Boundary-Layer Separation in Aircraft Aerodynamics: Dedicated to Professor J .L. van Ingen

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Boundary-Layer Separation in

Aircraft Aerodynamics

Proceedings of the Seminar

held on 6 February 1997 in Delft

Dedicated to Professor J.L. van Ingen

Edited by

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Boundary-Layer Separation in Aircraft Aerodynamics

Tltoëift

Library

1111111111111111111111111111111111 C 3882828

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Boundary-Layer Separation in

Aircraft Aerodynamics

Proceedings of the Seminar

held on 6 February 1997 in Delft

Dedicated to Professor

J

.L. van Ingen

Edited by

R.A.W.M. Henkes and P.G. Bakker

Faculty of Aerospace Engineering

Delft University of Technology

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Published and distributed by: Delft University Press

Mekelweg 4 2628 CD Delft The N etherlands

Telephone: +31 15 2783254 Telefax: + 31 15 2781661 . By the order of:

Faculty of Aerospace Engineering Delft University of Technology Kluyverweg 1 2629 HS Delft The N etherlands Telephone + 31 15 2785907 Telefax + 31 15 2781822 ISBN 90-407-1476-2

No part of the material by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without permission from the publisher:

Delft University Press, Mekelweg 4, 2628 CD Delft, The Netherlands. Cover plate:

Smoke visualization for the separating boundary layer along a cylinder by Dobbinga and Van Ingen.

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v

Preface

by

the Editors

This book contains the proceedings of lectures that we re given at the one-day seminar, that was organized on the occasion of the 65 birthday and retirement of Professor van Ingen. For more than 40 years he has played a major role in the Faculty of Aerospace Engineering at Delft University. He was the he ad of the Low-Speed Aerodynamics Laboratory, and during many years he was also involved in the management of the Faculty.

His main scientific interest was, and is: boundary layers. In fact he has always been enormously inspired by the classical inventors of boundary-Iayer theory, such as Prandtl, Von Kármán, and Schlichting. Professor Van Ingen as weIl has given a, what has now become, 'classical' contribution to the boundary-Iayer theory, namely the en method for the prediction of boundary-Iayer transition. He proposed these ideas already at the beginning of his scientific career in 1956, and since then his work has become a standard reference in papers and books on stability and transition.

In December 1995 the first editor and Professor van Ingen organized a three-day colloquium for the Royal Netherlands Academy of Arts and Sciences, entitled

Transitional Boundary Layers in Aeronautics. The leading researchers on this topic were brought together and Professor van Ingen gave the lecture Some introductory remarks on transition prediction methods based on linear stability theory. From the discussions that followed, it was clear that the en method is still actual, though new generations of prediction methods are underway.

Besides transition, Professor Van Ingen has also given scientific contributions to the topic of boundary-Iayer separation. Together with Professor Dobbinga, he has performed experiments to measure the separation angle of the flow along various configurations, and he developed a simple engineering method to predict separation bubbles.

On 6 February 1997, the Faculty of Aerospace Engineering, and particularly the Aerodynamics Group, has taken the initiative to honour Professor van Ingen with a seminar on the topic of separation. Professor T. Cebeci from McDonnell-Douglas Aerospace opened the seminar with an overview of the different aspects of separation and stall for the flow along aircraft, followed by presentations of researchers from the NLR and from Delft University. More than 100 participants attended the seminar, among which Professor Van Ingen's family, colleagues fr om in si de and outside university, and present and former students.

The seminar has shown that the topic of separation is still very challenging, and requires further analysis particularly with respect to turbulence modelling and three-dimensional aspects. Advanced experiment al techniques (such as laser-Doppier anemometry, and other optical methods), as weIl as theoretical analysis of the flow topology and numerical approaches using high-speed computers are expected to further improve the knowledge of a topic that is of great practical importance for the aerodynamic design of aircraft.

All the contributors have delivered a written version of their presentation, collected in the present volume. A personal introduction by Professor H.

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Witten-Vlll Pref ace by the editors

berg, being for a long time a close colleague of Professor Van Ingen, precedes the collection of papers. The last word is to Professor Van Ingen, and he ends this book with an over view of his own involvement in the research of flow separation. The editors thank all who contributed to the seminar and the proceedings. The fiTSt copy of the book has been handed out to Professor Van Ingen af ter his farewell lecture on 30 May 1997, entitled Een halve eeuw in stroming en sturing.

We are sure that the work on transition and separation in boundary-Iayer flows needs to be continued in the spirit of Professor Van Ingen.

Delft, May 1997,

R.A.W.M. Henkes and P.G. Bakker Editors

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lX

Prof. dr ir J.L. van Ingen:

Aerodynamicist and Dean

by H. Wittenberg

With much pleasure I have accepted the invitation of the editors to write an introduction to this Liber Amicorum for Professor Jan van Ingen, knowing him since the time that he was a student at the Aeronautical Department of Delft U niversity.

Jan Leendert van Ingen was bom on January 30,1932 in Puttershoek, a small village in the Hoekse Waard, an area with an agricultural environment south of Rotterdam. Af ter the primary school he received his secondary education at a high school in Dordrecht, where he obtained the diploma in 1949. At this school one of his teachers was the late Dr S.J. van Veen, who later on was appointed professor of mathematics in Delft and in this quality Jan would meet him again. Having left the secondary school with high marks, it was obvious that a university study would follow. The choiee was Delft University of Technology. Opting for an education in aeronautieal engineering, he enrolled at the university in September 1949. At that time the Aeronautical Department at Delft was in the building-up phase under the energetic leaders hip of Prof. dr ir H.J. van der Maas, who was always looking for young talent. It thus often happened that a bright student was asked for a assistantship already before he got his final degree. In this position Jan joined the academie staff in 1952 as one of my assistants. I remember he worked on methods for aircraft-design studies and he performed a study on wing characteristies with ground effect. In May 1954 Jan obtained the Delft degree in Aeronautical Engineering, cum laude. His thesis subject was on the classification of stalling characteristies of three-dimensional wings; Van der Maas was his supervisory professor.

The start of his boundary-Iayer research is a story in itself. In the early years af ter World War II the Aeronautical Department did not have its own wind tunnel. Aerodynamic research, concentrating on wing-boundary-Iayer research, was performed in flight tests with a pre-war Koolhoven FK-43 plane. When this project was finished, some staff members tried to find new goals for research topics and prepared large posters with every thinkable topic. This search failed completely in opening new insights in the way to go. However, in the meantime the large low-speed, low-turbulence wind tunnel of the Department was com-pleted and was waiting for work. It was in the spirit of Professor van der Maas to start working anyway and in doing so, to gain new ideas and further impetus to proceed. In that spirit I sketched a two-dimensional wing with boundary-Iayer suction through slots and aporous surface with the objective to start its testing in the new tunnel. This project was the beginning of Jan van Ingen's professional career in aerodynamics.

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x Aerodynamicist and dean

Af ter the year 1954 Jan van Ingen was continuously promoted at the Univer-sity, becoming senior-lecturer in 1967 and fuil-professor in aerodynamics in 1971. His inauguration speech was entitled Theorie en experiment in de stromingsleer. Already earlier, in 1965, the results of his research had led to his doctor's thesis Theoretical and experimental investigations of incompressible laminar boundary layers with and without suction. The promotor was Prof. dr ir J .A. Steketee of the Department of Aeronautical Engineering and the Ph.D. degree was honoured cum laude. One ofthe topics ofthis research was the prediction ofboundary-Iayer transition based on the amplification of Toilmien-Schlichting waves. Transition had already been shown experimentaily in the flight tests withthe Koolhoven FK-43 aircraft. Boundary-layer investigations are the leading thread running through his work, which resulted in many publications, as listed at the end of this book.

During many years Professor van Ingen was in charge of the Low-Speed Windtunnel Laboratory, which was considerably extended in fiool' space, equip-ment and experiequip-mental set-ups. Over the years he cooperated closely with the late Prof. ir E. Dobbinga. It was a fine combination of Dobbinga's spiritual and experiment al gifts and van Ingen's theoretical knowledge, thoroughiless and leadership. One of their weil-known research projects was the investigation of separation bubbles on airfoils.

The research of Professor van Ingen did not only bring advancements in boundary-Iayer aerodynamics, but laid also the foundations for practical ap-plications. As a result of discussions, in which my own disciplinary group on aircraft design was involved, the choice was made to concentrate on sailplanes. Under the leaders hip of Professor van Ingen new airfoils and other aerodynamic refinements for sailplanes were developed by ir L.M.M. Boermans, who is now a senior staff member at the Low-Speed Windtunnel Laboratory. Although no sailplanes are manufactured in the Netherlands, several modern sailplanes from abroad (e.g. Germany) have wing sections developed in Delft.

The research of Professor van Ingen attracted also international scientific attention. As an effect of this he was offered in 1966 a one year's stay as a con-sultant at Lockheed Georgia Research Laboratory in the U.S. There he developed computerized design programs for airfoils. He was also asked to become member of several national and international gremia, of which I mention his long-standing membership of the AGARD Fluid Dynamics Panel (since 1970) and the reader is referred to the Curriculum Vitae in this book for further details.

In addition to his research Professor van Ingen performed a heavy task in teaching: lecturing in aerodynamics at severallevels and supervising the thesis work of many students, who had chosen low-speed aerodynamics as option for their graduation. His vast knowledge, experience and thoroughness has certainly valued the student's education.

However, Professor van Ingen has not only been activein his professional field. It was inevitable that he was asked to support the management of the Faculty of Aerospace Engineering (formerly the Department of Aeronautical Engineering). He served as a member of several internal committees and was Dean of the

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H. Witten berg Xl

Faculty in the years 1972-1974 as successor of the late Prof. ir G.J. Spies. That was in the 'roaring' seventies of the universities in the Netherlands and ot her European countries. After the introduction of a new democratie law for the Dutch universities, Professor Spies was chosen as the first Dean, because of his personality and of the faith the Faculty community put in him. It will not have been easy for Professor van Ingen to take over from this predecessor, but his quiet and wise leadership did also provide the foundation for the cooperation between the academie staff, the supporting personnel and the students, which has characterized the atmosphere in the Faculty since then. I was pleased that Professor van Ingen was willing to act for a second term as Dean of the Faculty af ter my retirement in 1991, an assignment he too fulfilled until his retirement in 1997. In his second period as Dean he met other problems than in his first period such as those related to a reduced number offreshmen (and -women), that enroiled for aerospace engineering; among others this had serious consequences for the financial budget of the Faculty. In the last years of his professional career he had to guide a radical reorganisation of the Faculty. In addition to this the activities of the Faculty were hampered by the temporary movement of staff and services from the Main Building to elsewhere, because of an 'asbestos' problem which required a complete internal rebuilding of theFaculty's home.

N evertheless under his leaders hip , Professor van Ingen succeeded with the help of his staff members to keep the Faculty in the air. His merits for the Faculty were honoured in 1995 with a royal decoration as Knight in the Order of the Netherlands Lion.

As a last item in this introduction the special interest of Professor van Ingen in the cooperation with Indonesia has to be mentioned. He presented several lectures at the University of Bandung and supported the exchange of staff mem-bers as weil as the study of Indonesian students at the Faculty in Delft. To strengt hen the position of the Faculty he will continue his activities to attract foreign students for the study in aerospace engineering in Delft. I am sure that Professor van Ingen will also continue to contribute in the advancements on his life-time interest: boundary-layer research. We all wish that his knowledge and experience in this field will bear further fruits.

Above all, on behalf of his many friends in the Netherlands and abroad, Ilike to wish him, his wife, Mrs Ans van Ingen, his son Johan and his family, many happy years together. During these years this Liber Amicorum may stay in the study room at Professor van Ingen's home to remember him on the thanks of his friends for his important contributions in aerodynamics and his leaders hip as Professor at the Faculty of Aerospace Engineering.

April 1997,

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Prediction of Airfoil Stall at

Low and High Reynolds Numbers

T. Cebeci

Advanced Transport Aircraft Systems McDonnell Douglas Corporation Long Beach, CA

90807,

USA

Abstract

1

This paper describes an efficient and accurate approach to the prediction of air-foil stall at low and high Reynolds numbers. In this approach, the inviscid flow

solutions are coupled with solutions obtained from the boundary-Iayer equations with Veldman's interaction law. The boundary-Iayer method includes an im-proved Cebeci-Smith eddy-viscosity formulation and computes the ons et of the transition location using the en-method of van Ingen and AMO Smith. Re-sults are presented for a wide range of flow conditions, and recommendations are made for the preferred approach for predicting the stall angle and maximum lift coefficient of single and multielement airfoils and wings.

1. Introduction

I am honoured and pleased to attend this meeting on the occasion of Professor van Ingen's retirement af ter a distinguished forty plus year career. He has made significant contributions to low-speed aerodynamics, and it is appropriate that in this meeting I address one of his particularly favourite areas: the task of predicting airfoil performance, including stall and post stall, at low and high Reynolds numbers.

Such a task requires the calculation of laminar flows, the prediction of the onset of transition location and the calculation of turbulent flows, both on the airfoil and in the wake. Our ability to perform such calculations has improved significantly in recent years. For example, in the 1960's such calculations for predicting the lift characteristics could only be done by a panel method and profile drag by a combination of inviscid and boundary-Iayer methods. In the

former case, the accuracy of the lift calculations was limited to small angles of at

-tack on relatively slender airfoils. In the lat ter case, the profile-drag calculations

were also limited to small angles of attack containing no flow separation. The important airfoil characteristics near stall and post stall could not be calculated. Even in the calculation of profile drag of airfoils, the boundary-Iayer and transition methods were rather crude; boundary-layer calculations could only be performed by using integral methods and the onset of transition could only

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2 Prediction of airfoil stall

be predicted by correlations. Furthermore, the transition calculations were re-stricted to high Reynolds number flows since at low Reynolds nu mb er flows, the onset of transition location can occur inside the separation bubble and the avail-able correlation formulas cannot be used to predict transition. The en-method, due to van Ingen (1956) and Smith and Gamberoni (1956), could not be used to predict the onset of transition on airfoils at low as weil as high Reynolds numbers, since in those days the differential methods for solving the boundary-layer equations we re not available to calculate the velo city profiles needed in the en-method.

Much progress, however, has been made since the 1960's. Modern methods for solving the Navier-Stokes equations have been developed for obtaining the complete airfoil flow field and computing the performance parameters of airfoils for a wide range of angles of attack, including stail and post stall. In addition, several interactive boundary-layer methods have been developed for the same purpose. These methods combine inviscid and boundary-layer solutions with an interaction law; by solving the boundary-layer equations in an inverse mode, the singular nature of the equations at flow separation is avoided and the solutions are also obtained for separated flow conditions.

Regardless ofwhether the Navier-Stokes approach or the interactive boundary-layer approach is used, ho wever , it is necessary to model the Reynolds stresses for turbulent flows and to calculate the onset of the transition location. In ad-dition to the numerical accuracy of the solutions, the solutions also dep end on the accuracy of the turbulence model and on an accurate determination of the onset of transition location.

In this paper, a method developed by the author and his associates is de-scribed for calculating the airfoil characteristics for a wide range of angles of attack, including stall and post stall, at high and low Reynolds numbers. It is based on an interactive boundary-layer method in which the onset of transit ion is determined with the en-method. It is applicable also for multielement airfoils as weIl as three-dimensional flows.

This method is described in detail in Cebeci (1997); for this reason only a brief description is given in the next section. Results are given in the foIlowing section 3 for a sample of airfoils at high and low Reynolds number in order to demonstrate the accuracy of the calculation method. The paper ends with a summary of the more important conclusions.

2. Description of the calculation method

In the application of the calculation method to airfoil flows, at first an in vis cid velocity distribution is obtained with a panel method for a given airfoil geometry and free stream flow conditions. The boundary-layer equations are solved in the inverse mode with transition determined with the en-method. The blowing velocity distribution, Vb( x), computed from

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T. Cebed 3

Figure 1: Interaetive boundary-layer seheme.

and the displacement thickness at the airfoil trailing edge,

6;e'

are then used in the panel method to obtain an improved inviscid velocity distribution with viscous effects as described in Cebeci (1997). The displacement thickness at the trailing edge is used to satisfy the Kutta con dit ion in the panel method at a distance equal to 8

_{te .}

In the first iteration bet ween the inviscid and inverse boundary-layer methods, Vb( x) is used to replace the zero blowing velocity at the surface (Fig. 1). At the next and following iterations, the difference in Vb( x)

in each iteration is added to the previous blowing velocity used as a boundary condition in the panel method. This procedure is repeated for several cycles until convergence is obtained which is usually based on the lift and total drag coefficients ofthe airfoil. Studies discussed in Cebeci (1997) show that, in general, with three boundary-layer sweeps for one cycle, convergence is obtained in less

than 10 cycles.

2.1. Inverse boundary-layer method

The inviscid method is a standard panel method developed by Hess and Smith as

described in Cebeci (1997). The inverse boundary-layer method is a differential method based on the solutions of the continuity and moment urn equations with a two-point finite-difference method due to KeIler (1970). These equations, using an eddy viscosity (ém ) concept for the Reynolds shear stress, can be written as

where OU

ov

_

0

ox

+ oy

-

,

b=V+ém . (2) (3)

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In the absence of mass transfer, the boundary conditions on the airfoil are

y

=

0; u

=

0, v

= 0,

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In the wake, where a dividing line at y

=

0 is required to separate the upper

and lower parts of the inviscid flow, the boundary conditions at y

=

0 are

y

=

0; v

=

0,

2.2. Solution procedure

au

=

o.

ay

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The equations of the previous subsection are first expressed in transformed co-ordinates. Two sets of transformed coordinates are used, one for the direct problem when the equations are solved for the prescribed pressure distribution, and the other for the inverse problem with the external velocity updated during the iterations. The Falkner-Skan transformation is used in the direct mode and

modified in the inverse mode. Cebeci (1997) presents the transformed equations

and their solution procedure. The airfoil is divided into upper and lower surfaces. For each surface, the calculations start at the stagnation point and proceed in

standard mode up to a certain specified location. Then, the inverse calculations

are performed from that switch location to the far wake.

2.3. Interaction law

To couple the inviscid and viscous flow solutions, an interaction law due to

Veld-man (1979) is used. According to this law, the external velocity is represented

by

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where u~ is the inviscid velocity computed by the panel method and is the

per-turbation velocity due to viscous effects, and 8ue is given by the Hilbert integral

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in the interaction region

(a,

b). The evaluation of this integral is described in

detail in Cebeci (1997).

2.4. Turbulence model

The calculation method uses an improved version of the eddy viscosity

formula-tion of Cebeci and Smith (1974). According to this formulation, the boundary

layer is treated as a composite layer with separate expressions in each region.

é

m

= {

(ém)i

=

(O.4

y

(1-

exp --;))

21~~I!tr

(émL =

a

11

00

(u

e -

u)

dyl

!tr!

o

~ y ~ Yc

(9)

Yc ~ Y ~ 8,

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T. Cebeci where 0.0168 O'=~, IJ A = 26-, UT 5 (10) Here F is related to the ratio of the product of the turbulence energy by normal stresses to that by shear stress evaluated at the location where the shear stress is maximum. It is given by

F

=

1 _

f3

aul ax ,

aulay

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where the parameter

f3

is a function of RT

=

Twl( -PU'V')mboxmax, which for

T w

2:

0, is represented by

~={

6

1+2RT{2-RT} l+RT

RT For T w ::; 0, RT is set equal to zero.

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Also, whereas the original intermittency expression was valid only for zero pressure gradient flows, the new expres sion based on Fiedler and Head's correla-tion (1986) is applicable for flows with favourable and adverse pressure gradients as weIl as zero pressure gradient flows. It is given by

'V

=

~

[1 -

erf(Y -

Y)]

I 2 ~'

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where Y and ()" are general intermittency parameters with Y denoting the value of Y where ,

=

0.5 and ()" the standard deviation.

The condition used to define Ye is the continuity of the eddy viscosity, so

that é m is defined by (ém)i fr om the wall outward (inner region) until its value is equal to that given for the outer region by (ém)o'

The expres sion represents the transition region and is given by

,tr

=

1-exp

(-G(x -

Xtr)

r

dX),

JXtr Ue

where Xtr is the onset of transition and G is defined by G

=

~

u~

R-1.34

C2 IJ2 Xtr '

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(15) where C is 60 for attached flows and RXtr =

(uex I

IJ )tr is the transition Reynolds

number. In the Reynolds number range from Re = 2 X 105 to Re = 6 X 105 where transition usually occurs within a separation bubble, the parameter C is given by

C

2

₌

₂₁₃

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6 Prediction of airfoiJ stall

The corresponding expressions for the eddy-viscosity formulation in the wake are

(17) where (émke. is the eddy viscosity at the trailing edge computed from its value on the airfoil and (ém)w is the eddy-viscosity in the far wake given by the larger of and I

l

Ymin (ém)w=0.064 -00 (ue-u)dy

(ém)~

=

0.064100 (ue - u) dy, Ymin

with Ymin denoting the location where the velocity is minimum.

2.4. Transition prediction

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At high Reynolds numbers and low-to-moderate angles of attack, if the flow is attached, the onset of transition can be calculated with the en-method or by Michel's criterion, as described in Cebeci (1997). At higher angles of attack, the flow may separate downstream of the pressure peak before either method can be used. In such situations, the onset of transition is chosen to coincide with laminar separation.

At low Reynolds numbers (less than 106

), rather large separation bubbles may

occur on the airfoil with the location of transition occurring inside the bubble. In that case, the only available method for predicting the onset of transition is the en-method as is discussed in the following section.

3. Results and discussion

3.1. Accuracy of the en-method for fiows with separation

Before we present a sample of results for several airfoils at high and low Reynolds numbers, it is useful to discuss the accuracy of the en-method for separated flows. Although this method has been extensively explored for attached flows on two-dimensional and axisymmetric bodies, including heat transfer, as discussed by Wazzan (1975), there has been less activity in flows with separation. Nayfeh et al. (1986) reported one ofthe few attempts to apply the method which they did in the context of the corrugalated-plate flows of Fage (1943). Cebed and Egan (1989) addressed the same problem with detailed differences in the application of the en-method and provided results which suggested that the method can represent the effects of separation on the location of transition in a manner which can be used for flows such as those addressed here. In a subsequent study, Cebed (1989) applied the calculation method of the previous section with the onset of transition computed with the en-method to airfoil flows with separation

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T. Cebeci 7 E F G 0.862 0.916 0.961 separation A C

p

~Ff1

1

bubble 2.0 1.6 y(mnV 1.2 a) : :::

:

:!

c===:===~-=-

0.8 0.4 b)

Figure 2: Comparison of calculated (--) and measured (0) velo city profiles for the ONERA-D airfoil for 0'

=

0, Re

=

3 X 105, a) airfoil and' profile locations and b) velo city profiles. XÉ.. 10.0 ₀_.304_---.-. 0.273 8.0 0.243 6.0 0.229 n 4.0 2.0 0.0 0.2 0.4 0.6 0.8 xlc

Figure 3: Variation of amplification rates on the upper surface ofthe ONERA-D

air-foil at different frequencies originating at four different chordwise locations.

~ .2 U'" .0 0.8 0.6 0.4 Cr x 102 0.2 0.0 1.0

Figure 4: Results for the upper surface of the ONERA-D airfoil. Symbols denote experimental data.

bubbles. A sample of results presented here is taken from that reference in

order to demonstrate the accuracy of the en-method to flows with separation. Additional results are given in Cebeci (1997).

We first show results for the ONERA-D airfoil examined by Cousteix and

Pailhas (1979) in a wind tunnel with a chord Reynolds number of 3 X 105 at zero

angle of attack. The airfoil, mean velocity profiles, variation of amplification rates, and distributions of free stream velocity and skin-friction coefficient are shown in Figs 2 to 4. In this case, the measured and calculated results are in close agreement with appreciabie differences only in the velocity profiles immedi-ately upstream of boundary-Iayer separation where we may expect cross-stream pressure gradients and normal stresses to have a locally-important role. In this case, transition occurred within the separated flow region and caused

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reattach-8 0.080 0.020 y/c 0.010 SEPARATION BUBBLE A • • " . H

B~?EFG

_---'-~[

--L

!

i [[

i

~---A xlc=O.367 o E F D 0.774 0.810 0.730 0 0 G H 0.841 0.946

Figure 5: Comparison of calculated (solid lines) and measured (symbols) velo city profiles for the NACA 65-213 airfoil.

Prediction of airfoil stall

~ 1.2 UG lO ~ UG 0 7.5 0 0.8 5.0 0.6 Cr xlO' Cr 2.5 0.4 0 0.0 0.2 0.4 0.6 .8 lO xlc

Figure 6: Comparisoll of calculated ( - ) and measured (0) freestream velo city and skin-friction coefficients for the NACA 65-213 airfoil.

ment shortly thereafter. The calculations revealed transition at x/c = 0.79 for

n

=

8, at x/c = 0.81 for n

=

9 in comparison with measurements which revealed transition at x / c

=

0.808.

We next consider the experiment al work of Hoheisel et al. (1984) who were also concerned with zero angle of attack, this time with a NACA 65-213 airfoil at a chord Reynolds number of 2.4 x 105 _sa_{that the flow was}_separated_from

x / c of around 0.6 to 0.80. The experiments were carried out in the wind tunnel of the French-German Institute at St. Louis which had a freestream turbulence intensity of 0.2%. The airfoil and velocity profiles and distributions offreestream velocity and skin-friction coefficient are shown in Figs 5 and 6. The results in Fig. 6 show a slightly lower calculated variation in freestream conditions between the

x / c-stations corresponding to laminar separation and turbulent reattachment which we re reported to occur at 0.609 and 0.774, respectively. The velocity profiles imply separation at a similar location with reattachment slightly down-stream of the measured value. The location of onset of transition was calculated at x/c of 0.721, which is consistent with an experiment al measurement of maxi-mum fluctuations in the near-wall region at the reattachment location of around 0.774.

3.2. Airfoils at high Reynolds numbers

In this subsection the calculation method of the previous section is applied to airfoils at high Reynolds numbers with the onset of transition location com-puted with the en-method, except where the boundary-Iayer separates upstream of this location, in which case transition is assumed to correspond to the sep-aration point. A sample of results is presented here for the NACA 0012 airfoil to demonstrate the accuracy of the method. Results for additional airfoils are given in Cebeci (1997).

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T. Cebeci 9 2.0 0.040 1.5 00 0.030 Ce 1.0 0 Cd 0.020 0.5 0.010 0.0 0.000 .0 5.0 10.0 15.0 20.0 0.0 0.5 1.0 1.5 a Ce a) b)

Figure 7: Comparison between calculated (--) and experiment al values (0) of: a) lift

coefficient vs 0', and b) drag vs lift coefficient. NACA 0012 airfoil at Re

=

3 X 106.

Figs 7 to 9 show the results for the NACA 0012 airfoil, with Figs 7 and 8 corresponding to a ehord Reynolds number of 3 X 106 and Fig. 9 to Reynolds

numbers of 6 X 106 and 9 X 106 • Fig. 7 shows the variation of the lift and drag

coefficients of the NACA 0012 airfoil for a chord Reynolds number of 3 X 106 . As

can be seen from Fig. 7a, viscous effects have a considerable effect in reducing the (ct)max of the airfoil, which occurs at a stail angle of around 16, and the calculated results agree weIl with measurements.

Fig. 7b shows the variation of the drag coefficient with lift coefficient. As ean be seen, the measurements of drag eoefficients do not extend beyond an angle of attack of 12 degrees and at smaller angles agree weil with the calculations. The nature of the lift-drag curve is interesting at higher angles of attack with the expected increase in drag coefficient and reduction in lift coefficient for post-staIl

angles.

Fig. 8 shows the variation of the local skin-friction coefficient cf and dimen-sionless displacement thickness 6* / C distribution, for the same airfoil at the same

Reynolds number. As can be seen from Fig. 8a, flow separation occurs around a

=

10° and its extent inereases with increasing angle of attack. At an angle of attack a

=

18°, the flow separation on the airfoil is 50% of the ehord length. The variation of dimensionless displacement thickness along the airfoil and wake of the airfoil shown in Fig. 8b indicates that, as expected, displacement thickness increases along the airfoil, becoming maximum at the trailing edge, and decreases in the wake. For a = 10°, 8* / c at the trailing edge is around 2% of the chord, becoming 4% at a

=

14° and 7% at a

=

16°. With increase in angle of attack, the trailing-edge displacement thickness increases significantly, becoming 12% of the chord at a

=

17° and 16% at a

=

18°. However, what is quite interesting,

aside from this rather sharp increase in displacement thickness, is the behaviour of the maximum value of the dis placement thickness. While for angles of attack up to and including stall angle, a

=

16°, its maximum value is at the trailing

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10 0.004 Cf -0.001 ';;---''--;:'::---"--::'-;-,---:'-:~--:-':-~-:c' QO Q2 Q4 Q6 Q81~ xJc a) b) 0.14 0.12 0.10 ö· 0.08 C 0.06 0.04 0.02

Prediction of airfoil stall

xJc

Figure 8: Variation of a) local skin-friction coefficient and b) dimensionless displacementthickness distribution. NACA 0012 airfoil at Re

=

3 X 106.

edge, at higher angles of attack corresponding to post-stall, its maximum is aft of the trailing edge.

Fig. 9, together with Fig. 7, shows the effect of the Reynolds number on the lift coefficient. In accord with the measurements, the calculation method satisfactorily accounts for the effects of Reynolds number. The results show that the maximum lift coefficient, (cz)max increases with an increase in Reynolds number in agreement with measurements.

3.3. Airfoils at low Reynolds numbers

In recent years the subject of low-Reynolds-number airfoils has received consid-erabie interest in both civil and military applications including remotely piloted vehicles, propeller and wind-turbine aerodynamics, aircraft with high-aspect ra-tio wings, and ultralight human-powered vehicles. The behaviour of these air-foils differs from those at high Reynolds numbers, in that rat her large separation bubbles can occur some way downstream of the leading edge with transition taking place within the bubble prior to reattachment. The length of the bub-bIe increases with a decreasing Reynolds number and strongly influences the performance characteristics of the airfoil.

We now apply the calculation method of the previous section to the Eppler '387 airfoil at low Reynolds numbers. At low-to-moderate angles of attack the onset of transition is again calculated with the en-method. At higher angles of attack, it is not possible to calculate the onset of transition with the en-method as in high Reynolds number flows. For this reason, the onset of transition is assumed to correspond to the location of laminar flow separation.

Figs 10 and 11 show a comparison between calculated and measured results for a chord Reynolds number of 2 x 105_. _{The experiment al data for this airfoil}

were obtained by McGhee et al. (1988) in the Langley Low- Turbulence Pressure Tunnel (LTPT). The tests were conducted over a Mach number range from 0.03

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T. Cebed Ce a) 2.0 1.5 0 1.0 0 0.5 o.oJ!j.o=---~5"".0~....,1:-;f0".0~·15;!-;.0;;-'-....,2:;;(0.0 ct 11 2.0 1.5 0 Ce 1.0 0 0.5 \0.0 15.0 20.0 ct b)

Figure 9: Effect of Reynolds number on the lift coefficient. NACA 0012 airfoil at a)

Re = 6 X 106 and b) Re

=

9 X 106.

Table 1: Experimental and calculated chordwise laminar separation (LS), and turbulent reattachment (TR), and transition locations on the upper surface of the Eppler airfoil for Re = 2 X 105. Calculated Experiment a L5 (xjc)tr

TR

L5

TR

-2 0.56 0.748 0.835 0.53 0.80 0 0.51 0.688 0.785 0.48 0.74 2 0.46 0.624 0.716 0.43 0.67 4 0.415 0.564 0.65 0.40 0.62 5 0.40 0.526 0.60 0.38 0.59 6 0.39 0.467 0.52 0.37 0.55

to 0.13 and a chord Reynolds number range from 60 X 103 to 460 X 103. Lift and pitching-moment data were obtained from airfoil surface pressure measurements and drag data from wake surveys. Oil flow visualization was used to determine

laminar-separation and turbulent-reattachment locations.

Fig. 10 presents a comparison bet ween measured and calculated distributions of pressure coefficients and local skin-friction coefficients for angles of attack of 0, 4 and 8°. As can be seen, at lower angles of attack, the separation bubble is long and located away from the leading edge, and becomes smaller with increasing

angle of attack as the separation bubble moves towards the leading edge.

Fig. 11 shows a similar comparison for the lift and drag coefficients up to the stall angle. In general, the calculated results agree remarkably weU with the measured ones. Further details of the results shown in Figs 10 and 11 are presented in Table 1. The calculated values of the chordwise location of

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lami-12 Prediction of airfoil stall -LO 0.04 -0.5 0.00 Cp _0.0 Cr 0.02 0.01 0.5 _0.00 1.0 0.0 0.2 0.4 0.6 0.8 1.0 -0.01 110 0.2 0.4 0.6 0.8 1.0 a) xJc xJc -L5 O,W! -LO 0.015 Cp -115 Cr 0.010 0.0 0.005 0.5 0,<XXl LO -0.005 110 0.2 0.4 0.6 0.8 LO 0.0 0.2 0.4 0.6 0.8 1.0 b) xJc xJc -4.0 0.015 -3.0 _0.010 -2.0 Cp Cr 0.005 -1.0 .;l 0.0 0.<XXl -11005 c) 0.2 0.4 _xJc0.6 118 10 0.0 0.2 0.4 _xJc0.6 0.8 10

Figure 10: Comparison of calculated (- ) and measured (0) pressure-coefficient and

local skin-friction-coefficient distributions for the Eppler airfoil at a) Q'

=

0°, b) Q'

=

4°,

and c) Q'

=

8° for Re

=

2 X 105.

nar separation (L8), turbulent reattachment (TR), and the onset of transition are given for several angles of attack_ The experimental results of this table are subject to some uncertainty because of difficulties associated with the sur-face visualization technique_ With this proviso, comparison bet ween measured and calculated values must be considered outstanding_ It should be noted that when there is a separation bubble, the transition location obtained from the en_{_} method occurs within the bubble in all cases, and, in accord with experiment al observation, leads to reattachment some distance downstream_

4. Concluding remarks

The results obtained with the interactive boundary-layer approach show that our ability to calculate the performance characteristics of airfoils has substantially

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T. Cebed 13 15 0.10 0 0.08 10 00 0.06

ce

Cd 0.04 0.5 0 0.02 0.0 0.00 -2.0 2.0 6.0 10.0 14.0 -5.0 0.0 5.0 10.0 15.0 a a a) b)

Figure 11: Comparison of calculated (--) and measured (0) a) lift, and b) drag

coef-ficients for the Eppler airfoil at Re

=

2 X 105.

improved since the early 1960's. The prediction ofthe lift and drag characteristics of airfoils, including stalI, can now be routinely performed. Similar capabilities

also exist for multielement airfoils but the overall accuracy of the results for

stall conditions is not yet as good as those for single airfoils. Furthef theoretical

work as weIl as experimental work is needed in this area. The extension of the

calculation method for predicting the stall characteristics of single and

multi-wing configurations is also within our reach. Thanks to the en-method of van

Ingen and AMO Smith, the onset of transition distributions on these geometries

can be calculated together with the fiowfield calculations. The progress in this

area, however, has not advanced to a stage that calculations for three-dimensional

can be performed with the same accuracy as for two-dimensional fiows.

References

Cebed, T. and Smith, A.M.O. 1974 Analysis of turbulent boundary layers,

Academic Press, N.Y.

Cebed, T. 1989 Essential ingredients of a method for low Reynolds-number

airfoils, A/AA J. 27, 1680-1688.

Cebed, T. and Egan, D. 1989 Prediction of transition due to isolated roughness,

A/AA J. 27,870-875.

Cebed, T. 1997 An engineering approach to the calculation of aerodynamic

fiows, to be published.

Cousteix, J. and Pailhas, G. 1979 Etude exploratoire d'un processus de

tran-sition laminaire-turbulent au voisinage du décollement d'une couche limite

laminaire, T.P. No. 1979-86. Also La Recherche Arospatiale No. 1979-3,

pp. 213-218.

Fage, A. (1943), The smallest size of spanwise surface corrugation which affects

(26)

Fiedler, H. and Head, M.R. 1986 Intermittency measurements in the turbulent boundary layer, J. Fluid Mech. 25, 719-735.

Hoheisel, H., Hoeger, M., Meyer, P. and Koerber, G. 1984 A comparison of laser-doppler anemometry and probe measurements within the boundary layer of an airfoil at subsonic flow, in: Laser Anemometry in Fluid

Me-chanics - lI, Selected Papers from the Second IntI. Symp. on Applications of Laser Anemometry to Fluid Mechanics, Lisbon, Portugal, LADOAN, pp. 143-157.

Keller, H.B. 1970 A new difference scheme for parabolic problems, in: Nu-merical solution of partial differential equations, Vol. lI, ed. J. Bramble, Academie, New Vork.

McGhee, R.J., Jones, G.S. and Jouty, R. 1988 Performance characteristics from wind-tunnel tests of a low Reynolds number airfoil, AIAA Paper 88-0607. Nayfeh, A.H., Ragab, S.A. and Al-Maaitah, A. 1986 Effect of roughness on the

stability of boundary-layers, AIAA Paper No. 86-1044.

Smith, A.M.O. 1956 Transition, pressure gradient, and stability theory, Pro-ceedings IX International Congress of Applied Mechanics, Brussels, Vol. 4, pp. 234-24.

Van Ingen, J .L. 1956 A suggested semi-empirical method for the calculation of the boundary-layer region, Report No. VTH71, VTH74, Delft, Holland. Veldman, A.E.P. 1979 A numerical method for the calculation oflaminar

incom-pressible boundary layers with st rong inviscid interaction, NLRTR 79023L, 1979.

Wazzan, A.R. 1975 Spatial stability of Tollmien-Schlichting waves, Progress in Aerospace Sciences 16, 99-127.

(27)

Similarities and Differences of Turbulent

Boundary-Layer, Pipe and Channel Flow

F.T.M. Nieuwstadt

J .M. Burgers Centre for Fluid Mechanics, Lab. of Aero and Hydrodynamics

2868 AL Delft, The Netherlands

P. Bradshaw

Dept. of Mechanical Engineering Stanford University, USA

1. Prologue

15

There is no better way to start this contribution to the book in honour of the retirement of professor van Ingen by a quote from the book "Grenzschicht The-orie" by H. Schlichting. This book has formed the source of inspiration for the course on boundary layers given by professor van Ingen during the whole period that he worked and taught at the University of Technology in Delft.

Of course Schlichting, being one of the last direct heirs of Prandtl, should only be quoted in German and on p. 563 of the "fünfter Auflage" he says of turbulent internal flows,l

... Es sei noch darauf hingewiesen, dafl die beiden universellen Ge-schwindigkeitsverteilungen Gl. (20.23) and (20.24) nach den Betra-chtung das vorigen Kapitels für die ebene Strömung in einem Kanal aufgestellt würden. Dafl sie trotzdem gut für die rotationssymmetrische Rohrströmung gelten, wie der vergleich mit Messungen zeigt, kan als ein Beweis für die weitgehende Ä nlichkeit der Geschwindigkeitsverteil-ungen im ebenen und rotationssymmetrischen Fall angesehen werden. Wir erinneren bei dieser Fall daran, dafl auch im laminaren Fall beide die gleiche parabolische Geschwindigkeitsverteilung haben ...

lTranslation according to Kestin of H. Schlichting " Boundary Layer Theory" (1968). p.

571:

lts is worth pointing out here that both universal velocity distributions laws ... have been obtained ... for two-dimensional flow in a two-dimensional channel. The fact that they nevertheless agree weil with experimental results for the case of pipe flow with axial symmetry can be taken as proof that there is a far reaching similarity between the velocity distribution in two-dimensional and axisymmetric cases. ft will be recalled that in laminar flow the velocity distribution is parabolic in both cases· ..

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16 Boundary-layer, pipe and channel flow

Here Schlichting draws attention to an interesting similarity between two geometrically totally different flows: the two-dimensional pipe flow, to be denoted further as channel flow, and the three-dimensional axisymmetric pipe flow, to be further denoted as pipe flow. Af ter Schlichting nobody seemed to have been interested in this similarity. One will look in vain for any remarks on it in the books of Hinze (1975), Townsend (1976), Tennekes and Lumley (1972) and even in Monin and Yaglom (1971).

However, Schlichting was already aware of the fact that this similarity was not perfect, as he points out on p. 506 of the same edition mentioned above an aspect in which the laminar channel and pipe flow are totally different2

... es ist schwierig einzusehen, dafJ das parabolische

Geschwindig-keitsprofil im Kanal gegen kleinen Störungen instabil sein soU (Kap.

XVlc) dasjenige im Rohr jedoch nicht . ...

In defense of this seemingly inconsistency in Schlichting's book, one may perhaps rem ark that the first quotation on p. 563 has appeared in all editions

starting with the first one whereas the second quotation on p. 506 can be found only in the "fünfter Auflage" onwards.

In the present note we examine the rem ark of Schlichting regarding the sim-ilarity of a turbulent pipe and channel flow in more detail with the help of results of numerical simulations. lt will turn out that this similarity fails beyond the second-order moments, i.e. the variance of the velocity fluctuations. Subse-quently, we shall offer an explanation of these differences with the aid of a simple model first proposed by Dean and Bradshaw (1976).

2. DNS of a 2-D and 3-D pipe flow

A technique which was not available at the time that Schlichting wrote his book, is the numerical simulation of turbulence. Nowadays, simulation has established itself as a tooI to investigate turbulent flow. This is in particular the case for so-called Direct Numerical Simulation (DNS) in which the complete Navier-Stokes equations are solved as a function of time and space. lts results are considered to be as trustworthy as experiment al data. The only disadvantage of DNS is that it is limited to rather low Reynolds numbers.

Here, we shall not go into the details of numerical simulation of turbulence but for this refer to the literature, e.g. to Kim et al. (1987) for the channel flow and to Eggels et al. (1994) for the pipe flow. An advantage of DNS is that it is not difficult to perform a computation of a pipe and channel flow at exactly

2Translation according to Kestin of H. Schlichting " Boundary Layer Theory" (1968). p.

515:

... it is difficult to visualize the fact that the parabolic velocity profiles in channels

can - but parabolic profiles in pipes can not - be made unstable by very small

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F. T.M. Nieuwstadt & P. Bradshaw 20 15 + 10 ~ 5

o

10.1 ._ -- Channel - --Pipe 2.5*ln(y.) + 5.1 / / 17

Figure 1: The mean velocity profile of a channel and pipe flow at Re. = 360; the dashed line is the logarithmic velo city profile.

the same Reynolds number. Here, we will present data obtained for a DNS of a channel and pipe flow at Re.

=

360, where for a channel flow Re. is defined as Re.

=

u.h/v and for a pipe flow as Re.

=

u.D /v. Here h is the width of the

channel, D the diameter of the pipe, and u. is the friction velocity defined with

the help of the wall shear stress.

The profiles of the mean velocity obtained from our simulation data are illustrated in Fig. 1 where the mean value has been computed as an average over the homogeneous flow directions and also as an average over various time steps. The velocity profiles of both the channel and pipe are indeed almost equal in the entire flow domain. Note also that both profiles differ from the standard logarithmic profile shown in the figure. This is because the Reynolds number is too low for the existence of a matching region between the inner and outer law in which the logarithmic layer is supposedly valid. However, this does not affect our basic argument regarding the similarity of the channel and pipe profile.

In Fig. 2 we show the profiles of the root-mean square of the streamwise velocity fluctuations for the channel and pipe flow. From our computational data for the pipe we have also estimated the statistical errors of this parameter and these are indicated by the vertical bars in Fig. 2. We again find that the results for the channel and pipe flow are quite similar and we may perhaps say that from the viewpoint of experiment al results in which error bars are usually

(30)

18 3 2.5 Cf)

E

L Q) 2 Cf)

'

5 E

~ 1.5 Q) L +-' Cf)

Boundary-layer, pipe and channel flow

Channel

Pipe

0.5 ... ' ~--'--'-~~ ... ~-'--'-~~-'---'-~'--'

o

0.1 0.2

0.3

0.4 0.5

y/D

Figure 2: The profile of the root mean square of the streamwise velo city fluctuations in a channel and pipe flow at Re.

=

360, normalized by u.; the vertical bars indicate the range of statistical errors.

larger, the two profiles are identical. The shear-stress profiles are of course exactly the same in the two cases so it also follows that the distributions of the structural parameter -u'v' ju2 _{are equal.}

Let us next move to the higher-order structural parameters, the dimensionless third- and fourth-order moments. In Figs 3 and 4 we show the skewness and the

kurtosis ("flatness factor") of the streamwise velocity fluctuations, respectively. Again the statistical errors in these parameters have been estimated and are indicated by vertical bars. In the neighbourhood of the wall the curves for both

flows are quite similar, and this is in agreement with the scaling hypothesis of the "law of the wall". However, in the centre region of the channel or pipe, the profiles of the skewness and kurtosis are no longer comparable. In other

words the similarity for the higher-order moments breaks down and statistically significant differences bet ween the two flow geometries are apparent.

Let us concentrate further on the profiles of the kurtosis for both flows. The conventional picture for wall-bounded shear flows, such as the channel and pipe flow, is that the production of turbulence is concentrated in the neighbourhood of the wall, in particular in the buffer layer. The turbulent eddies produced in this layer are subsequently transported towards the centre of the pipe or channel. The turbulence in the centre region appears to be approximately homogeneous,

(31)

F.T.M. Nieuwstadt & P. Bradshaw

o

~

-0.2 Q)

c

5

~ -0.4 Cf) Q) Cf)

5

-0.6

E

m

~ -0.8 -+-' Cf) -1

o

0.1 0.2 0.3

y/D

Channel Pipe 0.4 19 0.5

Figure 3: The profile of the skewness of the streamwise velo city fluctuations in a channel and pipe flow at Re* = 360; the vertical bars indicated the range of statistical errors.

as e.g. follows from Fig. 2. One may then perhaps expect the turbulence to be close to Gaussian, as is usually found for homogeneous turbulence. In other words the kurtosis should be close to 3 but we see from Fig. 4 that this is not the case. For both flow geometries the kurtosis is clearly larger than 3, values for the channel flow being even larger than in the pipe flow.

To explain this behaviour we make use of a simple model which was first proposed by Dean and Bradshaw (1976). Let us concentrate first on the channel geometry. For this flow Dean and Bradshaw argue that it can be interpreted in term of two interacting "boundary layers" generated at the opposite walls. The two "boundary layers" are separated by an interface across which little mixing occurs. This implies that at each point in the centre region one should be able to distinguish whether a flow has originated from the farthest or nearest wall. A schematic illustration of this model is shown in Fig. 5.

Given this model, let us interpret measurements at, for instance, a point x in the lower half of the channel (see Fig. 5). For a fraction of the time, say

J,

this point is immersed in the turbulence generated at the nearer wal! and for a fraction 1- Jin turbulence generated at the farther wall. Let us now assume that the turbulence intensities in the two cases are different. Turbulence generated at the farther wall has travelled for a long distance and finds itself in an opposing mean velocity gradient (i.e. a velocity gradient of the opposite sign to that at

(32)

20 4 Cf) Cf) 3.5

o

t ::J ..Y Q) 3 Cf)

5 E

(\:Î ~ 2.5

tn

2

o

0.1 0.2

Boundary-layer, pipe and channell10w

0.3

y/D

Channel Pipe

OA

0.5

Figure 4: The profile of the kurtosis of the streamwise velo city fluctuations in a channel and pipe flow at Re* = 360; the vertical bars indicate the range of statistical errors.

the position of production), which will on average lead to negative production and attenuation of the turbulence. Therefore, we may expect the turbulence intensity in this case to be weak. In contrast the turbulence generated at the nearer wall at position x is still able to draw energy from the mean flow and therefore, we expect it to be more vigourous. In other words we can interpret the turbulence condition at position x as a timesharing between two processes with different intensities. Given the statistics of the two individu al processes, one can then directly compute the statistics of the complete process. Let us con si der the extreme case, in which the turbulence generated at the upper wall has completely decayed when it reaches position x. It then follows that the total kurtosis can be written as

T.( = J(u+

L! u

f '

where J( u+ is the kurtosis of the turbulence generated at the lower wall. Even if this kurtosis is equal to 3, the kurtosis of the total process clearly becomes larger than 3, in agreement with our results.

How then to explain the difference bet ween the channel and pipe flow geom-etry implied by Fig. 4? We repeat that the argument introduced above is based on turbulence generated at the wall which is subsequently transported toward the centre of the channel or pipe. In the case of the channel there is enough space

(33)

F. T.M. Nieuwstadt & P. Bradshaw 21

Boundary Layer Pipe or channel

2---Figure 5: Schematic drawing of the structure of a channel or pipe flow according to the model of Dean and Bradshaw (1976).

to allow for both turbulent flows separated by an interface. However, this is not the case for a pipe geometry. Here, the space decreases when the turbulence produced at various azimuthal positions along the wall, is transported towards the cent re region. As aresult there is more interference and the distinction be-tween the production at various positions on the wall becomes less dear. One could say the turbulence becomes less organized in terms of the two processes than in the case of the channel flow. The turbulent flow, so to speak, becomes more chaotic and this would explain the smaller kurtosis level for the pipe flow because one would identify a value 3 for the kurtosis with a pure chaotic flow. Moreover , as the central region of the pipe receives contributions from all round the circumference and not just from points diametrically opposite the position

x, some packets will carry a contribution to shear stress at an angle to the mean

shear at point x, and will therefore not be as strongly attenuated as in the chan-nel. This effect would also result in a value of the kurtosis closer to 3 than for the case of the channel flow.

3. Epilogue

We have found that the similarity bet ween the velocity profile in a channel and pipe flow, first noticed by Schlichting, is confirmed by the results obtained fr om a DNS. However, we have also found that this similarity breaks down for statistics higher than the second-order moment, such as skewness and kurtosis. Based on a model proposed by Dean and Bradshaw in which the turbulence near the cent re line can be separated into two processes, we have offered a conceptual explanation for these results. However it will be dear that more detailed investigation is needed to show whether such a simple picture is indeed a valid description of reality.

Nevertheless, one condusion to be drawn from this small study stands firm. The book by Schlichting remains a source of inspiration, to us as it was to Prof. van Ingen.

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22

Boundary-layer, pipe and channel flow

Acknow ledgement

The authors are indebted to ir. B.A. van Haarlem for carrying out some of the computations.

References

Dean, R.B. and Bradshaw, P.1976 Measurements ofinteracting turbulent shear layers in a ducts. J. Fluid Mech. 78,641-767.

Eggeis, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M. 1994 Fully developed pipe flow: a comparison bet ween direct numerical simulation and experiment. J. Fluid Mech. 268,

175-209.

Hinze, J.O. 1975 Turbulence, McGraw-Hill second ed., New Vork, pp. 790. Kim, J., Moin, P. and Moser, R. 1987 Turbulence statistics in fully developed

channel flow at low Reynolds number. J. Fluid Mech. 177, 133-166. Monin, A.M. and Yaglom, A.M. 1971 Statistical Fluid Dynamics - Mechanics

of Turbulence. The MrT Press, Cambridge Mass, pp. 769.

Schlichting, H. 1968 Boundary-Layer Theory. McGraw-Hill (translated by J. Kestin), sixth edition, New Vork, pp. 744.

Tennekes, H. and Lumley, J.L. 1972 A first Course in Turbulence. The MrT

Press, Cambridge Mass, pp. 300.

Townsend, A.A. 1976 The Structure of Turbulent Shear Flow. Cambridge Univ. Press, second ed., Cambridge, pp. 429.

(35)

Wing-Fuselage Design of

High-Performance Sailplanes

L.M.M. Boermans

Delft University of Technology, Faculty of Aerospace Engineering

Kluyverweg 1, 2629 HS Delft, The Netherlands

K. K

U

brynski

Technical University of Warsaw,

Institute of Applied Mechanics and Aviation ul. Nowawiejska 22/24, Warsaw, Poland

F. Nicolosi

University of Naples, Faculty of Engineering

Via Claudio 21, 80125 Napels, ltaly

Abstract

23

The' paper describes the interference effects on a high-performance sailplane wing-fuselage combination and the way the negative effects were encountered in the design of two wing-fuselage combinations. One combination has a wing with camber changing flap and the second one has a wing with spanwise camber. Prototypes of both configurations are being produced.

1. Introd uction

The aerodynamic quality of high-performance sailplanes has reached a high level;

for instance the best glide ratio of 25 m span sailplanes is about 60 which

corre-sponds to a glide angle of about 10

• Wings, tailplanes and fuselages have been

squeezed out for low drag, using advanced theoretical design methods. When a wing and fuselage are combined, however, the flow in the junction is very complicated and not yet theoretically predictable with the required accuracy (Devenport, 1992). Hence, the design of a proper wing-fuselage junction has to be based on a judicious mixture of computational and experiment al results, examples of which are shown in this paper.

In the next section the wing-fuselage interference effects for a sailplane

(36)

24 Wing-fuselage design of high-performance sailplanes

Figure 1: Alpha-floweffects.

Figure 2: Viscous floweffects.

encounter the negative interference effects, as weil as a brief description of the two- and three-dimensional design tools used for the design of two wing-fuselage combinations presented in the next sections. The first configuration has a wing with camber changing flap, and the second configuration has a wing with span-wise camber.

2. Wing-fuselage interference effects

The interference effects of the flow on a high-performance sailplane wing-fuselage combination can be distinguished in non-viscous and viscous effects (Boermans, 1984).

2.1. Non-viscous efJects

Due to the displacement effect of the fuselage the streamwise pressure distri-bution on the wing changes towards the junction, depending on the relative

Boundary-Layer Separation in Aircraft Aerodynamics: Dedicated to Professor J .L. van Ingen

Boundary-Layer Separation in

Aircraft Aerodynamics

Proceedings of the Seminar

held on 6 February 1997 in Delft

Dedicated to Professor J.L. van Ingen

Edited by

Boundary-Layer Separation in Aircraft Aerodynamics

Tltoëift

Boundary-Layer Separation in

Aircraft Aerodynamics

Proceedings of the Seminar

held on 6 February 1997 in Delft

Dedicated to Professor

J

.L. van Ingen

Edited by

R.A.W.M. Henkes and P.G. Bakker

Faculty of Aerospace Engineering

Delft University of Technology

Contents

Preface

by

the Editors

Prof. dr ir J.L. van Ingen:

Aerodynamicist and Dean

by H. Wittenberg

Prediction of Airfoil Stall at

Low and High Reynolds Numbers

T.

Cebeci

90807,

6;e'

te .

ov

_

ox

+ oy

-

,

(4)

=

=

= 0,

=

=

=

=

au

=

o.

ay

(7)

(a,

= {

=

(O.4

(1-

21~~I!tr

a

11

(u

u)

dyl

o

(9)

=

f3

aul ax ,

aulay

f3

=

2:

~={

(12)

=

~

[1 -

Y)]

(13)

_{te .}

₌

₂₁₃