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August 22, 2012, 03:43 
stagnation point at the trailing edge of the airfoil

#1 
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mahzad_kh
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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 Cpx 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! 

August 22, 2012, 12:55 

#2 
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Gonzalo
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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 

August 22, 2012, 14:10 

#3  
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mahzad_kh
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Quote:
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! 

August 22, 2012, 21:03 

#4 
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Gonzalo
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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 

August 23, 2012, 01:34 

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mahzad_kh
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August 23, 2012, 07:17 

#6 
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Gonzalo
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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.


August 23, 2012, 12:02 
Hi

#7  
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Dynampally Pavitran
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Quote:
Cp=(p_nodep_infinity)/q_infinity Cp=(q_infinityq_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 

August 24, 2012, 03:23 

#8  
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mahzad_kh
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