2D PANEL METHODS
The solution is obtained by combining two separate calculations, an inviscid panel method prediction of flow velocities and pressures and a viscous boundary layer theory prediction of surface flow displacement and momentum loss due to friction.
Because the presence of a boundary layer does modify the aerofoil's displacement effect on the freestream, it is more accurate to iterate between the results of these two solutions and obtain a final, converged solution. However in many cases, numerical problems may arise due to the number of iterations required and the possibility of an unstable iteration.
In the Reynolds number range that is the case for small to large aircraft, the boundary layer is very thin and a reasonable result is generally obtained by just using a single pass of each solution component. The solution software below does just one inviscid flow solution for velocities and then one boundary layer integration pass to obtain a solution. More complex panel method solutions are available in the reference material listed below.
Inviscid Panel Method
A potential flow solution of any general aerofoil section can be modeled by discretising the surface contour using singularity panels. Many different techniques are possible but for the programs used on this site, the following configuration has been employed for the panel modeling. It is based on using straight panels with a linear distribution of vorticity between end points.
A boundary condition of no flow through surface ( Vn=0 ) can be applied at the center of each panel. This produces N equations in N+1 unknowns. In order to correctly solve for the extra unknown vorticity, a Kutta condition must be applied at the trailing edge.
The Kutta condition, equation N+1, can be applied in terms of trailing edge tangential velocities which means that the vorticity at the trailing edge is zero,
The lift coefficient can be calculated, assuming a small angle of attack, as the integration of surface pressure coefficient acting in the y-direction, ie. projected on the x axis.
Solutions only need to be calculated for one or two angles of attack as the lift curve will be linear. Stall and boundary layer effects are not predicted by the first part of the process as it deals only with inviscid flow.
APPLICATION : 2D Panel Code Computer Program.
The following program accepts ASCII data files which consist of a list 2-D aerofoil section coordinate points (x,y). The format of these aerofoil input data files is the same as that produced by the NACA section generation program.
The data file structure used is shown below,
N (Number of Data Points describing section)
There is an initial header line, followed by a line giving the number of data points used to describe the aerofoil and then pairs of surface coordinate points (x,y). The order of surface points is anti-clockwise, starting at the trailing edge, going back over the upper surface around the nose and then forward along the underside back to the trailing edge. Data files for other aerofoil sections can be created using a spreadsheet or text editor to give a data file in the correct format.
From the surface coordinate data file, the program calculates an inviscid flow solution. The 1-D momentum integration is run to predict the boundary layer near the aerofoil surface. The program can predict CL, Cm(1/4c) and CD for the specified aerofoil section at a given angle and Reynolds number.
- Executable Program : 2-D Panel Method Solution MS Windows downloadable
- Executable Program : 2-D NACA Aerofoil Section Generator MS Windows downloadable
- Virtual Wind Tunnel System : Program Suite to allow a number of different solutions
- Alternately for a more elaborate section solver try the XFOIL program, visit the Marc Drela GPL Aerofoil Solution System site at MIT XFOIL site.