Abstract of "A new e^N database method for transition prediction"

It is nearly 50 years ago that the present author and independently Smith and Gamberoni published their first versions of a method to predict transition of two-dimensional boundary layers in incompressible flows. The method used linear stability theory to calculate the ratio of the amplitude of the amplified disturbances to the initial amplitude for a range of frequencies. The most amplified disturbance was assumed to cause transition. It was found from a comparison with experimental data that in a real flow transition always occurred for about the same value of the amplitude ratio (e⁹ for Smith and Gamberoni and e^7.8 to e¹⁰ for Van Ingen).At first the method has become known as “e⁹ “ method. Later it was realised that the amplitude ratio should depend on the magnitude of the initial disturbances as for instance indicated by the turbulence level in the free stream. This observation led to the present name e^N method where N is a function of the initial disturbances; say turbulence level in the free stream.
Over the years a number of different versions of the method have been used at the Low Speed Laboratory at Delft University of Technology for the design of airfoils for (sail)planes and wind turbines. It was demonstrated that the method was also applicable to laminar boundary layers with suction and to transition in laminar separation bubbles.
Not all of these versions have been published in detail, the progress made over the years at Delft can be found in the papers on the CD-ROM.
At the 50^th anniversary of the method it seems that even after 50 years the method is still considered to be useful. Therefore the author decided to put some of his “50 years with the e^N method” on record.  

For a long time the various versions of the method have been used for the design of low speed airfoils by L.M.M. Boermans, former student of the author and now associate professor at Delft Aerospace. The art and science of airfoil design has now advanced to such a level that further benefits from “laminarization by shaping” are no longer possible. Therefore recently Boermans started work on the design of airfoils with laminarization by suction with a possible application to sailplanes and general aviation aircraft.
It was realised that the existing versions of the  e^N method concentrated more on the prediction of transition than on the design of optimum suction distributions to prevent transition. Therefore it was decided to develop a new version with special attention to the design of optimum suction distributions and re-stabilisation by strong suction.

Because of the drastic increase of the computational capabilities over the past decades it was considered useful to take a fresh look at the method. This new version is presented in the second part of the report. The discussion is based on a MATLAB version as implemented by the present author; a FORTRAN version has been made by J. Bongers, then student at Delft Aerospace, who also removed some flaws from the original version and suggested some improvements.