Scanned versions of previous
articles published concerning the e^N method
Download Adobe Reader to view
pdf files
Matlab .m files containing
figures for further clarification
Thesis by Bongers with examples
of the use of the new e^N method
The article: "A new eN database
method for transition prediction method" in pdf format
Interesting links
Contact information
Abstract of the report: "A new eN
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 e7.8 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 eN 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 50th 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 eN
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 eN
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.
|