Hi All! Thanks for taking the time to watch the video. If you found it useful, you should check out my other video on Temperature/Thermal Wall functions, which are very similar (but critically different) to velocity wall functions: th-cam.com/video/2bJ-5gaeSE0/w-d-xo.html Im also in the process of making another video for Turbulence Wall Functions for k, epsilon and omega. With this video you should be able to better understand some enhanced wall treatment models (such as non-equlibrium wall functions) that are offered by some CFD codes. As always, thanks for your support and I look forward to hearing from you Aidan
@@fluidmechanics101 it is super amazing work. Hope the science community support this work (funding) and appreciate your effort. We are waiting for OpenFOAM cases since I am using it frequently :)
@@fluidmechanics101 first of all thanks for all these videos. Requesting you to put more videos like this with simple explanations.. kudous to you.. excellent
Bro....I have seen many videos but urs one is the nost clear ....precise and accurate as well as practical....Plz keep on doing the good work.. and also I subscribe......Like
Hey Aidan! Thanks a lot for this great tutorial! It helped me a lot to understand the wall function approach better. Although i think there are some small mistakes on the slide 14 in equation 8. First of all the gradient should get multiplied by the dynamic viscosity mu, instead of the kinematic viscosity nu. And therefore the term on the right hand side should also get multiplied by the density to be consistent with the unit of the wall shear stress in pascal. Greetings from Switzerland! :)
Kinematic viscosity is equal to density / dynamic viscosity right? These equations makes sense to me. If you want to choose the density just express the equations in terms of density over dynamic viscosity instead.
This lecture clarified my confusion. I thought the wall function was specifying the velocity at the first grid centroid. However, through this video, I found that the wall function is not giving the velocity value to the first grid centroid, rather, it uses the velocity at the first grid calculated by the conservation equation and the wall velocity (=0) to get the modified wall stress.😀
I just finished the first two courses of "Computational Fluid Dynamics Fundamentals Course", they were so informative and helpful but I had some doubts about wall function, I looked for more information and I found you again, now I understand everythig more clearly. Great work and thank you I hope that you could touch topics like LES or FGM. Have you thought in making a free or paid course of OpenFoam? I would purchase it, no doubt.
Hi Geovany, fantastic im so glad you found my courses useful. I really wanted to make the best course that i possibly could and as clearly as possible, so everyone would understand. This is quite difficult, especially for wall functions 😂 yes, i am going to do some LES videos in future, but i need to do some more research first, as it is quite hard! Hmmmm, yes i have been thinking about making an OpenFOAM course. I am probably going to start making it at the end of the summer, as the course take me a long time to make! Thanks again for supporting the channel, i really appreciate it
Listen, Aiden you are the best in this CFD or whatever seems to be iterative. Tell you what, I would love it if you explain about creating various meshes for CFD tools such as Ansys and OpenFoam or SU2. It will be brilliant
@@fluidmechanics101 Meshing tools for OpenFoam or SU2 I think are free. But for ANSYS I will personally give you my proffessor's licence since he has been rounding around the bush all along the course.
Thanks for the offer but I don't think I can accept. ANSYS tend to not be very happy about people sharing licenses. Maybe I will give OpenFOAM or SU2 a go. BlockMesh and snappyHexMesh are pretty good but take some getting used to!
Thank you, Aidan. Well explained particularly on the implementation of wall functions. Slightly confusing when you say "by substituting in the logarithmic profile" to evaluate the wall shear stress - Eq. (8). In fact, the velocity gradient, at the wall, can only be worked out by using the linear wall function u+ = y+ and the logarithmic profile is obviously not applicable in the viscous sublayer. Forcing the logarithmic profile to pass (yp, Up) is here to just figure out the "right" velocity scale utau. Anyway, very high-quality video!
Very understandable expression, thanks. I was wondering why we try to y+ value lower than 1 when y+ is already higher than it until watched this video.
Very good information. The wall function in OpenFOAM are too many. It is difficult to understand the exact form of wall function. can you plz make one lect on that?
Hello Aidan, your videos are very clear and helpful! I am working on a case in which I want to resolve the boundary layer entirely (up to viscous layer, so y* = 1). I could use some help on better understanding the "Two-Layer" model and "Menter-Lechner" model used in ANSYS (as part of k-eps model wall treatment). As far as I understand, these are actually still wall functions, adapted to work for y* = 1. Would you consider creating a video on this topic? Thanks
Hi Aidan, many thanks for this educational and entertaining video! In the slide from 06:30 the calculation starts with u_tau based on tau_w (the wall shear stress). But isn't the wall shear stress the value we want to model with the wall-function approach? At first sight this seems to me like a circular reference - what did I miss?
Thank you for the wonderful explanation. A quick question : You mentioned that we already know the cell centroid velocity (u_p). How do we know the cell centroid velocity?
Maybe I mispoke in the video! Up is the main unknown in the matrix equation we are solving for the velocity (so in this sense it is unknown). However, it is a variable that we can express other variables in terms of. The wall shear stress for example does not appear in any of the equations, so we need to rewrite it in terms of Up and the other variables we know. Sorry for the confusion!
@Fluid Mechanics 101 First of all thanks for this excellent lecture. I have a query. The motivation of this lecture is to reduce the aspect ratio of cells closer to the wall but it seems we cannot reduce the number of cells as often we may need to resolve our mesh to get minimum y+. So could you please shed some light whether we have achieved our aim of reducing cell count. Eagerly waiting for your reply if u have time to clarify my query.
Have a look at your y+. If it is in that range, either make the first cell height smaller or larger, then check the results again. Repeat until you are in the range you want
This video clarifies so much for me! Thanks a lot Dr. Whimshurt. One thing I am trying to understand is scalable wall functions in k-epsilon model. I understand that it is different than automatic wall functions presented in this video. It solves log-law equations by scaling them no matter which region your first cell is at. I am using CFX but assuming Fluent does the same. And for my model I am still aiming y+
Hi Mehmet, Great, im glad you found it useful! From the user guide, it looks like CFX and Fluent do the same thing for scalable wall functions. www.afs.enea.it/project/neptunius/docs/fluent/html/th/node99.htm More specifically, it looks like they force the value of y+ to be 11.25, if your value of y+ falls below 11.25, so that wall functions will always be used and you won't get viscous sub-layer resolved treatment. As you are aiming for y+ < 1, I wouldnt use scalable wall functions, as the scalable treatment will force y+ to be 11.25, which will give you the wrong answer. I would therefore go for standard wall treatment with the k-epsilon model instead, so that you can get the correct viscous sub-layer behaviour. Alternatively, If you are really concerned with correctly computing the wall shear stress and near wall behaviour and need y+ < 1 (this will depend on your application, perhaps you have an external aerodynamics application), then the k-omega SST model is widely considered to give more accurate predictions of the wall shear stress and near wall behaviour, when y+ < 1. I will be doing a video on this soon, so keep watching this space! Hope this helps, Aidan
@@antanas9015 Yes, but there is also an enhanced wall treatment formulation in Fluent for the k-eps turbulence model. In this approach, the flow is "divided" in a viscous affected region and a fullty turbulent region. In the viscous affected near wall region , the one-equation model of Wolfstein is employed, insetad of wall functions. in this way it is still possible to solve cases with low y+ when using the k-eps turbulence model. I hope it can help:)
I want to purchase some of your lectures but the ones I need are in seperate lecture groupings. Isn't there a way to purchase slides of specific lectures that we need?
Hi Soroush, yes the slides are available. You can download them from my website or patreon account. Just follow the links in the description of the video 😊
Wow!! This was nicely explained. You are a blessing in disguise. I have question for you. Towards the end of the video, you say that conventional wisdom is to have y+ ~ 1. This indirectly means that we are in the viscous sub-layer. If that is the case, then why would we use wall functions? We can resolve (i.e. numerically solve the equations) the viscous sub-layer isn't it? Anyway, Thanks for the video. Cheers :)
Hi Mihir. Surprisingly the reason is often cell quality. As the cells get thinner (to reduce y+ to less than 1) their aspect ratio and non-orthogonality gets a lot worse. This reduces the stability of the equations and can often lead to divergence, which can be very frustrating! So it is usually possible to get y+~1 for smooth aerofoils and wings. However for more complex geometries, the poor cell quality and high cell count forces engineers to use larger cells and have y+> 30. Despite the loss of solution accuracy, at least we can get a solution ... 😄
@@fluidmechanics101 ok. So, my question is that suppose we have made a very fine mesh (y+ ~ 1). Now, we are no longer having a "big wall cell i.e. y+>30 " as you have mentioned at the start of the video. Now, Purpose of using wall function is to reduce the mesh count by having that big wall cell. Now, since i have very fine mesh i can actually resolve the flow. Why would i use wall function in that case? So, basically, what i think is that wall function will be used only when we are in y+>30 region ( I suppose that is what you meant in the above comment for complex geometries) . And When we are in y+~1 region then the turbulent equations will be solved and thus we won't use wall function. What do you think?Let me know. Cheers :)
Hi Mihir, sorry if you have been waiting a while for a reply. I think the key misconception here is that the 'wall function' only acts on the face of the cell in contact with the wall. If this cell has y+ = 1 then there are no modifications to the cell face and the wall flow is 'resolved'. The cells that are further away may have y+= 30 but they are not in contact with the wall (only the face of the cell in contact with the wall is affected) so no change is made to those cells. The phrase 'wall function' is misleading as it is not a continuous function but just a modification to the face in contact with the wall. As it sounds like your case has y+ = 1, then there are no modifications and you are good to go. I think my video on 'enhanced wall functions' would be useful for you. Maybe give it a watch?
@@fluidmechanics101 Actually I still don't get it Sir. So, after all, the wall functions only works when the y+ of wall-adjacent cells are larger than 30? And when the y+
I always lose it at eqn 8. I have no freaking idea where that expression for the wall shear stress comes from? Also how does it make any dimensional sense? (its m2/s2). Also should not shear stress be dynamic viscosity x velocity gradient?
Sorry there are a few errors in this talk (it is quite old)! There is a missing density in the equation for the wall shear stress. Note that: wall shear stress = density * kinematic viscosity X velocity gradient at the wall (because kinematic viscosity = density X dynamic viscosity). I think you might find it helpful to watch my more recent video on 'Enhanced Wall Functions' where I go through this again (but a bit more recently)
Great explaination.... just one query..if I put my first cell in the log law region then the effect of viscous sub layer and buffer layer is ignored. correct?
Yes, the effect of the viscous sub layer and buffer layer are ignored and the viscosity on the cell face is increased to ensure that you get the correct wall shear stress 👍
Hi Aidan thanks for the video.. i have a question about the adjacent wall cell.. when you say is better to avoid to place y+ in the buffer layer do you mean that the centroid of the first cell has to be at a y+ greater than 30 right? Thank you
Hello sir, I am an undergraduate Mechanical engineer and am very much interested in learning CFD. I am finding this playlist extremely useful. I just want to know how to begin my career with CFD as most of the CFD engineer jobs demand a higher degree in the same...
You can always try and find a graduate engineer position and then indicate you are interested in fluid mechanics? You might be able to move internally into a CFD team in a company
Hi Aiden! Nice video and thanks for the superb introduction. I have a small doubt and wonder if you would like to share some wisdom. If in CFD y+ is way smaller than 1 (say 0.02), other than high aspect ratio, will wall function also predict wrongly?
They should be fine because the velocity profile is linear in the viscous sub-layer. So you can go as close to the wall as you want, the profile will always be linear
Hi Adian Sir, Good Morning Could you please make the videos about the mesh cell quality with respect to ICEM CFD. what it should be? How to correct it? etc.?????
The ICEM CFD quality metrics are a bit weird. I usually just focus on non orthogonality quality as this is the most important metric for CFD. But yes, i think a good video is required here 👍
@@fluidmechanics101 After unstructured meshing, generally I maintain the quality more than 0.14 but wanted to know your approach how do you check the quality of the mesh means what parameter, what values do you check for tri, quad, prism and other elements in ICEM CFD? what values should be maintained for different mesh cells?
ICEM has lots of different metrics because you can also use it for FEA. For CFD the most important metrics are non-orthogonality and aspect ratio. If you make sure non orthogonality quality is greater than 0.1 and aspect ratio is less than 100 (unless you are doing high speed aero) then you should be fine
Remember that the solution also changes, so the wall shear stress will change each time ... out of interest, how large is your y+? This is more common at higher y+ values
Hi zeeshan, the y+ plot is always shown with a logarithmic scale, as it helps to see the shape of the curves in the logarithmic region. 10^1=10 and 10^2 = 100, so you want to look between 10^1 and 10^2 👍 it is the third increment along, because the increments go: 10,20,30 ... 90,100
Hi, Thanks for your videos!! these are the best I've ever seen on the web. One question! I didn't get why we need to check y+ while there are some wall functions that fit through all layers such as the one you mentioned "Spalding's wall function". It can calculate the right value regardless of the mesh size, I mean no need to worry if some cells are in the buffer layer.
Spaldings wall functipn and the other wall functions are only accurate if you have a flow that is pretty much a straight pipe or flow over a flat plate. If you have a complex flow (impingement, separation etc) then these models will give the wrong answer and you need to reduce the y+ into the viscous sub layer, as the viscous sub layer is always laminar if you are close enough to the wall. It is the only solution you can rely on for a complex flow. So the answer is: it depends on what your flow is doing 😊
@@fluidmechanics101 So, suppose I want to model a turbulent flow in a return duct (180-deg return duct) Do I need to generate grids somehow in order to get y+ in the viscous sublayer?? Even if I use enhanced wall function??? Thank you for your time
It sounds like you will be getting some pretty significant separations and the enhanced wall functions were developed for attached flows. So ... if you want the best results, better to try and get y+ in the viscous sub-layer
You said that CFD codes choose appropriate wall function on the fly, i.e. switch between linear and logarithmic behavior. But, for example, in ansys cfd codes' (cfx, fluent) manuals it is said that wall functions should never be used if y+ < 30, i.e. we should locate the first node (cell) in the log-layer. For me this means that linear (viscous) sublayer is not modeled at all with wall function approach (because we don't have places to store corresponding values), so only logarithmic wall function is used. And automatic wall treatment is automatic switching between wall function approach and direct resolving of the viscous sublayer in omega-based turbulence models, but not between linear and logarithmic wall functions. What do you think?
Its useful to remember that as the code converges, the values of y+, wall shear stress etc. will be changing all the time. So the CFD code needs to have a continuous treatment that can handle any y+ at all times. Otherwise it would suddenly get floating point exceptions, which would be very annoying! The comment that the user guides make is about the accuracy of the final solution. Once the code is converged, we have a final solution with a fixed value of y+, wall shear stress etc. For this converged solution to be accurate, you should follow the guidelines for where y+ should be. For example, y+ > 30 if you are using the k-epsilon model. Does this help?
Thank you for posting these videos. These have been incredibly helpful. Quick question, in equation (7), shouldn't you be using 'mu' (dynamic viscosity) instead of 'nu' (kinematic viscosity)? And what is u_t in equation (8), (9) and (10)? Is it u_tau, or something else?
I also noticed that. The u_t you mentioned was exactly u_tau, and the multiplication of rho was missing. The equation Aidan wanna express was tau_w=rho*(u_tau)^2
Hi Aiden, thanks again for these very informative videos, and for your previous responses. I'm afraid I have another clarification I would like you to help with please: 1 - this is more of a clarification, am I right in saying that a cell with a Y+ of >30 refers to a cell which starts at the wall and extends into the Y+30 range, or, does Y+30 only refer to cells that are not touching the wall but are situated within this Y+ range? 2 - If it is the former (of Q1, a cell that is touching the wall but so large it reaches the >30 Y+ zone), then why make a cell that is so big that it has to use the log-law equation, and as such will not record any of the viscous sub-layer info? 3 - if it is the latter (of Q1, as in referring to cells that happen to be in the Y+ >30 zone but are not touching the wall), then how is it possible not to put cells in the buffer zone? As it would be impossible to have cells in the Y+30 zone without having cells in the buffer zone.
When talking about y+ and wall distance, we are only talking about the cell that is touching the wall. The cells above it are not considered. More specifically, we are talking about the distance of the centroid of this cell normal to the wall. You can check this in the post-processor. There will only be values of y+ computed for the cells that are touching the wall. Usually we would always like to have y+ < 5. However at high Reynolds numbers, the cells get very thin! This can reduce their quality and make the solution unstable or too slow to solve. So y+ > 30 is only really used when we have no choice. Im not sure about the spalding wall function. Perhaps it is more difficult to code or is less stable? I would have to look into this
Hi! fantastic explanation. Just to confirm here. When we use equation 3 calculating the yplus, the kinetic viscosity here is identical to the so-called near wall viscosity. So, with each iteration, the Up is updated first then update the near wall viscosity according to the wall function (instead of the constant value for laminar viscosity or the turbulence viscosity relationship) till at last get a convergence. Is this the procedure? And when we split the near wall viscosity into laminar and turbulence parts, does this near wall turbulence viscosity still satisfy the equation for turbulence viscosity (turbulence viscosity=Cmu(TKE^2)/epsilon)?
Hi Chang, you have almost got it! I feel like i have missed a bit of the explanation out, so here goes. y+ is always calculated with the laminar viscosity (the material property of the fluid), which does not change. You are correct that the CFD solver starts by calculating the value of Up (the cell centroid value). We then calculate the value of y+ for each boundary cell face using the value of the laminar viscosity. Once we know y+, we calculate the near wall viscosity (nut) for each boundary cell face. The reason we calculate a seperate value for each boundary cell face is that one cell may have multiple faces that are walls (see my previous video on the epsilon wall functions)! The near wall viscosity is calculated at the wall, and it is this value that is used to compute the wall shear stress on that boundary face. The turbulent viscosity at the cell centroid is not affected. This value is computed using C k^2 / epsilon, as you pointed out :) The part where the near wall viscosity is split into laminar and turbulent parts is purely for convenience in codes like OpenFOAM and is used to emphasise that the laminar viscosity remains constant across the cell and is not modified by the wall function. Only the turbulent component is modified on the boundary cell face. I hope this helps clarify things! I will be releasing another video in a few weeks on the difference between y+ and y*, which should help clarify things a bit more. In the meantime, check out my video on epsilon wall functions. This should help explain why boundary faces are treated individually All the best Aidan
@@fluidmechanics101 Thanks, Aidan. I have tried to extract the TKE, epsilon, and turbulence viscosity value at the near wall cell in Fluent, but found it does not follow the equation C k^2 / epsilon. I am not sure if I did it in the right way. Does it mean the near wall modification of viscosity is also only applied to the turbulence viscosity in Fluent (same to OpenFOAM)? So when it calculates velocity from the momentum equation, we switch to the near wall modified viscosity as the effective viscosity at the near wall cell for the coefficient of diffusion term? And is this how wall function affects the wall adjacent velocity Up?
Yes you are correct! I think the difficulty might be having is that a near wall damping function is applied in the k - epsilon model ( mut = rho f C k^2 / epsilon, where f is a damping function which varies between different versions of the k - epsilon model) Have a look here: www.cfd-online.com/Wiki/Low-Re_k-epsilon_models
The k omega and k omega SST models dont have this damping function. This is why they are often preferred for wall bounded flows. Also, it is always difficult to know exactly what fluent is up to, as the source code is hidden ... but your explanation is exactly what OpenFOAM does :)
A question bothers me: If I set the no-slip boundary condition on the wall, and I set the viscosity to be 0 at the same time, would the boundary condition be slip? If not, what the physics looks like ? Thank you very much!
@@fluidmechanics101 Thank you very much for your reply! For no slip condition with 0 viscosity: the first layer of fluid still adheres to the wall, but the second layer of fluid can move freely. However for slip condition with ideal fluid: the first layer of fluid can move freely. Based on this, I still don't understand why these two situation is equivalent.🤣🤣🤣
Surely with 0 viscosity, the fluid does not adhere to the wall in the no slip case? Physically it is the action of viscosity which sticks the fluid molecules to the wall, so zero viscosity is equivalent to the fluid not sticking to the wall
Thank you so much! I'm also watching other videos. I still confuse the difference between wall function and dumping function in k-e model... Both are used for treating near wall characteristics. what's the critical difference?
The key difference is that wall functions are applied to the faces of the cells in contact with the wall. Damping functions are applied to all cells, even the cells that aren't in contact with the wall 👍
@@fluidmechanics101 I see! Now I understand. Thanks for quick and cordial reply. It is a really helpful video channel. I also introduce to my friends :)
Hello Aidan, First of all I would like to thank your for your effort with making such excellent videos. However, I am not sure about the correctness of the relation in the outer layer (log-law region). When I equate both of the expressions, I am getting a different value for the intersection, see time 10:20. Based on the formula and constants (kappa and E) you use for the log-law region, I am getting smaller value of this intersection, i.e. below 4. Am I doing something wrong? Could you elaborate more on this issue? Thank you in advance for your response!
Hi jack, to get the intersection point you will need to solve this equation numerically ie. Y+ = 1/kappa log(E y+) Rearrange: Y+ - 1/kappa log(Ey+) = 0 Take an initial guess of Y+ = 11 E = 9.793, kappa = 0.4187 Solve using bisection/newton-raphson Y+ ~ 11.25 If you are interested, i go through the full derivation and explanation in more detail in my 2nd fundamentals course, which you can get from my website, udemy or skillshare 👍 but im sure you have just made a small error somewhere
@@fluidmechanics101 I see your point, but in my opinion we seem to be talking at cross purposes. I think I figured that out. To get the correct result, you need to use the natural logarithm "ln" rather than the common logarithm "log" with the base of 10. I have been taught all my life that log(x) usually means the base 10. It is common practice that in some pieces of software the term log(x) means implicitly ln(x) with the base of e, so it needs to be the reason for this misunderstanding. I am glad we have resolved it. Thank you for your videos and stay blessed!
@@fluidmechanics101 Hey, thanks for the response. This series would be complete with compressible flow solver videos too. I'd surely recommend this to anyone learning CFD. Also, I have a doubt regarding y+. I am trying to simulate an incompressible turbulent flow and it was given in previous research to have Y+ < 1 in the Boundary layer. How do I ensure this during the mesh generation itself? Should I simulate a flow first, plot y+ and go about refining the mesh or is there an empirical relation that can be used as a good first estimate?
Hello there! Many thanks to the channel and everyone there. As fas as I understand, in case of turbulent flow, with a good mesh with growth rate near the walls, if yoy achieve y+ value near 1, you don't need enhanced wall functions. Do I get it right? Thanks in advance.
i dont get (at slide 15) how we are allowed to simplify Up, which in one case (eq.9) is the value of the velocity at the first cell if we suppose its y+30. Anyone has a clue?
The trick is that we aren't specifying the value of Up. Up is calculated by solving the momentum equations. We are actually modifying the viscosity on the near wall face, which is then used in the solution of the momentum equations during the next iteration
@@fluidmechanics101 Thank u very much. i also checked the reference you gave at the end of the video and now i think i really grasped for the first time how this kind of wall functions work (at least the main part of it!). Thanks
Hello, Thanks for the Video. Its explain much and there are things that I didn't understand before, but now they look a little bit cooler. Also, I may have questions that, even if that look clearer, I fail to understand it: 1- the equation (8). I tried to recover how you did the derivative, but I didn't find the same things. If you can send me a link where I can read it or explain it here, that would be great. 2- From that page, I think I understood just the half of what you said. I mean, I heard the explanation clearly, but I didn't understand. And I REALLY want to understand as clearly as possible as you do 3--I'am using a cfd Software for a while now, but what I find difficult, is to put the right value of y+. I do understand that at the beginning we don't know the value and that the value change during the simulation. I saw that. The problem is "HOW DO I CORRECT IT"?. Read somewhere that you change it at the end of the simulation. But it's complicated, since I'am evaluated the drag of the boat, and it's taken 4 to 6 hours to run one simulation. So my question is: how I may ensure the value of y+ before letting the simulation run until the convergence? Thanks in advance if you find time to answer me and sorry for my english if it is not good enough.
Hi Brice! So glad you found my video useful. In answer to your questions: 1) you can find the derivation in the Jonas Bredberg paper (link 4 in the description of this video) and you want equation 75 and 76. The trick is to rearrange for utau, rather than differentiate. 2) I am thinking of doing a follow up video to explain this in more detail, as i have had lots of comments! What do you think? 3) To reduce y+ you have to go back and refine your mesh. The only way you will know y+ is after your simulation, so the process is iterative: make a mesh, run computation, find y+, remesh, repeat etc. However, you can make this process quicker by having a good guess for y+ before you mesh. There are some tools online which can help you with this. Try googling ‘CFD online y+ calculator’. There is a really good tool which can help you guess y+ before you run your simulation. Hope this helps! Aidan
@@fluidmechanics101 Aidan First of all thanks for this excellent lecture. I have a query. The motivation of this lecture is to reduce the aspect ratio of cells closer to the wall but it seems we cannot reduce the number of cells as often we may need to resolve our mesh to get minimum y+. So could you please shed some light whether we have achieved. our aim of reducing cell count. Eagerly waiting for your reply if u have time to clarify my query. Also requesting you to post more such lectures.. it is fortunate that i have found your channel which is very helpful.
Hi Siva, i think i might not have explained it well enough in the video, so here goes! The optimum mesh is always a mesh with all cubes (aspect ratio 1) that are aligned with the flow direction. However, if we were to use all cubes, the cell count would be really high (particularly at high Reynolds number). So what we do is note that the gradients normal to the wall are steeper than the steeper than parallel with the wall. So we increase the aspect ratio of the cells and stretch them out. However, if the aspect ratio is too high (say over 1000) then the computations start to become unstable. So we would like to make the wall adjacent cell (which has the largest aspect ratio) larger in the wall normal/y+ direction. This will reduce its aspect ratio and make the computations more stable. In addition, it will also reduce the cell count as all the other cells will be the same size or larger than this cell. I hope this makes a bit more sense now 😊 and yes, i have lots more videos to come, so stay tuned!
Clear, clean and practically sound explaination! Amazing work, keep it up. Please do make more videos explaining the basic terms as well👍👍 such as RANS, NS equations etc. would love to see your approach!
I have more than one thing to ask! In the "What value of y+ should I aim for?" section, you said that we should avoid placing cells which have a value of 5< y+
Hi Osman, you are correct. We only need y+ to be either < 5 or between 30 and 200 for the first cell close to the wall. All the other cells are computed by the cfd solver using a linear variation of variables across the cell.
If you are doing a study related to species mixing which is more of a phenomenon in the turbulent flow region there you mostly can go with first cell height that can lie at y+>30 and you can use k-e turbulent model without activating wall functions but if you want to solve for lift on wing using k-e turbulent model then it is a good practice to put first cell height at y+
All credits goes to Fluid Mechanics 101, my knowledge on turbulence models was like raw metal it is your lectures that polished it Please keep spreading knowledge
Hi Aidan. Great video a thank you a lot for your simple and clear explanation :). I have just one remark. You should write tau=rho * nu * du/dy. Or you can just divide the shear stress by rho. Also the dimensions of the two sides of the equations would be incorrect if you don't include rho. Anyway, great video!:)
Yes, I found exactly the same thing when I did the derivation. If you watch my video on enhanced wall functions, I think I do a better job of the derivation there
That's a very clear explanation of something not so obvious! The thing is, in CFD, a lot of cases are complex, with detachment/attachment, acceleration/deceleration etc... This will inevitably lead to 5 < y+ < 30 in some regions. Second thing: When we talk about y+, do we talk only about the first cell height? Because even with a nice y+ = 1, the 3rd or 4th cells might be in the buffer layer. That is a problem or not? Didn't get this.
Hi Lili An, yes you are absolutely correct. CFD cases are complex and and y+ may be in the region of 5 < y+ < 30 in some places in the mesh and < 5 in others. Usually we adopt a compromise and try and get y+ < 5 in the main area we care about. For example, when simulating an aerofoil/wing we usually try and get y+ < 5 near the trailing edge of the suction surface, as this is where seperation inception begins and will have the most signifciant affect on the solution. This normally leads to y+ > 5 near the stagnation point (and hence not an accurate solution), but we dont care about the solution as much here, as the integrated lift and drag are more significantly affected by the suction surface boundary layer. 2) Yes you are correct, the second and third cells may be in the buffer layer. But this is normally fine because the variation across the cells in the mesh is linear and the CFD solver compute the rest of the profile through the boundary layer for us. Conventional wisdom is to try and have 10 cells through the thickness of the boundary layer (a growth ratio less than 1.2) with a y+ < 5 for the 1st cell and this is normally fine to get an accurate solution. As always, check your solutions with a mesh convergence study, as every case is different! Hope this helps
@@fluidmechanics101 So, let's clarify more. Wall functions are used to compute values at the first near wall mesh node only and values at all other nodes are solved by the solver from the flow equations. Am I correct? If so, then it's not optimal approach IMO. Or do wall functions are used for all mesh nodes within ranges y+
Yep, you are correct. The cfd code only uses wall functions for the cell closest to the wall (often called the wall adjacent cell). The rest of the mesh will be solved by the cfd solver by assuming a linear variation across the cells. So ... you will still need a relatively fine mesh near the wall as the gradients are steep. This is why yo should try and use a growth ratio of 1.2 or lower normal to the wall to make sure you have enough cells :)
Well spotted! You still need enough cells to capture the velocity profile (and other gradients) away from the wall. Remember that the variation across cells is linear, while the velocity profile is definitely non linear! So you need enough cells to make the linear approximation sensible. People usually advise 10 cells through the boundary layer. However this is not useful to us when we are making a mesh .... so my colleagues and i tend to find that a growth ratio of 1.2 normal to the wall is about right to get the right number of cells through the boundary layer. For external aerodynamics applications where you really need a good answer, i would drop this to 1.1 or even 1.05. I hope this helps!
Great video. I got a bit confused in the part "interpolation in CFD between cell center and its faces is linear", but I got the point, it is often, but not strictly linear. Thank you for the high-quality content!
Thanks for this content! Somehow you made everything very clear in the span of 20 minutes :) It is rare to find someone in this field which is able to explain these topics in such a simple manner.
I'm glad you like the content. Generally the courses have a lot more detail and examples in them than the TH-cam lectures, so they are great if you want to dig into the matrices and the detail. The TH-cam lectures are best if you are looking for a good overview of a topic and trying to work out what buttons to press in ANSYS or OpenFOAM 😃
This is a difficult question, as there arent many good books on turbulence modelling at all! I would suggest ‘turbulent flows’ bu stephen pope. It is quite an advanced book that goes through turbulence theory in detail and should have eveything you need. The application to CFD however, is limited in this book and i would read Hrvoje Jasaks thesis instead for this 👍
The video is awesome thank you very much ...... I have 2 questions please 1) The curve of the log low region makes a nonlinear curve from the wall to Up, from where did you know that this nonlinear curve is going to have the right slope of the wall shear stress (I think the green line should reach the origin to satisfy this but in the graph in the video it doesn't reach the origin) is that right ? 2) when you equated the 2 equations of the linear and log low region you cancelled "Up" in the left side with the right side although "Up" of the linear equation should be different from the "Up" of the log low equation to equate them right?
Hi Hatem, in answer to your questions, it is important to remember that it is the product of the viscosity and the velocity gradient that gives the wall shear stress. As the variation across a cell is linear, the velocity gradient will be incorrect when we are in the log law region. But this is ok, as long as the product of the (now incorrect) velocity gradient and viscosity gives the correct wall shear stress. This is why we modify the viscosity :) the green line doesnt need to reach the origin, as it is the gradient that we care about. For question 2, remember that it is the CFD solver that calculates the value of Up, so we assume that we know this and it is a constant. Remember remember, we are modifying the viscosity here to get the correct wall shear stress, not computing the value of Up. I hope this helps! Im thinking of doing a follow up video to clarify these points, what do you think? Would that be helpful? Aidan
"Thank you for your awesome video! could you please tell me which y+ in In OpenFOAM, should be between 30 < y+ < 300? Is it the minimum, maximum, or average ?
It is the y+ in the region that you care about (or affects your solution the most). For example, on an aerofoil it is the y+ on the trailing edge of the aerofoil which has the greatest effect on the separation point. You care less about the y+ near the stagnation point at the nose of the aerofoil, as this has a smaller effect on the drag calculation. So you need to use some engineering judgement. Have a look at your geometry and try and deduce which region in the most important. If you are unsure, you can always test it by creating a few different meshes and see what effect it has on the results
Aiden, I had a doubt, Till what value of y+ is the wall function to be applied for in the mesh? Ypu have mentioned that for y+ > 30, use wall functions But till what y+ value is that to be used, above which is the resumption of normal CFD interpolation?
This will depend on the CFD code you are using. Often there is a hard switch between the viscous sublayer and log law at y+ = 11.25. It's really worth checking the user manual
y+ and u_t require wall shear stress to be known which is part of solution. As we don't know wall shear stress yet Equation 9 is an implicit equation. So, there must be some kind of iterative approach required to solve it unless there is another way to estimate y+ and u_t. You didn't explain how it is done I think.
Yes we'll spotted. If you choose y+ based on wall shear stress, rather than turbulent kinetic energy you need iteration. You can either just take the wall shear stress from the previous iteration of the SIMPLE algorithm itself or you can do the iteration locally. You can find this iterative equation either in the OpenFOAM source code, or checkout the book by Weller and Greenshields 'notes on computational fluid dynamics'
Thank you so much for your wonderful explanation! Your explanation is excellent, and I have gained a lot. However, I don't understand how equation(8) is derived and what ut in equation(8) represents?
Hi Aidan, thanks so much for the video and lectures. It is really awsome and very helpful. I would like to ask you ine thing if I may. One thing is not clear to me that, how this calculated effect of the wall sheer streas is then fed into the momentum equation. Is it done by modified turbulent viscosity, which is then used in the momentum equation? So that the velocity at the first grid can take into account the effect of the (total) boundary viscosity? I appreciate your help in advance!
Yes, that's correct. The modified viscosity is accounted for in the summation over the faces of the cell when calculating the diffusion contribution to the A matrix of the momentum equation
Hi Aidan, I really appreciate these high-quality videos and I love how you bridge the gap between coursework from schools and commercial CFD codes. Thank you and keep up the good work! In equations 7 - 11 (slides 13, 14, and 15), why is it nu (kinematic viscosity) and not mu (dynamic viscosity)? Is that an error or am I missing something?
Thanks Kevin 😊 the wall functions are always written in terms of nu (kinematic viscosity) and alpha (thermal diffusivity). To get back to mu (dynamic viscosity) and k (thermal conductivity), just multiply by rho (density) and rho cp (for temperature). Maybe check out my vid for temperature wall functions and this will make more sense 🙃
@@fluidmechanics101 Aidan, I have watched that video as you have suggested and it looks like equation 7 in that video has a rho (density) term in front of nu (kin. visc.). I believe you are missing a rho term in equation 7 of this video.
hello I am korean cfd user I am pleasure to see your you-tube and it make me to help I have a question about wall-function you said that "Always avoid placing y+ in the buffer layer (5 < y+
Yes, you are correct. The automatic wall treatment does improve the accuracy a bit (compared to standard w f with switching) in the buffer region but it is still not very accurate and you should try to use either y+ < 5 or > 30 if you can 👍
@@fluidmechanics101 Thank you for your attention It is helped me to be assured about "automatic wall function" Could I more give some questions? 1. if I not use "wall function", ansys's manual recommend y+ < 1. so for it, recommend to make more than inflation layer 10. but I am not sure if it's right. So, I think it need mesh dependence test about how inflation layer make instead of manual guide. I am wondering your opinion 2. I learned my superior that y + is not important in case of "airflow analysis" (such as analysis of ventilation inside the house, outdoor airflow etc) because force arise for velocity profile around wall is weak compared to total airflow force so it not much impact I also not sure if it's right. I also wondering your opinion thank you for reading my questions. Your help is a great strength to me.
A simple answer to both questions would be: yes you should always try and do a mesh dependence test. You can try different values of y+ and different numbers of layers and see how much it affects the solution. The general guidance that people give (around y+ and number of layers) is useful as a starting point but then you should try it for yourself. For point 2, I have often been given vague advice like this from supervisors / advisors / reviewers over the years. It is often difficult to understand what they mean and you can't really argue back. The best thing you can do is run your own tests (compare different values of y+ for example) and then show them the results. You can then let your results do the talking for you 😄 this is a very useful trick for addressing review comments as well. Better to discuss the results than your thoughts / ideas / what you saw on s TH-cam video ....
Thanks Aidan for this video. In summary, velocity profile is computed as piecewise linear in CFD due to values at cell centroids. However, turbulent velocity profile is non linear. In order to bridge the gap, wall functions are used. For y+
![[CFD] What are Thermal (Temperature) Wall Functions?](http://i.ytimg.com/vi/2bJ-5gaeSE0/mqdefault.jpg)
![[CFD] What are Thermal (Temperature) Wall Functions?](/img/tr.png)
![[CFD] How Fine should my CFD mesh be?](http://i.ytimg.com/vi/60fDz2cVdy8/mqdefault.jpg)
![[CFD] What is the difference between Upwind, Linear Upwind and Central Differencing?](/img/n.gif)
Hi All! Thanks for taking the time to watch the video. If you found it useful, you should check out my other video on Temperature/Thermal Wall functions, which are very similar (but critically different) to velocity wall functions:
th-cam.com/video/2bJ-5gaeSE0/w-d-xo.html
Im also in the process of making another video for Turbulence Wall Functions for k, epsilon and omega. With this video you should be able to better understand some enhanced wall treatment models (such as non-equlibrium wall functions) that are offered by some CFD codes.
As always, thanks for your support and I look forward to hearing from you
Aidan
Very very very useful and you are very good at explanation ❤🌹
Thanks for the feedback 😊 im glad you enjoyed the video
@@fluidmechanics101 it is super amazing work. Hope the science community support this work (funding) and appreciate your effort. We are waiting for OpenFOAM cases since I am using it frequently :)
@@fluidmechanics101 first of all thanks for all these videos. Requesting you to put more videos like this with simple explanations.. kudous to you.. excellent
Thanks for making these videos. These are very helpful. Can you make one video on chemical reaction in porous media?
I couldn't believe such high quality lectures available for free. Great work, deep insight, and vivid explanations.
Bro....I have seen many videos but urs one is the nost clear ....precise and accurate as well as practical....Plz keep on doing the good work.. and also I subscribe......Like
I finished my master thesis with your video. I should use CFD in my doctoral thesis and I keep going to watch again :D
best cfd channel ever.. thank you sooooo much!!
Merci, grazie mille, THANK YOU! Your channel is a blessing, the ray of sunlight in my broken grad student life!
Excellent lecture, I have seen many videos of these channel and learned a lot, thanks.
It would like very much to see one lecture of dynamic mesh.
Hey Aidan! Thanks a lot for this great tutorial! It helped me a lot to understand the wall function approach better.
Although i think there are some small mistakes on the slide 14 in equation 8. First of all the gradient should get multiplied by the dynamic viscosity mu, instead of the kinematic viscosity nu. And therefore the term on the right hand side should also get multiplied by the density to be consistent with the unit of the wall shear stress in pascal.
Greetings from Switzerland! :)
Yep, well spotted!
@@fluidmechanics101 Wouldn't that mean the succeeding equations 9, 10,...have a missing density term too?
Kinematic viscosity is equal to density / dynamic viscosity right? These equations makes sense to me. If you want to choose the density just express the equations in terms of density over dynamic viscosity instead.
Kinematic viscosity= dynamic viscosity / density (your fraction is upside down)
Excellent explanation Dr. Aidan. It's very clear. Thank you very much.
This lecture clarified my confusion. I thought the wall function was specifying the velocity at the first grid centroid. However, through this video, I found that the wall function is not giving the velocity value to the first grid centroid, rather, it uses the velocity at the first grid calculated by the conservation equation and the wall velocity (=0) to get the modified wall stress.😀
Exactly!
I just finished the first two courses of "Computational Fluid Dynamics Fundamentals Course", they were so informative and helpful but I had some doubts about wall function, I looked for more information and I found you again, now I understand everythig more clearly. Great work and thank you I hope that you could touch topics like LES or FGM. Have you thought in making a free or paid course of OpenFoam? I would purchase it, no doubt.
Hi Geovany, fantastic im so glad you found my courses useful. I really wanted to make the best course that i possibly could and as clearly as possible, so everyone would understand. This is quite difficult, especially for wall functions 😂 yes, i am going to do some LES videos in future, but i need to do some more research first, as it is quite hard!
Hmmmm, yes i have been thinking about making an OpenFOAM course. I am probably going to start making it at the end of the summer, as the course take me a long time to make!
Thanks again for supporting the channel, i really appreciate it
Love the rhyme in the beginning: Hello Everyone, This is Aidan from FM 101. (Y)
😂👍
Listen, Aiden you are the best in this CFD or whatever seems to be iterative. Tell you what, I would love it if you explain about creating various meshes for CFD tools such as Ansys and OpenFoam or SU2. It will be brilliant
I would love to do something like this. The problem is meshing tools are expensive and I really can't afford an ANSYS license 😔 any suggestions?
@@fluidmechanics101 Meshing tools for OpenFoam or SU2 I think are free. But for ANSYS I will personally give you my proffessor's licence since he has been rounding around the bush all along the course.
Thanks for the offer but I don't think I can accept. ANSYS tend to not be very happy about people sharing licenses. Maybe I will give OpenFOAM or SU2 a go. BlockMesh and snappyHexMesh are pretty good but take some getting used to!
Congrats, this is so clear and concise !
Thank you, Aidan. Well explained particularly on the implementation of wall functions.
Slightly confusing when you say "by substituting in the logarithmic profile" to evaluate the wall shear stress - Eq. (8). In fact, the velocity gradient, at the wall, can only be worked out by using the linear wall function u+ = y+ and the logarithmic profile is obviously not applicable in the viscous sublayer. Forcing the logarithmic profile to pass (yp, Up) is here to just figure out the "right" velocity scale utau.
Anyway, very high-quality video!
Very nice explanation. your channel deserves to have more subscribers! Keep it up.
Thank you so much 😊
Excellent Presentation and explanation
Great explanation 🙂
Thanks a lot for it 🙏🏼
Very understandable expression, thanks. I was wondering why we try to y+ value lower than 1 when y+ is already higher than it until watched this video.
Very good information.
The wall function in OpenFOAM are too many. It is difficult to understand the exact form of wall function.
can you plz make one lect on that?
Thanks to youtube for recommending me this video
thanks for your lecture. its really detailed and practical!
Hello Aidan, your videos are very clear and helpful! I am working on a case in which I want to resolve the boundary layer entirely (up to viscous layer, so y* = 1). I could use some help on better understanding the "Two-Layer" model and "Menter-Lechner" model used in ANSYS (as part of k-eps model wall treatment). As far as I understand, these are actually still wall functions, adapted to work for y* = 1. Would you consider creating a video on this topic? Thanks
Excellent lecture!
Hi Aidan, many thanks for this educational and entertaining video! In the slide from 06:30 the calculation starts with u_tau based on tau_w (the wall shear stress). But isn't the wall shear stress the value we want to model with the wall-function approach? At first sight this seems to me like a circular reference - what did I miss?
Yes, it is circular! The CFD code uses iteration to calculate tau_w and u_tau.
Thank you for the wonderful explanation. A quick question : You mentioned that we already know the cell centroid velocity (u_p). How do we know the cell centroid velocity?
Maybe I mispoke in the video! Up is the main unknown in the matrix equation we are solving for the velocity (so in this sense it is unknown). However, it is a variable that we can express other variables in terms of. The wall shear stress for example does not appear in any of the equations, so we need to rewrite it in terms of Up and the other variables we know. Sorry for the confusion!
Thank you, very awesome material!
Can you put in order of your lessons? Like Lesson 1, 2 ...
Great idea! I am looking for ways to improve the channel. Perhaps a playlist might be a good idea with the lessons in order? What do you think?
@@fluidmechanics101 Yes, i think it will be very helpful for student and any begginers!
@Fluid Mechanics 101 First of all thanks for this excellent lecture. I have a query. The motivation of this lecture is to reduce the aspect ratio of cells closer to the wall but it seems we cannot reduce the number of cells as often we may need to resolve our mesh to get minimum y+. So could you please shed some light whether we have achieved our aim of reducing cell count. Eagerly waiting for your reply if u have time to clarify my query.
Nice Video Aidan..... How can i avoid the situation having (5 < y+ < 30) ?
Have a look at your y+. If it is in that range, either make the first cell height smaller or larger, then check the results again. Repeat until you are in the range you want
This video clarifies so much for me! Thanks a lot Dr. Whimshurt. One thing I am trying to understand is scalable wall functions in k-epsilon model. I understand that it is different than automatic wall functions presented in this video. It solves log-law equations by scaling them no matter which region your first cell is at. I am using CFX but assuming Fluent does the same. And for my model I am still aiming y+
Hi Mehmet, Great, im glad you found it useful! From the user guide, it looks like CFX and Fluent do the same thing for scalable wall functions. www.afs.enea.it/project/neptunius/docs/fluent/html/th/node99.htm More specifically, it looks like they force the value of y+ to be 11.25, if your value of y+ falls below 11.25, so that wall functions will always be used and you won't get viscous sub-layer resolved treatment. As you are aiming for y+ < 1, I wouldnt use scalable wall functions, as the scalable treatment will force y+ to be 11.25, which will give you the wrong answer. I would therefore go for standard wall treatment with the k-epsilon model instead, so that you can get the correct viscous sub-layer behaviour. Alternatively, If you are really concerned with correctly computing the wall shear stress and near wall behaviour and need y+ < 1 (this will depend on your application, perhaps you have an external aerodynamics application), then the k-omega SST model is widely considered to give more accurate predictions of the wall shear stress and near wall behaviour, when y+ < 1. I will be doing a video on this soon, so keep watching this space! Hope this helps, Aidan
@@fluidmechanics101 Thank you for your time. I'll be waiting for the new videos. Great work.
If I'm not mistaken, if you're aiming at y+
Yep! I agree
@@antanas9015 Yes, but there is also an enhanced wall treatment formulation in Fluent for the k-eps turbulence model. In this approach, the flow is "divided" in a viscous affected region and a fullty turbulent region. In the viscous affected near wall region , the one-equation model of Wolfstein is employed, insetad of wall functions. in this way it is still possible to solve cases with low y+ when using the k-eps turbulence model. I hope it can help:)
I want to purchase some of your lectures but the ones I need are in seperate lecture groupings. Isn't there a way to purchase slides of specific lectures that we need?
Send me an email (fluidmechanics101@gmail.com) and I will sort it out for you
@@fluidmechanics101 Okay
@@fluidmechanics101 I've made the payment. Please check mail.
Great instructional video! thanks! by the way, are the slides shared anywhere? if not, is it possible to share them?
Hi Soroush, yes the slides are available. You can download them from my website or patreon account. Just follow the links in the description of the video 😊
Wow!! This was nicely explained. You are a blessing in disguise.
I have question for you.
Towards the end of the video, you say that conventional wisdom is to have y+ ~ 1. This indirectly means that we are in the viscous sub-layer. If that is the case, then why would we use wall functions? We can resolve (i.e. numerically solve the equations) the viscous sub-layer isn't it?
Anyway, Thanks for the video.
Cheers :)
Hi Mihir. Surprisingly the reason is often cell quality. As the cells get thinner (to reduce y+ to less than 1) their aspect ratio and non-orthogonality gets a lot worse. This reduces the stability of the equations and can often lead to divergence, which can be very frustrating! So it is usually possible to get y+~1 for smooth aerofoils and wings. However for more complex geometries, the poor cell quality and high cell count forces engineers to use larger cells and have y+> 30. Despite the loss of solution accuracy, at least we can get a solution ... 😄
@@fluidmechanics101 ok. So, my question is that suppose we have made a very fine mesh (y+ ~ 1). Now, we are no longer having a "big wall cell i.e. y+>30 " as you have mentioned at the start of the video. Now, Purpose of using wall function is to reduce the mesh count by having that big wall cell. Now, since i have very fine mesh i can actually resolve the flow. Why would i use wall function in that case?
So, basically, what i think is that wall function will be used only when we are in y+>30 region ( I suppose that is what you meant in the above comment for complex geometries) . And When we are in y+~1 region then the turbulent equations will be solved and thus we won't use wall function. What do you think?Let me know. Cheers :)
@@mihirmakwana2026 Hi Mihir. Have you found an answer to your question?
Hi Mihir, sorry if you have been waiting a while for a reply. I think the key misconception here is that the 'wall function' only acts on the face of the cell in contact with the wall. If this cell has y+ = 1 then there are no modifications to the cell face and the wall flow is 'resolved'. The cells that are further away may have y+= 30 but they are not in contact with the wall (only the face of the cell in contact with the wall is affected) so no change is made to those cells. The phrase 'wall function' is misleading as it is not a continuous function but just a modification to the face in contact with the wall. As it sounds like your case has y+ = 1, then there are no modifications and you are good to go. I think my video on 'enhanced wall functions' would be useful for you. Maybe give it a watch?
@@fluidmechanics101 Actually I still don't get it Sir. So, after all, the wall functions only works when the y+ of wall-adjacent cells are larger than 30? And when the y+
I always lose it at eqn 8. I have no freaking idea where that expression for the wall shear stress comes from? Also how does it make any dimensional sense? (its m2/s2). Also should not shear stress be dynamic viscosity x velocity gradient?
Sorry there are a few errors in this talk (it is quite old)! There is a missing density in the equation for the wall shear stress. Note that: wall shear stress = density * kinematic viscosity X velocity gradient at the wall (because kinematic viscosity = density X dynamic viscosity). I think you might find it helpful to watch my more recent video on 'Enhanced Wall Functions' where I go through this again (but a bit more recently)
@@fluidmechanics101 Thank you! Sorry for the outburst, I was really frustrated what I was missing. I really like what you are doing, great videos!
Great explaination....
just one query..if I put my first cell in the log law region then the effect of viscous sub layer and buffer layer is ignored. correct?
Yes, the effect of the viscous sub layer and buffer layer are ignored and the viscosity on the cell face is increased to ensure that you get the correct wall shear stress 👍
Hi Aidan thanks for the video.. i have a question about the adjacent wall cell.. when you say is better to avoid to place y+ in the buffer layer do you mean that the centroid of the first cell has to be at a y+ greater than 30 right? Thank you
Yes exactly!
Hello sir, I am an undergraduate Mechanical engineer and am very much interested in learning CFD. I am finding this playlist extremely useful. I just want to know how to begin my career with CFD as most of the CFD engineer jobs demand a higher degree in the same...
You can always try and find a graduate engineer position and then indicate you are interested in fluid mechanics? You might be able to move internally into a CFD team in a company
Hi Aiden! Nice video and thanks for the superb introduction. I have a small doubt and wonder if you would like to share some wisdom. If in CFD y+ is way smaller than 1 (say 0.02), other than high aspect ratio, will wall function also predict wrongly?
They should be fine because the velocity profile is linear in the viscous sub-layer. So you can go as close to the wall as you want, the profile will always be linear
@@fluidmechanics101 Thank you very much for your answer!
Hi Adian Sir, Good Morning
Could you please make the videos about the mesh cell quality with respect to ICEM CFD. what it should be? How to correct it? etc.?????
The ICEM CFD quality metrics are a bit weird. I usually just focus on non orthogonality quality as this is the most important metric for CFD. But yes, i think a good video is required here 👍
@@fluidmechanics101 After unstructured meshing, generally I maintain the quality more than 0.14 but wanted to know your approach how do you check the quality of the mesh means what parameter, what values do you check for tri, quad, prism and other elements in ICEM CFD? what values should be maintained for different mesh cells?
ICEM has lots of different metrics because you can also use it for FEA. For CFD the most important metrics are non-orthogonality and aspect ratio. If you make sure non orthogonality quality is greater than 0.1 and aspect ratio is less than 100 (unless you are doing high speed aero) then you should be fine
Godd!!!! This is so good
Thanks!
God bless you. Nice work. I did not understand how the equation:8 came out. Can you please explain?
What could be the reason if the refinement and improvising the mesh still do not reduce the Y+ with reference to the reduction in the cell size?
Remember that the solution also changes, so the wall shear stress will change each time ... out of interest, how large is your y+? This is more common at higher y+ values
at 5:10 you said y+ values greater than 30 but in plot where is 30 on y+ that is x axis has logarithmic scale 10^0,10^2 can you explain me
Hi zeeshan, the y+ plot is always shown with a logarithmic scale, as it helps to see the shape of the curves in the logarithmic region. 10^1=10 and 10^2 = 100, so you want to look between 10^1 and 10^2 👍 it is the third increment along, because the increments go: 10,20,30 ... 90,100
Hi, Thanks for your videos!! these are the best I've ever seen on the web. One question! I didn't get why we need to check y+ while there are some wall functions that fit through all layers such as the one you mentioned "Spalding's wall function". It can calculate the right value regardless of the mesh size, I mean no need to worry if some cells are in the buffer layer.
Considering you want to use such function, you still need to compute y+ because Spalding's wall function is correct up to y+
Spaldings wall functipn and the other wall functions are only accurate if you have a flow that is pretty much a straight pipe or flow over a flat plate. If you have a complex flow (impingement, separation etc) then these models will give the wrong answer and you need to reduce the y+ into the viscous sub layer, as the viscous sub layer is always laminar if you are close enough to the wall. It is the only solution you can rely on for a complex flow. So the answer is: it depends on what your flow is doing 😊
@@fluidmechanics101 So, suppose I want to model a turbulent flow in a return duct (180-deg return duct) Do I need to generate grids somehow in order to get y+ in the viscous sublayer?? Even if I use enhanced wall function???
Thank you for your time
It sounds like you will be getting some pretty significant separations and the enhanced wall functions were developed for attached flows. So ... if you want the best results, better to try and get y+ in the viscous sub-layer
You said that CFD codes choose appropriate wall function on the fly, i.e. switch between linear and logarithmic behavior. But, for example, in ansys cfd codes' (cfx, fluent) manuals it is said that wall functions should never be used if y+ < 30, i.e. we should locate the first node (cell) in the log-layer. For me this means that linear (viscous) sublayer is not modeled at all with wall function approach (because we don't have places to store corresponding values), so only logarithmic wall function is used. And automatic wall treatment is automatic switching between wall function approach and direct resolving of the viscous sublayer in omega-based turbulence models, but not between linear and logarithmic wall functions. What do you think?
Its useful to remember that as the code converges, the values of y+, wall shear stress etc. will be changing all the time. So the CFD code needs to have a continuous treatment that can handle any y+ at all times. Otherwise it would suddenly get floating point exceptions, which would be very annoying! The comment that the user guides make is about the accuracy of the final solution. Once the code is converged, we have a final solution with a fixed value of y+, wall shear stress etc. For this converged solution to be accurate, you should follow the guidelines for where y+ should be. For example, y+ > 30 if you are using the k-epsilon model. Does this help?
Thank you for posting these videos. These have been incredibly helpful. Quick question, in equation (7), shouldn't you be using 'mu' (dynamic viscosity) instead of 'nu' (kinematic viscosity)? And what is u_t in equation (8), (9) and (10)? Is it u_tau, or something else?
I also noticed that. The u_t you mentioned was exactly u_tau, and the multiplication of rho was missing. The equation Aidan wanna express was tau_w=rho*(u_tau)^2
Yes!
Could someome give a hint how to arrive at equation 8?
Great video and excellent content!
Thank you! Im so glad you found it useful :)
Hi Aiden, thanks again for these very informative videos, and for your previous responses. I'm afraid I have another clarification I would like you to help with please:
1 - this is more of a clarification, am I right in saying that a cell with a Y+ of >30 refers to a cell which starts at the wall and extends into the Y+30 range, or, does Y+30 only refer to cells that are not touching the wall but are situated within this Y+ range?
2 - If it is the former (of Q1, a cell that is touching the wall but so large it reaches the >30 Y+ zone), then why make a cell that is so big that it has to use the log-law equation, and as such will not record any of the viscous sub-layer info?
3 - if it is the latter (of Q1, as in referring to cells that happen to be in the Y+ >30 zone but are not touching the wall), then how is it possible not to put cells in the buffer zone? As it would be impossible to have cells in the Y+30 zone without having cells in the buffer zone.
Ooo, also I forgot to ask, why does cfd use the linear/loglaw equations at all? It looks like the Spalding equation is superior in every way.
When talking about y+ and wall distance, we are only talking about the cell that is touching the wall. The cells above it are not considered. More specifically, we are talking about the distance of the centroid of this cell normal to the wall. You can check this in the post-processor. There will only be values of y+ computed for the cells that are touching the wall.
Usually we would always like to have y+ < 5. However at high Reynolds numbers, the cells get very thin! This can reduce their quality and make the solution unstable or too slow to solve. So y+ > 30 is only really used when we have no choice.
Im not sure about the spalding wall function. Perhaps it is more difficult to code or is less stable? I would have to look into this
Hi! fantastic explanation. Just to confirm here. When we use equation 3 calculating the yplus, the kinetic viscosity here is identical to the so-called near wall viscosity. So, with each iteration, the Up is updated first then update the near wall viscosity according to the wall function (instead of the constant value for laminar viscosity or the turbulence viscosity relationship) till at last get a convergence. Is this the procedure? And when we split the near wall viscosity into laminar and turbulence parts, does this near wall turbulence viscosity still satisfy the equation for turbulence viscosity (turbulence viscosity=Cmu(TKE^2)/epsilon)?
Hi Chang, you have almost got it! I feel like i have missed a bit of the explanation out, so here goes. y+ is always calculated with the laminar viscosity (the material property of the fluid), which does not change. You are correct that the CFD solver starts by calculating the value of Up (the cell centroid value). We then calculate the value of y+ for each boundary cell face using the value of the laminar viscosity. Once we know y+, we calculate the near wall viscosity (nut) for each boundary cell face. The reason we calculate a seperate value for each boundary cell face is that one cell may have multiple faces that are walls (see my previous video on the epsilon wall functions)! The near wall viscosity is calculated at the wall, and it is this value that is used to compute the wall shear stress on that boundary face. The turbulent viscosity at the cell centroid is not affected. This value is computed using C k^2 / epsilon, as you pointed out :) The part where the near wall viscosity is split into laminar and turbulent parts is purely for convenience in codes like OpenFOAM and is used to emphasise that the laminar viscosity remains constant across the cell and is not modified by the wall function. Only the turbulent component is modified on the boundary cell face.
I hope this helps clarify things!
I will be releasing another video in a few weeks on the difference between y+ and y*, which should help clarify things a bit more. In the meantime, check out my video on epsilon wall functions. This should help explain why boundary faces are treated individually
All the best
Aidan
@@fluidmechanics101 Thanks, Aidan. I have tried to extract the TKE, epsilon, and turbulence viscosity value at the near wall cell in Fluent, but found it does not follow the equation C k^2 / epsilon. I am not sure if I did it in the right way. Does it mean the near wall modification of viscosity is also only applied to the turbulence viscosity in Fluent (same to OpenFOAM)? So when it calculates velocity from the momentum equation, we switch to the near wall modified viscosity as the effective viscosity at the near wall cell for the coefficient of diffusion term? And is this how wall function affects the wall adjacent velocity Up?
@@fluidmechanics101 I recognized that in Fluent, they use ystar instead of yplus. So I look forward to your new video. Thanks!
Yes you are correct! I think the difficulty might be having is that a near wall damping function is applied in the k - epsilon model ( mut = rho f C k^2 / epsilon, where f is a damping function which varies between different versions of the k - epsilon model) Have a look here: www.cfd-online.com/Wiki/Low-Re_k-epsilon_models
The k omega and k omega SST models dont have this damping function. This is why they are often preferred for wall bounded flows. Also, it is always difficult to know exactly what fluent is up to, as the source code is hidden ... but your explanation is exactly what OpenFOAM does :)
Your channel is great ❤️
Thanks Mostafa!
A question bothers me: If I set the no-slip boundary condition on the wall, and I set the viscosity to be 0 at the same time, would the boundary condition be slip? If not, what the physics looks like ? Thank you very much!
Yep, you would have a slip boundary
@@fluidmechanics101 Thank you very much for your reply! For no slip condition with 0 viscosity: the first layer of fluid still adheres to the wall, but the second layer of fluid can move freely. However for slip condition with ideal fluid: the first layer of fluid can move freely. Based on this, I still don't understand why these two situation is equivalent.🤣🤣🤣
Surely with 0 viscosity, the fluid does not adhere to the wall in the no slip case? Physically it is the action of viscosity which sticks the fluid molecules to the wall, so zero viscosity is equivalent to the fluid not sticking to the wall
@@fluidmechanics101 Thanks a lot!😅 Hope that OpenFOAM would run as you suggest!
What is u_t in equation 8?
Typo. It's meant to be u_tau (the friction velocity)
@@fluidmechanics101 And how do u get Eq. 8? I mean if I enter the U value using eq. 2 and 3 I end up getting a different result.
What does it means y+ equal to one? That the first mesh reach that value?
Y+ is the distance of the cell centroid from the nearest wall. It is a dimensionless distance, so a y+ of 1 is smaller at higher Reynolds numbers.
Fluid Mechanics 101 So the value is calculated on the first cell from the wall (in the centroid)?
Yes!
Thank you so much! I'm also watching other videos.
I still confuse the difference between wall function and dumping function in k-e model... Both are used for treating near wall characteristics. what's the critical difference?
The key difference is that wall functions are applied to the faces of the cells in contact with the wall. Damping functions are applied to all cells, even the cells that aren't in contact with the wall 👍
@@fluidmechanics101 I see! Now I understand. Thanks for quick and cordial reply.
It is a really helpful video channel. I also introduce to my friends :)
Hello Aidan,
First of all I would like to thank your for your effort with making such excellent videos. However, I am not sure about the correctness of the relation in the outer layer (log-law region). When I equate both of the expressions, I am getting a different value for the intersection, see time 10:20. Based on the formula and constants (kappa and E) you use for the log-law region, I am getting smaller value of this intersection, i.e. below 4. Am I doing something wrong? Could you elaborate more on this issue? Thank you in advance for your response!
Hi jack, to get the intersection point you will need to solve this equation numerically ie.
Y+ = 1/kappa log(E y+)
Rearrange:
Y+ - 1/kappa log(Ey+) = 0
Take an initial guess of Y+ = 11
E = 9.793, kappa = 0.4187
Solve using bisection/newton-raphson
Y+ ~ 11.25
If you are interested, i go through the full derivation and explanation in more detail in my 2nd fundamentals course, which you can get from my website, udemy or skillshare 👍 but im sure you have just made a small error somewhere
@@fluidmechanics101 I see your point, but in my opinion we seem to be talking at cross purposes. I think I figured that out. To get the correct result, you need to use the natural logarithm "ln" rather than the common logarithm "log" with the base of 10. I have been taught all my life that log(x) usually means the base 10. It is common practice that in some pieces of software the term log(x) means implicitly ln(x) with the base of e, so it needs to be the reason for this misunderstanding. I am glad we have resolved it. Thank you for your videos and stay blessed!
Amazing playlist to learn CFD! Add compressible flows too?
Coming soon 🙃
@@fluidmechanics101 Hey, thanks for the response. This series would be complete with compressible flow solver videos too. I'd surely recommend this to anyone learning CFD.
Also, I have a doubt regarding y+. I am trying to simulate an incompressible turbulent flow and it was given in previous research to have Y+ < 1 in the Boundary layer. How do I ensure this during the mesh generation itself? Should I simulate a flow first, plot y+ and go about refining the mesh or is there an empirical relation that can be used as a good first estimate?
Yep, thats the one 😊
Hello there! Many thanks to the channel and everyone there. As fas as I understand, in case of turbulent flow, with a good mesh with growth rate near the walls, if yoy achieve y+ value near 1, you don't need enhanced wall functions. Do I get it right? Thanks in advance.
Yes correct 👍
i dont get (at slide 15) how we are allowed to simplify Up, which in one case (eq.9) is the value of the velocity at the first cell if we suppose its y+30. Anyone has a clue?
The trick is that we aren't specifying the value of Up. Up is calculated by solving the momentum equations. We are actually modifying the viscosity on the near wall face, which is then used in the solution of the momentum equations during the next iteration
@@fluidmechanics101 Thank u very much. i also checked the reference you gave at the end of the video and now i think i really grasped for the first time how this kind of wall functions work (at least the main part of it!). Thanks
Hello,
Thanks for the Video. Its explain much and there are things that I didn't understand before, but now they look a little bit cooler.
Also, I may have questions that, even if that look clearer, I fail to understand it:
1- the equation (8). I tried to recover how you did the derivative, but I didn't find the same things. If you can send me a link where I can read it or explain it here, that would be great.
2- From that page, I think I understood just the half of what you said. I mean, I heard the explanation clearly, but I didn't understand. And I REALLY want to understand as clearly as possible as you do
3--I'am using a cfd Software for a while now, but what I find difficult, is to put the right value of y+. I do understand that at the beginning we don't know the value and that the value change during the simulation. I saw that. The problem is "HOW DO I CORRECT IT"?. Read somewhere that you change it at the end of the simulation. But it's complicated, since I'am evaluated the drag of the boat, and it's taken 4 to 6 hours to run one simulation. So my question is: how I may ensure the value of y+ before letting the simulation run until the convergence?
Thanks in advance if you find time to answer me and sorry for my english if it is not good enough.
Hi Brice! So glad you found my video useful. In answer to your questions:
1) you can find the derivation in the Jonas Bredberg paper (link 4 in the description of this video) and you want equation 75 and 76. The trick is to rearrange for utau, rather than differentiate.
2) I am thinking of doing a follow up video to explain this in more detail, as i have had lots of comments! What do you think?
3) To reduce y+ you have to go back and refine your mesh. The only way you will know y+ is after your simulation, so the process is iterative: make a mesh, run computation, find y+, remesh, repeat etc. However, you can make this process quicker by having a good guess for y+ before you mesh. There are some tools online which can help you with this. Try googling ‘CFD online y+ calculator’. There is a really good tool which can help you guess y+ before you run your simulation. Hope this helps! Aidan
@@fluidmechanics101 Aidan First of all thanks for this excellent lecture. I have a query. The motivation of this lecture is to reduce the aspect ratio of cells closer to the wall but it seems we cannot reduce the number of cells as often we may need to resolve our mesh to get minimum y+. So could you please shed some light whether we have achieved. our aim of reducing cell count. Eagerly waiting for your reply if u have time to clarify my query. Also requesting you to post more such lectures.. it is fortunate that i have found your channel which is very helpful.
Hi Siva, i think i might not have explained it well enough in the video, so here goes! The optimum mesh is always a mesh with all cubes (aspect ratio 1) that are aligned with the flow direction. However, if we were to use all cubes, the cell count would be really high (particularly at high Reynolds number). So what we do is note that the gradients normal to the wall are steeper than the steeper than parallel with the wall. So we increase the aspect ratio of the cells and stretch them out. However, if the aspect ratio is too high (say over 1000) then the computations start to become unstable. So we would like to make the wall adjacent cell (which has the largest aspect ratio) larger in the wall normal/y+ direction. This will reduce its aspect ratio and make the computations more stable. In addition, it will also reduce the cell count as all the other cells will be the same size or larger than this cell. I hope this makes a bit more sense now 😊 and yes, i have lots more videos to come, so stay tuned!
@@fluidmechanics101 thank you very much for your time and reply...
thank you man ♥
Thanks 👍🏼
Great video
Thanks Ali!
to be honest I lost it in the middle
first
Well done useful video 👍👍
Great! Glad you found it useful
Thanks Harry Potter
🧙♂️✨
Clear, clean and practically sound explaination! Amazing work, keep it up. Please do make more videos explaining the basic terms as well👍👍 such as RANS, NS equations etc. would love to see your approach!
I have more than one thing to ask! In the "What value of y+ should I aim for?" section, you said that we should avoid placing cells which have a value of 5< y+
Hi Osman, you are correct. We only need y+ to be either < 5 or between 30 and 200 for the first cell close to the wall. All the other cells are computed by the cfd solver using a linear variation of variables across the cell.
If you are doing a study related to species mixing which is more of a phenomenon in the turbulent flow region there you mostly can go with first cell height that can lie at y+>30 and you can use k-e turbulent model without activating wall functions but if you want to solve for lift on wing using k-e turbulent model then it is a good practice to put first cell height at y+
Yep! 👍
All credits goes to Fluid Mechanics 101, my knowledge on turbulence models was like raw metal it is your lectures that polished it
Please keep spreading knowledge
Hi Aidan. Great video a thank you a lot for your simple and clear explanation :).
I have just one remark. You should write tau=rho * nu * du/dy. Or you can just divide the shear stress by rho. Also the dimensions of the two sides of the equations would be incorrect if you don't include rho.
Anyway, great video!:)
Yep, completely agree 👍
congratulations for your work. Each of your presentation is so helpful and comprehensible. However, how is Eq. 8 derived?
Yes I don't get it either. The derivative of the log should be 1/y and not 1/log ?
Yes, I found exactly the same thing when I did the derivation. If you watch my video on enhanced wall functions, I think I do a better job of the derivation there
@@fluidmechanics101 Will do thanks ! Excellent work btw !
That's a very clear explanation of something not so obvious!
The thing is, in CFD, a lot of cases are complex, with detachment/attachment, acceleration/deceleration etc... This will inevitably lead to 5 < y+ < 30 in some regions.
Second thing: When we talk about y+, do we talk only about the first cell height? Because even with a nice y+ = 1, the 3rd or 4th cells might be in the buffer layer. That is a problem or not? Didn't get this.
Hi Lili An, yes you are absolutely correct. CFD cases are complex and and y+ may be in the region of 5 < y+ < 30 in some places in the mesh and < 5 in others. Usually we adopt a compromise and try and get y+ < 5 in the main area we care about. For example, when simulating an aerofoil/wing we usually try and get y+ < 5 near the trailing edge of the suction surface, as this is where seperation inception begins and will have the most signifciant affect on the solution. This normally leads to y+ > 5 near the stagnation point (and hence not an accurate solution), but we dont care about the solution as much here, as the integrated lift and drag are more significantly affected by the suction surface boundary layer.
2) Yes you are correct, the second and third cells may be in the buffer layer. But this is normally fine because the variation across the cells in the mesh is linear and the CFD solver compute the rest of the profile through the boundary layer for us. Conventional wisdom is to try and have 10 cells through the thickness of the boundary layer (a growth ratio less than 1.2) with a y+ < 5 for the 1st cell and this is normally fine to get an accurate solution.
As always, check your solutions with a mesh convergence study, as every case is different! Hope this helps
@@fluidmechanics101 So, let's clarify more. Wall functions are used to compute values at the first near wall mesh node only and values at all other nodes are solved by the solver from the flow equations. Am I correct? If so, then it's not optimal approach IMO. Or do wall functions are used for all mesh nodes within ranges y+
Yep, you are correct. The cfd code only uses wall functions for the cell closest to the wall (often called the wall adjacent cell). The rest of the mesh will be solved by the cfd solver by assuming a linear variation across the cells. So ... you will still need a relatively fine mesh near the wall as the gradients are steep. This is why yo should try and use a growth ratio of 1.2 or lower normal to the wall to make sure you have enough cells :)
@@fluidmechanics101 So why should I put enough cells to capture boundary layer?If I just focus on wall shear stress then one layer will be enough?
Well spotted! You still need enough cells to capture the velocity profile (and other gradients) away from the wall. Remember that the variation across cells is linear, while the velocity profile is definitely non linear! So you need enough cells to make the linear approximation sensible. People usually advise 10 cells through the boundary layer. However this is not useful to us when we are making a mesh .... so my colleagues and i tend to find that a growth ratio of 1.2 normal to the wall is about right to get the right number of cells through the boundary layer. For external aerodynamics applications where you really need a good answer, i would drop this to 1.1 or even 1.05. I hope this helps!
This is an excellent video. You explain far clearer than my proffesor.
saw your video for the first time. Excellent presentation and was truly helpful. I'm glad that you gave some references in the description.
Great video. I got a bit confused in the part "interpolation in CFD between cell center and its faces is linear", but I got the point, it is often, but not strictly linear. Thank you for the high-quality content!
Thanks for this content! Somehow you made everything very clear in the span of 20 minutes :) It is rare to find someone in this field which is able to explain these topics in such a simple manner.
Thanks Peter!
Super useful and clear.
I paid 13 bucks for your cfd fundalmentals course and you just put this for free here :(.
Ok, I gess I don't gonna buy the 3° part. jajajaja
Than you!
I'm glad you like the content. Generally the courses have a lot more detail and examples in them than the TH-cam lectures, so they are great if you want to dig into the matrices and the detail. The TH-cam lectures are best if you are looking for a good overview of a topic and trying to work out what buttons to press in ANSYS or OpenFOAM 😃
great video / guide thanks mate!
Great! Glad you found it useful
please suggest a readable book on turbulence modeling to understand turbulence theory and its implementation using CFD code.
This is a difficult question, as there arent many good books on turbulence modelling at all! I would suggest ‘turbulent flows’ bu stephen pope. It is quite an advanced book that goes through turbulence theory in detail and should have eveything you need. The application to CFD however, is limited in this book and i would read Hrvoje Jasaks thesis instead for this 👍
@@fluidmechanics101 Thank you so much for your response.
The video is awesome thank you very much ...... I have 2 questions please
1) The curve of the log low region makes a nonlinear curve from the wall to Up, from where did you know that this nonlinear curve is going to have the right slope of the wall shear stress (I think the green line should reach the origin to satisfy this but in the graph in the video it doesn't reach the origin) is that right ?
2) when you equated the 2 equations of the linear and log low region you cancelled "Up" in the left side with the right side although "Up" of the linear equation should be different from the "Up" of the log low equation to equate them right?
Hi Hatem, great questions! Im going to have to get back to you on these as im quite busy at the moment. Glad you found the video useful!
Hi Hatem, in answer to your questions, it is important to remember that it is the product of the viscosity and the velocity gradient that gives the wall shear stress. As the variation across a cell is linear, the velocity gradient will be incorrect when we are in the log law region. But this is ok, as long as the product of the (now incorrect) velocity gradient and viscosity gives the correct wall shear stress. This is why we modify the viscosity :) the green line doesnt need to reach the origin, as it is the gradient that we care about. For question 2, remember that it is the CFD solver that calculates the value of Up, so we assume that we know this and it is a constant. Remember remember, we are modifying the viscosity here to get the correct wall shear stress, not computing the value of Up. I hope this helps! Im thinking of doing a follow up video to clarify these points, what do you think? Would that be helpful? Aidan
@@fluidmechanics101 Yes plz do
"Thank you for your awesome video! could you please tell me which y+ in In OpenFOAM, should be between 30 < y+ < 300? Is it the minimum, maximum, or average ?
It is the y+ in the region that you care about (or affects your solution the most).
For example, on an aerofoil it is the y+ on the trailing edge of the aerofoil which has the greatest effect on the separation point. You care less about the y+ near the stagnation point at the nose of the aerofoil, as this has a smaller effect on the drag calculation.
So you need to use some engineering judgement. Have a look at your geometry and try and deduce which region in the most important. If you are unsure, you can always test it by creating a few different meshes and see what effect it has on the results
That was really informative and explained in a Lucid manner. Great work.
Aiden, I had a doubt,
Till what value of y+ is the wall function to be applied for in the mesh?
Ypu have mentioned that for y+ > 30, use wall functions
But till what y+ value is that to be used, above which is the resumption of normal CFD interpolation?
This will depend on the CFD code you are using. Often there is a hard switch between the viscous sublayer and log law at y+ = 11.25. It's really worth checking the user manual
y+ and u_t require wall shear stress to be known which is part of solution. As we don't know wall shear stress yet Equation 9 is an implicit equation. So, there must be some kind of iterative approach required to solve it unless there is another way to estimate y+ and u_t. You didn't explain how it is done I think.
Yes we'll spotted. If you choose y+ based on wall shear stress, rather than turbulent kinetic energy you need iteration. You can either just take the wall shear stress from the previous iteration of the SIMPLE algorithm itself or you can do the iteration locally. You can find this iterative equation either in the OpenFOAM source code, or checkout the book by Weller and Greenshields 'notes on computational fluid dynamics'
Thank you so much for your wonderful explanation! Your explanation is excellent, and I have gained a lot. However, I don't understand how equation(8) is derived and what ut in equation(8) represents?
thank you very much
Thank you so much! 😀
Hi Aidan, thanks so much for the video and lectures. It is really awsome and very helpful. I would like to ask you ine thing if I may. One thing is not clear to me that, how this calculated effect of the wall sheer streas is then fed into the momentum equation. Is it done by modified turbulent viscosity, which is then used in the momentum equation? So that the velocity at the first grid can take into account the effect of the (total) boundary viscosity?
I appreciate your help in advance!
Yes, that's correct. The modified viscosity is accounted for in the summation over the faces of the cell when calculating the diffusion contribution to the A matrix of the momentum equation
@@fluidmechanics101 Thanks a lot for the clarification!
GREAT ! MERCI !
May I kindly suggests you to make your explanations understandable to newbees 🙏
Yes, I understand that my talks can be a bit too much for newbies. I am going to make some dedicated videos for beginners soon!
@@fluidmechanics101 thank you soo much for your acknowledgement
Exactly what I need. Thanks!
Hi Aidan, I really appreciate these high-quality videos and I love how you bridge the gap between coursework from schools and commercial CFD codes. Thank you and keep up the good work!
In equations 7 - 11 (slides 13, 14, and 15), why is it nu (kinematic viscosity) and not mu (dynamic viscosity)? Is that an error or am I missing something?
Thanks Kevin 😊 the wall functions are always written in terms of nu (kinematic viscosity) and alpha (thermal diffusivity). To get back to mu (dynamic viscosity) and k (thermal conductivity), just multiply by rho (density) and rho cp (for temperature). Maybe check out my vid for temperature wall functions and this will make more sense 🙃
@@fluidmechanics101 Aidan, I have watched that video as you have suggested and it looks like equation 7 in that video has a rho (density) term in front of nu (kin. visc.). I believe you are missing a rho term in equation 7 of this video.
@@xGenezhi Thanks for pointing this out.
sir thanks for giving all these important information for us
hello I am korean cfd user
I am pleasure to see your you-tube and it make me to help
I have a question about wall-function
you said that "Always avoid placing y+ in the buffer layer (5 < y+
Yes, you are correct. The automatic wall treatment does improve the accuracy a bit (compared to standard w f with switching) in the buffer region but it is still not very accurate and you should try to use either y+ < 5 or > 30 if you can 👍
@@fluidmechanics101 Thank you for your attention
It is helped me to be assured about "automatic wall function"
Could I more give some questions?
1. if I not use "wall function", ansys's manual recommend y+ < 1.
so for it, recommend to make more than inflation layer 10.
but I am not sure if it's right.
So, I think it need mesh dependence test about how inflation layer make instead of manual guide. I am wondering your opinion
2. I learned my superior that y + is not important in case of "airflow analysis" (such as analysis of ventilation inside the house, outdoor airflow etc) because force arise for velocity profile around wall is weak compared to total airflow force so it not much impact
I also not sure if it's right. I also wondering your opinion
thank you for reading my questions.
Your help is a great strength to me.
A simple answer to both questions would be: yes you should always try and do a mesh dependence test. You can try different values of y+ and different numbers of layers and see how much it affects the solution. The general guidance that people give (around y+ and number of layers) is useful as a starting point but then you should try it for yourself. For point 2, I have often been given vague advice like this from supervisors / advisors / reviewers over the years. It is often difficult to understand what they mean and you can't really argue back. The best thing you can do is run your own tests (compare different values of y+ for example) and then show them the results. You can then let your results do the talking for you 😄 this is a very useful trick for addressing review comments as well. Better to discuss the results than your thoughts / ideas / what you saw on s TH-cam video ....
@@fluidmechanics101 Thank you for reply my question~^^
Thank you so much, very clear and on point explanation
Great tutorial, thank you for the time you invested to share your knowledge!
Thanks Brandon, much appreciated 😊
Awesome explanation. Great. Thanks a lot.
New subscriber here! Great slides!
Great video! Thank you!
Thanks Aidan for this video. In summary, velocity profile is computed as piecewise linear in CFD due to values at cell centroids. However, turbulent velocity profile is non linear. In order to bridge the gap, wall functions are used. For y+
Yes! 100% correct