If you linked your numerical solutions, I would suggest to check carefully the velocity field at Re=20 as I see a pattern of streamlines that does not seem symmetrical to the center lines. You are solving a laminar flow and you should get very accurate solutions. In this range the drag coefficients simply decreases as the Re number increases.

Thanks Filippo for your reply

As I checked, ther results are accurate, because I validated them with literature. the figures are plotted not very accurate but the solution is correct.

And what about the resulting Cd at Re =10 and 20? Are you sure that the upper and lower boundaries does not affect the solution?

Yes. I have validated them with available data. You can check the CD diagram in fluid mechanics book (like M. White) that is mentioned CD=2.4 for Stocks relation (CD=24/Re) that has a little error with the exact data. my CD is 2.91 and I think that is correct.

Also I have investigated the effect of upper and lower boundaries.

Do you think that my results are wrong according to physics? i.e. CD sohld not be decreased with Re?

Stokes law 24/Re is quite far from real solution at Re=10 and 20 and is applied for 3D body, see Fig 7.16(b) in White. Is your problem 2d?

Yes. I mentioned Stokes just for being sure that the results are in a correct limit.

my problem is 2D and the results are similar to Fig 7.16(b) in White

Show your results - do you see Cd which is not decreasing? what is your pressure if it's not like in the cited references?

Cd decreases for a simple reason that the drag force, which is increasing of course, is normalized by V^2 which, in turn, is increasing stronger (or faster).

We know that separation occurs due to positive pressure gradient along the flow and transition occurs due to increase of Reynolds number beyond a critical value. Now on a bluff body separation occurs when pressure forces that overcome the frictional forces do not have sufficient inertia to keep the boundary layer attached on the wall. At the same time when you increase Reynolds number transition occurs simultaneously and that causes the turbulent flow to happen. So this means you will have an active boundary layer which tries to reattach the separate streamlines to the surface and this causes to decrease the drag coefficient at that point.

Dear Mohsen, the topic is just for laminar flows, Re=10 and 20 implies a steady laminar 2D flow pattern.

I agree with Alex Liberzon, please show the details of your numerical solution

Dear Alex

Thanks for you reply.

You can see my P distribution around cylinder in a special case!

http://uupload.ir/files/x66_p-teta_in_re=10,20.jpg

see the trend of P distribution. I expected to see a constant value for P after separation like literatue:

http://uupload.ir/files/kk4h_tubes_crossflow_over_fig5.gif

2nd point: you can see the pressure drop (between rear and front stagnation points) is decreased in Re=20 rather than Re=10. So CDp should be decreased! this is against what I expected: When you increase Re, separation point should be place in lower angle, so pressure drop should be more and CDp should be more!

about your last sentence I should tell you that I changed the Re in 2 cases Re=10 , 20 just with changing viscosity and inertia (0.5*rho*V^2) is the same between these two cases.

Regards,

Ali

Dear Ali Minaeian,

you plot of the pressure distribution does not extend along a sufficient region behind the cylinder, you should extend the range up to the outlet section

Dear Filippo

Could you plz explain more?

I have plotted P distribution on the cylinder surface from(*) teta=0 to teta=180 (degree). If I extend it we will come back from teta=180 to teta=360 (=teta=0). and you can see that in teta=180 to teta=360 the plot is similar to teta=0 to teta=180, just it's vise versa!

(*) teta=0 is on rear stagnation point.

No, I mean that I want to see the plot that after theta=180 is done along the fluid region (centerline), not along the cylinder. I want to see how is the behaviour towards the outlet, if the pressure increasing still continues.

Ok

I plotted now. this is the pressure (ono-dimentioned with inertia(0.5*rho*V^2) on center line (y=0) from cylinder surface (x=0) to right hand boundary (x=25*D).

You can see that P* is increasing at first and then would be constant.

This figure is plotted in Re=20.

http://uupload.ir/files/n4ps_screenshot_from_2018-08-09_11_25_42.png

If I understand correctly the plot, you recover totally the p_inf value (Cp=0) along the centerline far from the cylinder. I never explored personally such a case at such low Re number and I would expect that the relevant viscous effects would introduce a more relevant pressure dissipation. What about your BC.s? Have you already compared to other published results for pressure and velocity?

here is a solution at your Re numbers

ftp://161.24.15.247/Andre%20Fernando/AED-25/SU2/TestCases/navierstokes/cylinder/Numerical%20Solutions%20of%20Flow%20Past%20a%20Circular%20Cylinder%20at%20Reynolds%20Numbers%20up%20to%20160.pdf

I have investigated what you mentioned it. I thought that viscous force had to be dominant. but this is for lower Re like 1.

Yes, I have investigated 3 BCs and all of them gave me the same results (a little sifference).

What about the extension of the domain, how many diameters? Are you sure the computations run until a steady state is reached?

I was very careful about these numerical aspects. Yes, I run the problem for some wider domains and results changed very small. upper and lower boundaries are in a 20D space, left boundary is in 15D and right boundary (outlet) is in 25D.

Yes . I'm sure that the problem reached to steady state.

Well, I think that something in your setup is wrong..the inlet profile is uniform? lateral BC are based on free stream conditions? have you tried to compare your solution at least at Re=1 and get a result comparable to published ones?

Of course. I compare my results in many Re:

Re=1, 5, 10, 20, 40, 46, 50, 60, 100

Even I checked CD, CL, St, wake wide, wake length and all of them are in agree with a couple of papers.

So can we conclude that numerical aspects are passed?

Not completetely, as you are using integral quantities. You should have also a pressure distribution that correctly accords to the reference solution. From your pressure solution I don't see a good accordance. Could you plot the pressure distribution of your solution at Re=1 superimposed to a published one?

Yes I can but I don't have a published paper in which the P distribution is plotted. if you have please send it to me to compare my results with that.

There are a lot of paper you can find in literature. I attach just one reporting the pressure distribution at Re=2. Compare to it, check that your profile matches the behaviour

Dear Filippo

I added the P diagram of this paper to my plot. There is a difference between my results and paper. Also it's Cd and stagnation angle in some Re are different from mine. Of course I know some other papers that their results are very similar to mine.

http://uupload.ir/files/a9xz_export.jpg

Method for time-dependent simulations of viscoelastic flows: vortex shedding behind cylinder - by Paulo J. Oliveira

The paper you cited illustrates only the case Re=100 for a Newtonian flow. In the other cases viscoelastic effects are considered

Yes, This was just an example. There are some other paper like the reference paper of Oliveira research make me sure that the accuracy of results are good.

Z. Lilek, S. Muzaferija, M. Peric, V. Seidl, Numer. Heat Transf. B 32 (1997) 403–418.

Dear friends,

I studied all of my results and found that this kind of reasoning (when separation point angle increases, pressure drop between front and rear of cylinder will be less, therefore pressure drag will decrease) is just usable for high Reynolds number like the Reynolds near transition Re from laminar to turbulent and is not true for low Re. In high Re flow, the wake region is turbulent, so momentum transport is very efficient (in presence of turbulent eddies), so when you plot the Cp around cylinder you can see (almost) constant value for Cp after separation point:

http://uupload.ir/files/kk4h_tubes_crossflow_over_fig5.gif

so we usually read in references that the pressure of separation region is equal to separation point pressure.

But in low Re flows, wake region is still laminar and still we have a big stable wake the there is a pressure gradient in it.

http://uupload.ir/files/x66_p-teta_in_re=10,20.jpg

So we can't compare the P value between front and rear of cylinder and conclude that pressure drag should be increased or decreased!

This was just my conclusion and may not be true!

So I'm waiting to see you ideas.

Of course my main question is still remain that:

Why does CDp decrease with increasing Re in low Re flows:

http://uupload.ir/files/03ru_untitled.jpeg

Dear Ali Minaeian

Have you found the answer clearly?