e-to-the-N

In 2006 it was 50 years ago that emeritus professor J.L. van Ingen published his first version of the e^N method for transition prediction. Over the years different versions have been developed. The most recent version is specially adapted to the application of laminarisation by suction.

To celebrate the 50^th anniversary of the method the new method is available on CD-ROM together with a number of older publications.

Some further information on the contents of the CD-ROM is presented below.

Copies of the CD-ROM may be requested from the author.

Contact:

e-mail:         prof.J.L.van.Ingen@planet.nl

cc:               B.W.vanOudheusden@tudelft.nl

Website:

www.lr.tudelft.nl/aerodynamics/e-to-the-N

In the future the website will provide:

• Additional information on the CD-ROM
• Answers to questions
• Correction of possible errors
• Etc.

Postal address:

Prof. J.L. van Ingen

Faculty of Aerospace Engineering

TU Delft

P.O. Box 5058

2600GB Delft

The Netherlands

Preface with a personal touch

It is nearly 50 years ago that I published my first version of the e^N method for transition prediction in two-dimensional incompressible flows. Independently and simultaneously Smith and Gamberoni presented essentially the same method.

During my study for aeronautical engineer at the Technical University of Delft I had enjoyed lectures on boundary layer theory by Burgers and Timman. In these lectures the subject of linear stability theory had aroused my interest that led to the idea for the e^N method. I graduated in 1954 and since then theoretical and experimental boundary layer research has been my favourite topic.

In the spring of 1955 Timman invited me to join him to attend the conference on “Boundary Layer Effects in Aerodynamics” held at the National Physical Laboratory (NPL) at Teddington, UK. Here I had the wonderful experience of meeting some of the well-known researchers in the boundary layer community of that time, such as Eichelbrenner, Glauert, Görtler, Head, Küchemann, Lachmann, Legendre, Lighthill, Lilley, Owen, Pankhurst, Pearcy, Preston, Raspet, Ross, Schubauer, Stewartson, Stratford, Thwaites, Trilling, Young, etc. Some of them were already known to me by name, many I would get to know personally later in my career. Especially impressive to me was a private discussion with G.B. Schubauer, famous for his experimental proof of the existence of Tollmien-Schlichting instability waves in a flat plate boundary layer. To him I could show the preliminary results of my research on what later would become the e^N method. His appreciation for this idea was of course extremely stimulating for me as a young aeronautical engineer who was working on what was going to be his first international publication. In later years I had the pleasure of meeting Schubauer again at other conferences and to visit him at the National Bureau of Standards in Washington in 1959.

My initial work on e^N was published in two reports of the Department of Aeronautical Engineering of Delft University in July and September 1956. In September 1956 I presented the method at the First European Aeronautical Congress at Scheveningen, the Netherlands. Before I started my (first ever) presentation before an international forum, somebody pointed out to me a very special person in the audience, namely the famous Hermann Schlichting. The fact that he nodded with appreciation during my presentation was of course very stimulating. Afterwards he told me that A.M.O. Smith had given a similar presentation at the International Congress for Mechanics at Brussels the week before. Later I got to know A.M.O. Smith very well. I have always appreciated his acquaintance and that of his colleague and later successor at the Douglas Company, Tuncer Cebeci.

The development of the e^N method was the start of a life-long commitment to boundary layer research in which the contacts with many colleagues and friends have enriched my life. In 1996 I had the honour to present the Prandtl Memorial Lecture on the combined invitation of the German GAMM and DGLR. In this lecture I gave an overview:” Looking back at forty years of teaching and research in Ludwig Prandtl’s heritage of boundary layer flows”

The e^N method remained one of my favourite topics. The present collection of papers on CD-ROM illustrates the history of work in this field at the Low Speed Wind Tunnel laboratory of Delft University. The original presentation is included because, although it is still quoted very often, not many readers will have a copy readily available.

Finally a recent new version of the method for two-dimensional incompressible flow (in MATLAB) will be presented. The author is indebted to Jeroen Bongers for invaluable assistance with the preparation of the final version of this report and for the design and realisation of the CD-ROM.

Applications of this new method to the design of suction airfoils using the FORTRAN environment of the XFOIL program are presented in the Masters Thesis by Jeroen entitled: Implementation of a newtransition prediction method in XFOIL (August 2006). The thesis is also included on the CD-ROM.

In addition a recent summary paper is included.(“The eN method for transition prediction. Historical review of work at TU Delft.” By J.L. van Ingen. AIAA 2008-3830, 23-26 June 2008, Seattle.

The CD-ROM has been organised in such a way that from the report on the new method direct access to the relevant older publications is gained by clicking on a special icon.

The CD-ROM also contains a number of MATLAB programs and data files so that, while reading the report on the new version of the method, illustrative MATLAB programs can be run by means of an “N_factor_show”

The author is indebted to the Dean of Delft Aerospace Prof. B.A.C.Droste and the Head of the Aerodynamics Group, Prof. P.G. Bakker for providing the funding to realise the CD-ROM.

Introduction to the new version of the e^N method.

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 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 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. Moreover the new version could be based on a set of tabular stability data that had been calculated by Arnal. A report on this new version is included on the CD-ROM. 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.

Contents of the CD-ROM

Preface with a personal touch

Introduction to the new version of the e^Nmethod.

A series of earlier publications by J.L. van Ingen

(sometimes with co-authors as mentioned).

1 A suggested semi-empirical method for the calculation of the boundary layer transition region. (The original 1956 report ,VTH-74)

2 A method of calculating the transition region for two-dimensional boundary layers with distributed suction. Paper presented at the 6th European Aeronautical Congress Munich, Sept 1-4, 1965

3 Theoretical and experimental investigations of incompressible laminar boundary layers with and without suction. PhD Thesis Delft, 1965

4 On the design of airfoil sections utilising computer graphics. De Ingenieur, vol 43, 24 October 1969, pp L110-118

5 Some research on two-dimensional laminar separation bubbles. AGARD CP 102, Lisbon 1972 (With E. Dobbinga, and J.W. Kooi).

6 On the calculation of laminar separation bubbles in twodimensional incompressible flow. AGARD CP168 Göttingen, May 1975

7 Transition, Pressure Gradient, Suction, Separation and Stability Theory. AGARD CP-224, Copenhagen 1977

8 Transition, Pressure Gradient, Suction, Separation and Stability Theory. Rand Corporation P-6119, 1978

9   Low-Speed Airfoil Section Research at Delft University of Technology. Paper ICAS-80-10.1, Muenchen 1980, (With L.M.M. Boermans and J.J.H. Blom)

10   Research on laminar separation bubbles at Delft University of Technology in relation to low Reynolds number airfoil aerodynamics., Conference on Low Reynolds Number Aerodynamics, Notre Dame, Indiana, USA, June 1985. (With L.M.M. Boermans)

11   Experimental aerodynamic characteristics of the airfoils LA 5055 and DU 86-084/18 at low Reynolds numbers. , Low Reynolds Number Aerodynamics, Notre Dame, Indiana, USA June 1989. (With L.M.M. Boermans, F.J. Donker Duyvis and W.A. Timmer))

12 Experimental investigation of Tollmien Schlichting instability and transition in similar boundary layer flow in an adverse pressure gradient. IUTAM Symposium, Toulouse, 1989 (with F.J.M. Wubben and D.M. Passchier).

13   Research on laminar separation bubbles at Delft University of Technology. IUTAM Symposium, Novosibirsk, 1990

14   Some introductory remarks on transition prediction methods based on linear stability theory. In “Transitional boundary layers in Aeronautics”, KNAW, Amsterdam, 1996

15   Boundary layer research in relation to airfoil design at the Faculty of Aerospace Engineering of Delft

University of Technology. 2^nd Int. Symposium on Aeronautical Science and Technology in Indonesia, ISASTI ’96. Jakarta 1996.

16   Looking back at 40 years of teaching and research in Ludwig Prandtl’s heritage of boundary layer flows. 39^th Ludwig Prandtl Memorial Lecture, Prague, 1996. ZAMM 78 (1998) 1. 3-20.

17   Part of my forty years of teaching and research in boundary-layer flows: the laminar separation bubble. Seminar on “Boundary layer separation in aircraft aerodynamics” dedicated to Prof. J.L. van Ingen on occasion of his retirement  Editors R.A.W.M. Henkes and P.G. Bakker, 1997

Contents of the CD-ROM (continued)

Three new reports

1. J.L. van Ingen: A new e^N database method for transition prediction. 2006

2. J. Bongers: Implementation of a new transition prediction method in XFOIL (August 2006).

3. J.L. van Ingen: “The e^N method for transition prediction. Historical review of work at TU Delft”. AIAA paper 2008-3830, 23-26 June 2008, Seattle.

MATLAB programs and data files

Computer requirements and instructions for use of the CD-ROM

• After inserting the CD-ROM in your PC it should be self-starting in a Windows environment. Your web browser may ask if you want to activate/ allow the ActiveX components, as the application contains some AcitiveX components. This can be done safely.

• Non-Windows users can start the application by opening the “start.htm” file found on the CD-ROM in any web browser.

• To use the CD-ROM you need Adobe Reader; when starting up the CD-ROM you will see an icon that helps you to download the latest free version of this software. The CD-ROM was optimized for use with version 8 of Adobe Reader.

• Because the CD-ROM contains interactive elements it’s stopping and starting during use may slow down the interaction in an unacceptable way. Therefore it is advised to copy the contents of this CD-ROM to a file on your hard disk.

• Further instructions may be found in the read.me file on the CD-ROM and, if found necessary, on the website mentioned on page 6.