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August 4, 2012, 13:55 
calculating pressure coefficient on airfoil surface

#1 
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mahzad_kh
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Hi every one I am modeling an airfoil in an incompressible low Re flow! I set pressure in my outlet boundary condition as 1. I also set velocity in x and y direction at inlet. my question is when I solve the flow for example for a 10 degree angle of attack and when the flow reach a steady state condition, Are all the far field boundaries and inlet boundary supposed to have a pressure as same as the outlet boundary(it means 1)? if I want to calculate pressure coefficient, am I allowed to use P_out=1 instead of P_infinity or not? otherwise which pressure must be used for P_infinity for calculating pressure coefficient on the airfoil surface? Thanks for any word in advance!


August 4, 2012, 21:07 

#2 
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Mehdi
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I recommend you to read "Computational Fluid Dynamics Principles and Applications" by J Blazek. in chapter 8, I think you can find answer of your question.
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August 5, 2012, 01:20 

#3 
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mahzad_kh
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I checked this book, in chapter 8 of this book the method which must be used to set the boundary condition at inlet or outlet for subsonic or supersonic flow is explained! it is not my question?!!! I don't have any problem with setting the boundary condition, my problem is that when I solve the flow over airfoil, and the solution is steady, can I expect the boundaries to have the same pressure as that which is set in outlet or not? if not, why this is so? because in most of the books and papers P_infinity which is needed to calculate Cp is set from upstream, it means inlet pressure! Is inlet pressure different from that of outlet?


August 5, 2012, 03:55 

#4 
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Why do you care so much about absolute value of the pressure coefficient? Adding a constant (shift) to the pressure coefficient does not change total forces/ moments.
When your computation domain is infinite, the inlet and outlet pressures are the same. For finite size domains the shift in the pressure coefficient is inverse proportional to the domain size, (or the domain size squared, I am not sure). 

August 5, 2012, 06:43 

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August 5, 2012, 07:38 

#6  
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Yes, and for 20c domain it could be quite negligible. To have an idea about the shift value you could compare values of inlet and outlet pressure in your simulations, i.e. their difference divider by rho v^2/2 

August 5, 2012, 08:02 

#7 
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mahzad_kh
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So you mean that, in case of any differences I can add (p_outp_in)/(rho*V^2/2) to the Cp values over the airfoil surface?


August 5, 2012, 09:22 

#8 
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August 5, 2012, 09:46 

#9 
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mahzad_kh
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ok thanks, another question is that when my solution reach a steady state condition, the pressure is not exactly 1 at inlet, it's for example 1.12 and also it is not 1.12 at every node on inlet boundary, it decreases and reach to 1 as the nodes get farther from the node which has a pressure of 1.12 . If I want to use inlet pressure as P_infinity for calculating Cp,can I average the pressure at inlet nodes? Is it correct? or it is better to use a greater domain, the problem with the use of greater domain is that it increases my grid size and the amount of calculation needed!


August 5, 2012, 10:49 

#10 
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It is not a good idea to average pressure at inlet, the error is rather determined by the maximal difference. Try to increase domain (it does not cost much computational time if you are using unstructured grids on outer part of the grid with spacing increacing towards the outer boundaries)


August 5, 2012, 10:56 

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August 5, 2012, 20:30 

#12 
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Mehdi
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Hi;
One of my problem is in this area. in Fact, I want to apply constant pressure as a outlet boundary condition in structured grid with collocated arrangement. I used dummy cell to do it, but I can not find out how ap should be calculated? (ap=L/ape; ape=(ap+apE)/2) ap is coefficient of main cell and apE is coefficient of neighbor cell (there is dummy (guest) cell ), my problem is calculating apE, because ap=Σ an and in guest cell, we don't have an, or I don't know how to calculate it. Thanks in advance
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August 6, 2012, 03:05 

#13 
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Hi Mahzad, if your problem is how to calculate the pressure coefficient over the airfoil, why don't you use the inlet velocity as the reference value? Then you'll come up with something like this:
where p is the pressure over the airfoil, and and are the density and velocity imposed far upstream (which you know becase you have set them). What do you guys think? Cheers. 

August 6, 2012, 03:36 

#14 
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