# How to calculate pressure distribution over an airfoil from its coordinates?

I need to compute the pressure distribution over an airfoil (I have the coordinates, but any will do) with the streamline curvature method. Unfortunately, I cannot find much on the web.

Can someone point me in the right direction or walk me through it? I understand it qualitatively (the concepts) but have a hard time quantifying it (actually solving the flow field).

• Another detailed source can be found in this paper by Mark Drela on xfoil (web.mit.edu/drela/Public/papers/xfoil_sv.pdf). For your purpose, you can stop at section 2.1, assuming source strengths at every panel to be 0.
– JZYL
Apr 20, 2020 at 15:25

What helped me was the book "Theoretical and Computational Aerodynamics" by Jack Moran (ISBN 0-471-87491-4). That was 30 years ago, but the physics haven't changed since then. And it is still available.

An online source would not go deep enough to cover all what you need. My advice is to get the book and work through the exercises. It worked for me, and if even I could code a 2D potential code after having read this book, you should have no problems.

There is one trick: At one point you will end up with n equations for n+1 unknowns. Bummer! What you need to do is to prescribe flow direction at the trailing edge, and then you will have n+1 matching conditions for those n+1 unknowns, n being the number of panels you divide the airfoil surface into. Google "Kutta condition" for an explanation.

EDIT

Now you have quite a different question:

by CFD i meant RANS. how does it compare to RANS methods in term of stall prediction and pressure distribution

@toshiba: The comparison is like between a Volkswagen Beetle and a Mercedes. A potential code is simple, robust and gets you there, like the Beetle. Pressure distribution is good until separation starts. Compressibility can be modelled until locally the speed of sound is reached. Stall prediction is a bit tricky, but with a bit of experience and an added boundary layer calculation you will get good results.

RANS is a simplified Navier-Stokes algorithm which is used for modelling turbulent flows. Like the Mercedes, it needs much more effort to code and run (and computing power - it requires a mesh where the potential code only needs panels on the airfoil surface) but also produces better predictions if the mesh is laid out well. Drag and stall approximation is included while potential flow needs some extra effort for boundary layer modelling. A Navier-Stokes code can also be used for transsonic flow.

If you want to build your own, assume you get the parts only and have to assemble the cars. No plans included. The VW Beetle heap is much smaller and you can figure out quite quickly how it fits together (did that once with a Beetle engine that someone else had disassembled and left behind). When you are finished, the car will run and require little maintenance.

With the Mercedes, there are many more parts, more complicated looking and requiring special tooling. It takes much longer to get assembled and in the end you will have some parts left over and others in the wrong place if nobody experienced guides you along. Maybe the car runs, but it will break down quickly unless you put much effort into maintaining it.

In other words: Start with a potential code. MUCH easier.

• will this allow me to compute the pressure distribution over the entire airfoil only, or the entire flow field as well? Also, how accurate is this method vs experiments or CFD? Apr 20, 2020 at 16:15
• @toshiba: The method uses potential theory, so you get a solution for every point in the flow field. It is the boundary conditions which have to be met on the airfoil surface. Potential theory only works well for attached flow and is inviscid. However, Moran also includes a simple boundary layer calculation so you will also get an approximation of drag. And it is CFD (but a rather simple variety of it). Apr 20, 2020 at 16:34
• great thx. by CFD i meant RANS. how does it compare to RANS methods in term of stall prediction and pressure distribution. Can it successfully model compressibility effect? Im sorry about the question but i need to write a code and i chose potential flow theory beacause i was under the impression that accuracy would be sufficient. but im having doubts now. how good is that drag approximation? Apr 21, 2020 at 21:31
• @toshiba: That is a new question altogether. See the edit. Apr 21, 2020 at 22:11
• thx. however i must add: i just read the book you recommended. It is based on potential flow yes, but not streamline curvature method. Apr 25, 2020 at 18:57