Aerofoil pressure drag calculation

[lc05]

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...

 

[eljose79]

Thank you for your post and for sharing your question with us. It sounds like you have a very interesting and complex problem at hand, and I appreciate your detailed description of your approach.

Firstly, I would like to clarify that the pressure drag coefficient is defined as the ratio of the pressure drag force to the dynamic pressure of the flow, and is typically denoted as Cd_p. It is not the same as the pressure coefficient, Cp, which is the ratio of the local pressure to the free stream pressure. I just wanted to make sure we are on the same page with the terminology.

Now, onto your question. As you have correctly pointed out, pressure drag is primarily caused by boundary layer growth and separation at the trailing edge of the airfoil. However, it is important to note that the pressure distribution over the entire airfoil also plays a significant role in determining the overall pressure drag. In other words, even though the boundary layer effects may be more pronounced at the trailing edge, the pressure distribution over the entire airfoil can still contribute to the overall pressure drag.

In your approach, you are integrating the pressure coefficient along the chord at each station, which is a valid method. However, it is possible that the negative pressure drag term you are seeing on the upper surface is a result of the pressure distribution in that region. It could be that the pressure distribution on the upper surface near the leading edge is such that it contributes negatively to the overall pressure drag. This could be due to a variety of factors, such as the shape of the airfoil, the angle of attack, or even the boundary layer characteristics. Without more information, it is difficult to pinpoint the exact cause.

One suggestion I have is to check the pressure distribution over the entire airfoil and see if there are any regions where the pressure coefficients are significantly negative. If so, this could explain the negative pressure drag term you are seeing. Another suggestion is to compare your results with experimental data or other numerical simulations to see if they are in agreement.

I hope this helps and I wish you the best of luck in your research. Please feel free to reach out if you have any further questions or concerns.