[CFD] y+ for Laminar Flow

A comprehensive summary of the calculation of wall shear stress, y+ and y* for laminar and turbulent flows. The following topics are covered:
1) 3:51 How is the wall shear stress calculated for globally laminar flows?
2) 10:38 How is the wall shear stress calculated for globally turbulent flows?
3) 16:09 How is the wall shear stress calculated for locally laminar flow?
#y+ #fluidmechanics101 #laminarFlow
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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.

[@user-it1qu2on5l]

Whenever I find some specific topics, the last place I'm in is this channel. Thank you!

[@johnluffman7954]

The best CFD channel. Can't wait to see more videos.

[@sauliusr]

After 5 years of searching this is best videos so far in regard to CFD theory. Promoting your chanel left and right.

[@AnandSinghS]

One of the best channels I have heard about CFD and A good explanations on topics...cheers

[@rochakbadyal1856]

U r such a genius . U make very tough things easily understandable. Thank you so much

[@user-mg7cz9mr8r]

You are awesome. I got lot more information about CFD from you then University. Thanks!

[@lorenzocarlesso]

Great explanation, as always!

[@nikhilnick8886]

Thank you Dr.Aidan🙂

[@aminubukar308]

Very good CFD lecture.

[@ibragim_on]

Thank you!!

[@YensR]

Great video, just one errata:
7:49 there is a NOT missing in the third line - you say the not, but it's missing in the text.

[@murchanabaruah4484]

yes exactly! I got so badly confused as my ears were listening to one thing but I could see something else on the screen. But the video is as always excellent!

[@ProfWill-ip1wz]

Very good video. It would be even better if you add some examples to demonstrate how the theory applies in practice! Like in this video it would be helpful to see how the wall shear stress is actually calculated in numbers not just equations.

[@fluidmechanics101]

Thanks Prof. Will! I will try to do this a bit more in my future videos 😄

[@haiderh2052]

For globally laminar flow, how would I know the required sufficient cells to capture the profiles

[@RatDota]

Hi, you mentioned that for globally laminar flow, the wall shear stress does not depend on y+ based on the result of a flat plate moving at velocity V. In this case, the velocity profile is linear, so the velocity gradient is the same regardless of y+, which makes sense. However, for pipe flows, the velocity profile is quadratic as you show on the next slide. In this case, wouldn't the velocity gradient depend on how fine our mesh is? The gradient would get steeper and steeper as we approach the wall, so wouldn't the wall shear stress depend on y+?

[@fluidmechanics101]

Yes, but the CFD solution is always piecewise linear. The piecewise linear solution will only approach the limit of a quadratic velocity profile as the mesh size tends to zero. In practice that means that the solution (y+, wall shear stress etc) will keep changing as you refine the mesh. However once the error is small enough then we are happy to just leave the solution there 👍

[@RatDota]

​ @fluidmechanics101 Oh right, I think I was accidentally interchanging y+ with mesh size. So the shear stress will still depend on the size of the mesh, but not on the actual value of y+ since the gradients are small in laminar flow, and hence the linear solution from the CFD is basically good enough. Please let me know if I'm still misunderstanding it.

[@fluidmechanics101]

Yes, exactly!

[@mounarahal256]

heello, do we need prism layers mesh in a global laminar flow in a pipe or just a fine mesh in all the fluid domain?

[@fluidmechanics101]

Layers are still needed in a laminar flow. They probably just don't need to be as fine close to the wall. I would aim for 15 cells across the boundary layer and you should be fine

[@parasghumare5502]

So the viscous sublayer approach will be used by the code only till y+ < 11.25 or for the whole locally laminar region even beyond y+ >11.25.

[@fluidmechanics101]

Yes, with a classic wall function approach based on switching

[@parasghumare5502]

@@fluidmechanics101 Well then it is nothing new, is it? Just same as a globally turbulent flow....just that the viscosity is of this other fluid.

[@RamKumar-to5ip]

HI, a small doubt,... for nonnewtonian fluid, the shear stress is not directly proportional to shear strain right?, so, how shall we compute shear stress in that case

[@fluidmechanics101]

I have a video on Non-Newtonian flows. I think I explain it in that video

[@nassersabet8846]

Thanks Aidan for your great videos! I have learned a lot from them. Keep up the excellent work.
I have a question about y* in laminar flow. As we don't calculate k and eps in laminar flow, the value of kp is unknown. So, how can we estimate y* if we want to estimate it instead of y+?
Also, I appreciate it if you could introduce me a paper or a book that I can learn about the initial conditions of k and eps in turbulent flow.

[@fluidmechanics101]

Well spotted, that is a good question. I think the usual convention is to make y+ not available to the user if we run a full laminar simulation (no turbulence model at all). But if you have a turbulence model turned on and the KE is very low (essentially locally laminar flow) then it will be able to give you y* and y+

[@nassersabet8846]

@@fluidmechanics101 Thanks Aidan!

[@parasghumare5502]

19:18 How will you use extrapolated nu from centroid to wall to calculate nu_w? I didn't understand this point. Or you mean they are same?

[@fluidmechanics101]

Linear extrapolation would work

[@parasghumare5502]

@@fluidmechanics101 No i mean once u extrapolate how will u calculated nu_w?

[@mahmoudabdullah5414]

Thank you. Please what is the recommended value for y+ for laminar flow over a flat plate in ANSYS FLUENT. Is it (Y+ = 1) or (Y+

[@fluidmechanics101]

Hi Mahmoud, i think this is answered in the video but perhaps i didnt explain clearly enough. To summarise, you do not need a specific y+ if your flow is laminar. However, you should still ensure that you have sufficient cells to resolve your velocity/temperature/species profiles with sufficient accuracy 😊

[@mahmoudabdullah5414]

@@fluidmechanics101 Thank you very much. Really, your channel is the best.

[@parthchavan1030]

@@fluidmechanics101 Hello Dr. Aidan It was an amazing video. Please let me know how to calculate y+ for thermal boundary layer. I looked for the answer but could not find much content on y+ calculation for thermal boundary layer.
Thank you.

[@fluidmechanics101]

Hi Parth, y+ is calculated in the same way for the thermal boundary layer. The only difference is the thermal profiles also depend on the Prandtl number (which is a material property that you can look up in a text book).

[@parthchavan1030]

@@fluidmechanics101 thank you. Keep sharing your knowledge. CFD is the best career option for mechanical engineers.

[@ammarlaichi8474]

Hello Dr, have you a channel for simulation with Ansys fluent or anothor information about this?

[@fluidmechanics101]

I don't have ANSYS fluent tutorials or demonstrations yet. Maybe in the future ☺️ for now I only have theory presentations

[@ammarlaichi8474]

@@fluidmechanics101 thank you very much Dr

[@sauliusr]

After 5 years of searching this is best videos so far in regard to CFD theory. Promoting your chanel left and right.

[@sauliusr]

After 5 years of searching this is best videos so far in regard to CFD theory. Promoting your chanel left and right.

[@fluidmechanics101]

Fantastic! Thank you so much for the support :)