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The Science Behind The Virtual Wind Tunnel

Many people ask how the virtual wind tunnel works. So here it goes...

Step 1: Panelize To Get Velocities

The key to estimating a non-stalled airfoil's aerodynamic coefficients is to accurately predict the surface pressure. And the key to finding this is to know the air velocities on the airfoil surface. Back in the 1960's, a couple of researchers at the Douglas Aircraft Company developed a technique that was robust enough for arbitrary airfoil shapes and fast enough to be solved on existing digital computers. These two researchers, J. L. Hess and A.M.O Smith, developed a method that takes a smooth airfoil and breaks it up into many flat facets, or panels. Then they distributed sources (the potential flow kind) on each of the panels and, via a tri-diagonal matrix solver, backed out the strength of those individual sources. With that knowledge, they predicted the surface velocities. This method proved to be very accurate for non-stalled airfoils.

The method has been improved through the years, but the general panelizing of airfoils is called a panel method and is still the technique of choice for most fast preliminary analysis software packages. It can even be extended to three-dimensional surfaces; products like CMARC and VSAERO use these techniques. DesignFOIL uses a modern variation on the Hess & Smith method that is proprietary.

Once you know surface velocities, you can calculate surface pressure coefficients with the following equation:

Cp = 1-(V/Vinf)^2

Step 2: Lift & Pitching Moment Coefficients

With an accurate representation of the pressure coefficients, you can accurately measure the non-stalled lift and pitching moment coefficients. It's just a matter of summing around the airfoil panels. The drag coefficient, however, is much more complicated.

Step 3: Boundary Layers & Drag Coefficient

Given a velocity distribution, one can use an integral method for predicting the shape of the boundary layer profile at various stations along the airfoil. DesignFOIL uses an incompressible approximation method based on von Karman and Pohlhausen. With boundary layer thicknesses known near the trailing edge, the drag coefficient is then calculated using the method developed by Squire and Young.

Step 4: Maximum Lift Coefficient

An accurate prediction of maximum lift coefficient is the holy grail of 2D airfoil analysis routines. The reason it is difficult is because separated flow is nonlinear, time-dependent, and very difficult to model. As such, several techniques have been developed by various people. DesignFOIL takes a new and novel approach of basing maximum lift coefficient on statistical analysis of empirical data. By analyzing an enormous amount of data, taking a look at geometric factors and Reynolds effects, I've developed a technique that predicts a maximum lift coefficient and blends it into the polar plots seemlessly. Generally you will find that DesignFOIL predicts conservative maximum lift coefficients.