Pressure drag calculation

lc05 · October 26, 2010, 15:41

Hi everyone, this being my first post I will take this opportunity to say that you seem to have a very interesting forum going here!

I have a question with regards the calculation of pressure drag over an aerofoil (or airfoil if you prefer).

I am using a panel method coupled with an inverse boundary layer solver to calculate the velocity distribution and boundary layer profiles. The inverse boundary layer solver accounts for interaction of the boundary layer with the inviscid outer flow and can calculate separation bubbles. It gives as an output the modified pressure distribution as a result of boundary layer growth (and separation where it occurs).

In order to calculate the pressure drag coefficient I resolve the pressure coefficient term at each station into its axial component and integrate along the chord. For each station (i) this is done using:-

Cd_p(i) = Cp(i) * dy(i)

I then sum these terms over the upper surface, and do the same for the lower surface; the total pressure drag coefficient is then giving by adding the upper surface component to the lower surface component.

The problem that I am having is that the upper surface contribution is giving a negative pressure drag term, and is of larger magnitude than the lower surface term (which is positive) giving me the clearly nonsensical result of negative pressure drag.

This problem is due to the terms near the leading edge. This seemed counter-intuitive to me as pressure drag arises due to boundary layer growth and separation which are effects that only become significant in the region of the trailing edge.

Any suggestions are much appreciated.

Thank you for reading and apologies for the long post...

akhokhay · October 29, 2010, 09:28

I Prefer airfoil

I am not sure if understand ur question correct,
but why u don't use absolute pressure to over come negative pressure problem(I think you MUST use absolute pressure but not sure). and if u already used absolute pressure then some error in ur code?

lc05 · November 1, 2010, 08:50

Hi akhokhay, thanks for your reply. Integrating the pressure coefficient in this manner is fine and should result in the correct answer; the method is equivalent to using absolute pressure. Its all in the first chapter of Anderson's text (Fundamentals of Aerodynamics).

Anyways, I found that my problem was that when using the coupled inviscid boundary layer method as I am the integration is swamped with numerical noise and leads to innaccurate drag predictions. Using some wake based method such as the Squire-Young formula seems to sort the problem out; this also seems to be the method used by others using inviscid-viscous methods (x-foil for example).

October 26, 2010, 15:41	Pressure drag calculation	#1
lc05 New Member Anonymous Join Date: Oct 2010 Posts: 2 Rep Power: 0	Hi everyone, this being my first post I will take this opportunity to say that you seem to have a very interesting forum going here! I have a question with regards the calculation of pressure drag over an aerofoil (or airfoil if you prefer). I am using a panel method coupled with an inverse boundary layer solver to calculate the velocity distribution and boundary layer profiles. The inverse boundary layer solver accounts for interaction of the boundary layer with the inviscid outer flow and can calculate separation bubbles. It gives as an output the modified pressure distribution as a result of boundary layer growth (and separation where it occurs). In order to calculate the pressure drag coefficient I resolve the pressure coefficient term at each station into its axial component and integrate along the chord. For each station (i) this is done using:- Cd_p(i) = Cp(i) * dy(i) I then sum these terms over the upper surface, and do the same for the lower surface; the total pressure drag coefficient is then giving by adding the upper surface component to the lower surface component. The problem that I am having is that the upper surface contribution is giving a negative pressure drag term, and is of larger magnitude than the lower surface term (which is positive) giving me the clearly nonsensical result of negative pressure drag. This problem is due to the terms near the leading edge. This seemed counter-intuitive to me as pressure drag arises due to boundary layer growth and separation which are effects that only become significant in the region of the trailing edge. Any suggestions are much appreciated. Thank you for reading and apologies for the long post...

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October 29, 2010, 09:28		#2
akhokhay New Member Amir Khodabandeh Join Date: Oct 2010 Location: Sweden Posts: 10 Rep Power: 16	I Prefer airfoil I am not sure if understand ur question correct, but why u don't use absolute pressure to over come negative pressure problem(I think you MUST use absolute pressure but not sure). and if u already used absolute pressure then some error in ur code?

November 1, 2010, 08:50		#3
lc05 New Member Anonymous Join Date: Oct 2010 Posts: 2 Rep Power: 0	Hi akhokhay, thanks for your reply. Integrating the pressure coefficient in this manner is fine and should result in the correct answer; the method is equivalent to using absolute pressure. Its all in the first chapter of Anderson's text (Fundamentals of Aerodynamics). Anyways, I found that my problem was that when using the coupled inviscid boundary layer method as I am the integration is swamped with numerical noise and leads to innaccurate drag predictions. Using some wake based method such as the Squire-Young formula seems to sort the problem out; this also seems to be the method used by others using inviscid-viscous methods (x-foil for example).