PABLO
Potential flow around Airfoils with Boundary Layer coupled One-way

KTH- The Royal Institute of Technology
Department of Aeronautics
Stockholm, Sweden

Programmed by Christian Wauquiez, 1999
Contact : Prof. Arthur Rizzi, rizzi@flyg.kth.se

Conditions :
The program is freeware. Anyone is free to develop it further. It comes with NO GUARRANTEES and NO SERVICE.
The purpose of the program is education. It has been sucessfully used as a lab material at KTH / Department of Aeronautics.

Description of the program :

Pablo is a pedagogical low-speed airfoil analysis program written in MATLAB. It uses a one way coupled
inviscid + boundary layer model.

The inviscid flow is solved using a Panel Method [1]. Three different kinds of singularity distributions can be used.

The boundary layer equations use the inviscid flow velocity provided by the panel method, but the effect of the
boundary layer on the inviscid flow is not taken into account, as in Panda [2]. The boundary layer model is
described in [3]. It uses Thwaites' equations for the laminar part of the flow, and Head's equations for the
turbulent part. Michel's criterion is used to locate transition. The drag coefficient is computed using the
Squire-Young formula.

[1] Katz and Plotkin : Low Speed Aerodynamics, From Wing Theory To Panel Methods. McGraw-Hill Inc., 1991
[2] Ilan Kroo : PANDA - A Program for Analysis and Design of Airfoils. © Desktop Aeronautics, 1988.
[3] Jack Moran : An introduction to Theoretical and Computational Aerodynamics. John Wiley and sons, 1984.
[4] I.H. Abbott and A.E. Von Doenhoff, Theory of wing sections, Dover Publications Inc,  NewYork, 1959

Program facilities :

* Three different kinds of geometries are implemented :
- Ellipse with prescribed axis ratio,
- NACA 4 digits airfoil library (see reference [4]),
- General airfoil library.

In the two first cases, the shape of the object is defined analytically. The user simply has to enter the proper information,
ellipse axis ratio or Naca 4 digits.

In the last case, the airfoils are defined in data files using a number of discrete points. Around 70 airfoils taken from well
known shape libraries are already recorded and ready to use. New data files can be added to the library with any airfoil
coordinates except that the airfoil trailing edge must be sharp.

*  Three different kinds of singularities are implemented :
- Constant-strength sources,
- Constant-strength doublets,
- Linear vortices.

* The user may change the flow angle of attack and Reynolds Number, as well as the number of panels used in the discretization.

* The solution computed by the program features :
- The Cp distribution,
- The aerodynamics coefficients CL, CD and CM,
- The coordinate of the center of pressure Xcp,
- The location of transition and eventual laminar or turbulent separation,
- The distribution of the boundary layer parameters.

* Miscellaneous :

It is possible to zoom in and out on the 2D plot. Get information by entering "help zoom" in Matlab.
It is also possible to hold on the previous plot by clicking on the button "Hold on (Cp)".
This is allowed only between solutions on the same geometry and at the same angle of attack.

Program download and installation :

The program can be obtained here, as a tar file.

To extract it, enter the following command :
> tar xvf pablo.tar

A directory called "pablo" is created. It contains all the MATLAB m-files,
and a number of airfoil data files.

To run the program, invoke MATLAB first, and then enter
>> pablo

Homeworks based on Pablo :

Handouts of homeworks based on Pablo are obtained below.
* Pedagogical Panel Methods (PDF)
* One-Way Coupled Integral Boundary Layer (PDF)

Created December 20th, 1999
Modified January 25th, 2000 (added links to lab handouts)