gif)
I come here whenever i have an interview. Thank you so much.
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Same! I'll put him in my undergraduate degree thesis.
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I am currently writing my master thesis on CFD an I can't tell how glad I am that I have found your channel. From my first pay check I am going to buy you a coffee (or 10). Great job and keep this up!
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I am just messaging to thank you for this channel and your exceptional videos. Really informative, easy to follow, and the additional reading references at the end of each video are just OUTSTANDING. Thank you so so much for this channel and for taking the time to make these videos. I can't thank you enough. Phenomenal.
Very clear explanation packed in 20 minutes. You inspired me. Thank you.
Hi! I'd just like to say that your videos have been very helpful and intuitive for me. I don't have much background in CFD as it was never really tackled in our university. I just want to say thank you and please continue to do what you are doing, you are amazing!
你是最棒的！我从没听过如此易懂的底层算法逻辑介绍，感谢您花时间为我们创造这个视频
Excellent clearance of the concepts, Best wishes
Thanks 🙂 have been binge watching ur videos lately 😅
Thank you so much for the explanation. it will help me a lot in my thesis.
Thank you a lot! Outsanding lectures!
Thanks for the video sharing. Easy to understand turbulent models owing to videos in your youtube channel.
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Excelent explanation. Thank you.
Thank you very much for your videos! You explanations are very useful for people who are just at the beginning of CFD!
Great, im so glad you find them useful! There really was no source of good CFD information when I started, so i thought i would try and create what was missing. Thanks again for the support!
@@fluidmechanics101 Thats true. i was looking for a YT channel and found yours; Just added your videos to my list. Thanks to put all this together
Thank you so much for your videos, very practical. very good explanation.
Thanks David! Im glad you like them 😊
thank you for explanations!
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thank you... it helped a lot
Excellent video, thanks for share your knowledge.
Thanks Daniel, im glad you found it useful!
This video is very helpful to me. Thank you so much
Thanks kounain! Im glad you found it useful 😊
@@fluidmechanics101 Hi Aidan thanks for another fantastic video. I have a doubt. How we could achieve flow separation by reducing both viscosity and wall shear stress. Because my understanding is only in laminar flow (viscous dominant flow) we will get flow separation. In that case how by reducing viscosity menter would have got the seperation. Sorry if I am wrong in not catching some fundamental part. I will be very happy if u have time to give a reply to my question. Thank u once again and I have became big fan of your channel.
Thank you for this video, this is very usaful knowledge, excellent.
Thanks Erhan! Im glad you found it useful 😊
Great content, You are my guru...
Your videos are prompt and right to the point. Can you make a video on the Under relaxation factors which are used on Fluent.
Thank you very much!!!
These videos are a perfect additional material for my course.
Also interesting topics would be other solving algorithms like PISO and other turbulence modeling approaches like reynolds stress models ;)
Fantastic, thanks Florian! Im glad you like them. Yes, more videos will be coming soon, they just take a little while to make as i want to make sure they are researched properly 😊 i think a video on the PISO algorithm and reynolds stress models would be really good, il see to it!
This video explains the blending funcitons in a so clear way! Thanks a lot!! Recent year, there is a scale-resolving mode called Scale-adaptive Simulation (SAS) based on SST which looks pretty interesting, hopefully you can make another video on that !
Yes! Coming soon😊
Fantastic work!
Please do a video on different kinds of mesh motion techniques: SRF, MRF, Sliding, Dynamic etc.
Yep i already have a video on MRF. The others will be coming soon!
Thank you so much.
thank you ... very effective
you are excellent ! thanks you
So helpful and interesting :D thank you so much :D
Thanks Nguyen!
I am so impressed with your work (y)
As people have mentioned, you did a great job explaining the model. Even though I've read few notes about K-w and K-e models, I failed to realize that there were functions that allowed the exchange between the models. Thank you!
Though, perhaps it's a bit out of topic question but, I see that there are 'limiters' and 'corrections' made in the models. A professor of mine mentioned that due to such dampings available in the models, it makes them unreliable when you are trying to simulate isotropic/anisotropic turbulent flows in order to see the propagation of the turbulence.
To be more clear, I've analytically calculated Re stresses and Kinetic Turb. Energy of a flow subjected to axi-symmetric contraction using the equations of Rapid Distortion Theory proposed by Batchelor and his colleagues. Then, I've used such various turbulence models from K-e to RST which yielded significantly different results (way lower Re stress values compared to analytical solution). Do you think the reasion behind such difference is due to the dampings introduced in the models?
Thank you once again.
Hi Onur, it could be due to the damping or simply due to the Boussnesq hypothesis. K-omega and k-epsilon based models are all isotropic in nature and will struggle to get the anisotropic components of the Reynolds stresses correct, regardless of the damping functions. Although we would need to do a more detailed comparison to be sure. Have you tried comparing the Reynolds stresses between the models?
@@fluidmechanics101 Im currently working on that but thanks for the insight. Its interesting stuff... I ll try to get more data on it for sure.
Thank you!
Thank You !
Good presentation.
Great, im glad you liked it 😊
Thank u so much for this video
No problem 😄
Very good
Really helpful video!! Could you please make a simple introduction about the PANS model? I'm confused about the saying "bridge between DNS and RANS" since it just modifies a source term.
Hello Aidan. First of all, great video as always. Both the format and the way you present the various topics are easy to follow even for some of us who are relatively new to the CFD world like myself. Secondly , I think a good video following this trend would be to expalin the Transition SST model used primarily in low Reynolds flows for it's ability to capture the laminar separation bubble and accurately predict the lift and drag coefficient in flow over smooth surfaces as well.
Lastly, keep it up, your videos are entertaining and educating!
Hi Daniel, thanks for your kind feedback, i really appreciate it. Yes, I am planning on releasing more videos for specific turbulence models, as they seem to be very useful for people. I am currently putting together a video on the k epsilon model (as it is probably the most popular turbulence model ever!) I am then going to look at some others, and I agree with you that a good transition turbulence model would be a great idea. Thanks!
It would be great to have a video on Reynolds stress transport model
AFAIK, k-omega model had been developed first, then k-epsilon, then Wilcox's k-omega, then k-omega-SST.
I think you might be right. There were plenty of turbulence models floating around at the time. K epsilon just seems to be the one which took off first
Great platform to learn CFD.....Sir I am looking for Fluid Structure Interaction related videos on your channel. Unfortunately could not find any thing related to FSI. Please make some videos related to FSI for Turbomachinery..
Hi, Aidan. Very very good presentation. But I think there might be an error at 8:00. The k and Omega are scalar variables, so the gradients of them are vectors rather than tensors as you mentioned in the video.
Hi Wenyang, yes you are right. K and omega are scalar variables. Taking the gradient of these variables results in vector variables . However when we take the tensor inner product of the vectors (the gradient of k and the gradient of omega) this results in a scalar variable again! It looks like my explanation was not clear enough ... Thanks for pointing this out!
Well, vectors are also tensor (1st order tensors). In this case, the tensor inner product of those two tensors/vectors results in the same as dot product of those two vectors/tensors. The two operations are valid, but I think tensor inner product results confusing.
i love you bro
Another excellent presentation! Would you be kind enough to make a video on Ansys Fluent Meshing concepts and visualization, please?
Yes, I am planning on doing some more code specific content in the future. I just need to get hold of a license first!
Great content, as always. So, does it make any sense to use the kOmegaSST model with wall functions, having y+ of around 300? Will it basically behave like k-epsilon everywhere in this case?
Yes, it will be pretty similar to k epsilon 👍
Thank you for a great lesson! I heard through several your videos today, which is though-provoking! With that being said, I do have a question about the SST k-w model. Do you by any chance now what the near wall mesh size should be (should y+ always be
This is a tricky topic, as it varies between solvers. I would check out my ‘Enhanced Wall Functions’ video if you are a Fluent or CFX user. If you can get y+ less than 1, perfect. If not then less than 3 is probably fine. The wall function approach (y+ between 30 and 200) is probably ok unless you are doing external aerodynamics / turbomachinery stuff where you need to get the separation point correct
@@fluidmechanics101 thanks for your promptly reply. I really appreciate it. I am using ansys fluent for my research. One thing the manual is not clear about is that, if y+ is larger than 30, does that mean that only k-e model plays the role in the sst k-w model? What is the critical distance from the wall whereby k-w starts phasing into k-e? I know it’s a hard question, have been searching for solutions online for a long time. So, any input is greatly appreciated!
the transition is based on the blending function F1, not y+. Im sorry if this hasnt been explained well! It really isn’t clear
@@fluidmechanics101 but blending function is a function of the distance between the cell center and the wall, right? Sorry the question is not clear enough. I think what I was really asking was what the critical distance from the wall should be whereby k-w phases into k-e or the other way around. I understand it varies depend on case, but is it possible to calculate it by hand?
It is not really possible to calculate this distance by hand. Why do you need to know it? Is this an input for a model or just for your own understanding?
Hi Aidan, excellent lecture!. I have a question, isn't the term in the note after Eq. 8 just the vector inner product of the two gradients? I don't see why the double dot (tensor product) is used since it would give a tensor and not a scalar. Thanks !
Correct! Sorry i have probably used the wrong notation. The term should evaluate to a scalar as all terms in the equation are scalar
@@fluidmechanics101 Thank you! Your lectures are fantastic!
Hello Adrian, I'm struggling with the lines you mentioned between 14:19 and 14:33. For me, separation, reminds me of the classic figure of the flow over sphere which people used to describe separation in classrooms.
1) The separation would depend on the "Molecular Viscosity " of the fluid, but over here we are calculating the "eddy viscosity" . So how is eddy viscosity related to the whole phenomena of separation? I mean I can imagine it helping to re energizing the flow and thus delaying separation, so by reducing "eddy viscosity" are you able to prevent that ? (thinking out loud)
2) How does reducing "eddy viscosity" mean our shear stress at the wall are going to reduce faster?
P.S (Your videos are amazing , keep them coming , All of us are very grateful to you )
Hi Shubham! In answer to your question remember that we are looking at a turbulent flow here. In a turbulent flow the velocity fluctuations transfer additional momentum towards the wall (this is why the velocity profile is broader in a turbulent flow). Subsequently this additional momentum needs to be overcome by the adverse pressure gradient if the flow is going to seperate.
In a turbulent flow the eddy viscosity increases the total shear stress at the wall (remember the wall shear stress has a laminar component and a turbulent component). This is why the limiter is concerned with the eddy viscosity, it is trying to reduce the turbulent component of the wall shear stress so that the flow seperates earlier (to match the experimental measurements).
I realise this can be quite confusing but i hope this helps 😊
@@fluidmechanics101 , I had to look up my basics and draw a couple of diagrams , but eventually was able to figure out what you were trying to say. Thanks for your response , it delivered home an important concept.
Hi Aidan thanks for another fantastic video. I have a doubt. How we could achieve flow separation by reducing both viscosity and wall shear stress. Because my understanding is only in laminar flow (viscous dominant flow) we will get flow separation. In that case how by reducing viscosity menter would have got the seperation. Sorry if I am wrong in not catching some fundamental part. I will be very happy if u have time to give a reply to my question. Thank once again and I have became big fan of your channel.
Hi Siva, you can get seperation in laminar flow and turbulent flow! It is the strength of the adverse pressure gradient that determines whether we can get separation or not 😄 as a result of the adverse pressure gradient, the wall shear stress reduces, until a point where it reaches zero. This is the seperation point. Maybe go and grab your favourite fluid dynamics textbook and have a quick refresher? It is a complicated topic, so dont worry if you get confused 👍
@@fluidmechanics101 thank u very much Aidan for your time to reply me. I got my doubt cleared. U r simply awesome.. keep.posting on such lectures for other turbulence models also.. keep up the good work. My best wishes 🙂
Sir please make video on largeeddy simulation with subgrid viscosity and subgrid heatflux.
By the way ur video are fantastic great man
LES will be coming soon. Im currently doing the research for it 👍
Thanks sir
Hi Aidan. Thanks for the insightful video. I have some doubts.
1) k-w SST model is blending of k-e and k-w with the viscosity limiter. Now, Since we are resolving the near wall flow by predicting accurately the wall shear stress , then i would suppose that our mesh should be wall resolved i.e. in viscous sub-layer ( y+ ~ 1). What do you think? Because i don't see any mention of y+ in the video.
2) What if we use k-w SST model with first cell in log-layer (30
Hi Mihir, yes you are right on both points! I didnt mention y+ in the video as i wanted to keep the video specific to the model itself. You can of course apply the model with any y+ you want (greater than 30 or less than 5) but the model generally gets the most accurate results when y+ < 5 (or even less than 1 for best results)! This is why it is most commonly used in external aerodynamics applications
@@fluidmechanics101 Thanks Aidan. That was helpful :)
how do i choose correct boundary conditions for k and omega? thanks
Dear Aidan,
I am using ANSYS fluent to model my 2 phase solid-liquid problems. My problems are steady-state in nature. I wish to know that in all the equations, such as continuity, momentum and the K-w model equations, the first term with dt in the denominator represents the unsteady part right? So I have a query, that in case of steady-state problems, how is this 'dt' term solved? Is it time averaged or neglected from the solution?
Hi Harman, the dt term is neglected completely. That term is ignored (or set to zero), so you dont need to worry about it. Iteration is used to ensure that all the other terms balance and a steady solution is achieved.
Hi Aidan,
first of, thank you for a very insightful video. However, I have never heard about the acronym BST. Where did you find it? Could your refer to the source? From what I gathered, it should be BSL, since it stands for BaSeLine. Can you clarify this issue, please? Thank you in advance.
Hi Jack, if you have a look in Florian Menter's original paper, you should see the BST (baseline stress transport) model. It is part of the development of the SST model but isn't really used much in practice
@@fluidmechanics101 Hello Aidan, unfortunately I did not succeed in finding the BST model you are referring to. By the Florian Menter's original paper did you really mean the paper Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
AIAA Journal, Vol. 32, No. 8, August 1994, pp. 1598-1605.? Thanks a lot for your effort!
Hey, you have highlighted the term external aerodynamics in the presentation. So, can't this model be used to simulate the flow in a gas turbine combustion chamber with swirler?
Expanation was excellent as usual. Thanks a lot.
Yep, the model will work fine for as turbine combustors. You might need to add the swirl source in fluent
Menter SST k-omega was initially developed for external compressible flows in 1994. But they were proved to be accurate for internal flows as well. Refer AIAA paper by John W Slater 2004 for the same info.
Also add video related to explaination of initial values, reference values and boundary conditions
Which model can I use for minichannel turbulent flow??kindly reply
*You must have recorded the video during Covid period. I can hear ambulances in the background.*
Please add video related to other turbulence model RSM, les dns
Hi Vivekanand. Yes i am definitely planning on doing videos for other turbulence models. However, there are many many turbulence models! So im going to try and do the most popular ones first. Next will probably be k epsilon? What do you think? What model would be most useful for you?
Can you please make a video for the K-Omega turbulence model ? Can we use this model for both Low-Re and High-Re (like in the video of K-Epsilon ) ?
Many Thanks
Ideally you would use this model for Low-Re only and then use k-epsilon for high Re. However, the model is quite resilient and you can use it for just about any y+ with reasonable success 👍
@@fluidmechanics101 Thanks
@@fluidmechanics101 I am modeling a structure in a river bed. As I did not know the y+ value at the first time, I built a guest mesh and run with k-w SST with a wall function and get 1
This depends on the CFD code you are using. In Fluent and CFX, the CFD code is clever enough to use wall functions when y+ is greater than 30 and will use the viscous sib layer solution when y+ < 5. What you need to do is make sure that y+ is in the range that you want in the region of the model that you care about most (the surface of the structure) 👍
Is the tensor of the gradient of k expressed as k[I] where I is the identity matrix, or is there a consideration where k is not isotropic?
For RANS models, k is isotropic. However you can use a non-linear eddy viscosity model, this allows the viscosity to be anisotropic, even if the turbulent kinetic energy is isotropic
@@fluidmechanics101 Thank you!
What is the physical interpretation of the word SST, meaning, how is the shear stress being transported in the flow field?
Great question. I have never understood this either and it isn't really explained in the original paper either! I suspect that they are claiming that the viscosity limiter is somehow limiting the transport of stresses, but I am not really sure. You are 100% correct with your observation that there is no transport equation for shear stress!
According to Versteeg you have a mistake in 8th equation where sigma omega 2 should be in denominator
Oops! 🤦♂️ well spotted!
I have just read Menter's original paper, and he puts sigma omega 2 in the numerator side
Hmmm, i think we need to use the NASA turbulence modelling source. This is usually the most reliable source as it points out the (numerous) typos that people make in their papers and keeps a record of the different versions of the models. Have a quick google search for ‘NASA turbulence modelling and you will quickly find it’ 👍
Is it the same equations in compressible and incompressible flwo?
Ive been having a look at the OpenFOAM manual and it looks like the equations are the same, except for an additional ‘rapid distortion theory’ term. I will look into this is a bit more detail and them get back to you! Remember also that in the compressible formulation of these equations, the variable inside the temporal derivative and convection terms is (rho * k), whereas in the incompressible form the variable is (k) as density is constant and can be cancelled out 👍
@@fluidmechanics101 ok thank you 👌
please make a video for k-omega model.
Coming soon!
Where does the identity epsilon = C_mu *k*omega come from? thank you! Top videos really helpful.
Disregard - found the answer in your k-omega video (Y)
Derive it from the equation: mu_t (turbulent viscosity) = (C_mu*roh*k^2)/epsilon = (roh*k)/omega
Its better if you recall omega as a specific turbulence dissipation rate i.e., imega = epsilon/(C_mu*k)
Can you make a vedio on RNG k epsilon model
Hopefully in the future if I have the time to make it 🙂
Is turbulent viscosity (13) a mathematical term or experimentally determined near the wall and away from wall?
it is kind of a virtual quantity, like a term introduced to predict the turbulent flow
Technically it is a mathematical term. If you had DNS data (or measurements) of a turbulent flow, you could calculate it.
However, for us, it is easier to think of it as a virtual term that we introduce to try and correct the mixing (accounting for the turbulence which isn't resolved) and the wall fluxes.
@@fluidmechanics101 thanks a lot
Do k-epsilon or k-omega ever get used in engineering applications since k-omega SST is superior?
K omega is rarely used as SST seems to be far better. You only really need to understand k omega, so that you understand the history and reasoning for developing it. K epsilon is sometimes used in heat transfer applications
What is BST ?
'baseline stress transport' according to Menter
@@fluidmechanics101 Thank you