stagnation point at the trailing edge of the airfoil
 

Hi every one
I am modeling an airfoil in an incompressible very low Re flow!In case of a fixed airfoil, for example when I solved the flow for Re500 alfa=10, and plotted the Cp-x diagram, I faced some problem with the pressure coefficient at the TE of the airfoil. It seems that it is fluctuating. I've attached the image here to clear the problem. It is not related to the grid used, because I've tried different grids, and by changing the mesh refinement, the problem didn't solved!For example when I use coarser grid at TE, the fluctuations are less, but on the other hand I cannot capture the wake correctly. And by using the finer grid the fluctuations at the TE are really high. I've validated my results by a cylinder and a duct, and the results were well matched. Has anyone faced such a problem? Does anyone knows how can I deal with such a problem? Is it related to the stagnation point at the trailing edge of the airfoil?
Thanks for any word in advance!

Hi, mi first question when I see your plots is why you have a Cp greater than 1 at the LE of the airfoil? Is that a mistake on your calculations? Second, does your airfoil have a blunt TE or a sharp one? I both cases, you may have a vortex sheedding at the TE and that causes the oscillation on the CP plot. You maust do a flow visualisations to be sure if it is happening or not. Last question, why do you think the Cp at the TE is fluctuating? Are you doing transient simulations? Your residuals converge? Regards
Gonzalo

Hi, thanks for your attention!
First, Cp at LE of the airfoil is greater than 1 for the very low RE numbers and this is so due to the viscous effect! There are some books such as Batchelor and paper named ''rise in total pressure in frictional flow'' which discuss this effect completely. The airfoil is naca0012 and the TE is sharp. at this Re number(Re=500) there isn't any vortex shedding, and I have compared my results by those which are available in the literature, so I'm sure that at Re=500 and alfa=10 naca0012 is not supposed to have shedding! The Cp is not fluctuating, what I mean by fluctuating, is that the Cp doesn't have a normal and smooth curve at TE as is shown on the attachments! I don't know how can I solve this problem? my problem is that I can't understand why this is so? because I've validated my results and there wasn't any problem!And also these are steady results and moreover the residuals have converged!

Hi again:
yes i forgot that of the Cp value in very low Re flows, sorry. Following with your problem, which solver or software are you using? If you use a FEM or FVM soft, what are the numerical schemes are you using?
Another question, why your Cp curve ends at one point if the TE if your airfoil is sharp? How do you calculate the Cp value at the TE? Because if you are using a FVM or FEM the pressure is calculated at the face centers, so it sholud not have a face center at the TE itself.
And the las thing, the definitions of all NACA folis are with blunt TE, be careful with that, because the sharp TE may be causing numericals problems inside the solver. Regards.
Gonzalo

Hi, I myself wrote a code based on a control volume based finite element method, also I used a collocated grid. I have nodes on the surface of airfoil and also just ONE node at TE. When the airfoil has a sharp TE there must be just one point at TE, I have attached the geometry of the airfoil. why my Cp curves must not end at one point? because I have just one point at the TE and also I calculate Cp by this formula at TE, Cp=(p_node-p_infinity)/q and p_node is the obtained value of the pressure of the node which is located at TE. Are you sure that the definitions of all NACAs are with blunt TE? I have seen many airfoils with sharp TE in different papers!!!! I've heard before that it may cause problem in inviscid flow, but I didn't know that it can cause problem in viscous flow as well. Why the sharp TE cause problem? What is the reason for that?

Hello, I never solved such a problem at very low Re Numbers, but I think that at high AOA even at that low Re N°, the velocity in the corner of a sharp TE o like a flat plate with zero thikness may be quite high so the Cp goes down (as in your case). And for the NACA airfoils definitions, please look at the NACA TR 824 where you can find the airfoil coordinates used in experiments. The sharp TE is used, i think, because is easier to generate a mesh in such a geometry than in a airfoil with blunt TE.

Hi
 

I believe for incompressible flows Cp definition mathematically is written as:

Cp=(p_node-p_infinity)/q_infinity
Cp=(q_infinity-q_node)/q_infinity
Cp=1-(q_node/q_infinity)

Which implies that the maximum Cp can be 1 and which occurs close to leading edge based on Angle of attack.

Cp usually goes more than 1 for transonic & supersonic flows where Stagantion pressure coefficient mathematically is

Cp=1+ M^2/4 + M^4/40 + .......
where M is Mach number

Hi, with regard to results which are available in the literature(and I have attached them here) I know that Cp must not go down. I think there is sth wrong with my results, but so far I couldn't find it. and because I've validated my results with cylinder and duct, and there were well matched, I cannot understand why this is so? maybe it is because of the sharp TE of the airfoil. but unfortunately I don't know how I can solve it!