Pressure around an airfoil in boundary-fitted coordinates

nw_ds · September 28, 2012, 16:16

I am trying to solve the viscous flow around an airfoil NACA 0012 using the vorticity streamfunction formulation in boundary-fitted coordinates , I have managed to find the velocity field everywhere but I can't seem to find a way to calculate the pressure field around the airfoil or at least on its surface to calculate the lift.

I have tried many things no thing seems to work. I started to doubt the velocity field,but the velocity field looks correct but I am not sure anymore.

So I would appreciate it if anyone can get me a version of the pressure equation ( static or total ) in boundary fitted coordinates with the appropriate boundary conditions

michujo · September 29, 2012, 13:27

Hi, this answer might seem a little dumb but, can't you use Bernouilli equation to calculate pressure at every point?

$p_{\infty}+\frac{1}{2} \cdot \rho U_{\infty}^2=p+\frac{1}{2} \cdot \rho U^2$

Where $p_{\infty}$ and $U_{\infty}$ are the pressure and velocity modulus far upstream of the airfoil.

This is valid for a incompressible flow (M<0.3). If your flow is compressible then you'll have to use the compressible version of the expression.

I don't think the fact that you're using body-fitted coordinates changes anything, you just calculate p (or p-p_infinity) at every point of your domain.

Was this answer helpful?

Cheers,
Michujo.

nw_ds · September 30, 2012, 11:06

Thanks but that's not what i am looking for

michujo · September 30, 2012, 12:21

I don't know if you speak spanish but you might want to check this MSc. Thesis. The algorithm to compute pressure (along with the appropriate boundary conditions) in body-fitted coordinates is all explained.

http://e-archivo.uc3m.es/bitstream/1...ranjo_2009.pdf

What she does essentially is to compute pressure at every point from the computed velocity field, regardless of the system of coordinates.

Could you explain your question a little bit more in detail?

Cheers,
Michujo.

September 28, 2012, 16:16	Pressure around an airfoil in boundary-fitted coordinates	#1
nw_ds New Member Mido Join Date: Mar 2011 Posts: 25 Rep Power: 15	I am trying to solve the viscous flow around an airfoil NACA 0012 using the vorticity streamfunction formulation in boundary-fitted coordinates , I have managed to find the velocity field everywhere but I can't seem to find a way to calculate the pressure field around the airfoil or at least on its surface to calculate the lift. I have tried many things no thing seems to work. I started to doubt the velocity field,but the velocity field looks correct but I am not sure anymore. So I would appreciate it if anyone can get me a version of the pressure equation ( static or total ) in boundary fitted coordinates with the appropriate boundary conditions

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September 29, 2012, 13:27		#2
michujo Senior Member Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 15	Hi, this answer might seem a little dumb but, can't you use Bernouilli equation to calculate pressure at every point? $p_{\infty}+\frac{1}{2} \cdot \rho U_{\infty}^2=p+\frac{1}{2} \cdot \rho U^2$ Where $p_{\infty}$ and $U_{\infty}$ are the pressure and velocity modulus far upstream of the airfoil. This is valid for a incompressible flow (M<0.3). If your flow is compressible then you'll have to use the compressible version of the expression. I don't think the fact that you're using body-fitted coordinates changes anything, you just calculate p (or p-p_infinity) at every point of your domain. Was this answer helpful? Cheers, Michujo.

September 30, 2012, 11:06		#3
nw_ds New Member Mido Join Date: Mar 2011 Posts: 25 Rep Power: 15	Thanks but that's not what i am looking for

September 30, 2012, 12:21		#4
michujo Senior Member Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 15	I don't know if you speak spanish but you might want to check this MSc. Thesis. The algorithm to compute pressure (along with the appropriate boundary conditions) in body-fitted coordinates is all explained. http://e-archivo.uc3m.es/bitstream/1...ranjo_2009.pdf What she does essentially is to compute pressure at every point from the computed velocity field, regardless of the system of coordinates. Could you explain your question a little bit more in detail? Cheers, Michujo.