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Renato N. Elias September 25, 2005 22:54

Drag and Lift in 3D flow around a cylinder...
Hello all,

It's my first time running the benchmark problem of the flow around a cylinder in my PhD's program. The program is based on the finite element method using tetrahedra elements (hence three dimentional) and I'm getting confusing about how do I go about computing the drag and lift forces. How could I compute shear stresses (due the drag forces) on the cylinder's wall if this wall is assumed to have no slip boundary conditions (ux=uy=uz=0.0)? The shear stresses would be null but it seems wrong for me...

any hint?

thanks in advance

Renato N. Elias

Praveen. C September 26, 2005 00:55

Re: Drag and Lift in 3D flow around a cylinder...
Note that the gradient of velocity is zero only along the wall but is not zero in any other direction.

jean-marie September 26, 2005 04:36

Re: Drag and Lift in 3D flow around a cylinder...
The drag is due to the normal gradient of the tangential velocities at the wall (wall shear stress), but mostly to the lower pressure on the downstream face in the detached flow region (integration of the pressure on the closed cylinder surface). This is very dependent on the angular location of the separation (this point oscillates with vortex shedding).

Mani September 26, 2005 13:01

Re: Drag and Lift in 3D flow around a cylinder...
I don't want to appear too critical, but if you pursue a PhD in fluid dynamics, this is really high time to review some of the basics. I would expect my undergraduate students to know this, not to mention a PhD student.

Renato N. Elias September 26, 2005 13:36

Re: Drag and Lift in 3D flow around a cylinder...
"Thanks a lot for your help"... I think, I should ask your under graduate students and they could be more helpful for me than you.

I was thinking that this forum should be used to discuss topics related with CFD...

If my question don't worth your atention please call one of the your students to help me.


ps.: Where have I told you that I had a PhD in Fluid Dynamics? I'm a PhD student in HIGH PERFORMANCE COMPUTING, so I'm still learning about CFD, parallel computing, solvers, preconditioners, etc...

Mani September 26, 2005 13:41

Re: Drag and Lift in 3D flow around a cylinder...
Nevertheless, take my friendly advice and read a textbook to get an introduction to fluid dynamics, if you will be dealing with fluid dynamic problems. It will not hurt you.

Renato N. Elias September 26, 2005 13:50

Re: Drag and Lift in 3D flow around a cylinder...
What do I have doing here?

I was just reading about the subjetc (or anybody that could take me a short cut) when you have posted your "helpful" message.

We are not struggling to know who knows more about anything. We are trying to help ourselves. I think so.


Renato N. Elias

Mani September 26, 2005 16:23

Re: Drag and Lift in 3D flow around a cylinder...
Dear Renato, have you not been helped by Praveen's and Jean-Marie's posts? If not, I cannot add anything except to suggest that you consult any fluid dynamics textbook for more detailed information on the subject, and that's what I suggested. No need to take offense as none was intended.

Renato N. Elias September 26, 2005 17:00

Re: Drag and Lift in 3D flow around a cylinder...
Dear Mani, you should think more before writing what you have written. Yes, I've taken your answer as an offense because I think that there isn't any basic question that doesnīt worth attention or a polite answer. BSc, MSc, PhD or any other "God of the knowledge" has your basic doubts about many things. We're always learning anything... and itīs impossible to know everything about a so huge topic as CFD is. Or do you know every basic detail about, compressible/incompressible flows, laminar/turbulent flows, Newtonian/non-Newtonian, Finite/diference/volume finites, etc..., etc..., etc... !?

Even so, I must be very grateful to Praveen's and Jean-Maries's answers. They've respected my basic doubt.

I know what equations are employed to compute the drag and lift forces, there are a bunch of books and papers with these equations. I was only in doubt about how to compute shear stresses in a surface with no-slip boundary condition, just it.

Best regards


zxaar September 26, 2005 20:07

Re: Drag and Lift in 3D flow around a cylinder...
well said :)

zxaar September 26, 2005 20:22

Re: Drag and Lift in 3D flow around a cylinder...
if you have access to peric's book, in its chapter complex geomteries it is nicely explained. if you do not have access to book please let me know.

Mani September 26, 2005 21:14

Re: Drag and Lift in 3D flow around a cylinder...
I do see your point, and you certainly deserve an answer to anything you ask. I saw that you already got the correct answer from others, so all I wanted to do is give a comment. That comment wasn't really meant to help you with this particular problem, just to give you some basic advice and criticism. When I am new to a field, the first thing I do is grab a book and get some basic understanding before I delve into it. I didn't need to answer your question, because you had already been helped, so I didn't worry about that. Instead, I was just stunned by the question, because it's actually not even about CFD, just elementary fluid dynamics. Let me explain why I say that. Drag is a force that acts on your cylinder in the direction of the free stream velocity. This force can be considered as consisting of two components: one from the pressure distribution over the cylinder surface, and one from the shear stress distribution over the same surface. In essence, it's all about stress, pressure just being the normal stress on the surface. By shear stress we mean those stress components which are tangential to the surface. They are determined by viscosity and velocity gradient normal to the wall. The linear relationship between shear stress and normal velocity gradient is a well-known (among fluid dynamicists, physisists, engineers and others) contribution by Sir Isaac Newton, and it is usually seen as the relation that actually defines viscosity (which, after all, is just a model for molecular interaction) for Newtonian fluids. I suppose my reaction was so strong because I could not imagine anyone touching CFD without being familiar with this basic law, fluid dynamicist or not. Anyway, if you do understand that the velocity varies in the normal-to-wall direction, and this is the gradient that matters, then your question doesn't pose itself. As you see, this has nothing to do with computational issues (CFD), and there is no problem whatsoever with no-slip, because it's the normal velocity gradient that's associated with shear stress. No-slip just means that the velocity itself (not the normal gradient) is zero on the surface. My citicism was based on the assumption that you asked the question because you really had no clue, and I guess that assumption was wrong, based on your explanation. To give an analogy for high performance computing: Not to know Newton's shear stress in fluid dynamics would be like trying to optimize your code for parallel computing without knowing about Amdahl's law. I am sure you understand my surprise, so forgive me. If you did know all this and just didn't trust your textbook I am sure glad to confirm that you were right. Just don't take criticism so emotionally, or it's no good for you.

Now let me also mention something else to make sure you know what physics you are dealing with. You are right to worry about shear stress, because shear stress does contribute to the total drag. However, in your case of a blunt body, that contribution is actually relatively small (shear stress almost doesn't matter, here). I hope you understand that the major cause of drag in this case is given by the normal stress, i.e. the pressure distribution with high pressure in front of the cylinder, and low pressure in the wake. You also should know that this flow is highly unsteady above a certain Reynolds number (about 47) based on the cylinder diameter. You'll need to know that in order to make sense of the drag. For example, solving the steady equations in the range of vortex shedding will not give you the correct (mean) drag.

Renato N. Elias September 26, 2005 22:09

Re: Drag and Lift in 3D flow around a cylinder...
Thanks a lot for your hint zxaar! I have this book and I've just found what I was looking for all day long.

Best regards


zxaar September 26, 2005 22:29

Re: Drag and Lift in 3D flow around a cylinder...
i have a phd thesis i wish to send it to you, please give me your email id where i can post it. Its very much relevant to your field of interest, just have a look.

Renato N. Elias September 26, 2005 22:40

Re: Drag and Lift in 3D flow around a cylinder...
Thanks again for your interest in helping me with this question being it basic or not.

You may send me messages through

Sincerely grateful


Renato N. Elias September 27, 2005 06:05

Re: Drag and Lift in 3D flow around a cylinder...
For whom that could be interested in this topic I've found 2 nice papers discussing the subject:

L. Baranyi, "Computation of Unteady Momentum and Heat Transfer from a Fixed Circular Cylinder in Laminar Flow", J. Comput. and Appl. Mech., 4(1):13-25, 2003

L. Baranyi, "Lift and Drag Evaluation in Translating and Rotating Non-Inertial Systems", J. Fluids and Struct. 20:25-34, 2005

The reference suggested by zxaar is very good too.



Renato October 4, 2005 11:32

Re: Drag and Lift in 3D flow around a cylinder...
I've got so disappointed and astonished by the answer that I've got for my question that I've been asking myself what happened...

I think I was not so well understood as I was expecting because some of the answered arguments were about that my question was not related with CFD but with the basics of fluid dynamics.

After researched a bit about the subject I've found several articles talking about the computation of drag and lift forces in unstructured discretized schemes (I think it's really related with CFD!!!) and I was feeling obligated to explain my question better.

let me try to explain it with an example:

imagine a very thin plate immersed in a fluid flow. If this plate is parallel to the fluid flow we will have drag force only due shear forces. Suppose that you are using triangles in a finite element scheme to discretize and solve your problem, thus you will have triangles with 2 or 1 nodes touching the plate and these nodes will have null velocities due the no-slip boundary condition. You will not get non null velocity derivatives if you compute the derivative at the baricentre of the element, thus the derivatives will be "averaged" with the node out of the boundary (MY QUESTION WAS ABOUT IT AND NOT ABOUT WHERE THE DRAG AND LIFT FORCES COME FROM). Of course this problem becomes much more complicated when you're dealing with complex geometries in 3D computations employing tetrahedra. In fact, I've found two ways of computing drag and lift forces: one by approximating the forces with the equations easily found in CFD textbooks and another one using the discretization scheme itself (I'm still reading about this...) where the former is less accurate.

For those interested by this topic I suggest the following articles where this subject is nicely explained:

Tabata, M. and Itakura, K., A precise computation of drag coefficients of a sphere, The International Journal of Computational Fluid Dynamics, Vol. 9, pp. 303-311, 1998


Tabata, M. and Tagami, D., Error estimates for finite element approximations of drag and lift in nonstationary Navier-Stokes flows, Japan Journal of Industrial and Applied Mathematics, Vol. 17, pp. 371-389,2000.

"...I think that some answers shouldn't be posted here because they discourage the participation of those people that are looking for any kind of CFD related help..."

Furthermore, if you think that the question you're reading is not well posed, please ask for the poster to explain it again and better before posting useless messages.

remember that you are in an open and international forum where not everybody is fluent in english.



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